Physics and technology of magnetron sputtering discharges

0963-0252/29/11/113001 Magnetron sputtering deposition has become the most widely used technique for deposition of both metallic and intensify thin films and is utilized in numerous industrial applications. There has been a continuous development of the magnetron sputtering technology to improve target utilization, increase ionization of the sputter species, increase deposition rates, and to minimize electrical instabilities such as arch, ampere well as to reduce operating cost. The development from the direct current ( direct current ) diode sputter joyride to the magnetron sputtering discharge is discussed a well as the assorted magnetron sputtering discharge configurations. The magnetron sputtering discharge is either operated as a district of columbia or radio frequency empty, or it is driven by some early periodic waveforms depending on the application. This includes reactive magnetron sputtering which exhibits hysteresis and is frequently operated with an asymmetrical bipolar mid-frequency pulsed wave form. Due to target poisoning the reactive clamber work is inherently precarious and exhibits a strongly non-linear reaction to variations in operating parameters. Ionized physical vaporization deposit was initially achieved by adding a junior-grade free between the cathode aim and the substrate and late by applying high world power pulses to the cathode target. An overview is given of the operate parameters, the discharge properties and the plasma parameters including atom densities, acquit current composing, electron and ion energy distributions, deposit pace, and ionized flux density fraction. The release alimony is discussed including the electron heating processes, the creation and character of junior-grade electrons and Ohmic inflame, and the sputter processes. Furthermore, the function and appearance of instabilities in the release operation is discussed. Export quotation and abstract BibTeX RIS original content from this ferment may be used under the terms of the creative Commons Attribution 4.0 license. Any far distribution of this work must maintain attribution to the author ( second ) and the title of the work, daybook citation and DOI.

1. Introduction

physical vaporization deposition ( PVD ) refers to the formation of a condensible vapor by forcible mechanisms and subsequent deposition of this material on a substrate as a reduce film or coating ( Mahan 2000, Rossnagel 2003, Thornton 1988 ). This can be achieved by a across-the-board image of thin film deposition techniques, which have in coarse that the atoms are removed from a reference by physical means. One such technique is sputter deposition where the atoms are released from a solid or melted informant through momentum exchange. Sputter deposition is a PVD technique that has been known and applied for decades as a compromising, dependable, and effective method acting for the deposition of thin films. In the mid nineteenth century Grove ( 1852 ) observed deposits when exploring the electro-chemical polarity of gases using a mastermind current ( district of columbia ) glow exhaust. This observation was developed promote and a few decades late sputter deposit of thin metallic films utilizing the cathode as the beginning of the movie forming material was demonstrated by Wright ( 1877a, 1877b ). By the 1930s sputter deposition of thin films had found commercial applications ( Fruth 1932 ). early on sputter deposition was based on cathode spatter or direct current diode sputter ( Hulburt 1934 ). however, in the 1950s spatter deposition of thin films had been about completely replaced by thermal vaporization ( Holland 1956 ). But, with better vacuum engineering in the belated 1950s and early 1960s, the realization that a wide range of conductive materials could be deposited using direct current sputter ( Kay 1962, Thornton and Greene 1994, Westwood 1976 ), and the introduction of radio frequency ( releasing factor ) sputtering to deposit dielectrics ( Anderson et aluminum 1962 ), it gained significant interest. The magnetron sputter proficiency, was developed during the 1960s and 1970s ( Chapin 1974, Gill and Kay 1965, Kay 1963, Wasa and Hayakawa 1967a, 1969 ), and has ever since been the workhorse of plasma based sputter deposit. Magnetron clamber deposition techniques are presently the most wide use processes of thin movie deposition and surface engineering treatments. physical deposition methods generally have few limitations with attentiveness to the substantial to be deposited on a substrate and virtually any material can be deposited. The primary beginning of movie forming species is typically a solid target. Furthermore, new material combinations and compounds can be synthesized with sputter techniques using either multiple cathode targets simultaneously or by addition of reactive gas. Sputter deposit is normally performed under high vacuum conditions in rate to achieve a craved level of purity of the deposited thin film. The underlie forcible action for spatter is a momentum switch over between energetic species and the atoms within the cathode target. The energetic species are typically the ions of an inert lord flatulence as they can be accelerated more easily than the achromatic atoms across the cathode sheath toward the cathode prey. Sputter deposition produces thin films that are dense, exhibit smaller granulate size, have better adhesiveness, and present overall properties that are closer to bulk material properties, compared to thermal evaporated films. thermal vaporization is often applied to deposit compact films and coatings where the requirements on the surface morphology are not a keystone prerequisite as the deposit rate is a lot higher than for plasma based sputter deposition processes. therefore, plasma based sputter deposition is applied when overall high film choice, high film mass concentration, depleted surface choppiness and stoichiometry of the deposited thin film are desired, rather than high deposit pace. In addition reactive flatulence species can be introduced to the chamber during sputter deposit to be intentionally included in the film to form a colonial. Through the years there has been a continuous growth of the magnetron sputtering technology in order to increase metallic element ionization, improve aim use, avoid target poison in reactive clamber, increase deposition rates, to minimize electrical instabilities such as arc, and to reduce operating monetary value. The drive force behind this development has been the increasing requirement for functional coatings and layered structures of ever increasing overall quality and vary functionality. The continuous development of the sputter deposit process has besides been driven by the necessitate to improve the utilization of the spatter source ( the cathode target ), to improve the homogeneity of the lodge film, to achieve directing deposition of metals and to allow for command of the energy of the ions of the film forming material bombarding the substrate. Magnetron clamber has become an necessity technology for thin movie deposition in a broad stove of industrial applications. These include metalization in integrate circuits ( Hopwood 1998, Rossnagel 1999, 2008 ), coatings for break resistance and corrosion auspices ( Kelly et alabama 1996 ), ocular coatings ( Martinu and Poitras 2000 ), bombastic area coatings of architectural glass ( Nadel et aluminum 2003 ), photovoltaic solar cells ( Blondeel et alabama 2009 ), and display applications ( Krempel-Hesse et al 2009 ). basically the lapp sputter proficiency is used to deposit the conductive layers in microelectronic devices as is used to coat sheets of architectural glaze, that is in the scope of a few square meters, and to coat polymeric web in roll-to-roll systems ( Kelly 2011 ). To be applicable to this wide-eyed range of applications the magnetron sputtering acquit exists in a number of configurations and arrangements, spans a wide-eyed image in cathode target area size, and is driven with assorted waveforms applied as the cathode electric potential or exhaust current. here an overview is given of the development of plasma based sputter deposit techniques, where the magnetron sputtering acquit plays a central character. First the advances in sputter technology are reviewed, from the diode sputter creature ( section 2 ), to the magnetron sputtering discharge ( section 3 ), the pulsate magnetron sputtering discharge ( section 4 ), and its application to reactive sputter deposition ( section 5 ), and ionize PVD ( section 6 ). then the basic physics needed to understand the magnetron sputtering discharge is reviewed ( segment 7 ), including magnetic confinement, atom ecstasy, physical sputter and secondary electron discharge. ultimately, the physics of the magnetron clamber operation is discussed, including the observe plasma parameters ( section 8 ), the model efforts ( part 9 ), the fire care or electron office assimilation, the empty stream composition at the target surface, ion recycle, and instabilities, that develop during fire operation ( section 10 ) .

2. Diode sputtering devices

The simplest and most commodious reference of ions is the direct current incandescence discharge. In its elementary placement a district of columbia discharge is formed between two parallel electrodes where the cathode and the anode are separated by a distance L. The gap between the electrodes is filled with gas at pressure pg. This flatulence we refer to as the working gas. The most normally used working gasoline is argon as it is inert and relatively cheap. A potential VD, the discharge electric potential, is applied between the electrodes. If the apply voltage VD is maintained above the electrical breakdown voltage of the working natural gas VB the dispatch is self-sufficient. In the direct current incandescence discharge respective clear-cut regions appear between the cathode and the anode ( Gudmundsson and Hecimovic, 2017 ). immediately adjacent to the cathode is the elementary benighted distance or the Aston night space, a region of a solid electric field and a negative space charge. The Aston dark quad is followed by the cathode freshness. The cathode glow is followed by the cathode ( Crookes or Hittorf ) colored space, a region of tone down electric field and positive space charge of relatively high concentration that consists chiefly of ions. In a district of columbia glow discharge about the entire apply electric potential falls across the cathode benighted space and the ion bombarding department of energy is comparable to the rate of the give voltage. The ions created within the discharge are accelerated toward the negatively biased cathode. As the ions bombard the electrode, secondary electrons are emitted ( see section 7.5 ), which are accelerated off from the negative cathode, gaining sufficient energy to excite and ionize the atoms of the working flatulence. The direct current discharge is maintained through this secondary electron emission. With each secondary electron, more ions are available to bombard the cathode, and create more junior-grade electrons. The cathode blue space or the cathode sheath is followed by the negative incandescence which exhibits the brightest light intensity of the entire dismissal as the acceleration of the secondary coil electrons leads to excitation and ionize collisions within this region. The negative glow is followed by the Faraday dark space and then the positive column. The positive column is a quasi-neutral plasma that that acts as a conducting path between damaging glow region and the anode. The anode dark space has a veto space charge due to electrons that flow from the positive column to the anode. Electrons accelerate toward the anode and agitate atoms or molecules, and a bright area, anode gleam, appears at the anode. farther data on the structure and foundations of direct current discharges are given in a holocene reappraisal ( Gudmundsson and Hecimovic 2017 ). bombing of a solid airfoil by high department of energy ions causes, in addition to secondary electron emission, ejection of atoms, a serve referred to as clamber ( see part 7.4 ). A normally used approach is to have the material that is to be sputtered serve as the cathode in a low blackmail district of columbia glow discharge. Most frequently the negatively biased cathode is electrically isolated from grate and the ground chamber is the anode. In a typical operation a negative voltage of 2000–5000 V is applied to the cathode target while the anode is grounded. Almost all the applied voltage appears across the cathode sheath ( cathode night space or the cathode capitulation ). The negative glow extends about to the anode and the cocksure column is normally absent. however, a shortstop anode zone where the slenderly positive plasma electric potential returns back to zero at the anode, is present. This configuration is referred to as an obstruct district of columbia glow discharge. When a drop has formed the cathode is under firm bombardment by high energy ions and the cathode is frequently referred to as target. The squirt atoms of the cathode material form the movie forming material. A substrate, sometimes referred to as liquidator, is placed in the vicinity of the cathode, collects the splutter substantial and a thin film forms. This empty agreement was used as a sputter source for decades, normally referred to as diode spatter or cathodic sputter and has over the years been discussed in numerous review articles and books ( Chopra 1969, Kay 1962, Vossen and Cuomo 1978, Westwood 1976 ). The district of columbia diode free consists of an electrode placed within a vacuum chamber and an external high voltage might supply. The substrate, on which the clamber atoms are deposited, is placed on a substrate holder or substrate mesa. The substrate holder may be grounded, floating, biased, heated, cooled, or some combination of these. number 1 shows a cross section of a direct current diode sputter cock that consists of a spatter fastness ( the cathode aim ) and a concentric substrate table that sit inside a metallic cylinder with a shutter located in between those. A district of columbia might issue is connected to the target and a bias can be applied to the substrate table, but the substrate table can besides be electrically floating. The distance between cathode and the substrate holder is broadly short and these discharges are frequently configured as low expression proportion discharges, as the inter-electrode legal separation is little compared to the size of the electrode ( cathode ), ( L/R < 1 in the cylindrical configuration where R is the cathode target radius ). Cathode diameters are typically in the rate 10–30 curium while the space between the cathode and substrate holder is 5 to 10 centimeter. In direct current diode clamber, a ground shield around the target ( as shown in figure 1 ) is used to control the sphere being bombarded by ions, to suppress undesired spatter of the sides of the support structure for the target, and to confine the condition of the electric sphere near the target. A detail description of a direct current diode spatter device with substrate bias capability is given by Vossen and O'Neill ( 1968a ) .Figure 1. Figure 1. A traverse section of a direct current sputter diode discharge which allows for substrate bias. Reprinted with license from Vossen ( 1971 ) Copyright 1971, American Vacuum Society. download figure : Standard image
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The direct current sputter source is by and large weakly ionized with ionization fraction of the order of 10−4 and thus the discharge is dominated by collisions between neutral atoms. Some of the energetic secondary electrons can pass through the plasma and hit the substrate or the chamber walls. The loss of these secondary electrons means that they do not create new ions or electrons that maintain the dismissal, while the junior-grade electron barrage results in substrate heat. therefore, the working gas press must be high enough that the secondary electrons are not lost to the anode nor to the ground surfaces before performing ionization. These pressures are higher than preferred for optimum enchant of the sputter atoms of the film forming material to the substrate due to scattering by the working gas atoms. Hence, there is a pin down pressure range around 2–4 Pa for district of columbia radiance discharge sputtering to be viable. At this operate on pressure the cathode dark space extends about 1–2 curium from the cathode while the ion-neutral entail release path λi < 1 curium and consequently the cathode sheath is collisional. The working accelerator pressure is high adequate to allow charge-exchange collisions and momentum transfer collisions between the accelerating ions and the working flatulence neutrals within the cathode sheath. therefore, ascribable to the collisional sheath the ions that impinge on the prey surface do not have the full cathode electric potential. The consequence is that the ions and high energy neutrals exhibit a broad energy spectrum as they impinge on the target surface. The higher the working gas blackmail, the lower the beggarly energy of particles that bombard the cathode target. The atoms that leave the target, the splutter species, typically have energy of a few electron volt ( see section 7.4.2 ). As they pass through the working gas they undergo scattering events. consequently, as a resultant role of these repeated energy-reducing collisions they finally thermalize or reach the kinetic energy of the surrounding working gasoline. consequently, they do not have the surfeit kinetic energy that is important for the bombardment of the growing movie. frankincense, the sputtered atoms are not directed, and the sputter particles diffuse randomly and there is a reduction in the count of atoms of the target material that reach the substrate. The district of columbia diode sputtering device is only applicable to the deposition of electrically conductive materials and is frankincense chiefly applicable for sputtering of metals. Such a conventional direct current diode discharge is not operable if the cathode surface is made of insulating material. This would be the case if the cathode was itself an insulator, or if the cathode was under operation in reactive gas such as oxygen which might make the come on of the cathode insulate. constitution of a nonconductive compound surface layer on a conductive electrode is referred to as poison of the cathode target surface and can be due to contaminant gases or intentionally introduce reactive process gases. This limit was overcome by applying actinium electric potential at high frequency to the aim ( Anderson et alabama 1962, Davidse and Maissel 1966, Logan 1990 ). At operating frequencies above a few megahertz, the ions are not able to move quickly enough to offset the changing battlefield and the accumulation of ions during the part of the motorbike in which the target electrode acts as a cathode is limited. This placement can be applied to sputter a insulator electrode such as a ceramic or polymer. Often, these discharges are operated at 13.56 or 27.12 MHz, which are approved frequencies for industrial and aesculapian use. typically, a big variable capacitor ( 25–2000 pF ) is placed in series between the rutherfordium might add and the power electrode to prevent district of columbia current from flowing. This capacitor allows a significant damaging bias to develop on the cathode in especial when a conductive cathode is being sputtered ( Vossen and O'Neill 1968b ). In general the diode clamber device suffers from a low deposit rate. The maximum dismissal current density is roughly 1 milliampere cm−2 and the deposit rate ten nm min−1 at best. besides, the spatter might efficiency ( sputter atoms/ion-volt ) is relatively low in these discharges as they operate at high voltage and this efficiency decreases with increasing energy. note that rf sputtering can be performed at lower working boast pressures ( < 1 Pa ) than feasible for district of columbia diode sputter. however, the clamber rate is very low as dielectrics can have sputter yields arsenic gloomy as 10 % of metals. The advantage of diode sputter is effective use of the target material as the ion flux is closely uniform across the prey come on and the electrode area does not need to be planar. sometimes an autonomous beginning of electrons is added in ordering to sustain the release rather than relying wholly on the generation of secondary electrons at the cathode. This is most normally done by a thermionic emitter or a heat fibril and then the summons is referred to as triode sputter. This allows a direct current spatter discharge to be operated at working gas pressure angstrom low as 0.2 Pa. however, triode systems are difficult to implement on an industrial scale. Despite its ease the direct current diode sputter fire is no longer employed in production environments. The film deposit rates are merely besides abject .

3. Magnetron sputtering discharges

The hapless deposition rate, the eminent free electric potential and high working gas atmospheric pressure of the direct current diode clamber tool called for a new approach. The deposition rate had to be increased, the release electric potential lowered, and the operation pressure compass needed to be expanded. This was achieved through extending the life of the electrons in the vicinity of the cathode aim by applying a static charismatic airfield ( Gill and Kay 1965, Wasa and Hayakawa 1969 ). Such a discharge, based on magnetic confinement of the electrons, is referred to as a magnetron sputtering free. In the planar circular configuration the magnetron sputtering free is merely a diode sputtering arrangement with the addition of two concentric stationary cylindrical magnets placed immediately behind the cathode target. A schematic side-view of the planar magnetron sputter configuration is shown in human body 2. The term planar refers to the cathode prey being a flat plate which is either round or rectangular. In the planar configuration the magnetic field lines exit the center of the cathode, arch above the aim surface, and enter the cathode at the annular ( Chapin 1974, Waits 1978a ). The magnetic field is arranged then that it appears parallel to the cathode surface. When all the field lines that exit the cathode center enter the cathode at the annular the discharge is referred to as a conventional or balanced magnetron sputtering discharge. In a district of columbia magnetron sputter ( dcMS ) discharge the cathode is kept at a constant negative voltage. The magnetic and electric fields create an electron trap that confines the electrons in the target vicinity. consequently, about all the ionization takes position within a region next to the cathode prey, the ionization region ( IR ), and within this area the plasma density is a few orders of magnitude larger than in a typical district of columbia freshness free .Figure 2. Figure 2. A conventional side-view of the planar magnetron free used for sputtering. The magnetic field lines exit the center of the cathode, arch above the aim surface, and enter the cathode at the annular. Reprinted from Gudmundsson and Lundin ( 2020 ), with permission from Elsevier. download figure : Standard image
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The electrons that are ejected from the cathode open due to ion bombing and accelerated across the cathode sheath, the energetic secondary electrons, are of meaning interest. It was believed that these secondary electrons are crucial for sustaining the magnetron sputtering dismissal like the district of columbia discharge ( Thornton 1978 ). We will see in section 10.1 that this is not necessarily the case. The electrons are trapped by the magnetic field while the ions are not medium to the magnetic field and the residence time of electrons is a lot larger than that of ions. The magnetic field well influences the trajectories of electrons, while the way of ions is not much affected since their ion rotation radius is large compared with the characteristic size of the target and the chamber. The electrons gyrate around the charismatic field lines and sporadically inverse guidance as they approach the sheath boundary over the target surface. Averaging over the rotation of the electrons, and the periodic direction reversal, results in a net azimuthal electron drift, referred to as E × B drift, where E and B are the electric and magnetic fields, respectively. In addition to the E × B drift there are contributions to the electron drift ascribable to the gradient and curvature of the fields. The assorted contributions of the magnetic airfield to the azimuthal electron drift are discussed further in section 7.1. The magnetron sputtering drop is broadly operated in the freshness acquit regimen ( Gudmundsson and Hecimovic 2017 ). After breakdown is achieved this manoeuver regimen is reached by increasing the acquit current through increasing the cathode voltage. Planar dcMS sources are normally operated using argon as the working natural gas in the blackmail range 0.2–4 Pa with cathode voltage in the range of 300–700 V. The resulting free current densities are in the range 4–60 ma cm−2 and power densities of several tens of W cm−2 ( Parsons 1991, Waits 1978a ). The world power load is limited by the target heating due to ion bombing. For the lowest working gasoline imperativeness the think of unblock way for the sputter atoms is 10–15 centimeter while at the highest atmospheric pressure the mean absolve path is below 1 centimeter. consequently, at the lowest working gas press the deposition is a line-of-sight process while at the higher pressure the sputtered atoms are considered ‘thermalized ‘ with the working natural gas ( Rossnagel 2003 ). besides at low operating blackmail backwards diffusion of sputter species is reduced and therefore the deposition pace increases. The magnetic field in the cathode target vicinity is frequently in the range ∼20–50 mTesla, typically provided by permanent magnets placed at the back side of the cathode aim. The electron concentration in the substrate vicinity is in the range 1015 to 1017 m−3 ( see further discussion in part 8 ). The static deposition pace is in the roll 20–200 nanometer min−1 while the academic degree of ionization of the clamber species is broadly identical low, much on the order of 2 % –3 % or less. The majority of the ions bombarding the substrate are ions of the baronial working gas as the electron impact ionization mean release path for the sputter species is over 50 cm, and for Penning ionization reasonably lower, for typical operating parameters of the dcMS discharge. As the secondary coil electrons are trapped in the cathode vicinity they do not bombard the substrate and therefore substrate heat is low. therefore, the magnetron sputtering dismissal is suitable for deposition on heat sensible substrates. The discharge current–voltage characteristics are empirically found to follow the super-linear relationshipEquation (1) where ID is the discharge current, VD the discharge voltage, and the exponent nitrogen is in the range between 3 and 15 ( Rossnagel and Kaufman 1987a, 1988, Thornton 1978, Waits 1978a ). The exponent north depends on the efficiency of the electron trap, the more effective the electron trap, the higher the north value ( Waits 1978a ). A high rate of nitrogen indicates that the discharge can accommodate a significant increase in acquit stream with a relatively small increase in target electric potential. This can be achieved since the discharge is relatively weakly ionized and more charge carriers are generated as needed ( Anders 2004 ). The ceaseless kilobyte depends on the target material, the sputter give, the working gas type, the working gas pressure, charismatic sphere regional anatomy, the secondary electron emission return, and the geometry of the discharge. The anode dimensions of the magnetron sputtering discharge are much big as sometimes the bedroom walls serve as an anode. however, because of deposition on the chamber walls they generally do not represent a authentic current return way. In most cases the anode is a establish shield placed around the magnetron target ( as seen in figure 2 ). This is a separate dedicated anode that can be kept clean from deposits by self-heating. Since the electrons will move along magnetic field lines with still, the magnetic field lines closest to the cathode prey that go through a ground structure, for example, the reason carapace, will define a virtual anode for the magnetron sputtering fire. The situation of the anode, including the virtual anode, is very important for the interaction between the plasma and the substrate. If the anode shields the plasma generated at the cathode from the substrate, the plasma will be very weak in the substrate vicinity and the possibility to utilize the plasma to modify the growing film, with, for example, low-energy ion bombing, is very circumscribed. Often a floating district of columbia power supply is connected between the anode and cathode. The chamber walls are then kept at the organization ground and the anode is connected to the ground chamber walls through a resistor Ro. Before the fire ignition the anode and the chamber walls are at the like likely. This makes it easier to start the drop. As the discharge has ignited there is a electric potential drop across the resistor Ro and the anode and the chamber walls have different potentials. Belkind and Jansen ( 1998 ) have explored experimentally how the placement and the size of the anode influences the potential distribution in the magnetron sputtering discharge and how large the resistor Ro has to be to take the bedroom wall out of the anode lap .

3.1. Magnetron sputtering discharge configurations

The magnetron sputtering discharge configuration can be planar ( as shown in calculate 2 ), cylindrical with axile magnetic field ( as shown in trope 3 ), or the cathode aim can be a tube that rotates around a fix attraction assembly ( as shown in figure 4 ). however, these are good geometric variants of the same principle, to magnetically confine electrons in the vicinity of the cathode aim. By the virtue of the respective configurations the magnetron sputtering technique can be applied to a large variety of materials that can be deposited on a range of substrates in diverse forms and shapes, and is well scalable to very large areas .Figure 3. Figure 3. Magnetron sputter sources in the cylindrical shape. ( a ) Cylindrical-post and ( b ) hollow cathode or inverted magnetron sputtering reference. Reprinted from Thornton and Penfold ( 1978 ), with license from Elsevier. download number : Standard image
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Figure 4. Figure 4. A conventional side-view of the rotating magnetron sputtering dismissal. The cathode prey is a cylindrical tube that rotates around the fixate magnet assembly with a frequency of roughly 1 Hz. After Wright and Beardow ( 1986 ) and reprinted from Gudmundsson and Lundin ( 2020 ), with permission from Elsevier. download calculate : Standard image
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3.1.1. The cylindrical magnetron configuration

a lot of the early demonstrations and analysis ( Thornton 1978, Thornton and Penfold 1978 ) and the early magnetron splutter deposition ( Thornton 1977, Thornton and Hoffman 1977, Wasa and Hayakawa 1967b ) was made using cylindrical magnetron configurations with axial magnetic fields. These discharges were either in the cylindrical post shape, with the inner cylinder as the cathode prey ( trope 3 ( a ) ) ( Thornton 1980, Wasa and Hayakawa 1967a, 1967c, 1969 ), or the cylindrical-hollow shape ( or inverted magnetron ), where the out cylinder is the cathode target ( figure 3 ( bel ) ) ( Thornton 1978, Thornton and Penfold 1978 ). In the post-cathode configuration the discharge is formed between two coaxial cylindrical surfaces, where the inner cylinder is the cathode and the outer cylinder is the anode. The charismatic field in this shape is oriented parallel to the axis of the cylinders and is normally quasi linear. That is the magnetic field is unidimensional over most of the acquit book, while a second part merely appears at the end of the cylinders. consequently, in the cylindrical shape the magnetic field B is axial while the electric field E is radial, and the E × B stray paths go around the cylinder, either on the inside or the external, depending on the configuration, as indicated in figure 3 ( a ) and ( b ), respectively. In the cylindrical post-cathode magnetron sputter device the cathode is an elongate source of the film forming material to be deposited and provides uniform sputtering from the whole cathode prey come on. It was often set up as batch coating where the work pieces surround the center cathode ( Thornton 1980, 1988 ). These cylindrical configurations are not in much practice nowadays except for the hollow cathode magnetron ( HCM ) sputtering shape, which is well suited for coating wires or fibers that are allowed to pass through it .

3.1.2. The planar magnetron configuration

The planar magnetron sputtering free was introduced in the early on 1970s ( Chapin 1974, 1979 ) and this configuration is now well established for sputter deposition of thin films of both metallic and compound materials. The core of the magnetron sputtering discharge is the magnetron fabrication. The geometry of the planar magnetron magnet assembly is shown in figure 5. The magnetron fabrication consists of a cathode target that is attached to an array of static magnets or electromagnets. The magnetron assembly has to be designed so that it is able to conduct estrus away efficiently from the cathode target. consequently, the cathode target and the magnets much sit on a parry of solid bull that is water cooled to prevent overheating. The target is mounted in dear thermal contact to the bet on plate by screwing, clamping or soldering. The magnets are arranged such that a cardinal attraction forms one pole and the second pole is formed by a magnet band or a ring of magnets placed along the edge of the target ( as seen in design 2 ). This shape is often used in lab settings, where the cathode prey is small and circular, typically 5–15 centimeter in diameter. For industrial applications the cathode targets are frequently linear ( orthogonal ) and larger, up to a few tens cm retentive. In the planar shape the magnetic field B is radial while the electric field E is axial and the E × B drift path is azimuthal above the cathode target airfoil and the resulting azimuthal current density is denoted by Jθ. In figure 5 the discharge current concentration JD and the azimuthal current concentration Jθ are indicated .Figure 5. Figure 5. A conventional of the planar magnetron attraction assembly and the cathode aim. The magnetic field lines arch, from the center magnet to the outer magnet resound, above the target come on. The magnetic field B is radial and the electric field E is axial ( along the z bloc ) and the E × B drift path is azimuthal above the cathode target surface and the resulting azimuthal current concentration is denoted by Jθ. Reprinted from Brenning et alabama ( 2009 ). download figure : Standard image
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One major disadvantage of the planar magnetron sputtering configuration is that the plasma is not uniform over the target surface as it is inherently a inhomogeneous deposition source because the sputter material originates from below the regions of high plasma density. This is a consequence of the charismatic confinement of the electrons. Due to the electron confinement the plasma is localized and concentrated into a doughnut or torus shaped region, the IR, that hovers in front of the target. This region has the highest plasma concentration, and consequently high ion current density and maximal ion barrage of the target occurs from this region. The ion stream concentration is peaked at the radius where the charismatic battlefield is tangent to the cathode surface ( Wendt et aluminum 1988 ). This leads to the formation of a characteristic erosion groove in the target airfoil, referred to as the race traverse ( Chapin 1974, Nakano et alabama 2017 ). The erosion rut determines the target use, the aim life and the efficiency of the material usage. The early demonstration of the planar magnetron sputtering discharge by Chapin ( 1974 ) reported target use of 26 %. however, the target use depends on the manoeuver parameters. As an case the top out in the ion stream distribution peaks more sharply for higher magnetic sphere force | B | as the width of the erosion groove has been found to scale as $\propto \sqrt{{r}_{\text{ce}}}$, where ${r}_{\text{ce}}\propto 1/\sqrt{\vert \mathbf{B}\vert }$ is the electron gyration radius, as has been determined experimentally using electrostatic probes that were embedded into the cathode target ( Wendt 1988, Wendt et alabama 1988 ). The issue of low target utilization in a planar magnetron sputtering free can be resolved to a large extent by using rotating attraction assemblies. These increase the target utilization significantly and improve the film thickness homogeneity dramatically ( Iseki 2006, 2009 ) and target use a high as 77 % for a planar aim has been achieved using an asymmetrical yoke magnet social organization ( Iseki 2010 ). besides, due to this non-uniformity the situate traffic pattern depends on the substrate position with obedience to the target. For a given target size the deposit model depends on the working accelerator press, the target–substrate distance, the material being sputtered, and the substrate geometry. The thickness distribution from the planar magnetron aim is like that from a ring source having a cosine discharge feature and is dictated by the ratio of the race track spoke rrt and the target-to-substrate distance ℓts. For ℓts ≪ rrt the film exhibits off-axis vertex in the film thickness, while for ℓts ≫ rrt the film is peaked on-axis. The optimum film uniformity is obtained when the race cut average radius is about 0.75 × ℓts or rrt/ℓts ≈ 4/3 ( Waits 1978b ). For industrial application of the process, issues such as aim use, throughput, deposition uniformity, and film properties are of significant concern ( Teer 1988 ). It is difficult to achieve uniform coating from a single cathode prey on complex structures. therefore, the magnetron sputtering systems used in industrial settings frequently consist of multiple long orthogonal cathode targets that surround rotating workpieces, in order to provide uniform deposit ( Monaghan et alabama 1993 ). such musical arrangement consisting of four magnetron assemblies is shown schematically in visualize 6 .Figure 6. Figure 6. A conventional showing a top horizon of the charismatic field shape and the rotating substrate holder in the close field unbalanced multi magnetron system, consisting of four magnetron assemblies, used for industrial applications. After Kelly et alabama ( 1996 ). download number : Standard image
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3.1.3. The rotatable cylindrical magnetron

For large area coatings of architectural glass and display panels boastfully cylindrical targets are normally used. The rotatable cylindrical magnetron sputtering target was primitively proposed to alleviate the trouble of low aim utilization ( Wright and Beardow 1986 ). The cathode target is a cylindrical tube and the magnet assembly is installed inside the cylinder ( McKelvey 1982, Wright and Beardow 1986 ) as seen in figure 4. The magnet assembly is stationary with regard to the exhaust chamber walls and so is the IR. It is alone the cylindrical cathode target that rotates during the sputter action and frankincense erodes uniformly as the target surface is continuously exposed to the plasma zone resulting in a consistent corrosion around 360° of the prey open. In this rotate shape the aim use can be angstrom high as 90 % and the target life increases substantially. For a cylindrical prey the coating uniformity can be in the range of a few percentage even for cathode target sizes in the image of meters. This proficiency is substantive for the deposition on large area glaze for architectural and automotive applications, for roll-to-roll web coat, ampere well as for the production of flat control panel displays and photovoltaic solar cells ( Blondeel et alabama 2009 ). In these big area in-line coaters, the substrate is moved proportional to the rotating magnetron cathode target in a linear fashion. The target surface sphere may be a big as hundreds and up to tens of thousands of square curium. In some cases the attraction fabrication is wobbled for improved layer thickness distribution ( Krempel-Hesse et al 2009 ). Insulating layers are deposited using a reactive sputter action where a metal is sputtered in the presence of a reactive gasoline. During reactive splutter ( see section 5 ), the active region of the rotatable target can be maintained exempt of a compound layer build up due to continuous sputtering with rapid rotation speeds ( 20 rev/min ) ( Nadel et alabama 2003 ). however, insulator layer can end up on the cathode target and on the anode, leading to process instabilities such as arcing and disappearing anode ( coating of the anode causes it to disappear from the circuit ). Both these issues can be resolved by sinusoidal alternating current or bipolar pulsed sputtering where the roles between cathode and anode are alternated between two rotating magnetron targets ( Blondeel and De Bosscher 2003, Christie 2013 ) ( see besides incision 4.2 ). The two targets alternate roles as cathode and anode, depending on the polarity of the exponent provision output. This eliminates the indigence for explicit, break anode. The anode is cleaned sporadically, even when dielectrics are deposited. This approach is normally referred to as double magnetron clamber ( DMS ) and it is wide used for the industrial production of coatings on methamphetamine in large-scale in-line coaters in a double rotate cylindrical magnetron setup located above a glaze transport system ( Brückner et alabama 2005 ) .

3.2. Balanced–unbalanced magnetron sputtering

Sputtered and evaporated films typically exhibit columnar microstructures when the adatom mobility is gloomy ( e.g. limited surface diffusion and no bulk diffusion ). As clamber is a line-of-sight summons, the film forming corporeal flow chiefly falls onto the surface that is facing the cathode coat and early parts lie in a ‘shadow ‘. such ‘shadowing ‘ can occur as the column or grains grow outward from the substrate/film interface, which leads to invalidate regions both within the grains deoxyadenosine monophosphate good as at the ingrain boundaries. The presence of voids and open grain boundaries reduces the film multitude density and therefore resistance to oxidation and corrosion. Two approaches can lead to the desired dense microstructure : ( i ) increase the substrate temperature and therefore the surface dispersion ; ( two ) apply ion assisted deposition, and thereby increased adatom mobility and permit atoms to move about on the coat and fill some of these voids, which results in a dense microstructure. however, for many applications, increasing the substrate temperature is deleterious to the substrate, leaving ion-assisted deposition as the only suitable option. variation in the magnetic field military capability and configuration powerfully influences the discharge properties and thus the process conditions such as plasma concentration, discharge electric potential and discharge current ( Ekpe et alabama 2009 ). By varying the magnet shape in the planar magnetron sputtering discharge it is potential to improve the ion barrage on the substrate during film deposition by extracting ions from the IR toward the near-substrate area ( Rohde 1994, Savvides and Window 1986, Window and Savvides 1986a, 1986b ). In a conventional or balanced magnetron sputtering acquit all the airfield lines of the magnetic trap form closed loops between the magnetic poles as seen in figure 7 ( a ). however, in world it is not easy to construct a perfectly balanced magnetron assembly. If one set of magnets is stronger than the other the magnetron assembly is said to be unbalance. To achieve unbalance attraction configuration, the central magnet can be strengthened with regard to the out magnet. In that font some of the field lines are directed to the chamber walls and the plasma density in the substrate vicinity is gloomy. This arrangement is called unbalance magnetron forum of type I ( Window and Savvides 1986a ) and is shown schematically in number 7 ( bacillus ). The magnetic airfield of the out perch can besides be intensified proportional to the cardinal pole. In that case, not all the battlefield lines are closed between the central and out attraction poles, and some discipline lines are directed toward the substrate, and some of the electrons are channeled along these airfield lines. consequently, the plasma is not only strongly confined to the IR, but it is besides allowed to flow out toward the substrate. thus, relatively high ion currents can reach the substrate. As the ions reach the substrate, by biasing the substrate, the ion bombing energy can be controlled. This musical arrangement of the magnetron assembly is referred to as unbalance magnetron forum of type II ( Window and Savvides 1986a ) and is shown schematically in figure 7 ( coke ) .Figure 7. Figure 7. A conventional of the magnet configuration in planar magnetron sputtering discharges. The three cases, ( a ) all the field lines that originate from the central magnet enter the annular attraction ( balanced ), ( boron ) all the field lines originate from the central attraction, while some do not enter the annular magnet ( unbalanced type I ), and ( carbon ) all the field lines originate from the annular magnet, and some do not enter the cylindrical cardinal magnet ( unbalanced type II ). Reprinted from Gudmundsson and Lundin ( 2020 ), with permission from Elsevier. download number : Standard image
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Despite the benefits of type II unbalanced magnetron, by increasing ion stream to the substrate, the exit of achieving uniform coat on complex components at acceptable rates from a single source remained an issue. therefore, in order to exploit the magnetron sputtering engineering commercially, multiple magnetron systems had to be introduced. In the multiple magnetron system, the attraction arrays in adjacent magnetron assemblies can be arranged with either identical, or opposition magnet polarities. The former arrangement is described as ‘mirrored ‘ and the latter musical arrangement is referred to as ‘closed ‘ field configuration ( Sproul et aluminum 1990 ). In the closed field configuration, the field lines are linked between the adjacent magnetron assemblies. then the losses to the chamber walls are low and the substrate sits in a high density plasma. It has been demonstrated that process in the close field shape results in a significant increase of the ion-to-atom proportion incident on the substrate as compared to single target unbalance magnetron, while the deposit rate is not importantly influenced ( Kelly and Arnell 1998 ). On the contrary in the mirror musical arrangement, the field lines are directed toward the chamber walls. In that subject some of the energetic secondary electrons follow these field lines and are lost from the exhaust, resulting in a low plasma density in the substrate region. initially, the industrial systems consisting of multiple long rectangular cathodes that surround the rotate workpieces ( as shown in figure 6 ) had all the magnetron assemblies balanced. due to the size of these systems this resulted in a significant decrease in the ion current density, that reached the substrate. The degree of ion current density at the substrates was simply besides low to produce dense enough coatings, in particular when depositing onto complex shapes. meaning improvements were achieved by varying the magnetic field configuration. rather of using the same polarity magnets on the out magnets of all the magnetron assemblies, the polarities were alternated, to achieve a join of the magnetic field lines between the neighboring magnetron attraction assemblies, as can be seen in calculate 6. In this arrangement the magnetic field lines are linked in arrange to maximize the trap of electrons. This arrangement is referred to as closed-field unbalanced magnetron sputter ( CFUBMS ), and leads to a significant increase in ionization in the substrate vicinity ( Monaghan et aluminum 1993 ). This design is immediately normally offered using even numbers of magnetron assemblies ( 2, 4, 6, 8 ). It allows the consumption of multiple magnetron assemblies with different target materials as sputter sources which then can be applied to deposit alloys or compounds consisting of few unlike metals. This besides means that by sputtering the versatile cathode targets simultaneously at different rates any hope admixture musical composition can be attained. This agreement can besides be applied to deposit layer debase structures, by alternate spatter of different targets. It has been claimed that the development of the unbalance magnetron and its incorporation into CFUBMS systems are the cause for the surface in importance of magnetron sputter deposition in versatile industries ( Kelly and Arnell 2000 ). The CFUBMS systems are presently widely applied to deposit wear and corrosion repellent surface coatings for assorted applications .

3.2.1. The magnetic field structure

A typical charismatic field distribution above a 76 millimeter diameter circular planar cathode target is shown in calculate 8. For a round target axile isotropy can be assumed. The magnetic airfield was produced by permanent magnets, a central attraction and an annular out ring attraction. The magnetic field was measured using a Hall probe with 1 millimeter steps in both radial and axial focus. The magnetic plain is tangential to the cathode surface at a spoke of about 21 millimeter. The magnetic nothing sharpen is the distance from the target come on to the point where the magnetic magnetic field density changes its steering and is denoted by znull. It can be seen that the magnetic null znull is 42 millimeter above the target surface and on the discharge center axis. As the human body indicates the magnetic field is largely confined to the cathode prey coat, and falls off with increase outdistance, and the field has reduced by approximately 80 % about 20 millimeter from the target come on. It is seen that the magnetic trap region is enclosed by the field lines that both embark and exit on the cathode target surface. We besides see in calculate 8 that there are field lines that connect the cathode to the substrate. Electrons can escape the magnetic trap region and can reach the substrate vicinity, when they are scattered onto these field lines. The magnetic field shape seen in figure 8 indicates a type II unbalance configuration as shown schematically in calculate 7 ( deoxycytidine monophosphate ). For a type II unbalanced shape, a magnetic nothing orient is always introduce and the far-field dipole moment is dominated by the out ring of magnets and the dominant electron losses are axile rather than radial. An analytic representation of the assume field shape for a cylindrical attraction arrangement consisting of permanent magnets, a central and an annular out ring magnets, in terms of generalized hyper-geometric function is given by Krüger et aluminum ( 2018 ). They demonstrate how these functions can be fitted to experimental data, like those presented in figure 8, with a least square method acting to achieve a fully analytic sphere exemplar for a given attraction arrangement .Figure 8. Figure 8. The confining magnetic field above a planar circular cathode aim. The data were taken using a Hall probe with 1 millimeter steps in both radial and axial direction. The solid lines with arrows represent the direction of the magnetic field, while the biased background represents the magnetic field force. The airfoil of the cathode target is located at z = 0 millimeter, the gloomy repair is the ground anode surround, and the brown fastness depicts the target clamp. number provided by Zanáška and Mainwaring ( 2020 ). download digit : Standard image
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3.2.2. Degree of balancing

The degree of unbalance can be varied by varying the proportional positions of the permanent magnets or having the magnetic field provided by electromagnets where the magnetic field lastingness is controlled by external stream. The degree of unbalance can be utilized to control the ion flux toward the substrate. consequently, there is a need to have a measure of the academic degree of balance. The charismatic null point znull can be used as a simple measure of the degree of derangement, but it gives identical limited data on the airfield regional anatomy. A abject rate of znull corresponds to a powerfully unbalance magnetron fabrication and high value znull corresponds to a balanced magnetron assembly. As a better meter to quantify the degree of imbalance Svadkovski et alabama ( 2003 ) introduced two parameters, a coefficient of derangement and a coefficient of geometric unbalance, that can be used to quantitatively estimate the degree of charismatic unbalance in a magnetron sputtering discharge. The coefficient of unbalance K is defined as the proportion of the charismatic fluxes from the cardinal and peripheral magnets at the aim airfoilEquation (2) where B⊥1 and B⊥2 are the components of the charismatic liquefy concentration perpendicular to the target surface from the out and inner magnets, respectively, and S1 and S2 are the cross-sectional areas of the knocked out and inside magnets, respectively. When the magnetic fluxes of the extinct and cardinal poles are equal and all the lines of the magnetic field are closed between the poles the magnetron assembly is balanced and K = 1. When K > 1 the magnetic flux at the out pole exceeds the magnetic flux at the cardinal pole, and some of the magnetic lines flow via the extinct slope of the magnetic system, and the magnetron assembly is unbalance of character II as shown schematically in trope 7 ( carbon ). type I unbalanced magnetron, as shown schematically in figure 7 ( boron ), has K < 1. The unbalance level of a magnetron fabrication can be estimated using a coefficient of geometric unbalance KG given byEquation (3) where rrt is the average radius of the erosion groove. For the magnetic field distribution shown in figure 8 the coefficient of geometric derangement is KG = 42/ ( 2 × 21 ) ≈ 1 .

4. Pulsed magnetron sputtering discharge

The dcMS discharge is ideal for depositing reduce metallic films from electrically conducting targets. The direct current baron supply can be operated as a office, current, or electric potential generator, depending on the regulation method desired. Furthermore, depending on the application the enforce target electric potential wave form can vary. The wave form is chosen so that instabilities such as arcing are avoided, the ionization flux fraction of the sputter species is increased, to allow sputtering from two targets, or to make it possible to sputter from insulating targets. The prey electric potential wave form can be sinusoidal releasing factor ( Nowicki 1977 ) or pulsed in diverse waveforms ( Schiller et alabama 1993 ). The pulse magnetron sputtering discharge can be driven by either an asymmetrical bipolar pulsed ( Kelly et alabama 2000, Scholl 1998, Sellers 1998 ), symmetrical bipolar, or unipolar pulsed ( Kouznetsov et aluminum 1999 ) wave form. For the deposition from blockheaded electrically insulating ( frequently compound ) target materials rf power needs to be applied to the cathode aim ( much 13.56 or 27.12 MHz ). however, the releasing factor magnetron sputtering discharge has by and large a very humble deposition rate for insulator films .

4.1. Asymmetric bipolar magnetron sputtering

The asymmetrical bipolar mid-frequency magnetron sputtering free was developed to optimize the deposition of insulating films from conductive targets with reactive sputter ( Sellers 1998 ). Bipolar pulsed refers to the mutual opposition of the aim voltage that is alternated between negative and positive. reactive splutter to deposit oxides, nitrides or carbides, in which a metal target is sputtered inside a discharge of reactive gas is of significant importance and will be discussed in department 5. In asymmetrical bipolar pulsed magnetron sputtering the discharge electric potential wave form has inadequate pulse amplitudes. The veto voltage pulse amplitude is larger than the convinced electric potential pulse amplitude, and there is no off time between the different polarities. typically, in asymmetrical bipolar mode the target is pulsed between the normal operate on voltage and a slenderly positive ( approximately 10 % –20 % of the negative electric potential amplitude ) electric potential for a short-circuit duration ( the pulse-off time period ). The width of the positive electric potential pulsate is only a divide of the negative pulse width, frequently 10 % –20 % of the width of the minus pulse. A schematic of this wave form is shown in figure 9. During the damaging pulsation, ions are attracted to bombard the aim surface, and sputtering takes position. however, in the presence of reactive boast an insulating level forms on the prey surface and this layer may not be significantly sputtered as the compound level can charge up as low-energy ions are collected on the top coat of the insulator. As the plasma facing surface becomes positively charged the ion acceleration is limited which ultimately reduces the sputter output ( Gudmundsson and Lundin 2020, Sellers 1998 ). As the polarity is quickly reversed to a positive value, the plasma-facing surface of the insulator is neutralized and even charges negatively during the convinced pulse as electrons from the plasma are quickly attracted to the target airfoil. As the pulsate once more reverses the convinced ions can sputter this region with an increased energy compared to the pure metallic target and thereby reduce the compound divide on the aim surface. A significant dowry of each cycle is spent in the splutter manner, and the deposition pace from an asymmetrical wave form can approach that of a dcMS. consequently, this approach is sometimes referred to as pulse direct current splutter .Figure 9. Figure 9. The asymmetrical bipolar wave form. The negative electric potential pulse amplitude is larger than the plus electric potential pulsate amplitude. Sputtering occurs during the negative pulsation. The width of the convinced electric potential pulsation is only a fraction of the negative pulsation width, and a significant part of each motorbike is spent in the sputter mode. The plus voltage amplitude is roughly 10 % –20 % of the veto electric potential amplitude. download figure : Standard image
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This type of wave form is applied to prevent arcing on the prey airfoil during the deposition of nonconductive film. As a insulator level is formed on the cathode aim surface the consequence is accumulation of positive mission on the cathode aim surface which can finally cause arcing. In sputter deposition using pulse power, the optimum frequency of pulse, the pulse duration, and the relative pulse heights depend on the target being sputtered and the film being deposited. typically, the magnetron sputtering fire is pulsed in the culture medium frequency range ( 10–250 kilohertz ) when depositing insulator films ( Schiller et aluminum 1993, Sellers 1998 ). It has been observed that operation in this frequency range importantly reduces the formation of arch, and therefore reduces the number of defects in the lodge insulator film .

4.2. Symmetric bipolar/mid-frequency ac magnetron sputtering

symmetrical bipolar or mid-frequency alternating current ( actinium ) waveforms are sometimes applied for the reactive deposition of oxide coatings from two targets ( Este and Westwood 1988, Heister et alabama 2000, Scherer et alabama 1992 ). Both waveforms use a voltage transposition at the cathode to offset appoint build up on the prey surface. then two targets, frequently placed side by side, are both connected to the lapp symmetrical bipolar pulser. One office run is connected to the first aim, while the early office lead is connected to the second target. In this arrangement, one prey is the anode for the system, while the other serves as the cathode target. When the discharge electric potential mutual opposition changes on the targets, the anode and cathode switch their roles. Sputtering from the cathode open during the damaging pulsation keeps the target come on clean, and when it switches its character to act as an anode, it is not covered with a insulator. This musical arrangement eliminates the disappearing anode problem, which is known to occur during pulsate district of columbia sputter of oxides when all surfaces including the chamber walls become report with an insulate oxide. This arrangement is referred to as DMS and is wide adopted by the architectural and automotive methamphetamine industries, with large rotating cathode targets, where the deposition runs tend to be long and therefore it is required that the process remains stable ( Brückner et aluminum 2005 ). The actinium frequency is nominally 40 kilohertz, however, sometimes the frequency is varied between 10 and 100 kilohertz to adjust the might delivered to the cathode by frequency modulation ( Scherer et alabama 1992 ) .

4.3. High power impulse magnetron sputtering

When a magnetron sputtering discharge is driven by unipolar pulses of high office it is referred to as a high exponent pulsed magnetron sputter ( HPPMS ). For gamey office density and short duty motorbike we talk about high power caprice magnetron splutter ( HiPIMS ) ( Gudmundsson et alabama 2012, Kouznetsov et alabama 1999, Sarakinos et alabama 2010 ). typically the repetition frequency is in the scope 50–5000 Hz, the duty bicycle 1 % –3 % and the extremum power concentration pt > 0.5 kilowatt cm−2. These discharges reach senior high school electron densities and expose significant ionization of the sputter species. The HiPIMS discharge is discussed promote in section 6.4. reactive HiPIMS utilizing symmetrical bipolar pulses of high power concentration, along with the benefits of DMS, has been demonstrated ( Čapek and Kadlec 2017, Zhou et aluminum 2018 ). More recently, Nakano et aluminum ( 2013, 2014 ) suggested applying a positivist pulse to the clamber target, right after the high office negative sputter pulse, to raise the plasma potential and accelerate ions out of the IR, toward the growing movie. This positivist pulse can be few tens to few hundred volts. This approach, sometimes referred to as bipolar HiPIMS or HiPIMS with a positive kick pulses, has been explored further by diverse groups ( Britun et alabama 2018, Hippler et alabama 2020, Keraudy et alabama 2019, Wu et alabama 2018 ) and has been reported to enhance the energizing energy of the ions of the sputter species, and thereby the application of the positive pulse provides an extra control knob for the deposit process .

4.4. Modulated pulse power magnetron sputtering

Modulated pulsation power magnetron sputter ( MPPMS ) is based on modulating the apply office pulsation such that during the initial phase ( a few hundred microseconds ) the office charge is mince ( like to dcMS levels ), followed by a high-octane pulsate ( lasting a few hundred microseconds up to a millisecond ). The resulting pulse is referred to as a macro-pulse. The pulse widths of the macro-pulse can be up to 3 master of science, at repeat frequencies in the lower end of HiPIMS operation, i.e. in the range between several 10 Hz and a few 100 Hz, leading to duty cycles well above 5 % ( up to 25 % ). The macro-pulse is composed of a train of shorter micro-pulses with frequencies in the range of several 10 kilohertz. The on- and off-times of these micro-pulses, which are typically up to respective 10 μs wide, a well as their frequency can be altered within the macro-pulses. Using this approach, varying the micro-pulse frequency and the on-and off-times, arbitrary tailored cathode electric potential and free current waveforms can be created including what appears to be a multi-step pulsate ( Chistyakov and Abraham 2009, Hála 2011, Liebig et aluminum 2011, Lin et alabama 2011 ). number 10 shows schematically the micro-pulses ( bottom ) and the result electric potential wave form on the cathode ( top ). A variation of the MPPMS proficiency is to apply packets ( or macro-pulses ) that dwell of a sequence of tightly packed micro-pulses whose duration is only a few μs. The light pauses between the micro pulses prevent the formation of discharge. This proficiency is referred to as deep oscillation magnetron sputter ( DOMS ) ( Ferreira et alabama 2016, 2014 ). By varying the cycle pulse on and off times, the peak target voltage and discharge current can be tailored. The duration of the macro-pulse in DOMS is 1–3 ms, and the repetition frequency is typically below 500 Hz .Figure 10. Figure 10. A conventional theatrical performance of the voltage wave form in MPPMS operation. The macro-pulse ( top ) is composed of a train of shorter micro-pulses with frequencies in the range of several 10 kilohertz. The voltage of the micro-pulses Vmp ( bed ) appears at the output of the pulser unit and the resulting discharge voltage VD ( acme ) appears on the cathode. From Hála ( 2011 ). download visualize : Standard image
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4.5. Arc detection and quenching

In magnetron sputter discharges instabilities can develop, in particular when operated at senior high school exponent density that can cause the large scale exhaust to collapse into a belittled bow of very high stream density. If left unhandled, the bow can begin to preferentially occur in the same location on the aim open, leading to damage to both the cathode target come on and the deposited film ( Christie et alabama 2004 ). In fact bow can be damaging for the films being deposited. These arcs normally leave in droplets being ejected from the aim open, and these droplets degrade the film choice. Therefore the exponent provision needs to have some means to detect and quench discharge, careless of the wave form desired. modern power supplies and pulsers normally have arc detection and suppression circuitry to reduce arc formation ( Christie 2004, Hubička et aluminum 2020a ). How the office provide handles the arch is crucial as if arcs are not stopped they lead to more arch. An arch can be detected by sensing a drop in the cathode electric potential or an addition in the discharge current. Once the arc is detected, the power provision cuts off power to the cathode and does not resume power pitch until the arch is cleared. As an bow is detected and power delivery to the aim is momentarily stopped, the baron stored in the ability delivery cable must be dissipated before the effect of the arc consequence is over ( Christie 2004 ) .

5. Reactive magnetron sputtering

Sputter deposition can be applied to deposit compound films either by sputtering a compound target or by sputtering an elemental target in a flatulence assortment of the inert working gas and a reactive natural gas ( e.g. O2, N2, CH4, etc ). The latter process is referred to as reactive splutter deposition or reactive spatter. A compound is the chemical bind between at least two chemical elements where at least one is a metallic element and the other is non-metal ( Strijckmans et al 2018 ). reactive splutter is attractive because a compass of compounds can be prepared from a low-cost metallic element target by addition of an allow reactive gas to the noble work flatulence. reactive spatter deposition is a topic of meaning industrial and technological relevance and the majority of commercially significant thinly films and coatings are compounds ( Kelly 2011 ). The most common compounds deposited by reactive clamber are oxides and nitrides ( Safi 2000 ) but other compounds such as borides ( Blom et alabama 1989 ), carbides ( Zehnder and Patscheider 2000 ), sulfides ( Hubička et aluminum 2020b ), and selenides ( Thornton et aluminum 1984 ) can be synthesized. such coatings are typically deposited by reactive magnetron sputtering using asymmetrical bipolar mid-frequency, reticular formation or unipolar pulsed ( HiPIMS ) waveforms. reactive sputter deposition is a huge and very significant topic and for further details the readers are referred to a holocene tutorial by Strijckmans et aluminum ( 2018 ) and a review by Sproul et alabama ( 2005 ). here, only a few fundamental concepts are reviewed. At the typical work gas pressures applied in reactive splutter deposition ( ⩽2 Pa ), reaction between the reactive accelerator and the sputter species can not occur in the gas phase as the energy and momentum can not be conserved in a two-body collision ( Strijckmans et al 2018 ). however, surfaces can act as a third base torso for the reaction, and consequently a surface is needed for the chemical reaction to occur. The reactive gas does not only react at the substrate and at the chamber walls, but besides at the cathode target. once a chemical reaction takes set at the prey surface, the overall sputter procedure is influenced, as both the sputter yield and the junior-grade electron emission concede are substantial dependant. Often the splutter yield of the compound material is substantially lower than the sputter render of the elementary target material. ascribable to this the deposition rate decreases as the menstruate rate of the reactive gasoline is increased. consequently, fewer atoms of the elementary aim material are sputtered and fewer reactive accelerator species are consumed, and a sudden and sharp rise in the reactive natural gas partial derivative blackmail occurs and the resulting deposit film becomes rich in reactive gas species. consequently, the kinship between the intensify film composition and the flow rate of reactive gas is non-linear. similarly, the deposition rate exhibits a non-linear addiction on the stream rate of the reactive boast. due to the varying spatter yields the deposition rate does not decrease and increase at the like prize of the stream rate of the reactive boast. This consequently results in hysteresis and the separation width between the decrease and increase denotes the width of the hysteresis region. This besides means that it is possible to deposit compound films of different stoichiometries and physical properties at two stable operating states, that correspond to the lapp value of the flow rate of the reactive accelerator, within the region of hysteresis. The hysteresis effect is therefore plainly due do to a competition between two opposing processes : the formation of a colonial on the target surface and sputter of the compound off the target open. formation of compound material on the target airfoil is frequently referred to as target coverage or target poison. The target poisoning occurs through several processes ( Strijckmans and Depla 2014 ) that include : ( one ) chemisorption of reactive boast with airfoil alloy particles, creditworthy for the formation of a compound layer on the aim open, ( two ) knock-on implantation of reactive species into the subsurface region as the incoming ion bombards the surface where chemisorbed reactive atoms occupy, ( three ) direct implantation of an ion of the reactive gas into the subsurface region, responsible for compound geological formation within the target surface, and ( intravenous feeding ) deposit of already sputtered material back onto the target surface, efficaciously transporting the underlying substantial into the subsurface region. therefore, in accession to surface reactions, subsurface reactions of deep-rooted ions of the reactive flatulence into the target has to be taken into report. During the reactive sputter process both nuclear and molecular ions of the reactive gas will be formed and accelerated over the cathode sheath. As they impact the target come on they are neutralized, will break up, and get implanted into the prey. Under typical operating discipline for reactive clamber deposition the implantation depth of the atoms or ions of the reactive accelerator ( such as oxygen or nitrogen ) can reach several nanometers ( e.g. 2.5–7 nanometer ) ( Abe et aluminum 2005, 2007, Güttler et aluminum 2004 ). due to target poisoning the reactive clamber serve is inherently unstable and exhibits a strongly non-linear answer to variations in diverse operating parameters. This non-linear response is normally represented as a hysteresis curve that shows, e.g. the deposition rate ( name 11 ( a ) ), the prey electric potential ( calculate 11 ( b ) ), or the overtone pressure of the reactive natural gas ( calculate 11 ( hundred ) ) versus the flow rate of the reactant molecular accelerator, as shown here for the encase of Ti sputtering in Ar/O2 atmosphere ( Kubart et aluminum 2020 ). In calculate 11 ( a ) three main regions of operation of a reactive magnetron sputtering process are indicated. For a broken reactive gasoline flow, or senior high school pumping speed, the reactive accelerator does not react with the cathode target, the deposition rate is high, and the work is referred to as alloy modality spatter. All the add reactive flatulence is incorporated into the deposited film ( the partial blackmail of the reactive gas is low ( see figure 11 ( coulomb ) ) ), and the surface of the sputter aim is spare from compound formation, and the addition of the reactive flatulence does not affect significantly the splutter process. As the hang of the reactive accelerator is increased the deposit rate increases slenderly as the mass of the reactive accelerator atoms adds to that of the deposit metal. With far increase in the reactive natural gas stream, the deposition rate drops abruptly as a intensify forms on the target and a transition from metal to compound mode ( poison mode ) occurs ( down arrow ). With a inactive further increase in the reactive natural gas flow rate the deposition rate remains low. When the reactive flatulence flow rate is decreased again a conversion back to the metal mode occurs as there is not enough reactive gasoline to convert all the sputter metal into compound. This leads to an enhance clean of the sputter aim surface and increased metal sputter as seen in figure 11 ( a ) ( up arrow ). here the reactive accelerator run can not maintain the compound layer on the target coat and the discharge is back in metal mode. This occurs at lower reactive gas flow rate than the transition from alloy manner to compound mood .Figure 11. Figure 11. Evolution of process parameters ( a ) deposition rate, ( bel ) dismissal electric potential, and ( coulomb ) oxygen partial derivative atmospheric pressure with the oxygen flow rate in reactive clamber of Ti in Ar/O2 atmosphere. The arrows indicate the direction of the transition. Reprinted from Kubart et aluminum ( 2020 ), with license from Elsevier. download figure : Standard image
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hysteresis is observed when the effective sputter rate of the compound is lower than for the pure metal which is normally the case. The consequence is besides a far reduced consumption of the reactive gas and therefore increased formation of the compound layer on the target surface. Such a positivist feedback explains the abrupt exchange in the deposition rate observed in number 11 ( a ) ( down arrow ). The presence of hysteresis means that the operate point within the transition region is ill defined. due to the hysteresis the operation conditions are not unique but depend on the operation history. For the same reactive gas flow rate, the deposition process may be either in the metallic element or the compound modality, depending on the process history. Furthermore, a noise in the spatter process can cause a transition from one to the early mood. The hysteresis is particularly austere for oxides due to the large deviation in sputter yields between metal and oxide surfaces and an regulate of magnitude reduction of the deposition rate is much observed ( Berg and Nyberg 2005 ). The width of the hysteresis with esteem to reactive flatulence flow is besides larger when the difference in spatter yields is larger. Taking the exercise of Ti, the sputter concede for 500 electron volt Ar+ ions is about 0.69 for the pure metal, but lone about 0.05 for TiO2 ( Kubart et aluminum 2010 ), while for TiN it is 0.42 ( Ranjan et alabama 2001 ). besides as a compound is formed there is a change in the secondary coil electron emission give and more or less of the empty current at the aim surface can be carried by the electrons rather than the ions ( Depla et alabama 2007b, 2009 ). This means that the dispatch current rises for some materials but decreases for others as the clamber mode transitions from metal modality to compound mode ( see section 7.5 ) .

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5.1. Theoretical description of reactive sputtering

A exemplar developed to describe the ID–VD characteristics of a reactive magnetron sputtering drop was the first one to demonstrate a hysteresis behavior by showing S-shape in VD versus ID characteristics ( Steenbeck et alabama 1982 ). This model included musical composition dependence of the reactive natural gas gettering by the substrate or chamber walls ( Steenbeck et aluminum 1982 ). This estimate was developed into what is now referred to as the Berg model which is a childlike analytic model of the reactive spatter serve. The Berg model was originally developed to study the reactive clamber work in dcMS operation ( Berg et aluminum 1987, 1989, Berg and Nyberg 2005 ). It is based on identical simplified description of the sputter system but captures the effect of the hysteresis for practical operational and material parameters. The model system is divided into three parts : the cathode target, the substrate, and the ( void ) chamber. For each of the three parts a single variable is defined, and for each of these variables, a remainder equation is developed which determines the prison term evolution of the variable. The variables followed are the compound coverage of the cathode prey, denoted by θt, the compound coverage of the substrate come on, denoted θs, and the fond pressure of the reactive boast pRG. The exemplary assumes a constant coat concentration of metal atoms that is independent of the reactive accelerator atom concentration. The surface consequently represents a constant density of surface sites, which can be either metallic or covered with compound. The responsiveness of the system is specified by surface reactions that occur both at the target side and at the substrate side. This chemical reactivity is here specified by a stick ( or internalization ) coefficient SRG which stands for the probability of a neutral reactive species to bind with a absolve metallic element site. The stick coefficient is often assumed to be close to integrity but it could have a importantly lower respect ( Kubart et alabama 2020, Strijckmans et al 2012 ). A single stoichiometric factor omega for the compound MRz is assumed and refers to the phone number of bounded reactive accelerator atoms R to a single metallic element atom M. Formation of the compound is a consequence of a flux of reactive boast ΓRG. The reactive accelerator flux to the surface assuming the working gas to be ideal is given byEquation (4) where kilobyte is the Boltzmann constant, Tg is the flatulence temperature, and MRG is the bulk of the reactive gasoline molecule. note that the reactive natural gas flux is proportional to the fond pressure of the reactive gasoline, and the constant of proportion is κ. The model describes the hysteresis under steady state conditions, and is based on a few poise equations. The state of the cathode target is described by a divide θt which represents the fraction of all available target surface reaction sites that have formed a certain compound state with the reactive gas. The balance equality for the compound divide θt on the cathode aim open is formulated assuming that chemisorption of reactive gasoline on the prey surface is counteracted by removal through sputter of the compound. Assuming atomic sputter, metallic element and reactive boast atoms are ejected as individual atoms from the surface, the compound is removed at a rate ( Ji/qe ) YCC, where YCC is the overtone spatter give of reactive gasoline atoms from the compound, and Ji/qe is the ion flux to the coat calculated from the discharge currentEquation (5) where At is the aim area and γsee is the secondary electron discharge yield. This gives a poise equality for a compound formation on the prey surfaceEquation (6) where the first terminus on the right-hand english accounts for the geological formation of the compound due to the flux of diatomic molecules of the reactive gas to the metallic function of the target surface, and the second term describes removal of the reactive boast off the surface covered by the compound by ion barrage. The time development of the compound divide θs at the substrate is described by the balance equalityEquation (7) were the beginning and third base terms on the right side represent the formation of compound on the metallic fraction of the substrate coat by thermal flux density of reactive gasoline ( inaugural terminus ) and by reactive gas atoms sputtered from the target with one sticking coefficient ( third term ). deposition of alloy atoms ( moment terminus ) over the compound part of the substrate provides clean metallic surface and reduces the compound coverage. The fluxes of sputter species from the target with an area At are distributed uniformly over the solid receive substrate sphere As. To describe the come of reactive gas within the dismissal chamber, the fond press pRG or the number of reactive gas molecules NRG is used givingEquation (8) where the add reactive gas menstruation QRG, total ( in molecules/s ) is consumed at the cathode target ( second condition ), substrate ( third term ), or removed by the pump with a pumping speed Sp ( in m3 s−1 ) ( fourth terminus ). In the subject of atomic splutter, extra reactive boast may be supplied by sputtering from reacted parts of the target surface ( fifth condition ). The consumption of the reactive gas ( number of molecules per unit time ) at the target QRG, thymine is obtained from equality ( 6 ) ,Equation (9) while the consumption at the substrate isEquation (10) and the remaining reactive natural gas will escape from the process chamber through the pump system. The reactive flatulence that is pumped out of the system is thenEquation (11) The entire provision of the reactive gasoline QRG, tot is the kernel of all reactive boast consumptionEquation (12) The system of equations ( 6 ) – ( 8 ) can be solved analytically assuming brace express ( Berg and Nyberg 2005 ). In firm department of state, all the express variables have ceaseless values, the time derivatives on the left-hand side are zero, and the system of equations simplifies to a bent of algebraic equations. A solution for a set of dispatch parameters is shown in figures 12 and 13. number 12 shows the partial pressure of the reactive flatulence pRG versus the reactive gas flow. In the model, the reactive accelerator partial pressure is used as a system varying to ensure a single-valued solution in each manoeuver item. therefore, it is potential to obtain solutions inside the conversion region, and rather of a hysteresis loop, an s-shaped curve is obtained. similarly s-shaped swerve is obtained when the compound fractions on the target and substrate θt and θs, respectively, are plotted versus the reactive natural gas flow pace in number 13. The positions labeled P1–P4 in figures 12 and 13 mark the region in which hysteresis occurs ( shadowed ). The mannequin results are characteristic for the reactive processes where hysteresis occurs. The Berg model gives a thoroughly understanding of the beginning of the hysteresis in reactive splutter and reproduces its forms, and its influence on the operation of the empty .Figure 12. Figure 12. Calculated partial pressure of the reactive natural gas pRG versus supply of the reactive gas, QRG, toddler. The parameters assumed for the calculations Sp = 80 l s−1, YCC = 0.3, YMM = 1.5, SRG = 1, At = 150 cm2, As = 2500 cm2 and ID = 0.5 A. Reprinted from Berg and Nyberg ( 2005 ), with license from Elsevier. download human body : Standard image
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Figure 13. Figure 13. Calculated compound fractions θt and θs for the target and substrate, respectively, versus supply of the reactive accelerator, QRG, total. P1–P4 are only marked for the θt-curve. The parameters assumed for the calculations Sp = 80 fifty s−1, YCC = 0.3, YMM = 1.5, SRG = 1, At = 150 cm2, As = 2500 cm2 and ID = 0.5 A. Reprinted from Berg and Nyberg ( 2005 ), with license from Elsevier. download figure : Standard image
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bill that the original Berg exemplar merely accounts for the process of chemisorption for the intensify shape on the aim and does not take into report some significant aspects like ion implantation of the reactive gas. More advanced models, that take into bill more interactions with surfaces, such as the reactive sputter deposition ( RSD ) exemplar, have been developed ( Depla et alabama 2007a, Strijckmans 2015, Strijckmans and Depla 2014 ). In the RSD model the target is assumed to have a top layer airfoil of one monolayer of metallic atoms. Below this acme level is a subsurface region that extends up to a certain astuteness under the target surface. This depth profiling of the target permits including target implantation of reactive accelerator ions adenine well as knock-on implantation of reactive flatulence chemisorb at the target by the bombardment of reactive and inert natural gas ions ( Strijckmans 2015, Strijckmans and Depla 2014 ). The depth is taken as the maximum depth that a reactive gas ion may be implanted. Keep in mind that once reactive boast atoms are implanted, they have the ability to react with the metal and therefore change the respective properties of the target .

5.2. Process control

Growth of stoichiometric compound films at relatively gamey deposition rates can be achieved in the intermediate target coverage regimen ( or the transition zone ) between the metallic and poisoned mood ( Sproul 1998 ). It is authoritative to identify a stable operate point within the transition regimen that provides suitable deposition conditions that give the craved film properties. early on bulk hang control was applied to control the flow of reactive gas into the chamber in attempts to achieve a static function bespeak. But using stream control of the reactive gas for process control can lead to problems. If the target is set at a situate power and the flow of the reactive flatulence is increased, initially all of the reactive gas will be consumed by reaction with alloy surfaces, including the cathode target and the chamber walls. consequently, several process parameters change simultaneously when increasing/decreasing the reactive gas flow rate. besides the preciseness of standard coerce gauges ( e.g. void ionization gauges ) is frequently inadequate for control of reactive sputter deposition, as their accuracy much depends on the type of gas. A better approach is to achieve this operate sharpen by active feedback control of the fond pressure of the reactive boast ( Sproul et alabama 2005 ). This can be achieved as there is a flat relation between the partial derivative pressure of the reactive natural gas pRG and the prey compound fraction θt without the appearance of hysteresis. The steadily submit relation between pRG and θt can be achieved from equation ( 6 ) by assuming brace submit and using equation ( 4 ) to getEquation (13) which indicates that the partial pressure of the reactive gas forms a smooth curve as a function of the target colonial divide, demonstrating that the overtone pressure is suitable as a control argument. The transition between the metal modality and the compound modality is continuous. It is therefore appropriate to use partial imperativeness see of the reactive gases as it is potential to control the partial blackmail of the reactive flatulence at any craved set operating point and no forbidden compositions exists ( Sproul 1998 ). The partial imperativeness of the reactive gas determines the reactive gasoline blend to all surfaces as indicated by equality ( 4 ). A feedback control loop requires a precise measurement of the argument that characterizes the process express. however, mastermind measurement of fond pressures requires specialize instrumentation, which is not always available. This can be realized by quadrupole batch spectroscopy of the reactive gas species ( Sproul et aluminum 2005, Sproul and Tomashek 1984 ), by ocular emission spectroscopy to detect the splutter metallic species ( Schiller et aluminum 1987, 1982 ), or by using the cathode voltage as the feedback bespeak ( Affinito and Parsons 1984 ). The mass mass spectrometer provides a calculate read of the particular reactive natural gas while the ocular emission spectroscopy read and the cathode electric potential are indirect measures of the partial press. Spectroscopic monitor of the discharge that forms above the cathode target gives data on the deposition march that can be applied in a feedback dominance loop ( Schiller et alabama 1987, 1982 ). The ocular emission mass spectrometer monitors the emission spectrum from the plasma release which is then used to adjust the reactive boast flow rate often through a piezoelectric valve. This method is referred to as a plasma-emission monitor. The optical discharge mass spectrometer detects the optical emission from metal species that are excited during the reactive clamber serve. The discharge measurement is typically performed through a collimator tube with the help of a character optics system that is oriented parallel to the target surface ( records the radial emission ) and the idle signal is fed into a photomultiplier. The electric signal form the photomultiplier is sent to a proportional built-in derivative instrument accountant that controls the piezoelectric valve that determines the reactive gas stream. The ocular emission mass spectrometer determines the ratio of the intensity of discharge from metallic species during reactive sputtering with deference to the full discharge intensity when operate in metallic sputter mode. In non-reactive sputtering the metal channel intensity increases linearly with dispatch current over a across-the-board range. This indicates that a flat relation exists between the intensity of an emission line and the deposition rate. A similar flat relation besides exists between the emission volume of a characteristic line of the sputter species and the degree of oxidation of the deposited layer. For reactive sputtering the alloy tune intensity exhibits a marked drop with increase compound coverage of the aim. The increased coverage is accompanied by a reduction in the ion stream onto the aim which, consequently, causes a reduction in the alloy clamber rate. The ocular discharge based techniques are relatively humble price and can be very effective as changes in the reactive environment can be detected and updated within 1 megabyte. therefore, a high stability of the reactive acquit is obtained at a relatively depleted installed pump capacity for the reactive flatulence. note that the pumping speed besides plays a significant function and for sufficiently high pumping speeds the hysteresis may be avoided ( Kadlec et aluminum 1986, Okamoto and Serikawa 1986 ). The reactive accelerator flowing into the deposition chamber is consumed by two mechanisms : ( iodine ) gettering by the clamber material, and ( two ) removal by the pump system ( Kadlec et alabama 1986 ). An equilibrium state exists between these processes and the intake reactive gasoline. The gettering of the reactive gas by splutter material QRG, getter depends on many operating parameters, including QRG, tot and pRG and the boast temperature in the chamber, the total work accelerator blackmail, the discharge stream and electric potential and the chamber geometry. The balance state can be expressed asEquation (14) The solution of equation ( 14 ) is static when the deriativeEquation (15) is positive and unstable if the derivative instrument is negative. A typical reactive gas consumption swerve can be divided into metallic, transition, and compound modes according to the target coverage by reaction products, θt. In the metallic manner ( low θt ), QRG, getter increases quickly with increasing pRG ascribable to the fact that about all the reactive gas molecules from QRG, tot are gettered by the flux of sputter target atoms that are deposited on the chamber walls. At the maximum of the curve, virtually all the sputtered atoms participate in the gettering of the reactive gas ( i, gettering limit ). In the transition mode, QRG, getter decreases with a further increase in pRG due to the decrease in the number of sputter metal atoms. The hysteresis effect is eliminated ( using boast flow regulation ) if the follow condition is quenched ( Kadlec et aluminum 1986 )Equation (16) where Sp, vitamin c is the critical pump rush of the deposition organization. The hysteresis can therefore be avoided if the pumping focal ratio is greater than the critical pump rush given by equality ( 16 ). however, this critical pump rush is frequently unrealistically high and therefore it is frequently practically impracticable .

5.3. Hysteresis free operation

The presence of hysteresis in reactive sputter is a significant technological challenge, so the initial reports on hysteresis-free operation of reactive HiPIMS work received much attention ( Kubart et aluminum 2020 ). Wallin and Helmersson ( 2008 ) compared the behavior of dcMS and HiPIMS while depositing Al2O3 films in Ar/O2 mix from an Al target. They demonstrated deposit of stoichiometric alumina by reactive HiPIMS in the absence of a transition to the oxide mode. Although, the compass of oxygen gas run was limited during the HiPIMS operation, the HiPIMS process could be operated beyond the dcMS critical oxygen flow, and Al2O3 was deposited at a deposit rate comparable to the metal manner value without process control. The authors tentatively attributed the lack of hysteresis to the pulse nature of the HiPIMS serve, the impregnable aim clean during the pulses and limited oxidation during the off-time. similar observation was made by Sarakinos et alabama ( 2007 ) that reported increase deposition rates when sputtering a TiO1.8 target in an Ar/O2 mixture by HiPIMS compared to dcMS. The operation was hysteresis-free which was attributed to a stronger gasoline rarefaction in HiPIMS than dcMS, which resulted in a shrink target oxidation as less reactive gas is available. For the reactive deposit of ZrOx from a metallic prey in an Ar/O2 assortment a polish hysteresis-free transition between the metallic element and oxide modes is observe which is in contrast to the equate dcMS summons that exhibits an abrupt transition ( Sarakinos et alabama 2008 ). More late study of a DMS using Ti and Al targets in Ar/O2 and Ti targets in Ar/N2 by Čapek and Kadlec ( 2017 ) explored the hysteresis in reactive HiPIMS as the duty hertz and pulsation frequency were varied. They demonstrated a reduce hysteresis with increasing extremum ability for both oxides. The increasing peak world power besides influences the nitride processes without a clear hysteresis, and the transition from metallic element to nitride mode becomes more gradual. The authors explained the reduced hysteresis by back-attraction of the sputter metallic element. similarly, using the RSD model Strijckmans et alabama ( 2017 ) prove that implantation of ionized species of the sputter substantial that returns to the target is the main cause for the reduce or eliminated hysteresis and rule out the role of accelerator rarefaction as contributing to the hysteresis reduction .

6. Ionized physical vapor deposition

In direct current, releasing factor and asymmetrical bipolar magnetron sputtering discharges the movie forming material at the substrate consists chiefly of neutral atoms that are ejected from the target surface. It is often desired to have ions bombard the substrate as it is well established that low energy ion barrage ( ${\mathcal{E}}_{\mathrm{i}}$ is below the lattice shift threshold, ∼20–50 eV depending upon the ion and lodge film ) during deposition, has a meaning charm on the microstructure and properties of the growing film, including the degree and management of orientation, granulate size, the epitaxial temperature, the film mass density, a well as stress in the film ( Greczynski et alabama 2019, Greene and Barnett 1982 ). Ion barrage of the substrate during film nucleation enhances the adatom surface mobility, referred to as surface diffusion. Surface diffusion is one of the key mechanism in the growth of dilute films, since due to the motion of the adsorb particles, they can find each other, equally well as find active sites and epitaxial sites, which then defines the social organization of the deposited thin movie. Ion-assisted PVD, using inert gas ions, provides the possibility to control and enhance the materials micro-/nanostructure and phase development through increase chemical responsiveness and increase kinetics ( surface diffusion and mobility ) of the condense particles as driving forces ( Greene and Barnett 1982 ). however, bombarding the growing movie with ions of the noble working gas creates remainder ion-induced compressive stress in the film, while bombarding the growing movie with the ions of the sputtered corporeal has respective advantages : improvement of the film choice, improved pace coverage and accord can be achieved in deposition on substrates with complex shapes ( Greczynski et aluminum 2019 ). By ionizing the sputtered atoms the ion energy at the substrate can be controlled by applying a substrate diagonal and besides a directing deposit and collimation of these ions with the plasma cocktail dress adjacent to the substrate surface is made possible. It was suggested by Greene and Barnett ( 1982 ) that self-ion bombing of a growing film leads to an increase in crystalline paragon. Working flatulence ion barrage, has been extensively studied, while the effects of metal-ion beam on sparse film properties has been less explored. This is due to humble metal-ion flux fraction ( a few percentage at most ) in dcMS process and difficulties in separating metal-ion from working gas-ion fluxes. A PVD process in which, for the splutter species, the flux of ions is larger than the flux of neutrals, or Γi > Γn, is referred to as ionize physical vapor deposition ( IPVD ) ( Hopwood 2000b ). assorted IPVD techniques have appeared over the by three decades that can deliver a high degree of ionization of the sputtered substantial ( Helmersson et aluminum 2006 ). It is coarse to all of these techniques that the splutter species are exposed to a higher concentration plasma than is available in a typical dcMS, rfMS or pulsed district of columbia discharge. initially the magnetron sputtering IPVD processes were based on placing a secondary fire between the source ( the cathode target ) and the substrate in otherwise dcMS tool. The secondary drop creates a dense plasma that has the function of ionizing a large fraction of the sputter species ( Gudmundsson 2008, Helmersson et alabama 2006 ). This IPVD proficiency was initially developed to deposit metal layers and diffusion barriers into trenches or vias of high aspect proportion in microelectronic lying ( Hopwood 1998, 2000b, Rossnagel 1999 ). other methods of creating highly ionized sputtered material include shaping the cathode target in a detail means, in club to confine the electrons, referred to as HCM sputtering fire ( Klawuhn et alabama 2000, Lai 2000 ). IPVD has besides been achieved by applying a high might unipolar pulses of moo frequency and low duty cycle to the cathode target in order to create very high plasma concentration in the cathode target vicinity ( Gudmundsson et alabama 2012, Helmersson et alabama 2006, Kouznetsov et alabama 1999, Macák et alabama 2000 ). This is referred to as HPPMS. There are a few variations of the HPPMS proficiency. In HiPIMS a short pulsation of very high baron concentration, an nerve impulse, is applied to the cathode target and a long pause exists between the pulses ( the duty cycle is short ). The presentation of the HiPIMS technique, which provides high metallic element ion flux fraction, has made it potential to utilize the alloy ion bombardment in thin film deposit ( Greczynski et alabama 2019 ). In the modulated pulsate office magnetron sputter ( MPPMS ) discharge the pulses are longer and the top out baron density lower. hera the diverse IPVD techniques are reviewed, but first the ask operational parameters are discussed, and then the respective approaches taken to achieve highly ionized flux of the film forming material are reviewed .

6.1. Ionization of the sputtered species

IPVD is a deposition process in which the lodge species are initially released by a forcible mechanism and subsequently ionized while passing through a dense plasma. The flush of ionization of the flow of the splutter species is the most critical feature when using IPVD deposit technology. This horizontal surface is normally expressed as a relative ionization of the film forming material. here we discuss how the degree of ionization of the sputter species is defined and what is required of the plasma parameters for ionization of the clamber species to take place .

6.1.1. Ionization mean free path

In rate to ionize the clamber atoms the average distance a impersonal atom travels before being ionized has to be sanely short ( Hopwood 1998 ). The ionization mean free path for electron impact ionization is given byEquation (17) where five is the speed of the sputter inert atoms, kiz is the electron shock ionization rate coefficient and nebraska is the electron density. To keep the entail detached path for ionization of the sputter atoms inadequate, the speed of the sputter species has to be depleted, and the electron density has to be high. low speed of the sputter atoms is achieved by thermalizing the sputtered flux which in reality means increasing the working accelerator pressure. To give an estimate of the ionization mean free way ( Gudmundsson 2010 ) the working accelerator is assumed to be argon, the electron temperature is assumed to be 3 electron volt and the target is assumed to be made of copper. The average speed of Cu atoms has been measured to be 1 kilometer s−1 as it escapes the magnetron sputtering aim at 0.2 Pa ( Britun et alabama 2008 ). For imperativeness above a few Pa some slowing down of the sputter species can be assumed. A typical dcMS discharge operates at working gas pressure of 0.1–1 Pa, and the electron density in the substrate vicinity is assumed to be 1017 m−3. Thus for a dcMS the ionization mean loose path of the metallic element calculated using equation ( 17 ) is 162 centimeter for non-thermalized species and 49 curium if the speed of the splutter species has dropped to 300 megabyte s−1. consequently, the fractional ionization of the splutter atoms in a dcMS is expected to be identical low and chiefly due to Penning ionization. If the sputter species have speed of 300 m s−1, and the electron concentration is of the order of 1018 m−3 a path of a few centimeters is required to ionize the metallic element atoms. These are the typical parameters for an IPVD systems based on a secondary inductively coupled plasma ( ICP ) or electron cyclotron resonance ( ECR ) discharge. These discharges have to be operated at relatively high pressure of 1–5 Pa in order to slow down the splutter species enough to get a sanely short ionization entail free path. For electron density of 1019 m−3 the ionization mean dislodge way is of the holy order of one centimeter. These are the electron densities achieved in the HiPIMS discharge. The high electron concentration is the key to achieve the high degree of ionization of the splutter material .

6.1.2. Degree of ionization

The academic degree of ionization of the movie forming material is authoritative to quantify. There are three approaches normally used to describe the degree ( or fraction ) of ionization : the ionize flow divide Fflux, the ionized density fraction Fdensity, and the divide of the clamber metallic atoms that become ionized in the plasma ( sometimes referred to as probability of ionization ) denoted as αt ( Butler et alabama 2018 ). The ionized flux divide is defined as the proportion of the ion flux of the sputter material and the total flux of the splutter material at a given localization ( Hopwood 1998 )Equation (18) where ${{\Gamma}}_{\mathrm{i}}^{\left(\mathrm{s}\right)}$ and ${{\Gamma}}_{\mathrm{n}}^{\left(\mathrm{s}\right)}$ are, the ion and neutral fluxes of the species s arriving at the substrate or a detector, in units of m−2 s−1, respectively. The ionized flux fraction is frequently measured using a gridded energy analyzer where the collector is configured with a quartz crystal rate monitor ( greens et alabama 1997, Kubart et alabama 2014 ) and the results of such measurements are discussed in section 8.5. The ionize density fraction of species s is defined asEquation (19) where ${n}_{\mathrm{i}}^{\left(\mathrm{s}\right)}$ and ${n}_{\mathrm{n}}^{\left(\mathrm{s}\right)}$ are the ion and impersonal densities of the species s in the volume, respectively. The ionize density divide can be calculated from ocular emission spectrum from the discharge ( Bernátová et alabama 2020, Bohlmark et alabama 2005a, Christou and Barber 2000 ). The probability of ionization ${\alpha }_{\mathrm{t}}^{\left(\mathrm{s}\right)}$ of species s was primitively introduced by Christie ( 2005 ) ( although he used the note β ) when describing his long-familiar aim material pathways model ( see section 9.2. ). It is defined as the fraction of the total total of sputtered atoms that are ionized in the magnetron sputtering discharge .

6.2. Magnetron sputtering with a secondary discharge

Highly ionized flux of the sputter species was initially achieved by the application of a secondary discharge to create a dense plasma in the region between the cathode target and the substrate. then a large fraction of the sputtered atoms are ionized as they pass through the dense plasma on their path to the substrate. The first sputter-based IPVD systems consisted of a dcMS for physical splutter of atoms and a secondary discharge which could be either inductively coupled ( Kim and Yeom 2019, Rossnagel 2000, Rossnagel and Hopwood 1993, 1994, Wang et aluminum 1999 ) or microwave-driven ( Musil et aluminum 1991, Takahashi et aluminum 1988, Xu et aluminum 2001 ) discharges. An ICP source can be added in the region between the cathode target and the substrate. The non-resonant induction coil is placed analogue to the cathode, in basically a distinctive dcMS apparatus, immersed or adjacent to the plasma as shown in digit 14. The magnetron assembly is located on the top of the chamber and is typically operated as dcMS. The clamber species transit the dense plasma, created by applying reticular formation office to the gyrate, where they are ionized ( Barnes et alabama 1993, Rossnagel 2000, Rossnagel and Hopwood 1993, 1994 ). The reticular formation coil is typically located 3–4 cm vertically from the cathode target airfoil and has diameter that is 1.2–1.4 times the substrate diameter ( Rossnagel 2000 ). The inductive handbuild is typically driven at 13.56 MHz using a 50 Ω reticular formation generator through a capacitive match network. The rutherfordium might is inductively coupled to the dismissal, frequently across a insulator window. Inductively coupled discharges are normally operated with lend oneself reticular formation exponent of 200–1000 W resulting in an electron density in the range of 1016 to 1018 m−3, which broadly is found to increase linearly with increased applied rutherfordium power ( Hopwood 1992, Hopwood et aluminum 1993 ). sometimes a faraday shield is located just inside the releasing factor coils but outside of the cathode diameter ( Dickson et alabama 1998 ). The Faraday harbor is a metallic blast that has minor slits or openings which allow the reticular formation fields to penetrate into the discharge chamber. The Faraday carapace besides takes over the problem of deposition and potential desquamation and flake from the rutherfordium coils. For this application the ICP assisted magnetron sputtering discharge is much operated at pressures in the range 2–4 Pa to shorten the ionization path for the film forming corporeal by thermalizing the clamber species ( Rossnagel 2000, 1999 ) .Figure 14. Figure 14. A conventional of an ICP-MS in which a radio-frequency-driven inductively coupled discharge is placed parallel to the cathode target in the region between the cathode and the substrate. download design : Standard image
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Another access to increase ionization of the sputter material is to use a supplementary ECR discharge. The ECR discharge can be located between the dcMS source and the substrate ( Xu et alabama 2001 ), the cathode target can be placed between the ECR exhaust and the substrate ( Berry and Gorbatkin 1995, Gorbatkin et alabama 1996, Musil et alabama 1991, Ono et alabama 1984, Takahashi et alabama 1988 ) or the microwave power can be introduced to the discharge through coaxial-type cavity that surrounds the cathode target ( Yoshida 1992 ). The ECR drop gives high plasma densities ( 1017 to 1018 m−3 ) and is normally operated at low working gas pressures ( 0.01–2 Pa ). In the ECR discharge wave absorption requires application of a potent stationary magnetic field ( 87.5 mTesla at rapport ). ECR discharges are typically operated at microwave frequencies ( for example, 2.45 GHz ) and the microwave power is injected as a right circularly polarized wave through a quartz glass window and propagates along firm charismatic field lines to a plangency zone. The introduction of a magnetic field leads to a resonance between the microwave frequency ( ω ) and the electron cyclotron frequency ωce = eB/me within the acquit. Due to the cyclotron resonance, the gyrating electrons rotate in phase with the polarized brandish and the wave energy is absorbed by a collisionless heat mechanism. calculate 15 shows a schematic of an ECR assisted magnetron sputtering discharge, where ECR discharges are placed between the cathode aim and the substrate. Two microwave ECR discharge chambers are placed on the opposite sides of the serve chamber. Electromagnets are placed around the periphery of each of the ECR dispatch chambers to create magnetic plain of 87.5 mTesla and a resonance zone within each of the chambers. With the lotion of microwave exponent a dense plasma is created that is then transported toward the region between the cathode target and the substrate, by the divergent magnetic battlefield. The sputter species travel through this dense plasma on their path toward the substrate and some become ionize. This IPVD technique has besides been demonstrated for thermal evaporate metallic that was ionized by passing through an ECR discharge ( Holber 2000, Holber et alabama 1993 ) .Figure 15. Figure 15. A schematic of an ECR-MS apparatus, two ECR fire chambers are located at the opposite sites of the chief process bedroom. A highly ionize plasma is created in the region between the magnetron sputtering cathode target and the substrate. Reprinted from Gudmundsson ( 2008 ). download digit : Standard image
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In sputter deposition systems, based on a secondary high density drop, it has been reported that a meaning divide of the sputter species is ionize and that the ionize flux fraction increases with increased office to the secondary discharge. The ionize flux divide for Cu has been reported to reach values higher than 80 % ( Holber et alabama 1993, Rossnagel and Hopwood 1994 ). The ions of the clamber material can subsequently be accelerated toward the substrate to a desired ion bombarding energy by applying a direct current bias. The ICP assisted magnetron sputter ( ICP-MS ) discharge is still very widely used in the microelectronics diligence for deposition of metallic element films such as conductors, dispersion barriers, and adhesiveness and seed layers .

6.3. Hollow cathode magnetron sputtering discharge

The HCM sputtering discharge is a high-density plasma device, developed for IPVD applications, that uses entirely a single district of columbia ability provision to both sputter and to ionize the movie forming species. The most common hollow-cathode magnetron spatter source is simply a magnetron sputtering discharge that is confined in an invert cup-shaped target ( Klawuhn et alabama 2000, Lai 2000, Wang and Cohen 1999b ). This cathode target shape is shown schematically in figure 16. The hollow-cathode magnetron sputter reference consists of the cup-shaped prey, permanent sidemagnets, and a turn out attraction. Due to the specific cup geometry of the target, the electrons are electrostatically ( target is negatively biased ) vitamin a well as magnetically confined within the volume of the generator ( see name 16 ). therefore, electron losses are minimized and a high plasma concentration is achieved. typically the width and astuteness of the cup are approximately the same which provides a high probability that sputtered atoms are either ionized by the dense plasma or re-deposited on the face-to-face wall. This cup-shaped HCM sputtering discharge can operate at an arrange of order of magnitude higher office densities than a planar magnetron and at pressures in the substitute 0.2 Pa government ( Wang and Cohen 1999a, 1999b ), which is subtantially lower operate pressures than potential in a planar magnetron sputtering exhaust operation. low pressure operation is desired for anisotropic deposition, long throw deposition, to minimize contamination from the working boast, and improve prey utilization ( Wang and Cohen 1999a, 1999b, Wang 1998 ). due to the effective electron caparison by the charismatic cusp mirror the advocate normality in equation ( 1 ) has a higher value than observed for a planar dcMS discharges when operating at lower power and working flatulence coerce > 1 Pa ( Lai 2000 ). consequently, when operated at sufficiently high blackmail, the HCM sputtering discharge can operate in a constant electric potential mode in which the cathode electric potential is about freelancer of the remark power ( Lai 2000 ). however, when operating at high might and low working boast coerce ( < 1 Pa ) the exponent approaches 1 and the discharge current increases slower with increasing cathode electric potential ( Lai 2000, Wang 1998 ). This has been attributed to the reduced knead gasoline density and rarefaction when operational at high power. A singular attraction geometry provides a confining charismatic field that sustains a magnetron sputtering discharge within the cup-shaped hollow cathode and gamey plasma densities are achieved ∼1019 m−3 ( Klawuhn et alabama 2000, Lai 2000 ) and the electric potential needed to sustain the release is reduced compared to a planar configuration ( Sagás et alabama 2011 ). With a proper magnet design, the ions can be extracted toward the substrate. This refers to a magnetic field regional anatomy where the magnetic null at the opening of the excavate cathode and a magnetic cusp mirror is created to trap electrons inside the cup-shaped container .Figure 16. Figure 16. A schematic of a HCM prey. The cup-shaped target and the magnetic field shape confine the primary electrons within the excavate cathode and a magnetic cusp near the target opening acts as an aperture for plasma origin toward the substrates. Reprinted from Helmersson et alabama ( 2006 ), with permission from Elsevier. download digit : Standard image
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6.4. High power impulse magnetron sputtering discharge

Highly ionize flow of the sputter material can besides be achieved by applying high world power pulses with low duty bicycle to a magnetron cathode target. This is referred to as HPPMS. By decreasing the duty cycle the pulsation might density increases, and consequently the electron concentration, while maintaining the same time averaged baron to the cathode prey ( Gudmundsson et alabama 2012 ). The high point might density is the key to achieve the dense plasma and the coveted high degree of ionization of the splutter corporeal. This high power density provides the electron density essential to ionized the sputter atoms. There is an upper limit on the office load applicable to the aim but when pulsed the acme power can be compensated for by a lower duty bicycle. The trade off between duty hertz and the acme power concentration ( at the prey ), platinum, is illustrated in calculate 17. In a typical dcMS exhaust the office loading is normally a few tens W cm−2 while in the HiPIMS discharge the power loading during the pulse can peak to several kW cm−2. here platinum = 0.05 kilowatt cm−2 is taken as a typical amphetamine limit for a dcMS discharge before target damage sets in. Pulsed magnetron sputtering discharges operated below the dcMS limit are denoted as pulse dcMS and include the asymmetrical bipolar pulsed magnetron spatter discharges, discussed in section 4. For all discharges operated at office densities above the dcMS limit the higher bill power must be compensated for by a lower duty motorbike. The HiPIMS crop in flower office density is defined to lie above an HiPIMS limit platinum > 0.5 kilowatt cm−2. thus, HiPIMS refers to very high extremum exponent concentration and very low duty cycle. MPPMS pulses ( see figure 10 ) typically begin at a low power flush, frequently in the dcMS compass, followed by a stronger pulse of intermediate office density ( 0.05 < platinum < 0.5 kW cm−2 ) or tied into the HiPIMS range .Figure 17. Figure 17. An overview of district of columbia and pulsed magnetron sputtering discharges based on the peak world power concentration at the target platinum, and the duty bicycle. The dcMS specify is platinum = 0.05 kW cm−2 and the HiPIMS limit platinum = 0.5 kilowatt cm−2. Reprinted with license from Gudmundsson et alabama ( 2012 ) Copyright 2012, American Vacuum Society. download figure : Standard image
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HiPIMS provides a highly ionized blend of the clamber material, while being compatible with about any magnetron sputtering deposition system ( Helmersson et alabama 2006 ). The only significant difference between dcMS and HiPIMS deposition systems is the accession of a pulser unit of measurement. however, in reality some change of the magnetron assembly and the electric system may besides be necessary. This can include increase isolation to handle higher potentials, weakening the confining magnetic field, and improved cool of the magnetron assembly. Various pulsed power supplies have been developed to drive the HiPIMS drop and there has been a continuous growth of these pulser units during the past two decades ( Hubička et aluminum 2020a ). In the early demonstrations of this proficiency ( Gudmundsson et alabama 2002, Kouznetsov et aluminum 1999 ) the discharge voltage and dismissal current waveforms were not identical well defined as the memory capacitor was small and throw was thyristor based. Therefore, the pulse length was not identical well defined and the repeat frequency was determined by the line mains and thus limited to 50 or 60 Hz ( Hubička et aluminum 2020a ). late developments led to improvements in the release electric potential and current waveforms, a good as allowing variation of the repeat frequency, and a better defined pulse distance. Modern pulser engineering is often based on a interchange capacitor bank in which an insulated-gate bipolar transistor throw is used to connect an energy storage capacitor to the load ( the dispatch ) to initiate the pulse and then disconnect it at the end of the pulsation. These pulsers have large storehouse capacitors and provide identical stable voltage pulse that can be up to few hundred μs long. In the earliest reports the senior high school exponent pulse was superimposed on a dcMS discharge that maintains the fire between the pulses ( Mozgrin 1994, Mozgrin et aluminum 1995 ). This we now refer to as pre-ionized HiPIMS ( Poolcharuansin et alabama 2010, Vaina et aluminum 2007 ). This leads to faster ignitation of the fire. For more information on the basic circuits that have been developed and are used to create the high power pulse and the circuit parameters the reader is referred to Hubička et aluminum ( 2020a ) .

6.5. Substrate bias

Biasing is the application of a voltage to the substrate during deposition such that the substrate experiences barrage by positive ions of control energy. The pelt energetic ions enhance adatom migration, promote desorption of physically adsorbed atoms and shallow ion implantation, and caparison of impinging atoms ( Takagi 1984 ). lotion of substrate bias is therefore an effective method to control the microstructural development such as film texture and grain size, and thereby to tailor the properties of the situate film. These effects control the film growth and improve step coverage a well as rule out formation of some defects such as microcracks. This implies that a substrate bias voltage can be a key parameter during film deposition. Substrate ion barrage can be either beneficial or harmful for the properties of the film being deposited. In magnetron spatter discharges, the substrate ( or anode ) sheaths are typically ⩽1 millimeter and basically collisionless. The modal ion bombarding energy at the growing film is ( Greczynski et alabama 2019 )Equation (20) where ${\mathcal{E}}_{\mathrm{i}}^{0}$ is the average energy of ions entering the anode sheath, normality accounts for the charge department of state of the ion, Vpl is the plasma electric potential and Vbias the applied substrate electric potential. For sputter-ejected species, ${\mathcal{E}}_{\mathrm{i}}^{0}\approx \frac{1}{2}{\mathcal{E}}_{\text{sb}}$ where ${\mathcal{E}}_{\text{sb}}$ is the coat binding energy of the aim fabric ( see discussion in section 7.4.2 ). Equation ( 20 ) implies that in principle the ion bombarding energy can be controlled by varying the amplitude of the substrate bias Vbias. For dcMS operation the substrate bias is frequently provided by a district of columbia power supply. recall that in dcMS and rfMS operation the majority of ions reaching the substrate are ions of the inert working gas. In IPVD meaning dowry of the ions reaching the substrate can be ions of the film forming species. not only direct current bias is of relevance during the IPVD process. early on in the growth of HiPIMS it was observed that there is a time transformation between working gas- and metal-ions as they appear at the substrate ( Macák et alabama 2000 ). While sputtering a Ti50Al50 target with argon as the working accelerator at 0.13 Pa and peak drop stream density of 1.1 A cm−2, using optical discharge spectroscopy, it was observed that the utmost emission from the working accelerator ions precedes that of metal ions. The ions of the function gas are detected about simultaneously with the emanation in the empty current, while the metal ions are generated after some delay. The dominance of clamber species in the latter part of the pulse is due to the higher might density in HiPIMS, which leads to a dramatic decrease in working gas atom concentration due to gas rarefaction ( see section 8.3 ) and therefore only metallic atoms are available belated in the pulse. These findings have lead to approaches to synchronize the substrate bias during HiPIMS and loanblend HiPIMS/dcMS deposit as discussed in a holocene reappraisal by Greczynski et aluminum ( 2019 ). It is possible to synchronize a pulse substrate bias with the HiPIMS discharge pulsate to selectively attract certain ionic species. Synchronizing the substrate bias with the pulse power supply was first demonstrated for deposition of diamond-like carbon paper films on bombastic substrates in a HiPIMS discharge with a cylindrical cathode ( Bugaev and Sochugov 2000 ). The substrate bias voltage was applied with a check of 60 μs with regard to the electric potential pulsation applied to the magnetron target. however, Bugaev and Sochugov ( 2000 ) observed that the negative bias electric potential falls with clock during the pulse. This is due to an addition in the plasma concentration ( approximately proportionately to the discharge current ) during the pulse, which loads the bias ability provision down as any deviation from the floating electric potential requires more and more current drive which appears as a shed in the bias voltage ( Hubička et alabama 2020a ). After the discharge pulse is off, the plasma concentration decays quickly, and the substrate lode cursorily increases to a identical eminent electric resistance and the average bias electric potential increases. sometimes mid-frequency pulse district of columbia voltage or rutherfordium power is used for substrate bias, but the problem of reduce diagonal electric potential when the ion current is large, during the HiPIMS empty pulse, remains. The winder to successfully generate a well-defined bias bespeak or bias pulses during HiPIMS mathematical process is to present the substrate with a low-impedance electric potential reservoir, switched on and off by a fast interchange. A low-impedance electric potential source is most easily achieved with a regular district of columbia power supply and a polish capacitance that can handle the pulse stream without excessively much devolve in the output electric potential .

7. The basic physics of magnetic confinement and plasma–surface interaction

The magnetron sputtering discharge is based on confining the electrons in the cathode prey vicinity using magnetic sphere. The magnetron sputtering discharge is basically an E × B device and the presence of both electric and magnetic field complicates the transport properties of charged particles within the empty. Plasma surface interactions are particularly significant in the magnetron sputtering dispatch. The cathode is the beginning of film forming material and the deposit pace depends on the splutter yield. The clamber yield depends on the target substantial and the energy of the bombard ions. besides the junior-grade electron discharge from the target, upon ion bombardment, plays some function in energy transfer to the electrons and in the ionization of the working flatulence atoms and the ions of the film forming material. here we review the basic physics of electron confinement by the magnetic discipline and the plasma surface interaction, including electron transport, physical sputter and secondary electron discharge .

7.1. Magnetic confinement

A distinct feature of the magnetron sputtering discharge is that an external magnetic field is applied to confine the electrons. In a magnetron sputtering discharge, crossed electric and magnetic fields, E and B, respectively, confine the electrons in close E × B drift loops in the vicinity of the negatively biased cathode prey. consequently, the way of the electrons in magnetron spatter discharges is complicated due to the presence of both a magnetic field B and an electric playing field E. The electric field E appears within the sheath and pre-sheath and the magnetic field B is provided by permanent wave magnets or by current-carrying coils. In the planar shape the charismatic field is arched above the cathode prey and traps the electrons. Whenever the electrons encounter the cathode sheath edge they are reflected back into the region equitable above the race traverse and therefore they bounce back and forth along the magnetic field lines in cycloid-like trajectories until a collision occurs. This leads to enhanced ionization within the dismissal, due to the longer path lengths of the electrons. therefore, the majority of the ionization events occur in the region where the energetic electrons are trapped, the IR. In the absence of electric battlefield, an electron will gyrate in the magnetic field with the electron cyclotron angular frequencyEquation (21) and the represent rotation radius isEquation (22) where ve, ⊥ is the electron speed perpendicular to the magnetic field B. typical values for rce in a magnetron sputtering free are < 1 millimeter for thermalized ( cold ) electrons and up to 20 millimeter for secondary ( hot ) electrons ( Krüger et alabama 2018 ). This means that electrons in the prey vicinity have rotation spoke that is a lot smaller than the characteristic size of the confining magnetic field social organization, that is the electrons are magnetized. As a comparison, ions have a rotation radius rci of the order of few tens of centimeter and up to 1 megabyte ( Krüger et alabama 2018 ), which is larger than the characteristic size of the organization, and frankincense the ions are not magnetized by the relatively fallible static magnetic field. In the presence of an electric field the electron exhibits a net drift perpendicular to both the B and E playing field vectors, much referred to as Hall drift or E × B -drift ( Chen 2016, Lieberman and Lichtenberg 2005 ), which is given byEquation (23) and the electrons perform trochoid movements. For a planar magnetron exhaust, this drift is in the azimuthal direction, with typical drift velocities around 104 molarity s−1 within the IR. The resulting azimuthal current is frequently referred to as Hall current ( Rossnagel and Kaufman 1987b, Thornton 1978 ). In addition to the Hall current there is a roll driven by the electron atmospheric pressure gradient ( or diamagnetic drift ) written asEquation (24) The Hall drift ( equality ( 23 ) ) and the diamagnetic drift ( equality ( 24 ) ) resultant role in an azimuthal current flowing above the prey rush path. This azimuthal current can at times be respective multiples of the fire current ( Lundin et aluminum 2008a, Rossnagel and Kaufman 1987b ). Complications arise due to the fact that the local electric plain is determined by the plasma and the plasma boundaries, which need to be taken into account in a self-consistent manner .

7.2. Electron transport

The gesture of charged particles is determined by the charismatic field B and the gradient in electron pressure ∇pe. Outside of the sheath regions most of the discharge stream is carried by the electrons. The azimuthal stream flowing above the aim subspecies track is an electron current. For an electron menstruation and transport, classical collisions are normally less significant than ‘anomalous collisions ‘. In a fluid description these can be represented by an anomalous effective ion–electron momentum exchange meter constant τeff which, however, only applies to the cross- B component of the electron–ion relative gesticulate ( alternatively expressed, the electric resistance is a tensor $\bar{\eta }$ with a little field-aligned component ) .

7.2.1. Classical electron transport

In the presence of a magnetic airfield that is oriented vertical to the electric field the electron drift speed parallel to E⊥, is reduced by a agent $\left(1+{\omega }_{\text{ce}}^{2}{\tau }_{\mathrm{c}}^{2}\right)$ with respect to the unmagnetized case and is given byEquation (25) where τc is the classical collision time due to electron–ion ( Coulomb ) and electron–neutral collisions. The E × B speed in the azimuthal direction is thenEquation (26) The dimensionless cross- B transmit parameter ωce τc is frequently referred to as the Hall argument. In the absence of collisions the argument ωce τc becomes infinite, and the drift speed parallel to the electric field becomes zero which indicates that the electrons are trapped around the charismatic airfield. Therefore the amplitude of | v E × B| approaches the collisionless specify E/B. An crucial relation, first proposed by Rossnagel and Kaufman ( 1987a ), can be derived for the sheath when the pressure term is negligible. In the plasma bulk the electrons have to move across the magnetic field lines in ordering to arrive at the anode. The currents ( i, the electron drift in the ion rest ensnare ) across B are given by the classical Hall and Pedersen conductivities, which can be obtained from the popularize Ohm ‘s law as functions of the Hall parameter ωce τc. The electric-field-driven separate of the cross- B fire current density and the electric field are related through the generalize Ohm ‘s lawEquation (27) where σP is the Pedersen conduction. This gives the stream density proportion ( Brenning et alabama 2009, Lundin et alabama 2008a, Rossnagel and Kaufman 1987a )Equation (28) where Je, θ is the azimuthal stream density, JD⊥ is the discharge current density, σP is the Pedersen conduction, and σH is the Hall conduction. The Hall parameter can be obtained from a measurement of the current proportion Je, θ /JD⊥. Furthermore, decision of Je, θ /JD⊥ gives a direct measure of ωce τc, and thereby all ecstasy parameters needed for fluid mold, including the cross mobility μ⊥, the cross electric resistance η⊥, the conductivities σH and σP, and the magnetic field dissemination coefficient D⊥. For definitions and how these parameters are related to ωce τc, the lector is referred to Brenning et alabama ( 2009 ) .

7.2.2. Anomalous electron transport

transport of charged particles in a magnetron sputtering free is affected by collisions and assorted collective phenomenon. Collisions and corporate phenomenon suggest that electrons can escape the magnetic trap and actually reach the anode to close the fire racing circuit, frankincense they are necessity for the magnetron sputtering discharge operation. classical hypothesis of dispersion and electrical conduction where collisions move electrons across the magnetic field lines results in diffusion coefficients that scale as 1/B2. Faster or anomalous loss of plasma across magnetic battlefield lines is caused by micro-instabilities and is referred to as Bohm dispersion. In Bohm dispersion the diffusion coefficients scales as 1/B or as described by the semiempirical Bohm dissemination coefficients ( Bohm et aluminum 1949, Chen 2016 )

Equation (29) Bohm diffusion can be ascribed as anomalous collisions, with an effective collision time τeff. The empirically found constant 16 in equation ( 29 ) is the anomalous Hall argument, i.e., ${\left({\omega }_{\text{ce}}{\tau }_{\text{eff}}\right)}_{\text{Bohm}}=16$. The azimuthal drift currents in a round planar dcMS have been measured for a image of parameters and values in the range Je, θ /JD⊥ ∼ 3–35 have been reported ( Bohlmark et aluminum 2004, Bradley et aluminum 2001c, Rossnagel and Kaufman 1987a, 1987b ). The azimuthal float current was found to vary approximately linearly with the fire current. furthermore, none or alone a watery dependence on the working gas species or the cathode target fabric is observed ( Rossnagel and Kaufman 1987a ). Electron cross- B transportation in the HiPIMS discharge is a lot faster than classically predicted through collisions deoxyadenosine monophosphate well as being faster than Bohm diffusion. Brenning et aluminum ( 2009 ) show that the dispersion coefficient is roughly a factor of 5 greater than what Bohm dissemination would predict, or in the range 1.5 < Jeθ /JD⊥ < 5.5. The early measurements by Bohlmark et aluminum ( 2004 ) indicated Je, θ /JD⊥ ∼ 2. later Lundin et alabama ( 2011 ) observed version of the transport parameter Je, θ /JD⊥ over time and distance and values arsenic low as Je, θ /JD⊥ ≈ 2 are observed 7–8 curium from the cathode target surface. The Je, θ /JD⊥ values then increase with decreasing distance from the aim airfoil and approach the values expected for Bohm dissemination. little variations in Je, θ /JD⊥ with time are observed. These results are shown in figure 18 where Je, θ /JD⊥ above the race track are shown for 30, 60, 85, 100, and 130 μs into the pulse. The gloomy value of Je, θ /JD⊥ observed for a HiPIMS empty indicates a much more efficient electron transport across the magnetic field lines than for a dcMS release which is a result of decrease cross electric resistance η⊥ and thereby increased cross- B conduction and dispersion of electrons .Figure 18. Figure 18. Measured values of Je, θ /JD⊥ ≈ ωe τeff above the race track at 30, 60, 85, 100, and 130 μs into the pulse versus the distance from the cathode come on in a HiPIMS dispatch with 15 cm diameter copper target and argon as the working boast at pressure of 0.53 Pa with a pulsate duration of 200 μs and a repeat frequency of 100 Hz. The Bohm-value Je, θ /JD⊥ = 16 is indicated with a dashed note. The datum is taken from Lundin et alabama ( 2011 ). download digit : Standard image
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7.3. Cathode sheath

ascribable to the different masses of electrons and ions a space charge region, a sheath, in which electrons are largely excluded, forms adjacent to all surfaces. The sheath properties determine the energy and flux of charged particles that bombard the surface. Such a sheath is formed future to the cathode target and most of the enforce discharge voltage is dropped across the cathode sheath, the cathode descend region. In the cathode fall area the stream is about entirely carried by ions. A relation between the current density, the voltage drop across the cocktail dress and the cocktail dress thickness was derived by Child ( 1911 ), assuming that the initial ion energy is negligible compared to the sheath potential ( see besides Gudmundsson and Hecimovic 2017, ( section 4.3 ) or Lieberman and Lichtenberg 2005, ( section 6.2 ) ), givingEquation (30) which is normally referred to as the Child law or the collisionless Child–Langmuir police. here Vc is the voltage drop over the cocktail dress and direct current is the cocktail dress thickness. The cathode cocktail dress width in dcMS discharges has been measured using optical emission ( Gu and Lieberman 1988, Miyake et aluminum 1992 ) and laser-induced fluorescence ( LIF ) ( Choi et aluminum 1996 ) and has been found to be in the range of few millimeter. At the distinctive function pressures the sheath width is modest compared to the ion–neutral collision mean unblock path and therefore it is collisionless. Gu and Lieberman ( 1988 ) applied optical emission to investigate the addiction of the thickness of the cathode dark quad on charismatic field forte, for respective drop currents and working gas pressures, and found that it scaled as the Child law thickness, but was approximately twice as thick. They proposed a scaling for the sheath thickness in a planar magnetron sputtering dispatchEquation (31) consequently the cocktail dress thickness is expected to be smaller for higher current density such as in HiPIMS process. But the cocktail dress thickness is not uniform over the target airfoil. Using particle-in-cell/Monte Carlo collisions ( PIC/MCC ) simulations Kondo and Nanbu ( 1999b ) found the sheath thickness in dcMS discharge to be few mm and to decrease with increasing magnetic field lastingness adenine well as with increasing secondary coil electron emission. They besides found the sheath thickness to vary in the radial focus, it is thin, and |Ez | is the largest, halfway between the magnetic poles ( or above the race cut region ). The electric airfield within the cathode cocktail dress has been measured in a magnetron sputtering release with helium as the working gasoline using LIF ( Choi et aluminum 1996 ). The measurements show that the electric field exhibits a linear decrease with outdistance from the target airfoil within the cathode sheath with a gradient that depends on the discharge current concentration. As the dispatch current was increased ( angstrom well as cathode electric potential ), the electric field within the cocktail dress increased and the sheath width decreased slightly. however, the electric sphere appeared to have little dependence on the working gasoline pressure or magnetic sphere lastingness .

7.4. Physical sputtering

Sputtering is the process when an atom is ejected from a solid or a melted due to bombardment by energetic particles, much ions ( Behrisch and Eckstein 2007 ). Sputtering is the consequence of a momentum transfer from the energetic bombard particles to the target atoms. There are a number of processes that occur at the surface due to ion barrage. The bombarding ion species may physically penetrate into the come on area, and the effects of collisions can be felt into the near-surface area. For distinctive apply acquit voltages the incident particle has sufficient energy to break bonds and shift atoms within the aim. Some of the atoms in the airfoil area, referred to as chief pink on atoms, may gain substantial sum of the energy, transferred from the incoming particle through the collision. They in twist rap other atoms in the target and transfer momentum yet again and a cascade of backfire atoms forms along the way of the incoming ion ( Behrisch and Wittmaack 1991 ). As a leave of this collision cascade some of the momentum is transferred to the surface atoms. If one or more atoms are removed from the solid target, are ejected ( sputtered ), they are referred to as sputtered atoms. The collision cascade can occur in one of three categories depending on the ion bombarding enegy ${\mathcal{E}}_{\mathrm{i}}$ and the mass ratio of the projectile and the target atoms Mi/Mt : a single-knock-on cascade, a linear shower and a spike heel cascade ( Greene and Barnett 1982, Mahieu et alabama 2008, Sigmund 1969 ). In the single-knock-on shower, the entrance atom transfers energy to the target atoms, after undergoing a few one-to-one collisions, which are then ejected from the surface. In the linear and ear cascade processes, the bounce target atoms achieve high enough energy to generate secondary coil and higher genesis recoils. Thus a cascade of recoils is generated, and atoms at the surface may be ejected from the solid. It is refereed to as a linear shower, when the concentration of recoils is low adequate to ensure that most collisions involve entirely one move and one stationary atom. This process is referred to as being linear since the sputter move over is found to be proportional to the first power of the projectile energy. In the spike cascade summons, the concentration of recoils is then high that collisions between two moving atoms are frequently occurring. For magnetron spatter, it is the lower energy function of the linear cascade action that is of chief concern since the bombard ions have energy in the image of respective hundreds eV. The number of these bounce atoms produced at any given location depends on the amount of energy lost by the entrance ion at that location ( Ruzic 1990 ). The divide of cascade sequences that actually result in sputter events is quite low and therefore a solid fraction of the energy ( 75 % –90 % ) of the primary pelt ions is dissipated in the prey as heating system ( Vossen 1971 ). When driving the discharge with a rutherfordium waveform the target is heated further by the waste of reticular formation exponent .

7.4.1. Sputter yield

The potency of the sputter action is described by the sputter succumb. The sputter succumb Y is defined as the entail number of atoms removed from a prey airfoil for each incident ion. The splutter output depends on the energy of the bombard ion, and its batch equally well as the angle of incidence, and the surface binding energy. The maximum movable energy in a collision has to be larger than the surface binding department of energy or ${\mathcal{E}}_{\text{th}}+{\mathcal{E}}_{\text{sp}}{ >}{\mathcal{E}}_{\text{sb}}/{\Lambda}$” src=””/> where <img align= is the surface binding energy ( heat of sublimation ) of the target material, ${\mathcal{E}}_{\text{sp}}$ is the binding energy of a projectile to the target coat ( ${\mathcal{E}}_{\text{sp}}=0$ for noble gas ions ) and ${\Lambda}=4{M}_{\mathrm{i}}{M}_{\mathrm{t}}/{\left({M}_{\mathrm{i}}+{M}_{\mathrm{t}}\right)}^{2}$ is the energy transfer factor in a binary collision and Mi and Mt are the masses of the projectile ion and the target atom, respectively ( Eckstein 2007 ). consequently, there is a threshold department of energy below which sputtering does not take stead. This minimum ion energy required for sputtering to occur is given by ( Yamamura and Tawara 1996 )Equation (32) In fact Yamamura and Tawara ( 1996 ) give respective empirical formula for the sputter give as a function of ion bombarding energy and data for versatile combinations of bombarding ions and target materials. To calculate the splutter give way for a given impact species on a given target, as a serve of the department of energy of the incident particle, calculator codes such as TRIM ( transportation of ions in matter ) ( Biersack and Haggmark 1980 ), SRIM ( stopping and range of ions in matter ) ( Ziegler et aluminum 2008, 2010 ) and TRIDYN ( A TRIM pretense code including dynamic musical composition changes ) ( Möller and Eckstein 1984, Möller et aluminum 1988 ) are normally used. These codes are based on a binary collision exemplar and follow the incidental particles and all of its cascade atoms until they sputter ( remove an atom ) or their energy is besides low to escape the surface potential. In the energy roll of elementary matter to here, 20–5000 electron volt, the sputter render increases with increasing incident ion energy. For a simpleton appraisal in this department of energy range the sputter output can be approximated byEquation (33) where a, a material dependent parameter, and b ∼ 0.5 are meet parameters that are given for a particular combination of bombarding ion and target materials ( Anders 2010, 2017 ). Examples of fitting parameters for a few common metallic targets are listed in table 1. The sputter yield of an oxide or oxidize surface can be importantly lower than that for a pure alloy. Table 1. Fitted parameters a and bel for clamber yields given by $Y\left({\mathcal{E}}_{\mathrm{i}}\right)=a{\mathcal{E}}_{\mathrm{i}}^{b}$, for Al, Cu and Ti targets calculated by the TRIM code. From Anders ( 2010 ) . 

Ar+ ⟶ Al0.02960.512Al+ ⟶ Al0.10420.370Ar+ ⟶ Ti0.04250.443Ti+ ⟶ Ti0.02850.484Ar+ ⟶ Cu0.14210.468Cu+ ⟶ Cu0.06910.556 The sputtered atoms are emitted with some energizing energy from the target surface and the energy and angular distribution of clamber atoms differs significantly from evaporated atoms. This is discussed further in section 7.4.2. furthermore, some of the bombard particles are reflected as high energy neutrals while others are implanted into the surface. These high energy reflected neutrals can leave the target with energies that range from a few electron volt to respective hundred eV, depending on the energy of the bombard ions and the relative masses of the target material and the working boast ions. These reflected particles can retain substantial fraction of their initial energy and frankincense represent a reference of high-energy neutral bombing onto the film being deposited. While some of this energy is lost to collisions with the working accelerator atoms, the end influences the growth of the growing film, through processes such as surface dispersion at the substrate .

7.4.2. Energy and angular distribution of sputtered atoms

Atoms that are sputtered off a cathode target are well more energetic than atoms that are thermally evaporated from a surface ( a few electron volt as compared to about a one-tenth of an electron volt ). Often this is desired as this initial kinetic department of energy of the sputtered atoms has favorable effects on the film increase ( Petrov et alabama 1993 ). depleted operate pressures are frequently desired to minimize scattering of the sputter atoms. At broken working flatulence coerce the splutter process is a line-of-sight procedure and the flux density of the splutter species can not be easily controlled, as it consists of achromatic atoms. A broad distribution has been measured for clamber neutrals ( Stuart et aluminum 1969 ) and this distribution has been predicted by the Thompson random collision cascade model ( Thompson 1968, 1981 ). According to the Sigmund–Thompson hypothesis the energy distribution affair can be approximated byEquation (34) where ${\mathcal{E}}_{\text{sb}}$ is the surface binding energy of the prey material and molarity is the advocate in the interaction likely applied V ( radius ) ∝ r−m ( Hofer 1991 ). Often thousand is taken to be 0.2. This model predicts an energy spectrum that peaks sharply at $\frac{1}{2}{\mathcal{E}}_{\text{sb}}$, followed by a gradual decrease to higher energies $\left(\propto 1/{\mathcal{E}}^{2}\right)$. The department of energy distribution of atoms ejected from a aim is expected to be mugwump of the nature of the incidental ion angstrom well as the crystal social organization of the prey. The Sigmund–Thompson sputter energy distribution function, given in equation ( 34 ), slenderly overestimates the probability to sputter-eject energetic atoms. A modified distribution officiate was introduced by Stepanova and Dew ( 2004 ), where a shortcut energy ${\mathcal{E}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ was added to better reflect experimentally measured profiles. The modify energy distribution function isEquation (35) typical values of the constants are normality = 1, thousand = 0.2 ( Stepanova and Dew 2004 ), and ${\mathcal{E}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=20$ electron volt ( Lundin et alabama 2013 ). Since ${\mathcal{E}}_{\text{sb}}$ is typically in the rate 3–6 electron volt, the sputtered atoms are emitted with energy in the scope 1.5–3 electron volt. The Sigmund–Thompson and the Stepanova–Dew energy distributions for titanium are shown in digit 19 ( a ). Both curves are normalized to the utmost rate for comparison .Figure 19. Figure 19. ( a ) The Sigmund–Thompson and the Stepanova–Dew energy distributions for titanium with binding energy of 3.30 electron volt and the cut-off energy set to 17 electron volt and the constants were chosen as north = 1 and m = 0.2. ( b ) The splutter angular distribution for ions under normal incidence calculated by equation ( 36 ). download figure : Standard image
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The particles ejected from single quartz glass targets exhibit prefer directions. This angular distribution of the exhaust particles depends on the direction of the entrance particles. The angular distribution of the clamber atoms is frequently stated to be proportional to cosn θ, where north is a constant that depends on the energy of the incident ions and the bulk of the bombarding working gasoline ion and the mass of the prey atoms, and θ is the emission slant. This is referred to as the cosine law and it results from an isotropic angular distribution of the recoil velocities. For low incidental ion bombarding energy, a collision shower is formed which leads to a non-isotropic angular distribution of the sputter species with an under-cosine ( normality < 1 ) or cordate distribution. For gamey ion bombarding energy, the angular distribution of the ejected atoms tends to be over-cosine ( n > 1 ). Yamamura et aluminum ( Yamamura 1981, Yamamura et aluminum 1991 ) give equations for the angular distribution of sputter species due to ion bombardment under normal incidenceEquation (36) where B is a fit argument. The cosine distribution corresponds to B = 0, while B > 0 and B < 0 harmonize with angular distributions of over-, under-cosine, and cordate types, respectively. The factor B defines the determine of the angular sputter distribution. Equation ( 36 ) captures the cordate distribution ( smaller negative values of B ) that match to very low ion bombarding energy, while cosn θ is not suitable in this case. The more under-cosine the distribution is, the larger is the redeposition probability. This is because more particles will be sputtered under larger angles compared with the surface normal and the deflection angle needed for the particles to return will decrease. In the font of over-cosine distribution the opposite is true. Examples of the sputter species angular distribution for ions bombarding under normal incidence are shown in visualize 19 ( b ). It has to be kept in mind that in world the angular distribution of the clamber species is not autonomous of the energy of the ejected atoms. For a more detail discussion of the ion energy and ion angular distribution of the clamber material the reader can consult the reviews given by Hofer ( 1991 ) and Gnaser ( 2007 ) or the original exploit of Thompson ( 1968 ), ( 1981 ) and Sigmund ( 1969 ). In an attempt to increase directivity of the sputter deposition work it has been suggested to add a geometric, spatial filter, a collimator, between the cathode aim and the substrate ( Dew et alabama 1993, Rossnagel 1999, 2003, Rossnagel et aluminum 1991 ). This technique allows patterned sputter deposition of metals and alloys using conventional lift-off lithography techniques. The collimator is typically an array of tubes or holes with an aspect proportion ( length of the tube/diameter ) in the range from 0.5 to 3. During the sputter action, atoms which travel with an slant far from normal incidence ( > ±5° ) will impact the collimator inner walls and deposit there. Thus only atoms that travel along the axis of the collimator tube transit the collimator and make it onto the substrate. The collimator array is grounded and appears as an effective anode for the discharge. however, this overture has a significant influence on the web deposit pace. A collimator with an expression ratio of 1:1 will exhibit a 70 % reduction in deposit rate compared to an open deposition system .

7.5. Secondary electron emission

bombing of a metallic surface by energetic electrons, ions or neutrals can lead to emission of electrons, referred to as secondary coil electrons. These electrons play a key character in dispatch physics. The secondary electron discharge give way or coefficient γsee is defined as the act of secondary electrons emitted per incidental species. The secondary electron discharge yield depends on the material being bombarded, its surface condition, the type of bombarding species, and the kinetic department of energy of the bombard species. In a magnetron sputtering discharge the cathode prey is kept at high minus potential. Thus the utter secondary electrons are accelerated away from the cathode target airfoil with initial energy roughly equal to the prey potential. For ions with low atom bombarding energy the secondary coil electron discharge yield is independent of the department of energy of the bombard particle and the electron discharge occurs due to transfer of the electric potential department of energy of the entrance ion or atom to an electron in the target ( Abroyan et aluminum 1967, Hagstrum 1954 ). This constant secondary electron discharge concede is attributed to an Auger process and is referred to as potential emission. At higher bombard particle energy the secondary electron emission yield becomes dependent on the energy of the bombard atom, and the secondary electron emission is referred to as kinetic discharge which dominates at higher bombard energies. Kinetic discharge occurs when a bombard particle transfers sufficient kinetic energy to an electron in the target. typically, it starts contributing to the total secondary electron emission yield at a threshold energy of around a few hundred electron volts. For ion bombard energies expected in magnetron sputter discharges, it is the potential department of energy of the arriving ion projectile rather than its kinetic department of energy that dictates the secondary electron emission yield. In accession to the energy of the affect atom, the secondary coil electron emission succumb depends on the cathode material, but it rarely exceeds 0.2 for ions bombarding with energy below 1 keV. The cathode target condition significantly influences the ion induced secondary electron emission yield. clean metals, i.e. metals release of oxidation, boast adsorption, and other contamination, generally have higher electric potential emission yield and lower energizing discharge yield than contaminated metals ( Phelps and Petrović 1999 ). Phelps et aluminum ( Phelps and Petrović 1999, Phelps et aluminum 1999 ) give fits for the secondary electron discharge yield for the ion energy roll 10–10 000 electron volt for both clean and dirty metallic element surfaces bombarded by Ar+ ions and Ar neutrals. For Ar+ ions bombarding at 400 eV their fit gives 0.07 for a clean alloy surface and 0.16 for contaminated alloy surface, which indicates that the target condition can play a meaning role in the discharge physics. Note that metastable atoms that are incident on a metallic surface may eject secondary electrons as their internal energy may be meaning. As an exemplar the secondary coil electron emission yield when a metastable argon atom bombards stainless steel is 0.21 ( Schohl et aluminum 1992 ). An empiric convention for secondary electron discharge output for diverse ions bombarding clean surfaces is given as ( Baragiola et alabama 1979, Baragiola and Riccardi 2008 )Equation (37) where ${\mathcal{E}}_{\text{iz}}$ is the ionization energy of the pelt ion, and ϕ is the work affair of the aim surface. This process can only occur when the condition $0.78{\mathcal{E}}_{\text{iz}}{ >}2\phi $” src=””/> is fulfilled. For electron emission to take place the ionization potential of the projectile has to be approximately twice the exploit routine of the target material. It was pointed out by Anders ( 2008 ) that for this reason, bombarding a distinctive metallic magnetron sputtering target, by individually charged metal ions can not execute potential emission. therefore, during self-sputtering of a metallic aim, no secondary electrons are emitted. The formation of oxide or nitride on a metallic surface has an influence on the secondary coil electron discharge output. A comprehensive examination review of the junior-grade electron emission coefficients for a scope of oxides has been given by Depla et aluminum ( 2007b ). They determined the secondary electron discharge yield from measurements of the discharge electric potential in dcMS discharge with argon as the working gasoline. Two groups of oxides, based on the variation of the secondary coil electron emission behavior with the surface oxidation, where identified. furthermore, they demonstrated that the open stoichiometry is crucial for dictating the secondary electron discharge. Compounds that form sub-stoichiometric oxides and are prone to discriminatory splutter of oxygen exhibit reduced secondary coil electron discharge upon oxidation. An model of this group of oxides is TiO2. The other group consists of oxides that do not lose oxygen preferentially and exhibit an increase in the electron emission upon surface oxidation. This group includes Al2O3. Depla et aluminum ( 2009 ) besides studied the influence of nitride formation on secondary electron discharge. They found that merely wide-band-gap semiconductor nitrides ( AlN and Mg2N3 ) showed a pronounce increase in the secondary electron emission output when a nitride is formed on the coat while other nitrides exhibited a decrease .</p>
<h2 class=8. Plasma parameters in magnetron sputtering discharges

The spatial and worldly variations of plasma parameters in magnetron sputter discharges have been explored extensively. The electrons are the main energy carriers in magnetron clamber discharges and they dictate the ionization processes and therefore the properties of the exhaust. The electrons are responsible for the ionization of the working boast atoms and the atoms of the splutter material, excitation of atoms to higher energetic levels, and in reactive clamber processes, excitement of molecules to higher vibrational or rotational states, dissociation of molecules, and creation of negative ions by attachment processes. In summation to electrons the empty consists of the neutrals and ions of the working boast, the neutrals and ions of the clamber species, and for reactive spatter, ions, atoms and molecules of the reactive natural gas. The flux of ions and neutrals and the energy distribution of these species influences the properties of the situate film. It is therefore important to know the energy and concentration of the versatile species .

8.1. Electron plasma parameters

The properties of electrons are described by the plasma parameters, the electron concentration northeast, the effective electron temperature Teff, and the plasma likely Vpl. There have been a issue of investigations of the spatial version of the electron plasma parameters in planar dcMS discharges ( Field et aluminum 2002, Rossnagel and Kaufman 1986, Seo et alabama 2004, Sheridan et alabama 1991, Sigurjonsson and Gudmundsson 2008, Spolaore et aluminum 1999 ). The electron density is highest in and near the magnetic trap above the race track area and is at a local minimum above the good region in the center field of the cathode target and near the edges of the cathode target ( Field et alabama 2002 ). The acme electron concentration measured in dcMS and mid frequency pulsed district of columbia discharges is shown versus fire current concentration in figure 20 ( toward the center of the graph ). The electron density measured in dcMS discharges, in the substrate vicinity, is typically in the range from a few times 1015 to a few times 1017 m−3. The electron energy distribution affair ( EEDF ) is found to be either Maxwellian like or bi-Maxwellian like, depending on the working boast pressure and spatial location ( Seo et alabama 2004, Sheridan et aluminum 1991, Sigurjonsson and Gudmundsson 2008 ). Maxwellian like electron department of energy distributions are found in or near the magnetic ambush ( the IR ) and bi-Maxwellian distributions are found farther away from the cathode target ( Sheridan et alabama 1991 ). The measure EEPFs along the exhaust center axis ( r = 0 ) in a dcMS operated with argon as the working gasoline at 0.4 Pa and a titanium target is shown in design 21. Two groups of electrons are apparent in the discharge and the EEPF is therefore bi-Maxwellian. The population of the high-energy electrons with ${\mathcal{E}}_{\mathrm{e}}{ >}$” src=””/> 3 electron volt decreases as the probe is moved away from the cathode target .<img alt= Figure 20. Compiled data showing the electron concentration versus the fire stream concentration measured in direct current diode and magnetron spatter discharges. Ta target Ar accelerator direct current diode ( Ball 1972 ), Cu target Ar gas dcMS ( Rossnagel and Kaufman 1986 ), Ag aim Ar flatulence dcMS ( Field et alabama 2002 ), Ti target Ar accelerator dcMS ( Seo and Chang 2004a ), Ti target Ar accelerator dcMS ( Seo et aluminum 2005 ), Cu prey Ar gas dcMS ( Sigurjonsson and Gudmundsson 2008 ), Cu prey He gasoline dcMS ( Sheridan et aluminum 1991 ), Al prey Ar gasoline direct current pulsed MS ( Bradley et aluminum 2001a ), Ti target Ar flatulence MPPMS ( Meng et aluminum 2011 ), Cu target Ar gasoline HiPIMS ( Gudmundsson et alabama 2009 ), Ti target Ar gasoline HiPIMS ( Meier et alabama 2018 ), Cu prey Ar boast HiPIMS ( Pajdarová et alabama 2009 ), and Ta aim Ar boast HiPIMS ( Gudmundsson et aluminum 2002 ). The blue horizontal dash-dotted line indicates electron concentration of 1017 m−3, below which Penning ionization dominates ionization of sputter species and above which electron impact ionization dominates ionization of sputter species. The loss smash vertical pipeline indicates JD, crit ≈ 0.2 A cm−2, to the left the clamber is ascribable to primary coil ions of the noble exercise accelerator and to the right recycle has to take target to provide the high free stream concentration observed. download visualize : Standard image
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Figure 21. Figure 21. The quantify EEPFs along the dispatch center axis ( gas constant = 0 ) in a dcMS operated with argon as the working gasoline at 0.4 Pa and a titanium target with a diameter of 50 mm and drop voltage of 350 V. Reprinted from Seo et aluminum ( 2004 ). ©IOP Publishing. Reproduced with permission. All rights reserved. download figure : Standard image
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The plasma potential is rather first gear < 2 V and is spatially uniform outside the magnetic trap in the distance > 20 millimeter from the target surface and decreases with increase working gasoline press. The abject and compressed distribution of the plasma likely traps the cold electrons. As the cold electrons are trapped by this plasma potential a bi-Maxwellian like electron department of energy distribution is observed in the downriver region as seen in calculate 21. For operate atmospheric pressure above 3 Pa the plasma likely falls below 0.2 V and the low energy electrons are lost and the EEDF transitions to become Druyvesteyn like ( Seo and Chang 2004a ). The electron temperature and the electron density are typically found to decrease with increase distance from the cathode target ( Rossnagel and Kaufman 1986 ). Outside the magnetic trap the plasma likely is broadly found to have weak addiction on spatial localization and working gasoline atmospheric pressure ( Field et alabama 2002, Sheridan et aluminum 1991, Sigurjonsson and Gudmundsson 2008 ). Sheridan et aluminum ( 1991 ) claim that the hot electrons observed are not energetic enough to be the secondary electrons emitted from the prey, but rather electrons created within the magnetic trap of the cathode spill region and roll to the downriver region under the influence of a divergent charismatic field ( Rossnagel and Kaufman 1986, Seo and Chang 2004b ). Sheridan et aluminum ( 1995 ) observe asymmetry in the measure electron speed distribution indicating a net electron drift away from the cathode with average speed of 1.9 × 105 meter s−1 ( 0.1 electron volt ). The asymmetrical bipolar pulsed magnetron sputtering fire typically exhibits higher time averaged effective electron temperature Teff ( Bradley et aluminum 2001a ) and increased time-averaged electron density compared to dcMS discharges, typically 30 % and 20 % for effective electron temperature and electron density, respectively ( Bradley et alabama 2001a, 2001b ). furthermore, this effect is more marked as the pulse frequency is increased. however, the electron concentration is typically of the club of northeast ∼ 1016 m−3 which is excessively low for the discharge to generate a hearty fraction of ionize sputtered material. It has been suggested that the increased electron heat is due to the pulse nature of the free and therefore stochastic inflame by the advancing sheath-edge during pulse-on, which may then heat the plasma globally through subsequent collisions ( Bradley et aluminum 2001a, Bradley and Welzel 2009 ). Measurements of the worldly variation of the effective electron temperature Teff and the electron density ne generally show a rapid ascent in Teff at both turn off and turn on, corresponding to the rapid transients in the fire voltage waveforms. The rapid rise in the electron density neon during the on time is observed to reach a utmost, coinciding with a minimum in the effective electron temperature ( Bradley et aluminum 2001b ). In accession a fusillade of hot or beam-like electrons, that appear shortly after the initiation of the negative splutter voltage pulse, have been observed ( Bradley et alabama 2001a, 2001b ). Modulated pulse ability magnetron sputter ( MPPMS ) discharges operate with relatively retentive pulses of high, but not extreme power densities, and allows the operator to play with the electric potential wave form, e.g. apply a bit-by-bit increase or decrease in the apply might ( Chistyakov et aluminum 2006, Lin et aluminum 2009, 2011 ). For the MPPMS operation the pulse duration is typically of the club of a few ms Because of this limited peak might density the bill plasma density is in the range 1017 to 1018 m−3 ( Meng et alabama 2011 ). Measurements of the temporal and spatial behavior of the plasma parameters in the HiPIMS discharge reveal a extremum electron density in the compass 1018 to 1019 m−3 ( Bohlmark et aluminum 2005b, Gudmundsson et alabama 2001, 2002 ). This is approximately two orders of magnitude higher electron density than normally observed in the substrate vicinity of a dcMS free. similarly, more recent work where the electron concentration in HiPIMS discharges is measured using THz time world spectroscopy reports peak electron concentration values that are in the range of 1018 to 1019 m−3, within the IR adjacent to the target, for empty current densities of 1–4 A cm−2 at 0.5 and 2 Pa with argon as the working gas ( Meier et alabama 2018 ). The top out electron densities versus the extremum discharge current concentration during HiPIMS operation are plotted in figure 20 for a few discharges and appear in the upper correct recess of the graph. The dense plasma, that is formed during the HiPIMS pulse, within the IR, expands from the aim as an ion acoustic wave, with a fixed speed that depends on the working gas pressure ( Gylfason et aluminum 2005 ). A high plasma concentration ∼ 1017 m−3 is normally observed to linger at large distances from the target surface for a quite long time after the pulse is off, up to a few master of science ( Gudmundsson et aluminum 2002, Horwat and Anders 2010 ). In bipolar HiPIMS operation a positive pulse follows the veto sputter pulse ( Keraudy et alabama 2019, Nakano et alabama 2013, 2014 ). In that case the floating likely is slenderly negative during the negative pulse, while the plasma likely is slenderly positive. When a positivist pulse follows the negative pulse the floating potential and the plasma likely ascent sharply to a boastfully value of few tens of volts ( Hippler et alabama 2020 ). The electron density increases during the damaging pulse and decreases during the positivist pulse and during the afterglow. furthermore, the electron concentration decays faster when a cocksure pulse is applied compared to when it is not ( Hippler et alabama 2020 ) .

8.2. Neutrals and ions

In accession to electrons the empty consists of the baronial cultivate gas and its ions equally well as the film forming corporeal. The movie forming material consists of neutral atoms sputtered off the target and its ions. In reactive clamber there are atoms, molecules and ions of the reactive natural gas that besides contribute to the film increase .

8.2.1. Neutral gas temperature

The setting working gasoline is frequently considered to be in thermal chemical equilibrium ( thermalized ) ascribable to collisions within the gas and with the walls of the vacuum chamber. For dcMS Britun et alabama ( 2007 ) find the argon working gas temperature to only weakly count on the give power, but to increase steeply with increasing working gasoline coerce from 700 K at 0.27 Pa to about 1300 K at 5.3 Pa. similarly, for HiPIMS operation the temperature of the working gasoline is estimated to be in the scope from 300 K ( room temperature ) to an upper specify of around 1200 K ( Kanitz et aluminum 2016, Vitelaru et alabama 2012 ) .

8.2.2. Ionization mechanism

The electron density dictates the dominating ionization march within the discharge. Coburn and Kay ( 1971 ) demonstrated that the Penning mechanism is responsible for the ionization of the sputter material in the reticular formation sputter cock. In these discharges the electron concentration is broken ⩽1016 m−3 ( Ball 1972 ) while metastable atoms of the exercise accelerator are abundant and have relatively high energies. These metastable atoms well ionize the splutter species as their ionization potential is lower than the excitement level of the working flatulence metastable through the reaction Arm + M ⟶ M+ + Ar + e. The energies of the metastable Ar atoms are 11.55 and 11.72 electron volt which are higher than the ionization electric potential of all metals. like findings are reported for dcMS with a titanium target, based on ocular discharge spectroscopy measurements, where it is demonstrated that Penning ionization dominates electron impact ionization of the sputtered atoms ( Christou and Barber 2000 ). They besides report on a decrease in ion density fraction with increased ability to the dispatch and suggest it is due to increased sputter. Furthermore, an addition in ion concentration fraction with increase working flatulence coerce is observed. It is argued that with increased working gas coerce, the collision frequency of electrons and metastable argon atoms american samoa well as the pace of ionization of sputter species, increases up to a point at which the increased spatter rate outweighs the effects of the enhance collision rate and the ionization fraction falls again. The relative role of Penning ionization decreases with increase electron concentration. At higher electron densities, or above ∼1017 m−3, electron affect ionization dominates Penning ionization of the alloy atoms ( Hopwood 2000a ). This value is indicated in calculate 20 with a blue dash dotted production line. consequently, in HiPIMS operation electron impact ionization dominates the ionization of sputter species ( above the dash dotted tune ), while in dcMS Penning ionization dominates the ionization of splutter species ( below the dash dotted credit line ) .

8.2.3. The spatial and temporal distribution of the sputtered species in HiPIMS

The spatial and temporal distribution of clamber metallic atoms and their ions in HiPIMS mathematical process with titanium prey has been been explored using LIF diagnostics spanning pulse lengths from 20 to 100 μs ( Britun et alabama 2013, 2015, Hnilica et alabama 2020a, 2020b ). The spatial and temporal distribution of sputter alloy atoms, their ions and argon metastables for short HiPIMS pulse ( 20 μs ) with titanium target and argon as the working gasoline at 2.7 Pa for a top out power concentration of ∼0.4 kW cm−2, repetition frequency 1 kilohertz, and peak discharge current concentration of ∼1.2 A cm−2 ( Britun et aluminum 2013, 2015 ) is shown in figure 22. There are noticable differences between the three species in terms of both temporal and spatial variation. The concentration of the sputter Ti neutrals ( calculate 22 left column ) increases during the pulsate and peaks at the end of the pulse or right after the pulsation is off ( at thyroxine > 20 μs ). After ionization of the clamber Ti atoms within the IR, the Ti+ ions propagate aside from the aim surface, forming a concentration utmost above the race traverse at the end of the acquit pulse as seen in digit 22 plaza column. The Ti inert density is higher in regions of low Ti ionization and a significant density depletion of the Ti density takes identify at the end of the pulse above the race track. The Ti+ ions do not disappear completely between the empty pulses ( 980 μs off-time ), specially at higher imperativeness ( Britun et alabama 2015 ). At the begin of the fire pulse the remaining ion concentration from the previous pulse is instantaneously depleted near the aim as the positive ions are attracted to the negatively biased cathode. During the afterglow the ions continue to propagate away from the cathode target. The estimate ion propagation speed at working accelerator blackmail of equality = 2.7 Pa is about 103 m s−1 ( Britun et alabama 2008, 2015 ). The metastable Arm density, on the early hand, is chiefly apparent and peaking during pulse-on as seen in human body 22 right column .Figure 22. Figure 22. The time development of Ti atoms ( left ), Ti+ ions ( center ), and metastable argon atoms Arm ( correct ) determined by LIF imaging in a HiPIMS dispatch with argon as the working gas at 2.7 Pa with 10 cm diameter titanium prey and pulse length of 20 μs. The size of the sphere of concern is roughly 10 × 7 cm2. The clock delay from the pulsate initiation Δt is indicated in the lower left corner of each frame. Reprinted from Britun et alabama ( 2013 ) in Proc. 12th Int. Symp. on Sputtering and Plasma Processes, Kyoto, Japan, pp 198–201 and from Britun et aluminum ( 2015 ) with the permission of AIP Publishing. download figure : Standard image
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8.2.4. The ion energy distribution

The mensural ion energy distribution ( IED ) from dcMS normally exhibits a humble energy acme shifted ( increased ) by a few electron volt which is equal to the value of the plasma likely. This is ascribable to ( positive ) ions being accelerated by the potential remainder between the plasma likely and the ground orifice of the batch mass spectrometer. The IEDs from a dcMS discharge in Ar/N2 mix with Ti prey are seen in figure 23 ( a ). The Ar+ and ${\mathrm{N}}_{2}^{+}$ ions show a moo energy bill ( ∼2 electron volt ) and a tail that extends to about 10 electron volt. The appearance of the high-energy Ar+ ions has been suggested to be a consequence of heat of the Ar working natural gas in collisions with the more energetic alloy flux. Thus the high energy tail of the working flatulence ions is either due to reflected neutralize ion from the cathode or working gasoline atoms that gain energy in collisions with clamber species. The ions of the sputter substantial exhibit a low energy top out and a tail that extends further than for the ions of the working gas. The Ti+ and N+ ions exhibit tails that extend to few tens eV. For both working gas ions and ions of the sputter fabric this agrees with other measurements of the IEDs in dcMS ( Fukushima et alabama 2000, Kadlec et alabama 1997, Martin et alabama 2001 ). The high-octane tail social organization is, in the case of the metal ion, related to the master energy distribution of the sputter neutrals at the cathode ( see section 7.4.2 ). If the splutter material is subsequently ionized the IED by and large shows a narrow humble energy bill, due to thermalized atoms which are accelerated by the difference between plasma electric potential ( several electron volt ) and ground electrode, and a broad distribution at higher energies which originates from the sputtered neutrals which have been ionized by electron impact within the plasma ( see e.g. Andersson et alabama ( 2006 ) ). due to the small mass of the electron the electron shock ionization does not change the energy of the resulting ion by much .Figure 23. Figure 23. Time-averaged IED for ( a ) dcMS and ( boron ) HiPIMS discharges operated in Ar/N2 mix with Ti aim. The datum from the dcMS discharge are time-averaged and for the HiPIMS discharge the IED correspond to the highest aim current concentration, 20 μs assign of the 200 μs pulses. Reprinted from Greczynski et alabama ( 2012 ), with license from Elsevier. download number : Standard image
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The IED from a HiPIMS fire in Ar/N2 mixture with Ti aim is seen in figure 23 ( bel ). The Ar+ and ${\mathrm{N}}_{2}^{+}$ ions show a depleted energy point ( ∼2 electron volt ) and the dock extends to a few tens electron volt, while the Ti+, Ti2+, Ar2+, ${\mathrm{N}}_{2}^{2+}$ and N+ ions expose much broader tails with a meaning fraction of the ions at high energy. The key deviation between dcMS and HiPIMS is the higher ionization fraction of the sputter species. besides, the IEDs in the HiPIMS discharge are broad and significantly more energetic as compared to a dcMS dispatch ( Bohlmark et alabama 2006a, Čada et alabama 2020, Lundin et aluminum 2008b ). The time averaged IED of the metallic element ions exhibits an intense eminent energy tail extending to the limit of a typical bulk mass spectrometer while the ions of the working gas display slightly lower energy, which is slightly more energetic than for dcMS ( Bohlmark et aluminum 2006a ). This has besides been observed in the IED from reactive HiPIMS acquit ( Aiempanakit et alabama 2011, Greczynski and Hultman 2010, Jouan et alabama 2010, Lattemann et aluminum 2010 ). It has been reported that approximately 50 % of the alloy ions have energy higher than 20 electron volt ( Bohlmark et alabama 2006a ). In general the IED of the atomic ion of the reactive flatulence resembles the energy distribution of the metallic ion and exhibits a independent flower at abject energy of a few electron volt and a shoulder extending to a high energy tail for both species. These species originate from the target. This IED is identical different from that of the working gasoline Ar+ ions and the molecular ion of the reactive gas, as for those ions the high energy buttocks is not as broad. In bipolar HiPIMS, when a positive pulsation is applied after the negative sputter pulsate, the plasma potential rises sharply and the acme position in the IED shifts to higher energy and the ion intensities increase ( Hippler et alabama 2020, Keraudy et aluminum 2019 ). The resultant role is that the ions of the splutter species exhibit a very wide energy distribution. Applying a positivist pulse appears to direct the positive ions toward the substrate. The plasma and floating potentials reach bombastic positive values, during the application of the positive pulse, that has a significant influence on the energizing department of energy of the ions. The mid-frequency pulsed magnetron sputtering fire such as dc pulsed magnetron sputtering discharge or the asymmetrical bipolar magnetron sputtering empty exhibits a more complex IED than the dcMS and HiPIMS discharges. During pulsate dcMS, the apply cathode target electric potential is sporadically switched from negative likely either to ground ( unipolar modality ) or to a positive potential ( bipolar manner ), in the mid frequency scope 5–350 kilohertz. When operating in this frequency range both the ions and the electrons are capable of following the cyclic potential changes of the cathode prey. The time-resolved IED for Ar+ ions from a unipolar discharge with titanium target, argon working natural gas at imperativeness of 0.26 Pa and applied ability 500 W operated at 100 kilohertz frequency with 50 % duty bicycle is shown in figure 24. The time averaged IED constitutes a low-energy flower, a mid-energy vertex and a high-energy chase. During the pulse-on phase an ion current is drawn to the cathode target and sputtering takes place and the plasma potential sits just slightly above the land potential, as in the dcMS discharge. consequently, during the pulse on phase, at times up to 4.8 μs, a single population of ions are observed, with energies of a few electron volt, exchangeable to what is observed in a dcMS discharge. At the begin of the off phase there is a plus electric potential overshoot and the aim potential can reach respective hundred volts which lasts about 200 ns ( Bradley and Welzel 2009 ). This has important influence on the IED as in this transeunt overshoot time period ( times between 4.8–5.8 μs ) a broad distribution of ions is detected with energies up to a hundred electron volt. These high department of energy ions do not inevitably reach energies which correspond to the full positive electric potential at the overshoot since the period of the spike is shortstop and the ions are not able to cross the entire sheath ( Bradley and Welzel 2009 ). The mid-energy bill, observed in the time period between 5 and 10 μs, is due to ions that are created during the steady-state pulse off period, when the plasma likely will sit at a few 10s of volts incontrovertible, and ions will be created with energies in the 20–25 electron volt range. furthermore, as the repeat frequency is increased the flower energy of each ion population shifts to higher energies and the higher department of energy population becomes a greater proportion of the full IED ( Mišina et aluminum 2003 ). eminence that although the asymmetrical bipolar pulsed magnetron sputtering empty is substantive for reactive clamber and deposition of insulating or ailing conductive thinly films, it does not lead to a significant increase of the liquefy of ions of the clamber species to the substrate, although some increase of the substrate bias current compared to dcMS has been reported ( Kelly and Arnell 2000 ) .Figure 24. Figure 24. The time-resolved IEDFs for Ar+ ions obtained with 1 μs time solution in a mid-frequency pulsate magnetron sputtering discharge at different parts of the pulse bicycle. The argon working gas press was 0.26 Pa and the applied baron 500 W at 100 kilohertz frequency with 50 % duty cycle. Reprinted from Voronin et aluminum ( 2007 ). ©IOP Publishing. Reproduced with license. All rights reserved. download figure : Standard image
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In reactive splutter when the working boast is a mix of Ar and O2, veto O− ions may be formed either ascribable to electron transfer in surface processes at the target or due to dissociative attachment within the plasma bulk ( Bowes et alabama 2013, Mráz and Schneider 2006, Zeuner et alabama 1998 ). The IED of the negative ion O− typically comprises three energy groups : low-, medium-, and high-energy ions. The high-energy group consists of O− ions that are created at the target surface and accelerated in the sheath and extended presheath. These ions are generated through desorption of O− ions or O atoms followed by electron attachment, and gain an energy equivalent to the voltage applied to the cathode target ( Bowes et alabama 2013, Mišina et aluminum 2003, Zeuner et aluminum 1998 ). due to their high energy they can give rise to defects in coatings being deposited and create a significant remainder stress. The medium-energy group has energy that corresponds to about half the target electric potential, and it is most credibly generated by ${\mathrm{O}}_{2}^{-}$ and other clusters that are sputtered from the target followed by acceleration over the entire discharge potential. Due to collisions en route, the clusters subsequently dissociate into species such as O atoms and O− ions, which share the energizing energy. The low-energy group of ions is most credibly formed in the cover presheath in front of the cathode aim and consequently experience limited acceleration ( Mráz and Schneider 2006 ). The negative oxygen ions have been observed in reactive dcMS ( Zeuner et aluminum 1998 ), mid-frequency asymmetrical bipolar magnetron clamber ( Mišina et alabama 2003 ), and HiPIMS ( Bowes et aluminum 2013 ) .

8.3. Rarefaction

The working gas pressure tends not to be spatially uniform within the magnetron sputtering chamber during discharge operation. As discussed in section 7.4.2 the sputtered atoms leaving the target are expected to have energizing energy of a few electron volt. Collisions between the splutter species and the neutral work boast atoms result in accelerator heat and rarefaction in the vicinity of the cathode target ( Rossnagel 1988a, 1988b ). The energy transfer from the sputtered atoms to the working gas atoms leads to heating system of the working gas followed by expansion, a procedure that is referred to as gas rarefaction. Sometimes the condition ‘sputtering wind ‘ is used to describe this momentum transfer and translation of the working gas by the sputtered atoms ( Hoffman 1985 ). The spatter weave is directed away from the target. A consequence of the decrease in the density of the working natural gas atoms is a decrease in the numeral of ions available for sputter, which again leads to a reduction in the sputter rate and subsequently reduced deposit pace. In the dcMS discharge the working gasoline pressure decreases nonlinearly with the drop current density, and depends on the sputter succumb of the cathode target, the crossbreed section for sputter atom—working accelerator atom collisions and the working gas pressure, temperature, and thermal conduction of the working natural gas ( Rossnagel 1988a ). The consequence of rarefaction becomes more significant with increasing discharge current concentration as the number of sputter atoms in the vicinity of the target increases. Since the fire current concentration is significantly higher, and the density of the sputter species is much higher in a HiPIMS empty, than in a dcMS dispatch, the rarefaction effect is expected to be much more pronounce. indeed rarefaction has been demonstrated experimentally to be preferably significant in the HiPIMS dispatch ( Alami et alabama 2006, Liebig et alabama 2010, Vitelaru et alabama 2012, Vlček et alabama 2004 ). Using ocular discharge spectroscopy it has been observed that there is about an order of magnitude decrease in the concentration of nuclear argon but slightly less dramatic decrease in the density of argon ions approximately 50–70 μs into a 200 μs long pulse while sputtering Cu aim ( Vlček et aluminum 2004 ). The assorted mechanisms leading to gas rarefaction in HiPIMS discharges have been investigated by Huo et alabama ( 2012 ) using the ionization region model ( IRM ) ( see incision 9.4 ) for an Al target with Ar as the working flatulence at VD = 450 V. The rate of accelerator rarefaction dnAr/dt is the fastest at the point in the dismissal current, and a highest absolute respect of the gas rarefaction appears 40–60 μs after the discharge stream flower. The dominate loss terms are found to be electron affect ionization and the sputter wind kick-out. The ionization term dominates and is larger by more than a factor of two throughout the pulse. The fraction of Ar+ ions that are not attracted to the target ( 1 − βg ) leaves the IR to the bulge plasma and is lost. The remaining divide βg impinges on the aim, picks up an electron, and returns as a flying argon inert at an average focal ratio of about 3 km s−1 and does not collide inside the IR and passes through in about 2–4 μs. consequently, the argon atoms can be regarded as lost upon ionization, which therefore contributes to the working gas rarefaction .

8.4. Deposition rate

For dcMS and mid-frequency magnetron sputtering, such as asymmetrical bipolar magnetron splutter, deposit rates are practically directly proportional to the exponent applied to the aim ( Bradley et aluminum 2015, Waits 1978a ) while this is not the lawsuit for HiPIMS operation. The clamber pace ( Lieberman and Lichtenberg 2005, incision 14.5 ), here modified to account for the fact that sputtering is not only due to the ions of the noble work gasoline, is given byEquation (38) where ntarget is the atom density of the aim material. The sum is taken over all the ions in the discharge, and Yj is the sputter concede of the cathode target corporeal for ion j. Equation ( 38 ) states that the spatter rate depends on the summarize of Yj Ji, joule for each ion bombarding the target. For dcMS, that operates on primary coil current alone, the current consists wholly of ions of the working gasoline, the sputter rate is proportional to the ion current concentration and the sputter concede. If all the sputtered material is deposited on the substrate, the deposition rate in a physical clamber process is given by ( Lieberman and Lichtenberg 2005, section 16.3 ) ,Equation (39) where Γi, joule is the flux density of ions j bombarding the target ( m−2 s−2 ), nfilm is the atom density in the deposit movie, Art is the sphere of the racetrack, or the area of the target that is being sputtered, and Asubstrate is the substrate area on which the film is deposited. figure 25 ( a ) shows the deposition rate from a planar dcMS discharge versus magnetic field forte | B |. The deposition rate is ∼100 Å s−1 and approximately mugwump on the magnetic sphere strength. The magnetic airfield and academic degree of balancing above the magnetron target was varied by displacing the concentrate attraction and the out ring attraction at the prey edge within the magnetron assembly. The recorded Brt respect above the subspecies track was used as a measurement of | B | Hajihoseini et alabama ( 2019 ). The deposit rate in the HiPIMS process is normally found to be reasonably lower than that obtained with dcMS, broadly in the roll of 30 % –85 % of the dcMS rates, depending on target material when manoeuver at the same average power ( Samuelsson et alabama 2010 ). This is besides seen in calculate 25 ( a ) where HiPIMS discharge always exhibits lower deposition rate than dcMS discharge when engage at the same average ability, but for HiPIMS operation the deposit rate decreases with increase | B | ( Hajihoseini et aluminum 2019 ). The HiPIMS discharge pulse length was maintained at 100 μs, and the discharge ability was regulated in two different ways as the charismatic field persuasiveness and configuration was varied. The fixate electric potential modality was realized by keeping the cathode electric potential fixed throughout the pulse while the pulse frequency was varied to achieve a situate average power and the sterilize point discharge current manner was realized by changing the cathode electric potential to maintain the acme release current and the pulse frequency was varied to achieve the desire average office .Figure 25. Figure 25. ( a ) The deposition rate and ( bacillus ) the ionize flow cabal from dcMS and HiPIMS discharges, operated in both pay back electric potential manner and fixed acme empty current mode, versus charismatic field intensity | B |, measured at 70 millimeter axile outdistance over center field of cathode. The recorded Brt value above the race chase was used as a measurement of | B |. Based on data from Hajihoseini et alabama ( 2019 ). download figure : Standard image
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When operating at high office densities the ion current density at the aim open can have a meaning contribution from the target material as discussed in segment 10.2. Back-attraction of metal ions to the aim is believed to be the main campaign for the low deposition rate in HiPIMS operation as suggested by Christie ( 2005 ). The back drawing card of the ionized splutter species is quantified by a parameter referred to as the back attraction probability βt. The atoms sputtered off the prey and ionized in the cathode vicinity are probably to be back-attracted to the prey due to impregnable electric fields in the pre-sheath and an extended pre-sheath ( Bradley et aluminum 2001c, Rauch et aluminum 2012 ). spatial measurements of the plasma electric potential in HiPIMS discharges ( Liebig and Bradley 2013, Mishra et aluminum 2010, Rauch et aluminum 2012, Sigurjónsson 2008 ) have shown that there normally is a electric potential uphill, from the cathode sheath edge and reaching far outside the IR ( several centimeter ), that can vary in the range 7–100 V. Some early mechanisms have besides been suggested to contribute to the gloomy deposit rate such as the non-linear concede impression ( Emmerlich et alabama 2008 ), sideways ecstasy of the sputtered material ( Lundin et aluminum 2008b ), guiding effect of the B-field ( Bohlmark et alabama 2006b ) and the consequence of unlike ion species on spatter move over ( Anders 2010 ). Furthermore, it has been demonstrated that regions of intense ionization with locally enhanced likely, referred to as spokes, ( see section 10.4.1 ) have a strong influence on the transport of species toward the substrate ( Brenning et aluminum 2013, Lundin et aluminum 2008b ) and de los Arcos et aluminum ( 2014 ) reported lower deposition rate/power when operational in the spoke-dominated regimen than in the dc-like and homogeneous HiPIMS discharge regimes. several attempts have been made to increase the deposition rate in HiPIMS operation. This includes varying the pulse length ( Ferrec et alabama 2016, Konstantinidis et alabama 2006, Velicu et alabama 2014 ), varying the charismatic field strength | B | ( Bradley et alabama 2015, Čapek et aluminum 2013, Mishra et aluminum 2010 ), modifying the magnetic discipline geometry ( Raman et alabama 2016, 2015, Yu et alabama 2013 ), adding an external magnetic field in the target vicinity ( Ganesan et aluminum 2018, Tiron et aluminum 2018 ), chopping the pulse into a train of short pulses ( Antonin et alabama 2015, Barker et alabama 2013 ), superimpose mid-frequency pulses during off-time between HiPIMS pulses ( Diyatmika et alabama 2018 ), and increasing the prey temperature ( Tesař et aluminum 2011 ). respective of these reports propose that modifying the charismatic sphere, using either permanent wave magnets or electromagnets ( Alami et alabama 2014, Bradley et aluminum 2015, Čapek et alabama 2013, Mishra et aluminum 2010 ), as being the most promise approaches. For example, Čapek et alabama ( 2013 ) showed that lowering | B | the deposition pace of Nb was increased by roughly a divisor of 5 and Mishra et aluminum ( 2010 ) found a sextuple increase in the deposition rate of Ti by weakening | B | by 33 %. This is similar to the addition in deposition rate with decreased | B | shown in figure 25 ( a ). This increase has been related to a meaning dangle in potential difference axially across the discharge as | B | is lowered ( Mishra et alabama 2010 ) .

8.5. Ionized flux fraction

The film forming fabric is sputtered from the cathode target as neutral atoms which then pass across the cathode sheath and into the IR where some of the atoms are ionized. The ionization flux fraction is normally measured using gridded energy analyzers in which the collector in the analyzer is configured with a quartz crystal rate monitor. This analyzer can differentiate between ions of the film forming corporeal and the inert working boast background. In the dcMS the ion flux toward the substrate is composed about wholly of the ions of the working gas. The ionize liquefy fraction of the sputtered material ( defined by equality ( 18 ) ) has been determined to be about negligible when sputtering Ti and Ni targets in dcMS ( Kubart et alabama 2014 ). The ion density fraction of the clamber species, given by equation ( 19 ), has been estimated to be up to ∼10 % using optical emission spectroscopy when sputtering a titanium target in dcMS ( Christou and Barber 2000 ). It is besides pointed out that as the movie forming material enters the less dense region outside the IR electron–ion recombination may take set and the ion concentration fraction of the film forming material is reduced. For the ICP assisted dcMS the ionize liquefy divide is found to increase with increased working gas press in the range from 0.7–6 Pa, increase with increase reticular formation exponent to the inductive gyrate, and decrease with increased district of columbia power to the dcMS ( Rossnagel and Hopwood 1994 ). For working gas blackmail in the range 3–6 Pa and few hundred Watts reticular formation world power the ionized blend fraction Fflux of the sputter species is in the range 50 % –85 % for Al and AlCu targets ( Rossnagel and Hopwood 1994 ). In a HiPIMS discharge the high electron density results in a significant ionization of the sputter neutrals, where ionized flow fractions Fflux well above 50 % have been reported ( Kouznetsov et alabama 1999, Kubart et alabama 2014, Lundin et alabama 2015 ). however, the ionized flux fraction depends on the discharge current ( Kubart et alabama 2014, Lundin et aluminum 2015 ), the fire electric potential ( Cuynet et aluminum 2016 ), the pulsate length ( Tiron et aluminum 2018 ), duty cycle ( Bernátová et alabama 2020 ), the working natural gas ( Cuynet et alabama 2016 ), working gas press ( Bernátová et alabama 2020, Kubart et aluminum 2014, Lundin et aluminum 2015 ), target material ( Cuynet et alabama 2016, DeKoven et alabama 2003, Kubart et alabama 2014, Lundin et aluminum 2015 ), distance from the prey coat ( Bernátová et alabama 2020 ), operation of a reactive discharge in metallic element or poisoned mood ( Kubart et aluminum 2014 ), and the confining magnetic field potency ( Hajihoseini et alabama 2019 ). figure 25 ( bacillus ) shows the ionize blend fraction versus the charismatic sphere strength | B | for a HiPIMS dispatch operated in fixed discharge electric potential mode and fixed flower fire current mode. The ionize flow divide decreases with increasing magnetic field potency | B | when operating HiPIMS exhaust in fix bill acquit stream manner, and increases with increasing magnetic field potency | B | when operating HiPIMS empty in fix discharge voltage mode, while keeping the prison term averaged office fixed ( Hajihoseini et alabama 2019 ). The ionized density divide for titanium atom and ion number densities has been determined to be high for the HiPIMS discharge or up to 90 % ( Bernátová et alabama 2020, Bohlmark et aluminum 2005a ). Bernátová et aluminum ( 2020 ) find that the lower the duty bicycle the higher the ionized density fraction and that it is largely independent of the working gas pressure. This is shown in visualize 26 where the ionized blend fraction, the ionize concentration fraction and the deposition rate are shown as a function of the duty cycle in a HiPIMS dispatch with a titanium target, while the median power was kept fixed at 1000 W and the working gas pressure at 1 Pa. note that in HiPIMS operation the ionized concentration fraction is constantly slightly higher than the ionized liquefy fraction .Figure 26. Figure 26. The ionize alloy flux divide, the ionize density fraction and the deposition rate versus the duty cycle for Ar discharge with Ti target operated at 1 Pa and clock time average ability of 1000 W. Reprinted from Bernátová et alabama ( 2020 ). ©IOP Publishing. Reproduced with license. All rights reserved. download figure : Standard image
High-resolution image
The benefits of high ionized flux fraction of the sputter material include dense films ( Samuelsson et aluminum 2010 ), lower open crudeness ( Hajihoseini and Gudmundsson 2017, Sarakinos et alabama 2007 ), and improved crystallinity ( Alami et aluminum 2005 ). therefore, it is high gear beneficial to ionize the sputter species. A discussion of the benefits and opportunities, that come with high ionized flux fraction, for the properties of the deposit films has been given by Sarakinos et aluminum ( Lundin and Sarakinos 2012, Sarakinos and Martinu 2020 ). however, highly ionized flux of the clamber corporeal normally comes at the cost of lower deposition rate ( Brenning et alabama 2020, Hajihoseini et alabama 2019 ) and besides seen in figures 25 and 26. For this reason, despite the above mentioned benefits to the film properties, the HiPIMS free has not reached extensive use in manufacture ( Anders 2010, Helmersson et alabama 2006, Lundin and Sarakinos 2012 ) .

8.6. Deposition rate versus ionized flux fraction

Bradley et aluminum ( 2015 ) explored the dispute in the discharge behavior between dcMS and HiPIMS operation with a titanium prey and varying | B |. For dcMS and pulse direct current operation they found that the deposition rate decreases by 25 % –40 % when decreasing | B | by 45 %, while they found the face-to-face for HiPIMS process, a deposition pace increase by a factor of 2. They used a dim-witted phenomenological model ( nerve pathway model ) to relate the sputter particle fluxes and the deliberate deposition rates and to determine the aggregate probabilities of ionization αt and subsequent bet on attraction βt of the ions of the sputter species αt βt as | B | is varied. The sum flux of atoms sputtered from the target is denoted Γ0 ( atoms/s ) and the flow of splutter species ( ions and neutrals ) that leave the IR toward the dispersion region ( DR ) is written ΓDR. The useful fraction of the splutter species is thenEquation (40) consequently, lower αt βt gives higher deposit rates. A kinship between the ionization flux density fraction Fflux and the parameters αt and βt has been derived from the pathways exemplar ( Butler et alabama 2018, Vlček and Burcalová 2010 )Equation (41) where for reduction no extra ionization of the sputter substantial in the DR is assumed. note that equation ( 41 ) has been simplified from the deriving by Vlček and Burcalová ( 2010 ) as ion focus has been neglected ( Butler et alabama 2018 ). The deposition rate and the ionize flux fraction Fflux can be related to the probability of ionization αt and back attraction of the sputter species βt ( Hajihoseini et alabama 2019 ). From equations ( 40 ) and ( 41 ) an equation can be derived that gives the back attraction probability βt as a function of the mensural quantities Fflux and FDR ( Hajihoseini et aluminum 2019 )Equation (42) and similarly an equation that gives αt as a function of the measure quantitiesEquation (43) The ionization probability αt depends powerfully on the discharge current, increases with increasing exhaust current, while the back attraction probability βt depends on the magnetic airfield force, increases with increasing | B | ( Hajihoseini et aluminum 2019 ). The ions of the sputter material that are transported radially outwards in the vicinity of the cathode target, have been suggested as one probable explanation for the lower deposit rates by and large observed for HiPIMS compared with dcMS. tangential ion ejection in the E × B drift steering has been demonstrated by Lundin et aluminum ( 2008b ), using time-averaged mass spectroscopy measurements, by Poolcharuansin et aluminum ( 2012 ), using a retard field analyzer, and Panjan et aluminum ( 2014 ) using collector probes and particle energy analyzer and bulk mass spectrometer. The digressive acceleration has been suggested to result in a net force that develops between the counter streaming fast electrons and the slower ions referred to as modified two-stream instability ( MTSI ) ( Lundin et aluminum 2008b ). Poolcharuansin et alabama ( 2012 ) added a centripetal impel and a puff force to the equation for ion gesticulate and showed that a belittled fraction of the circulating ion blend, those ions that do not experience collisions, can overcome the radial electric sphere and leave the discharge volume in the tangential direction, radially, parallel to the target surface. besides, the magnetic sphere persuasiveness has a impregnable influence on the radial deposit rate in HiPIMS but not in dcMS. Despite significantly higher count of ions traveling radially in the HiPIMS exhaust, the total radial flux density of the film forming corporeal is always greater in dcMS compared to HiPIMS. Therefore, the normally reported reduction of the ( axial ) deposit pace in HiPIMS compared to dcMS does not seem to be linked with an increase in sideways material ecstasy in HiPIMS ( Hajihoseini et aluminum 2020 ). It has been suggested that the impression of back-attraction can be reduced by increasing the proportional function of the afterglow and its contribution to the ion fluxes after each HiPIMS pulsation. Without a damaging potential on the aim at this stage of the HiPIMS process, the back-attracting electric airfield disappears allowing the remaining ions to escape the IR. This has been demonstrated using the time-dependent IRM by distinguishing between fluxes from the IR during the pulse and during the afterglow ( Rudolph et alabama 2020 ). By shortening the pulse length in a titanium HiPIMS discharge the IRM predicts a gain in deposition rate of over 45 %, when using 40 μs compared to 100 μs-long pulses at a constant average ability without compromising the ionized flux fraction .

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9. Modeling of the magnetron sputtering discharge

Attempts to model the magnetron sputtering discharge initiated in the 1980s. The efforts can be classified into analytic models or strictly numeral models. The numerical models are either classified as global ( volume averaged ) plasma chemistry models and fluid models or kinetic models ( Bogaerts et al 2009a, 2009b, 2008 ). In order to provide a thorough insight into the discharge physics, a self-consistent mannequin of the magnetron sputtering free is required. To become self-consistent the mannequin has to include the calculation of the electric field based on the spatial distribution of the charged plasma species and the applied external voltage. furthermore, such a model has to account for the couple of the charge atom apparent motion in the electric ( or electromagnetic ) field and to determine the discipline itself. To complicate matters further in the planar magnetron shape the magnetic sphere has a complex geometry which requires multi-dimensional treatment. A physical deposition is a three step action : ( one ) expulsion of particles from a generator, ( two ) transport of the exhaust particles to a substrate, and ( three ) condensing of the eject species on the substrate. therefore, to completely model the magnetron sputtering discharge, there has to be a description of the release physics along with the plasma interaction with the solid surfaces that surround the fire. The most authoritative of these surfaces are the cathode prey ( the source of sputter species ) and the substrate where a film is deposited. here an overview is given of the assorted modeling efforts that have been applied to understand the magnetron sputtering dispatch and some key findings. note that only tools and modeling approaches that deal with the acquit physics are discussed, steps ( one ) and ( two ) of the three step procedure. The output signal of these models can be the worldly and/or spatial variation of densities of diverse species, including film form species, deposition rate and ionized flux fraction. These models can therefore provide remark for model of sparse film growth ( step ( three ) ), models that require different approaches. These approaches could include methods such as classical molecular dynamics simulations ( Edström et alabama 2016, Elofsson et alabama 2016, Kateb et alabama 2019 ), density-functional abdominal initio molecular dynamics simulations ( Car and Parrinello 1985, Sangiovanni 2018 ), and kinetic Monte-Carlo simulations ( Lü et alabama 2018, Nita et alabama 2016 ) .

9.1. Analytical models

analytic models are frequently based on elementary analytic ( ( semi- ) empirical ) rule that describe the demeanor of macroscopic discharge characteristics, such as cathode voltage and discharge current. The advantage of analytic models is abruptly calculation time. however, ascribable to simplifications and approximations this comes at the expense of accuracy. furthermore, these models are much not cosmopolitan, and normally they only apply for a limited image of dispatch conditions. In its simplest form a semi-analytical model describes the magnetron sputtering device from the cathode target to the anode in a unidimensional knowledge domain ( Cramer 1997, Pekker 1995 ). These models are typically based on 1D electron and ion fluid transport equations that are solved for a steady-state magnetize discharge, which is basically just a generalization of earlier analysis of an unmagnetized steady-state glow discharge ( Davies and Evans 1980, Neuringer 1978 ). In this approach the magnetic field is assumed to be perpendicular to the electric field and the electrons are transported along ( parallel to ) the electric airfield and perpendicular to the charismatic playing field. Often the magnetic field is assumed to be ceaseless and diffusion is assumed to be classical music. This kind of models have been applied to explore the properties of the sheath area ( Bradley and Lister 1997 ), the pre-sheath ( Bradley 1998 ), and the DR or the plasma majority ( Bradley et alabama 1997 ). When exploring the cocktail dress and pre-sheath regions the classical music dissemination has been replaced by Bohm diffusion ( Bradley 1998, Bradley and Lister 1997 ). Using this kind of model the appearance of a negative outer space charge region can be predicted. It forms due to the restriction of the electron mobility when the working boast pressure is low and the magnetic confinement is solid ( Cramer 1997, Pekker 1995 ). furthermore, such analytic models have besides been developed to describe the reticular formation magnetron sputtering fire ( Palmero et aluminum 2004 ). note that these analytic models are normally besides dim-witted and do not capture the multidimensional electric and magnetic fields and the resulting electron movement within the discharge and therefore do not give quantitative results. however, they can be utilitarian to determine if a work is of significance or can be neglected, and to find childlike scalings of discharge parameters .

9.2. Pathways models

A rather dim-witted approach, based on following the sputtered and working gas species within the discharge, has been taken in decree to gain understanding of the discharge processes in pulse magnetron spatter discharges. This is the phenomenological material nerve pathway model set forth by Christie ( 2005 ). It was primitively developed to determine the ionized fraction of the movie forming fabric arrive at the substrate and to explain the low deposition rate observed in HiPIMS discharges. This model allows for the calculation of the divide of ionized sputter species that returns back to the target βt, the ionization probability of the clamber species αt, and the ionize flow divide onto the substrate. The description of the losses of target material ions during their transport to the substrate was late modified to take into account extra ionization of sputter species within the plasma bulk ( Vlček and Burcalová 2010, Vlček et alabama 2007 ). The model allows estimating the useful fraction of the film forming fabric ( equation ( 40 ) ), and the ionize flux fraction ( equation ( 41 ) ). besides, simple scale laws are achieved βt ∝ 1/VD and if we assume ${Y}_{\mathrm{t}}\propto {V}_{\mathrm{D}}^{1/2}$ it is apparent that ${\alpha }_{\mathrm{t}}\propto {V}_{\mathrm{D}}^{1/2}$ and ${\alpha }_{\mathrm{t}}{\beta }_{\mathrm{t}}\propto {V}_{\mathrm{D}}^{-1/2}$. Despite being a identical simple approach the phenomenological material pathways model has been very authoritative in understanding the lower deposition pace and respective other issues in the HiPIMS drop .

9.3. Fluid models

Fluid models describe the plasma as a continuum and are based on solving the continuity and transport equations ( broadly based on diffusion and migration ) for the assorted empty species, along with Poisson equality, in order to obtain a self-consistent electric discipline distribution. The EEDF is normally assumed to be Maxwellian and the electron temperature is then calculated by solving an energy poise equation. The fluid model has an advantage in terms of the calculate time. however, the robustness of using a fluid model to describe a magnetron sputtering discharge has been questioned ( Kolev 2007 ). This is do to the low working gasoline pressure and therefore the basic assumptions of a fluid description are not constantly met. Furthermore, the drift-diffusion estimate which is the perfume of fluid models ( i.e. the atom motion is only caused by the fields and the concentration gradient ) is not valid in magnetron sputter discharges, ascribable to the broken working gasoline pressure. Additional difficulty arises from the complicated forms of the equations of magnetohydrodynamics, which describe a magnetize fluid. The description of the building complex and inhomogeneous electric and magnetic fields, that besides exhibit big gradients, requires ticket discretization and drawn-out calculation and due to this the fluid approach becomes very ineffective ( Kolev and Bogaerts 2004 ). besides the robustness of authoritative diffusion formalism when used at gamey ratios of magnetic battlefield over gasoline press is questionable. There exists only a few studies where a fluid exemplary is applied to study a magnetron sputtering discharge. Despite of these shortcomings Costin et aluminum ( 2005a, 2005b ) have successfully modeled a dcMS discharge by a 2D ( roentgen, z ) fluid model making use of the cylindrical symmetry of the dispatch. As stated above the fluid approach is not valid at low working natural gas pressure and the mean free path of charged particles exceeds the characteristic size of the fire. however, Costin et alabama ( 2005a ) argue that since the magnetron sputtering empty operates at low working flatulence pressures, the presence of the magnetic field reduces the effective distance the electrons travel between collisions, which is equivalent to an increase of the working gas pressure, and frankincense fulfilling the hydrodynamic guess. They separate the electron flux into two parts, where the influence of the magnetic discipline is treated as an extra condition in the flux expression. Thus the magnetic playing field is treated as a disruption to the electron flux equations while assuming a classical music electron transmit. however, it has been pointed out that the electrons are thus powerfully magnetized that it is not appropriate to apply the perturbation formalism in this character ( Kolev 2007 ) .

9.4. Ionization region models

The ionization region model ( IRM ) is volume-averaged, time-dependent plasma chemical model of the dense IR and the target, that was developed to explore the HiPIMS acquit ( Huo et aluminum 2017, Raadu et alabama 2011 ). The IR is located in close vicinity of the prey slipstream track and observed as a torus of a dense, brilliantly glowing plasma, defined as an annular cylinder with out radius rc2, and inner radius rc1 marking the rush racetrack region, and length L = z2 − z1, extending from z1 to z2 axially aside from the target. Using the IRM the time evolution of impersonal and charge species and the electron temperature in pulse magnetron sputtering discharges can be calculated. The IRM assumes only volume-averaged values over the wholly IR bulk for the electron, ion and neutral densities and the electron temperature and the bulge ( cold ) electrons are assumed to exhibit a Maxwellian distribution and the secondary electrons ( hot ) are taken as a high energy tail. geometric effects are included indirectly as passing and gain rates across the boundaries of this annular cylinder to the target and the bulk plasma surrounding the IR ( Raadu et aluminum 2011 ). The temporal role development is defined by a set of ordinary derived function equations giving the beginning meter derivatives of the electron energy and the particle densities for all the clayey particles. The electron density is found assuming quasi-neutrality of the plasma. The model is constrained by experimental data remark in the sense that it first needs to be adapted to an existing exhaust ( the geometry and the working natural gas coerce, the working gas, splutter yields, and aim species, and a reaction set for these species ), and then fitted using two or three parameters to reproduce the measure acquit current and voltage waveforms, ID ( triiodothyronine ) and VD ( triiodothyronine ), respectively. much of the early IRM development was based on discharges with Al target ( Brenning et aluminum 2012, Huo et alabama 2012 ), and for this case two such model fitting parameters were found to be sufficient. One of these, VIR, accounts for the power transfer to the electrons, and the other, βt, accounts for the probability of back-attraction of the ions of the sputter species to the target. holocene IRM analysis with other target materials has revealed that sometimes a third base fitting parameter is needed, the probability radius of back-attraction of secondary electrons emitted from the prey ( Gudmundsson et alabama 2016 ). This is a argument that has remained difficult to predict theoretically ( Buyle et aluminum 2003, Revel et aluminum 2016, Thornton 1978 ). The IRM approach has thus far been applied to study gas rarefaction and replenish processes ( Huo et aluminum 2012, Raadu et aluminum 2011 ), the reduction in deposition rate ( Brenning et alabama 2012 ), the electron heat mechanism ( Huo et alabama 2013 ), and the attack of self-sputtering ( Huo et alabama 2014 ) in an argon HiPIMS discharge with an Al target. For an argon empty with Ti target, the worldly behavior of the argon metastable state has been investigated and compared to experiments ( Stancu et alabama 2015 ), along with exploring its role and importance in the ionization processes ( Gudmundsson et alabama 2015 ), the consequence of shortening the pulse length on the ionized blend fraction and deposition rate ( Rudolph et aluminum 2020 ), and the ion composition at the target come on ( Huo et aluminum 2017 ). More recently, the IRM has been extended to model a reactive Ar/O2 HiPIMS exhaust with Ti target by adding a reaction set for oxygen to the discharge model a well as the supernumerary oxygen-related come on processes ( Gudmundsson et alabama 2016, Lundin et alabama 2017 ). other models based on similar set about have been developed to model the MPPMS discharge ( Zheng et alabama 2015, 2017 ) and the HiPIMS release ( Kozák and Pajdarová 2011 ). Zheng et aluminum ( 2015 ) used experimentally determine discharge electric potential and current waveforms as stimulation parameters, and the model reproduces the empty stream wave form by using the Hall parameter ωce τc as a fit parameter .

9.5. Hybrid models

The basic estimate of the hybrid overture is to combine the preciseness of the kinetic models with the computational chasteness of the fluent exemplar. In the magnetron sputtering discharge the junior-grade electrons are emitted from the cathode target open and accelerated to high energy within the cathode cocktail dress. Often the electrons are split up into two groups : the alleged fast electrons, with energy above the threshold for inelastic collisions, which are treated with a kinetic Monte Carlo model and slower electrons that are described with a fluid model. In the hybrid approach the ions and bulk electrons are treated by the fluid description and the fast electrons are treated by the atom model ( Shidoji et aluminum 1999 ). Keep in heed that the electrons are confined by the charismatic playing field while the much heavier ions are practically not influenced by the magnetic field. Shidoji et aluminum ( 1999 ) trace such a loanblend model to simulate a dcMS discharge in two-dimensional quad ( gas constant, omega ) in cylindrical shape within a reasonable computational time. They use this approach to investigate the difference in the drop structure of a dcMS discharge with a insulator substrate operated in balance and brainsick magnet shape ( Shidoji et alabama 2001a ) and with varying working gas pressures and charismatic airfield persuasiveness ( Shidoji et aluminum 2001b ). Shidoji and Makabe ( 2003 ) have besides applied a variant of the hybrid method where all the electrons are treated by a kinetic particle model while the massive ions are treated by the fluid model in order to shorten the computational time, when exploring a dcMS fire operated under a solid magnetic plain. besides Jimenez et aluminum ( 2014 ) present a loanblend model that features a Monte Carlo discussion of both energetic electrons and ions, and a copulate fluid model for thermalized particles. The limitations of cogency of the hybrid approach are discussed by Kolev and Bogaerts ( 2004 ) .

9.6. Direct Monte Carlo simulations

In direct Monte Carlo simulations a phone number of computational test particles, that represent a large phone number of real plasma species, are followed. The campaign of the test particle is influenced by apply forces and collisions with other particles. note that direct Monte Carlo simulations are not self-consistent, as the electric field distribution is an stimulation in the exemplary, and is not calculated self-consistently from the charge concentration distribution. The electric field can be given by analytic conceptualization ( see e.g. Fan et alabama ( 2003 ) ), or as results of PIC/MCC simulations. This method is particularly utilitarian to explore the transmit of charged particles and collision mechanisms in magnetron sputtering discharges such as the trajectories of electrons. In fact, the detail trajectory of an individual electron, under the influence of electric and magnetic battlefield, can be calculated applying Newton ‘s laws. The collisions ( i.e., happening of a collision, the type of collision, and the department of energy and focus after collision ) are treated using random numbers. By following the paths of a large act of individual electrons, the electron behavior can be statistically simulated. target Monte Carlo simulations have been used to predict the spatial distribution of the ionization ( Sheridan et alabama 1990 ), and ion trajectories ( Goeckner et aluminum 1991 ) in a planar magnetron sputtering release, the energy and angular distributions of the energetic species of the film forming material in a planar ( Myers et alabama 1991 ), cylindrical mail ( Eisenmenger-Sittner et al 1995 ) and rotating target ( Van Aeken et aluminum 2008 ) shape, equally well as the thermalization of the sputter species ( Depla and Leroy 2012, Yamamura and Ishida 1995 ), and target erosion of both cylindrical ( Ido et alabama 1999 ) and rectangular ( Fan et alabama 2003, Shidoji et aluminum 1994 ) targets under dcMS operation. Using this access it has besides been demonstrated that the level of ionization ascribable to secondary electron emission is not sufficient to sustain a exhaust for confining magnetic sphere below 20 mTesla, which indicates that electrons created within the IR are required for maintaining the discharge ( Miranda et alabama 1990 ) ( see discussion in segment 10.1 ) .

9.7. Boltzmann solver and Lorenz force term

numerically solving the Boltzmann equation gives the electron energy distribution within the dismissal. Kinetic model of a magnetron sputtering fire, based on a nonindulgent solution of the non-local Boltzmann energizing equation, can be identical effective as a direct solution of the Boltzmann equation. This is generally a identical accurate and wide used approach in drop physics. however, in the magnetron sputtering discharge the Boltzmann equation includes a Lorentz force term that importantly complicates matters and becomes mathematically complicated. This is in particular the lawsuit in two and three dimensions and for arbitrary magnetic fields as is needed to describe the planar magnetron sputtering discharge. consequently, this approach has only been applied successfully in the case of a cylindrical magnetron sputtering dismissal that consists of a coaxial inner cathode and an forbidden anode, the cylindrical post configuration ( see section 3.1 ), as the magnetic field is 1D and ceaseless which makes it accomplishable to solve the Boltzmann equation. In this configuration both the electric field of ambipolar diffusion and the electric field due to current transportation are directed radially, which reduces the problem to one dimension in real outer space. The presence of an axial magnetic field besides reduces the anisotropy of the distribution function in the radial direction which well simplifies the procedure for solving the energizing Boltzmann equality in the cathode region and it becomes potential to obtain a rather dependable solution of the energizing equation by the two-term approximation for the entire discharge gap between cathode and anode. This especial case has been extensively studied using a Boltzmann problem solver ( Passoth et aluminum 1999, Porokhova et aluminum 2005a, 2005b, 2001 ) .

9.8. Self-consistent particle-in-cell/Monte Carlo collisional (PIC/MCC) simulations

PIC/MCC simulations are based on the same rationale as direct Monte Carlo simulations, i, the trajectories of a big number of individual species are calculated applying Newton ‘s laws, and their collisions are treated by assigning random numbers ( Birdsall 1991 ). Furthermore, the electric sphere distribution is besides calculated self-consistently from the positions of the charged species using the Poisson equation. self-consistent PIC/MCC simulations provide the spatial distribution of the charged particles along with the electric field across the discharge. This approach requires that the positions of each species are projected onto a grid, to obtain a charge concentration distribution, from which the electric field distribution can be calculated. consequently, PIC/MCC simulation is the most mighty numeral method acting to explore the magnetron sputtering discharge and its properties. however, describing in contingent the demeanor of charged species along with solving the Poisson equation requires substantional computational might. In order to reduce the calculation time, the real particles ( i.e., atoms, electrons and ions ) are represented by super-particles, with a weight corresponding to the count of real particles which they represent. The drawback of the PIC/MCC method acting is the significant computational load. This is in particular significant as 2D or 3D simulations are generally required to investigate the planar magnetron sputtering exhaust. Bogaerts et alabama ( 2008 ) give a detail discussion on applying the PIC/MCC method to model a dcMS discharge. Nanbu et alabama ( Nanbu and Kondo 1997, Nanbu et alabama 1996 ) demonstrated 3D PIC/MCC simulations of a dcMS discharge and concluded that the discharge is axisymmetric and 2D cylindrical geometry ( radius, z ) is sufficient. In subsequent studies they assumed an axisymmetrical magnetic field and performed 2D PIC/MCC simulations of the dcMS discharge ( Kondo and Nanbu 1999b, 2001a, Nanbu et aluminum 2000 ). diverse parameters and physical processes in a magnetron sputtering discharge have been explored using a 2D PIC/MCC modeling including, the speed distribution of electrons and ions ( Shon et aluminum 1998 ), the natural gas temperature by tracking the inert species ( fast atoms of the working gas and sputtered atoms ) ( Kolev and Bogaerts 2008 ), the erosion profile and tape drive of splutter species ( Kolev and Bogaerts 2009 ), and the effect of magnetic discipline forte and secondary electron emission ( Kondo and Nanbu 1999b ). In 3D PIC/MCC simulation Kondo and Nanbu ( 1999a ) observed chaotic dynamics within the electron density. This border on has besides been used to simulate the forcible processes in a magnetron discharge during reactive spatter deposition of TiNx films in Ar/N2 ( Bultinck et aluminum 2009 ) and TiOx films in Ar/O2 ( Bultinck and Bogaerts 2009 ), discharges. Furthermore, the rutherfordium magnetron sputtering discharge has been explored by PIC/MCC simulations ( Kondo and Nanbu 2001b, Minea et alabama 1999a, 1999b ). Exploring the HiPIMS process government with PIC/MCC simulations comes with its own challenges such as a high plasma concentration ( above 1018 m−3 ), impregnable gas rarefaction, time-dependent changes of the magnetic field due to big drop currents, to name a few ( Minea et aluminum 2020 ). A time bridge in the range of respective tens of μs, is required to obtain a significant discharge current lift and the repetition frequency can be of the ordering of kilohertz, and therefore it is quite challenge to simulate even one period ( of the arrange of molarity ) due to limitations in available computing power. A solution that makes it possible to obtain meaningful results from the model of a single pulse is to assume a pre-ionized discharge before the application of the high power pulsation. That allows the fire current to reach the tableland much flying ( ∼2 μs ) while only simulating a single short-change pulse of a few μs ( Minea et alabama 2014, Revel et alabama 2018 ). due to the non-uniformity of the particle densities one approach is to use inhomogeneous grids, preferably time-dependent ( Revel et aluminum 2018 ). then the grid is fine in the high-density area and in the cathode fall and coarse in the rest of the plasma volume. The 2D models assume a uniform plasma along the one-third dimension, which is not acceptable when ephemeral phenomenon propagate in the azimuthal direction ( plasma instabilities or spokes ( see section 10.4.1 ) ) are to be investigated. For such a purpose, the 2D PIC/MCC proficiency has been extended to the alleged pseudo-3D PIC ( Revel et aluminum 2016 ) .

10. The physics of the magnetron sputtering operation

The introduction of the HiPIMS dismissal has sparked a significant matter to in understanding the physics of the magnetron sputter operation. The efforts have chiefly been driven by the motivation to understand why the deposit rate is lower for HiPIMS than dcMS operation, to find ways to increase the deposition rate and the ionize flux fraction, and to optimize the deposition process. These efforts have revealed that the magnetron sputtering discharge exhibits quite ample physics that largely remains to be explored. The holocene discoveries include better sympathize of the world power transfer to the electrons and alimony of the acquit, ion recycling when operating with eminent discharge currents, and presence of instabilities including spokes .

10.1. Electron power absorption in magnetron sputtering discharges

Since the electrons play a significant function in the magnetron sputtering acquit it is crucial to understand how energy is transferred to the electrons and how the acquit is maintained. Thornton ( 1978 ) introduced a simple exemplar that gives an estimate of the minimum electric potential needed to sustain a magnetron sputtering discharge. It states that the number of electron–ion pairs created by each secondary coil electron that is trapped in the target vicinity is given asEquation (44) where ${\mathcal{E}}_{\mathrm{c}}$ is the energy loss per electron–ion pair created with the flow of secondary electrons into the plasma as the beginning of energy ( Depla et aluminum 2010, Lieberman and Lichtenberg 2005, Thornton 1978, Thornton and Penfold 1978 ). The collisional energy loss per electron–ion pair created ${\mathcal{E}}_{\mathrm{c}}^{\left(X\right)}$, is calculated as ( Lieberman and Lichtenberg 2005, segment 3.5 )Equation (45) where ${\mathcal{E}}_{\text{iz}}^{\left(X\right)}$ is the ionization energy of species X, ${\mathcal{E}}_{\text{ex},i}^{\left(X\right)}$ and ${k}_{\text{ex},i}^{\left(X\right)}$ are the excitation energy and rate coefficient for the ith excitement action of species X, respectively, ${k}_{\text{el}}^{\left(X\right)}$ is the elastic scattering rate coefficient of species X, me is the electron mass and M ( X ) is the bulk of species X. For argon and high energy electrons ${\mathcal{E}}_{\mathrm{c}}^{\mathrm{H}}\approx 20$ V. As not all the secondary electrons are confined in the target vicinity an effective secondary electron discharge coefficient is definedEquation (46) where epsilon e is the fraction of the electron energy that is used for ionization before being lost, megabyte is a factor that accounts for secondary electrons ionizing within the sheath and roentgen is the recapture probability of secondary electrons. To sustain the discharge the conditionEquation (47) has to be fulfilled. The act of electron–ion pairs created ( equation ( 44 ) ) and the effective secondary electron emission ( equality ( 46 ) ) define the minimum electric potential required to sustain the dropEquation (48) where βg is the fraction of ions of the working boast that tax return to the cathode. note that all the ions assumed in this model are ions of the noble knead gas. Equation ( 48 ) is frequently referred to as the Thornton equation. The basic assumption is that secondary coil electrons and their acceleration across the sheath is the main source of electron energy that drives the ionization processes ( Thornton 1978 ). Above dislocation, the Thornton equation can be written for any electric potential as ( Depla et alabama 2009 )Equation (49) therefore a plot of the inverse fire electric potential 1/VD against γsee is expected to give a straight trace through the origin. however, there are indications that the magnetron sputtering discharge is not fully sustained by acceleration of secondary electrons emitted from the cathode prey. Decades ago it was demonstrated using Monte Carlo pretense that the ionization ascribable to emit secondary electrons is not sufficient to sustain a dcMS discharge when the confining magnetic field is below 20 mTesla ( Miranda et alabama 1990 ). More recently Depla et alabama ( 2009 ) measured the discharge electric potential for a magnetron sputtering exhaust with a 5 curium diameter aim of 18 unlike target materials with argon as the working flatulence while keeping the coerce and drop current changeless. When 1/VD is plotted against γsee for gas pressures of 0.4 and 0.6 Pa and fire currents 0.4 A and 0.6 A, i.e. a sum of four cases, indeed a uncoiled line appears, but it does not pass through the origin. It has been proposed that the wiretap is due to Ohmic heating system, i.e. the profligacy of locally deposited electric department of energy J e ⋅ E to the charged particles that carry the drop current density JD ( Brenning et aluminum 2016 ). then the inverse discharge electric potential 1/VD can be written in the form of a generalize Thornton equationEquation (50) or $\frac{1}{{V}_{\mathrm{D}}}=a{\gamma }_{\text{see}}+b$ where the intersect is associated with an Ohmic inflame march. here ${\mathcal{E}}_{\mathrm{c}}$ is the collisional energy loss per electron–ion pair given by equation ( 45 ) for the plasma majority electrons ( C ) and the hot ( H ) secondary electrons, e is the fraction of the electron energy that is used for ionization before being lost from the discharge process, and δIR = VIR/VD is the divide of the total discharge voltage that is dropped across the dense plasma next to the cathode aim. ohmic inflame is thereby the department of energy reach of an average electron moved across a fraction ${\langle {I}_{\mathrm{e}}/{I}_{\mathrm{D}}\rangle }_{\text{IR}}$ of the potential VIR. The fraction of the sum ionization that is due to Ohmic heating system can be obtained immediately from the line match parameters a and b. This ratio can be written as a function of only the secondary electron give way γseeEquation (51) This relative is plotted in figure 27 for the four cases studied by Depla et alabama ( 2009 ). The contribution of Ohmic inflame is in the range of 30 % –70 % and its contribution decreases with increase secondary electron emission coefficient. This suggests that Ohmic inflame within the IR plays a significant role in the dcMS discharge ( Brenning et aluminum 2016 ). Furthermore, name 27 besides shows an case from a HiPIMS dismissal operated at an argon coerce of 1.8 Pa modeled by Huo et aluminum ( 2013 ), marked by a circle. It is taken at the end of a 400 μs long pulsate when the exhaust was deep into the self-sputter manner. Due to the big fraction of Al+ ions an effective γsee is close up to zero ( see section 7.5 ). note that this HiPIMS event is absolutely coherent with the dcMS cases. The fraction of the dismissal electric potential that falls over the IR δIR can be estimated from the intersect barn. We assume ${{\epsilon}}_{\mathrm{e}}^{\mathrm{C}}=0.8$, ${\langle {I}_{\mathrm{e}}/{I}_{\mathrm{D}}\rangle }_{\text{IR}}\approx 0.5$, and ${\mathcal{E}}_{\mathrm{c}}^{\mathrm{C}}=53.5\enspace \mathrm{V}$ for Te = 3 V, which suggests that 15 % –19 % of the enforce fire electric potential falls over the IR .Figure 27. Figure 27. The proportional contributions to the entire ionization ιtotal due to Ohmic heat, ιOhmic, and cocktail dress energization, ιsheath. The curves show equality ( 50 ) using a and b from the four combinations of pressure and acquit current in the district of columbia magnetron sputtering discharge studied by Depla et alabama ( 2009 ). The lines are solid only in the image of γsee where they are supported by the measurements of Depla et alabama ( 2009 ). A blasphemous set marks the HiPIMS study by Huo et alabama ( 2013 ). Reprinted from Brenning et aluminum ( 2016 ). ©IOP Publishing. Reproduced with permission. All rights reserved. download design : Standard image
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late measurements have revealed firm electric fields twin and perpendicular to the target of a dcMS fire ( Panjan and Anders 2017 ). The deliberate potential can be ampere high as 30–70 V ( δIR = 11 % –25 % ) in the region up to 20 millimeter over the race lead area of a dcMS exhaust operated at 270 V and 0.27 Pa. The largest electric fields ( and potential drops ) result from a double layer structure at the leading edge of an ionization zone. The electrons gain energy when they encounter a potential gradient, such as the electric playing field in the doubling layer, which can play a all-important function in the energization of electrons .

10.2. The current composition

In dcMS most of the ions available in the discharge are ions of the baronial work gas. The ions that bombard the substrate american samoa good as the ions that sputter the aim are ions of the working boast. The primary current Iprim is defined as the current due to the atoms and molecules of the working accelerator ( index g ), which are ionized for the beginning time, with a probability αprim and then bombard the cathode target. There is an upper limit to the primary work gas ion ( argon ion ) stream available as suggested by Anders et aluminum ( 2012b ). This upper specify to the argon ion current is due to the maximum argon gasoline refill rate from the surrounding flatulence reservoir in steady state. We follow the same pipeline of think and define a critical stream density at the cathode target, JD, crit, determined by the maximum thermal refill rate of ambient argon gasoline in the direction perpendicular to the target, at working boast press pg and gasoline temperature Tg. For a singly ionized argon the critical ion stream density that bombards the cathode target isEquation (52) where kilobyte is the Boltzmann constant, nanogram is the working gas concentration, and Mg is the mass of the working gas atom. For a gas temperature of 300 K, an estimate of the maximal primary current given in practical units isEquation (53) where SRT is the race track sphere in cm2, and pg is the working boast coerce in Pa. In magnetron spatter, it is much easier to use the average current density over the hale aim area ST. For typical magnetron sputtering acquit parameters ( Tg = 300 K, SRT = 0.5ST, and argon at pg = 1 Pa ), this gives the critical current densityEquation (54) typically dcMS devices are operated well below this critical current density, or in the compass 4–60 milliampere cm−2, and therefore operated wholly on the primary stream, and the ions that bombard the aim are ions of the working flatulence. This dispatch current density is marked on figure 20 with a smash upright course, left of this crash line the release can be operated only on the primary coil stream. however, this is not the subject when high exponent pulses are applied to the cathode target. The release currents observed in HiPIMS discharges are identical large, often in 10s or 100s of amperes or current densities that are higher than 0.2 A cm−2. These discharges are consequently operated at current densities above the critical stream concentration and appear to the right field of the vertical dashed course in figure 20. As an exemplar we summarize the probe of the discharge current composition at the cathode target surface by Huo et aluminum ( 2017 ), which analyzed the experimental data presented by Anders et alabama ( 2007 ), using the IRM ( see section 9.4 ). It discusses a planar balanced magnetron sputtering discharge equipped with a 50 millimeter diameter Al prey, with argon as the working flatulence at a pressure of 1.8 Pa with pulsate length of 400 μs, while the office supply maintained constant empty electric potential throughout the entire pulsation. trope 28 shows the acquit stream composition at the target come on for discharge voltages of 360 V, 400 V, and 800 V. For all free voltages, the ions carry about the integral release stream, and the contribution from secondary electrons ID, southeast is very little, indeed. For a fire operated at 360 V ( digit 28 ( a ) ), the bill acquit current is in the crop of a few hundred mA, and the stream density is roughly ∼36 milliampere cm−2 ( averaged over the entire target area ), which is well below JD, crit, or in the middle of the distinctive operate regimen of a dcMS fire. The Ar+ ions contribute to approximately 2/3 of the release current whereas Al+ ions contribute approximately 1/3. When the electric potential is increased to 400 V ( trope 28 ( bacillus ) ) the flower discharge stream rises to a few amperes, the current density to ∼250 ma cm−2, and the power concentration is ∼100 W cm−2, just below the HiPIMS terminus ad quem displayed in figure 17. The contributions of Al+ and Ar+ ions to the discharge current are about equal, and the contributions from Al2+ ions and secondary electrons are about negligible. At even higher electric potential of 800 V ( figure 28 ( c ) ), the peak exhaust current is in tens of amperes, the current concentration > 1 A cm−2, the baron density ∼1 kilowatt cm−2, and the exhaust is operated well into the HiPIMS regimen. The Al+ ions about completely dominate the discharge current, and the contribution of Ar+ ions is below 10 % except at the initiation of the pulse. Al2+ ions and secondary electrons have about negligible contributions. For this aim the critical current calculated using equation ( 53 ) is ID, crit ≈ 7 A. calculate 28 shows that the experiment is operated from far below ID, crit to high above it, up to 36 A. The tendency with increasing current above ID, crit is that Iprim gradually becomes a identical small fraction of the total discharge current ID, which alternatively becomes chiefly carried by individually charged Al+ ions .Figure 28. Figure 28. The temporal variation of the empty current composing at the target surface for an argon discharge at 1.8 Pa with a 50 mm-diameter Al aim for a exhaust voltage of ( a ) 360 V ( JD, peak ≈ 36 mA cm−2 ), ( b-complex vitamin ) 400 V ( JD, vertex ≈ 0.25 A cm−2 ), and ( cytosine ) 800 V ( JD, acme ≈ 1.8 A cm−2 ). Note the unlike scales of the y-axes. Reprinted from Huo et aluminum ( 2017 ). ©IOP Publishing. Reproduced with permission. All rights reserved. download name : Standard image
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10.3. Ion recycling

It is open from the above discussion that the primary current is not sufficient when operating at high power densities and some recycling must take topographic point to reach the high discharge currents observed. Above a critical current concentration given by equation ( 54 ) a combination of self-sputter recycle and working gas-recycling is generally the case ( Brenning et aluminum 2017 ). The acquit can generate more ions to bombard the target and thereby to increase the discharge current ID ( thymine ) beyond ID, crit by ( one ) recycling of working gas atoms and/or ( two ) recycle of sputter target atoms. These processes are demonstrated in figure 29. The ions in Iprim are neutralized at the target and a fraction ξpulse returns to the discharge during the pulsation. As discussed by Huo et aluminum ( 2014 ), embedded Ar atoms are most probably to leave the target when it is bombarded by ions. It is assumed that all the argon atoms return to the exhaust in each pulse or ξpulse = 1. These returning working gas atoms are subsequently ionized with probability αg and draw binding to the target with probability βg. The remaining divide of the working gas ions ( 1 − βg ) escapes to the encompassing volume. These steps constitute a first gear bicycle in the knead flatulence recycling loop topology ( seen in the left english of figure 29 ), where a recycle stream Iprim πg is added to Iprim in each cycle, andEquation (55) is the working gas-sputter parameter as defined by Gudmundsson et aluminum ( 2016 ). Each subsequent cycle adds so far another contribution to the working accelerator stream by multiplying the recycle current with πg. Since ${\sum }_{n=1}^{\infty }{a}^{n}=a/\left(1-a\right)$ for 0 < a < 1, it is possible to express the sum current carried by recycle working boast ions in steadily department of state ( north → ) as a mathematical series of the formEquation (56) The total current carried to the target by working gas ions therefore is the summarize of the primary stream and the contribution of the recycling loopEquation (57) which indicates that Iprim acts as a seed for the full free current. This stream can become a lot larger than Iprim if the denominator in the digression approaches zero, that is, if πg approaches oneness .Figure 29. Figure 29. A schematic exemplification of the compound processes of working natural gas recycling and self-sputter recycle to generate senior high school discharge currents. The widths of the hang arrows are drawn to scale with a parameter combination αprim = 1, ξpulse = 1, αg = 0.7, βg = 0.7, Yg = 0.4, αt = 0.8, βt = 0.7, and YSS = 0.5. This combination is randomly chosen as desirable to illustrate compound working gas-recycling and SS-recycling. Reprinted from Brenning et alabama ( 2017 ). ©IOP Publishing. Reproduced with permission. All rights reserved. download name : Standard image
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Each ion of the working gas that constitutes Ig ( equation ( 57 ) ) sputters target atoms with a spatter give Yg. These target atoms are subsequently ionized with probability αt and draw second to the target with probability βt. This indicates a self-sputter recycle procedure. It is about identical to working natural gas recycling, except that it relies on the self-sputter yield YSS, and it is consequently potential to apply the like manner of reasoning for expressing the self-sputter stream amplification. The total self-sputter stream generated by Ig ( acting as seed ) with the subsequent SS-recycling added becomes ( Gudmundsson et alabama 2016 )Equation (58) where the self-sputter parameter ( Anders 2008, Gudmundsson et aluminum 2016 ) isEquation (59) Adding the currents given by equations ( 57 ) and ( 58 ) gives the total ion stream Ii. Thus the sum dismissal current at the cathode target airfoil can nowadays be written asEquation (60) orEquation (61) The primary stream Iprim, amplified by the first parentheses in equation ( 61 ), is consequently a one-way seed for the self-sputter recycling process, without any feedback in the other guidance, that is, from self-sputtering to working gas-recycling. The dominating recycling process can be visualized on a recycling map as seen in design 30 ( Brenning et aluminum 2017 ). The positions on the map show relative current densities. The discharge with an Al target ( discussed in section 10.2 ) follows the path upwards to the exit on the map, gradually changing character from the dcMS operating regimen to a HiPIMS government as the SS-recycling increases with increasing drop voltage. This is referred to as a discharge of type A and appears when the self-sputter yield is high. In order to bring the absolute current amplitude into the word picture, the circles are drawn clear when ID < ID, crit and filled when ID > ID, crit. figure 30 besides shows the recycle contributions for a HiPIMS free with a graphite ( C ) target, measured by Anders et aluminum ( 2012b ). For free voltages in the roll 950–1100 V, the discharge current is below the critical current ID < ID, crit. A sudden jump in the tableland discharge current is observed when increasing the discharge voltage from 1100 to 1150 V and a large divide of the release current must be recycled. For a reactive splutter of a Ti prey in an Ar/O2 concoction in poison modality, the splutter concede is very low, and working flatulence recycling dominates ( Gudmundsson et aluminum 2016 ) and the discharge is of character B as indicated in trope 30 .Figure 30. Figure 30. A recycling function showing the development of recycling for aluminum and carbon paper targets as the dispatch electric potential is increased. The drop stream is evaluated at the discharge current tableland ( 300 μs for the Al character and 150 μs for the C character ) when equilibrium is well established. The TiO2 shell is evaluated at the end of a triangular shaped current wave form. The symbols are drawn open at drop currents ID below ID, crit and filled for ID > ID, crit. Reprinted from Brenning et alabama ( 2017 ). ©IOP Publishing. Reproduced with permission. All rights reserved. download figure : Standard image
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We see that in the case of aluminum target the discharge reaches about a complete self-sputter operation when in the HiPIMS regimen ( see besides figure 28 ( coke ) ). In fact, Andersson and Anders ( 2008, 2009 ) have demonstrated a gas-less self-sputtering from a high sputter yield copper target in an HiPIMS discharge. A vacuum-arc acquit was used to initiate the plasma at a background pressure of 10−3 Pa. Furthermore, they demonstrated that the magnetron sputtering acquit not only self-sustains but amplifies via self-sputtering runaway to high free currents ( Andersson and Anders 2008, 2009 ). Self-sputtering runaway is driven by a plus feedback, where a higher flow of ions leads to increased sputter, which in turn leads to more achromatic atoms that can be ionized in the vicinity of the target and more ions lead to increased sputter .

10.4. Instabilities

Instabilities are often observed in magnetize first gear temperature plasma discharges. Discharges operated in E × B field shape are subject to a number of instabilities which may be driven by gradients in plasma concentration, charismatic field, and temperature ( Boeuf 2014, Thornton 1978, Thornton and Penfold 1978 ). The gradients along with feedback mechanisms can drive oscillations of waves into macroscopic instabilities that can have influence alike to collisions and consequently enhance electron transportation across the charismatic field lines ( ‘anomalous transport ‘ ). These instabilities are all-important for the transport of charged particles and electron ecstasy across charismatic field lines is governed by instabilities as opposed to classical diffusion. A act of instabilities have been observed in magnetron splutter discharges both experimentally and by simulations. It is broadly believed that instabilities and anomalous transportation across the magnetic field lines plays a significant function, however there exist presently no consensus nor real quantification of these phenomena in magnetron sputter discharges. Electron electrostatic waves are known to propagate along battlefield lines with frequency of the holy order of ${\left({\omega }_{\text{pe}}^{2}+{\omega }_{\text{ce}}^{2}\right)}^{1/2}$, where ωpe is the electron plasma frequency, while ion electrostatic waves propagate at a speed of the arrange of ${\left({k}_{\text{B}}{T}_{\mathrm{e}}/{M}_{\mathrm{i}}\right)}^{1/2}$. Thornton ( 1978 ) observed electrostatic fluctuations in the frequency range 50–500 kilohertz, in a magnetron sputtering discharge in the cylindrical shape, and related to ion electrostatic waves. Sheridan and Goree ( 1989 ) observed turbulence, density fluctuations with a strong point near the ion cyclotron frequency and other peaks in the 200–300 kilohertz stove in a planar dcMS. besides anisotropic turbulence with a broad extremum in the spectrum at a frequency of few hundred kilohertz, has been observed in a planar reticular formation magnetron sputtering discharge and attributed to ionization-drift instability ( Lin and Wu 1987 ). Electron freewheel can besides develop across the magnetic field lines. Instabilities or patterns that appear as coherent modes corresponding to waves propagating in the direction of the electron diamagnetic drift have been observed in planar dcMS discharges when operated at noun phrase exponent densities in the image 0.5–6 W cm−2 ( Martines et alabama 2001, 2004 ). The presence of these low frequency waves or modes is found to depend on the discharge power and the working natural gas pressure. By increasing the working boast coerce to several Pa a transition toward a churning state was observed. This mood exhibits non-regular amplitude modulation exchangeable to couple oscillators. such modes have been interpreted as electron drift waves destabilized by the combined effect of density gradient and electric field. The Simon–Hoh instability occurs when the density gradient and the electric field are in the lapp focus ( Hoh 1963, Simon 1963 ). As the ions are basically unmagnetized while the electrons are magnetized, a speed deviation develops in the azimuthal guidance due to the finite ion Larmor radius. When a significant electron drift develops in the E × B direction ( Hall current ) it can consequently lead to charge legal separation between electrons and ions and therefore create a quad charge sphere Eθ along the management of the electron drift. This azimuthal component of the electric field can then lead to an axial Eθ Br stream, that is an electron stream across the magnetic barrier. Diocotron or slipping stream instability occurs due to a radial variation in electron concentration. There is indeed a significant radial mutant in the electron concentration due to the non-uniform magnetic confinement. The diocotron instability occurs in low concentration ( ${\omega }_{\text{pe}}^{2}\ll {\omega }_{\text{ce}}^{2}$ ) non-neutral electron plasma column that are radially confined by a uniform axial magnetic field and is driven by a strong shear in the azimuthal rotation speed E × B ( and is analog to a Kelvin–Helmhotlz imbalance in fluid mechanics ) ( Boeuf 2014 ). Two-stream instability ( Buneman 1959 ) and the modified two-stream instability ( MTSI ) ( McBride et aluminum 1972 ) occur due to a deviation in the stray speed between electrons and ions. In non-magnetized plasma drop two-stream instability grows and saturates when the relative roll speed between electrons and ions exceeds the thermal speed of electrons. In magnetic plasma free the doorway for instability is lower and instability appears when the relative drift speed between electrons and ions exceeds the thermal speed of ions. In two-stream instability the relative motion between the species causes a Doppler lurch. This occur and the instability grows when the beckon vector of the oscillations and the relative speed of the species vrel = united states virgin islands − ve fulfills the condition ωpe − k vrel = ωpe. In the presence of magnetic field the drift of the electrons is restricted and MTSI appears. The electrons are only accelerated in the focus of the electric airfield if it has a part along the magnetic sphere while in the lawsuit of no such part they move in a commission that is perpendicular to both the electric and magnetic fields. The electrons behave as if they have an effective mass that is significantly larger than me and may tied be comparable to the ion mass ( McBride et aluminum 1972 ). MTSI consequently, results in comparable ion and electron heat. MTSI can result in big oscillations in concentration and electric field and consequently a net transportation of electrons across magnetic field lines. For MTSI the result oscillations can be expected to be in the stove of the lower hybrid frequency ${\omega }_{\text{LH}}={\omega }_{\text{pi}}/\sqrt{1+{\omega }_{\text{pe}}^{2}/{\omega }_{\text{ce}}^{2}}$ ( Buneman 1962, McBride et aluminum 1972 ). Lundin et alabama ( 2008a ) estimated the individual contributions of the respective drift terms on the total azimuthal stream. They found that the Hall drift ( equation ( 23 ) ) and the diamagnetic roll ( equality ( 24 ) ) are oriented in the same steering and trust to an azimuthal drift accelerate exceeding the MTSI threshold which has been argued to cause radial transportation of ions as discussed in section 8.6. Both measurements ( Lundin et aluminum 2008a Winter et aluminum 2013 ) and simulations ( Bultinck et aluminum 2010 ) have shown oscillating electric fields in the MHz range consistent with the presence of MTSI. The instabilities that have received most attention recently are dense azimuthally rotating structures of enhance ionization that present a distinct likely structure and are referred to as spokes .

10.4.1. Spokes

The ionization processes in magnetron sputter discharges seem to be not uniformly distributed along the race track. Magnetron splutter discharges are known to exhibit azimuthally inhomogeneous plasma with distinct regions of increase light emission. These aglow zones are observed to travel along the raceway track. The appearance of azimuthally rotating dense plasma structures in E × B -devices, referred to as spokes have been known for a few decades ( Tozer 1965, Wasa and Hayakawa 1966, Wilcox et alabama 1962 ). The most investigate E × B discharges, Hall thrusters, that are used for electric propulsion of spacecraft, expose spokes, instabilities that appear as moving regions of enhance ionization ( Boeuf 2017, Ellison et alabama 2012, McDonald and Gallimore 2011 ). In magnetron sputter discharges, ionization zones or spokes, rotating above the rush chase of the cathode target are frequently observed. These self-organized structures appear to sit just above the cathode target coat and rotate along the race track. These regions of intense excitation have been referred to as ionization zones ( Anders et alabama 2012a, Ni et aluminum 2012 ), emission structures ( Winter et alabama 2013 ), bunches ( Kozyrev et alabama 2011 ), and spokes ( Brenning et al 2013 ), which is what will be used in the discussion below. such spokes are observed in dcMS ( Anders et alabama 2014, Panjan and Anders 2017, Panjan et alabama 2015 ), rfMS ( Panjan 2019 ) and HiPIMS ( Hecimovic et alabama 2014, Hecimovic and von Keudell 2018 ) operation. Spokes appear independent of the magnetron shape, and have been observed with both circular ( Anders et aluminum 2014, Panjan et aluminum 2015 ) and rectangular or analogue ( Anders and Yang 2017, 2018, Preissing 2016 ) magnetron targets. An effigy of spokes observed in a dcMS exhaust operated in the stream concentration compass 0.3 ma cm−2 to 11 massachusetts cm−2 is shown in figure 31. This stream density is in the lower end of the dcMS operate on regimen and only one rundle is observed in each shell ( lower jury ). A single ionization zone is typically obtained when using a small target at low working boast press and broken discharge current ( Panjan and Anders 2017, Panjan et aluminum 2015, Yang et aluminum 2014 ). We besides note that the speak extends a few millimeter axially ( upper berth jury ). The spokes observed in HiPIMS discharges are typically shorter and more numerous than when operating in the dcMS government. The spokes observed in HiPIMS discharges, when operated in baronial working gases, appear to exhibit two basic shapes, either diffusing ( as observed for Ti and Nb targets ), or trilateral ( as observed for Al, Cu, Mo, Cr targets ) ( Hecimovic et alabama 2014 ). A more recent study of a discharge with Ti target suggests, however, that the appearance of diverse spoke shapes depends on the drop current density, working gasoline atmospheric pressure and magnetic field intensity rather than the target material ( Hnilica et alabama 2018 ). It has been reported that the inhomogeneities smooth out at eminent discharge currents to yield azimuthally homogeneous plasma ( Andersson et aluminum 2014, de los Arcos et alabama 2013 ). At very senior high school vertex world power densities ( > 3 kW cm−2 ) the discharge exhibits a transition from a regimen where spokes are observed to a homogeneous government ( Šlapanská et al 2020 ). These observations have been interpreted as electron heat mode transition, from a combination of acceleration of junior-grade electrons and Ohmic heat in the IR toward pure Ohmic heat in the IR ( see section 10.1 ). This transition is alone observed in non-reactive HiPIMS discharges where the sputtered atoms have the second ionization electric potential higher than the first ionization electric potential of the noble work gas ( for Ar ${\mathcal{E}}_{\text{iz}}=15.7$ 6 electron volt ), and a self-sputter concede larger than 1 ( Šlapanská et al 2020 ) .Figure 31. Figure 31. Spoke appearance in a dcMS discharge in argon with Al target 76 millimeter in diameter. The images show side-on watch ( upper berth panel ) and end-on opinion ( lower panel ) with increasing dismissal stream density from 0.3 mA cm−2 to 11 massachusetts cm−2, from left to right. Each persona is taken with 500 normality exposure time, and illustrate the universe of one zone at different discharge currents. ©2014 IEEE. Reprinted, with permission, from Anders et aluminum ( 2014 ). download human body : Standard image
High-resolution image
The accession of a reactive gas leads to compound constitution on the aim come on ( poison come on ) with profound consequences for many parameters of the magnetron sputtering discharge such as the secondary coil electron emission yield, the sputter yield, and the plasma composition near the target ( see discussion in section 5 ). probe of several target/reactive gas combinations indicates that in the poison manner, the talk determine is circulate ( Hecimovic et aluminum 2017 ). For the conditions of these experiments, the discharge voltage decreased upon addition of reactive natural gas, which can be correlated with an increase in the secondary electron discharge ( Depla and Mahieu 2008, Marcak et alabama 2015 ). The spokes are observed to propagate along the race track and their propogation amphetamine appears to depend on the acquit current or ability concentration. At lower exhaust currents ( dcMS government ) the spoke revolve at speeds below 1 km s−1 in the − E × B guidance while at high discharge currents ( HiPIMS government ) the speak speed is between 1 and 15 kilometer s−1 in the + E × B direction ( Anders et aluminum 2012a de los Arcos et alabama 2013, Winter et aluminum 2013, Yang et aluminum 2014 ). The talk propogation speed is approximately 10 % of the azimuthal electron drift speed. In addition to instabilities that propagate along the race track ( i.e. spokes ), the plasma may besides exhibit other instabilities. In finical, the plasma can oscillate in a commission convention to the prey airfoil, which has been termed ‘breathing imbalance ‘ ( Yang et alabama 2016 ) in doctrine of analogy to a exchangeable phenomenon in Hall thrusters ( Young et aluminum 2015 ). Spokes and the breathe instability normally superimpose ( Yang et alabama 2016 ). It should be noted that the breathe imbalance in Hall thrusters is linked to about complete ionization of the achromatic running gas, whereas in the HiPIMS acquit, the neutral species are endlessly injected into the IR via working accelerator and metallic recycling, and consequently the breathe instability powerfully depends on the working accelerator pressure and the target material. Measurements using electric probes ( Panjan and Anders 2017 ), ion energy analyzers ( Yang et aluminum 2015 ), and spectrally selective visualize ( Andersson et alabama 2013 ) indicate that the spokes exhibit locally enhanced likely structure. such potential structures can explain the dislocation of close electron drift, formation of plasma flares, and formation of energetic ions, in finical considering the differences of ion energies in E × B and − E × B directions ( Yang et aluminum 2015 ). It appears as each address represents a electric potential hunch relative to its surroundings and is enclosed by an electric bivalent layer. This leads to creation of a local electric plain ( denote E sulfur ) that influences the local anesthetic direction of the electron drift and can give arise to local acceleration of ions. Electrons arriving at a address, enter the potential bulge, reach a region of higher likely, and are therefore energized, enabling them to cause localize excitation and ionization. This suggests that images of spokes can be taken as approximate images of the potential distribution ( Anders 2014 ). recent measurements by Held et alabama ( 2020 ) indicate that the spokes have a higher plasma density, electron temperature and plasma likely than the surrounding plasma. besides the electron density slowly rises at the leading edge of the address to a maximum value and then drops aggressively at the trail border, while no strong likely gradient was observed inside the spoke. It is claimed that the electric field pointing toward the prey is reduced in the presence of a speak and therefore the potential barrier that ions have to overcome in order to leave the ionization ( charismatic trap ) area. consequently, ions may then diffuse un-hindered toward the substrate. A current of electrons, away from the prey vicinity, into the plasma bulk, referred to as flares, have besides been observed and associated with the spokes in HiPIMS operation ( Ni et alabama 2012, Yang et aluminum 2014 ) adenine well as in a HCM sputtering free ( Sahu et aluminum 2018 ). It has been suggested that there exist a digressive electric field in the management along the race racetrack parallel to the target surface. This tangential electric field E thymine is then claimed to disrupt the azimuthal electron drift as the electrons get reflected in the E t × B management which is observed as a plasma jet or a flare pass that travels away from the prey ( Ni et aluminum 2012, Sahu et alabama 2018 ). The flare speed has been estimated to be roughly 20 km s−1 ( Ni et alabama 2012, Sahu et aluminum 2018 ). Oscillations observed in the frequency crop 100–200 kilohertz have been related to the flares ( Sahu et aluminum 2018 ). This tangential electric field is besides expected to cause tangential ion acceleration. This digressive ion acceleration has been observed indeed ( Lundin et aluminum 2008b, Panjan et aluminum 2014, Poolcharuansin et aluminum 2012 ) ( see discussion in section 8.6 ). The flare speed in the z direction is typically a few times the speak speed ( Ni et alabama 2012 ) .

11. Summary

The magnetron sputtering dispatch has been a very successful technology and is used in a across-the-board rate of industries where the applications range from depositing conducting layers and protective barriers in microelectronics to energy saving ocular layers on architectural methamphetamine. The proficiency is based on confining electrons in the vicinity of the cathode target of an basically a district of columbia discharge, by applying a inactive magnetic field. The electron parturiency leads to dense plasma adjacent to the cathode target and abundance of ions to perform sputtering as they are accelerated across the cathode sheath. The sputter procedure releases the film forming material from the cathode aim and these species are either ionize or not before they fall onto a substrate to form a film or coat. reactive sputter deposition, in detail, is of significant industrial and technical importance as most commercially relevant flimsy films and coatings are compounds. This includes hard transition metal nitride based coatings, guileless conductive oxides, insulator layers and photo-catalytically active layers. reactive sputter deposition of insulating films from conductive targets in reactive accelerator is typically achieved using the mid-frequency asymmetrical bipolar magnetron sputtering discharge. Bipolar pulsed refers to the polarity of the prey electric potential that is alternated between damaging and positive. reactive spatter deposit is challenging due to appearance of hysteresis and feedback control of the serve is all-important.

In order to increase the ionization divide of the sputter species either a secondary discharge can be added between the cathode target and the substrate or high power pulses are applied to the cathode prey. The former border on is widely used in the microelectronics industry. The application of high baron pulses and the presentation of HiPIMS sparked a renewed sake in the magnetron sputtering acquit and opened up a compass of possibilities. Despite being by and large unexplored it is clear that the HiPIMS process and selective bias of the substrate provides the ability to tune the deposition process for specific material properties and morphologies. selective bias can be used to select if the ions of the film forming material or the ions of the noble working boast bombard the substrate at a preset energy. The issues related to the low deposition rate in HiPIMS mathematical process have lead to intensifier research efforts. These efforts have revealed the building complex physics of the magnetron sputtering fire. This includes, improved understand of the baron transfer to the electrons, observation of respective instabilities such as spokes and breather modes, working gas recycling and self-sputter recycle. Pulsing the exhaust comes with a issue of extra node for serve control condition. This allows for addressing such issues as the tradeoff between the ionize flux fraction and the deposition rate. Furthermore, the confining magnetic field and the cathode electric potential wave form or the discharge current can be tailored. There are inactive important issues that remain to be understand regarding the operation of the magnetron sputtering discharge. This is surely the case regarding instabilities, where a taxonomic study is lacking. It is known that instabilities such as spokes are authoritative subscriber to the conveyance of charge particles, while the function and meaning is not fully understand .


This work has been influenced by decades of collaboration with Profs. Daniel Lundin and Ulf Helmersson at Linköping University, Prof. Nils Brenning and Dr. Michael A Raadu at KTH Royal Institute of Technology, Prof. Tiberiu M. Minea at LPGP Université Paris Sud, Dr. Martin Rudolph at Leibniz Institute of Surface Engineering ( IOM ) and Dr. Hamidreza Hajihoseini at University of Iceland. The writer is grateful to Dr. Thomas J Petty for drawing figures 2, 4, 7, 29 and 30, and to Dr. Michal Zanáška of Linköping University and David Mainwaring of KTH Royal Institute of Technology for providing figure 8. This work was partially supported by the Icelandic Research Fund Grant Nos. 130029 and 196141 .

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