Gas Rarefaction Research Articles

Gas rarefaction and the time evolution of long high-power impulse magnetron sputtering pulses

Model studies of 400 µs long discharge pulses in high-power impulse magnetron sputtering have been made to study the gas dynamics and plasma chemistry in this type of pulsed processing plasma. Data are taken from an experiment using square voltage pulses applied to an Al target in an Ar atmosphere at 1.8 Pa. The study is limited to low power densities, <0.5 kW cm−2, in which the discharge is far away from the runaway self-sputtering mode. The model used is the ionization region model, a time-dependent plasma chemistry discharge model developed for the ionization region in magnetron sputtering discharges. It gives a close fit to the discharge current during the whole pulse, both an initial high-current transient and a later plateau value of constant lower current. The discharge current peak is found to precede a maximum in gas rarefaction of the order of ΔnAr/nAr,0 ≈ 50%. The time durations of the high-current transient, and of the rarefaction maximum, are determined by the time it takes to establish a steady-state diffusional refill of process gas from the surrounding volume. The dominating mechanism for gas rarefaction is ionization losses, with only about 30% due to the sputter wind kick-out process. During the high-current transient, the degree of sputtered metal ionization reaches 65–75%, and then drops to 30–35% in the plateau phase. The degree of self-sputtering (defined here as the metal ion fraction of the total ion current to the target) also varies during the pulse. It grows from zero at pulse start to a maximum of 65–70% coinciding in time with the maximum gas rarefaction, and then stabilizes in the range 40–45% during the plateau phase. The loss in deposition rate that can be attributed to the back-attraction of the ionized sputtered species is also estimated from the model. It is low during the initial 10–20 µs, peaks around 60% during the high-current transient, and finally stabilizes around 30% during the plateau phase.

TRANSFLOW: An experimental facility for vacuum gas flows

The TRANSFLOW experimental facility represents a reliable tool for measuring the conductance of 1:1 scale components as typically used in vacuum systems in a wide range of the Knudsen number (e.g. 10−4≤Kn≤103). The main principle of this facility is the dynamic measurement of the pressure difference upstream and downstream of the duct by setting a constant mass flow rate through the test channel. Many experiments on fully developed and developing flows, based on long and short channels respectively, have been already completed and comparisons with corresponding numerical results have been successfully performed. It has been clearly proven that the TRANSFLOW experimental setup provides conductance results with overall uncertainty between 1 to 10% and it could be used as a benchmark facility for any new proposed scientific numerical method in rarefied gas dynamics and in the whole range of gas rarefaction.

Design of micro distribution systems consisting of long channels with arbitrary cross sections

Gas flows through long micro-channels of various cross sections have been extensively investigated over the years both numerically and experimentally. In various technological applications including microfluidics, these micro-channels are combined together in order to form a micro-channel network. Computational algorithms for solving gas pipe networks in the hydrodynamic regime are well developed. However, corresponding tools for solving networks consisting of micro-channels under any degree of gas rarefaction is very limited. Recently a kinetic algorithm has been developed to simulate gas distribution systems consisting of long circular channels under any vacuum conditions. In the present work this algorithm is generalized and extended into micro-channels of arbitrary cross-section etched by KOH in silicon (triangular and trapezoidal channels with acute angle of 54.74°). Since a kinetic approach is implemented, the analysis is valid and the results are accurate in the whole range of the Knudsen number, while the involved computational effort is very small. This is achieved by successfully integrating the kinetic results for the corresponding single channels into the general solver for designing the gas pipe network. To demonstrate the feasibility of the approach two typical systems consisting of long rectangular and trapezoidal micro-channels are solved.

Rarefied gas mixture flow between plates of arbitrary length due to small pressure difference

The linearized flow of a binary gas mixture between two parallel plates of any length driven by a small pressure difference is numerically solved based on the McCormack kinetic model. In this case the flow is not fully developed and the simulated flow field includes, in addition to the channel, efficiently large upstream and downstream regions significantly increasing the required computational effort. In the present work results are provided for one gas mixture, namely He-Ne with a specific concentration of 0.5 in a wide range of gas rarefaction. The ratio of the length over the height of the channel is taken to be equal to 0, 1 and 5 corresponding to flow through channels of very short (slit), short and moderate lengths respectively. Results are provided for the two kinetic coefficients related to Poiseuille and barodiffusion flow rates and the velocity profiles of each species. The effect of the length to height ratio and of the gas rarefaction on the flow quantities is investigated deducing that as the ratio in increased the separation phenomenon becomes more dominant, while a Knudsen minimum is observed at the ratio equal to 5.

Comparison of the numerical solutions of the full Boltzmann and S-model kinetic equations for gas flow through a slit

The pressure-driven flow of a rarefied gas through a two-dimensional slit is analyzed on the basis of the full Boltzmann equation and its kinetic S-model applying the discrete velocity method. The calculations are carried out for the gas rarefaction ranging from the free-molecular to the hydrodynamic regime and for the reservoir pressure ratios leading to the subsonic or supersonic flow behind a slit. The structure of the flow field, given by both numerical approaches, as a function of the pressure ratio and the rarefaction parameter is examined. The mass flow rate and the distributions of density, bulk velocity and temperature along the symmetry axis are reported. An applicability of the S-model kinetic equation via comparison with the Boltzmann equation is discussed.

Comprehensive computer model for magnetron sputtering. I. Gas heating and rarefaction

The complex interaction between several variables in magnetron sputtering discharges is a challenge in developing engineering design tools for industrial applications. For instance, at high pressures, rarefaction and gas heating should no longer be neglected for determining several parameters of the process. In this article, we use a comprehensive 3D reactor-scale simulator that incorporates most phenomena of interest in a self-consistent manner to simulate the transport of sputtered particles over a wide range of pressures and powers. Calculations of aluminum deposition rates and metal vapor densities are in reasonable agreement with experiments over a wide range of pressures and powers. Of the elements investigated (Al, Ti, and Cu), copper showed the greatest rarefaction (30%) due to its higher sputtering yield. Titanium, despite a slightly lower sputtering yield than Al, shows a greater rarefaction than aluminum as more particles are reflected from the target as high energy neutrals. In this case, a more efficient energy transfer process is responsible for the higher rarefaction observed in Ti sputtering when compared to Al. The authors also observed that by sputtering at a higher pressure, the probability of electron impact ionization of sputtered particles is increased and speculate about the role of this process in contrast to penning ionization, which is believed to be the dominant ionization mechanism in magnetron sputtering.

Rarefied gas flow through channels of finite length at various pressure ratios

A rarefied gas flow through channels (i.e. flow through parallel plates) of finite length has been modeled based on the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as function of the gas rarefaction, the length-to-height ratio and the pressure ratio upstream and downstream of the channel. The whole range of the gas rarefaction including the free-molecular, transitional and hydrodynamic regimes and a wide range of the length-to-height ratio representing both short and long channels have been considered. Several values of the pressure ratio between 0 and 0.5 have been used in the calculations. It is shown that the rarefaction parameter has the most significant effect on the flow field characteristics and patterns, followed by the pressure ratio, while the length-to-height ratio has a rather modest impact. The Mach belt phenomenon is discussed in detail.

Effects of Gas Rarefaction on Dynamic Characteristics of Micro Spiral-Grooved Thrust Bearing

The effects of gas-rarefaction on dynamic characteristics of micro spiral-grooved-thrust-bearing are studied. The Reynolds equation is modified by the first order slip model, and the corresponding perturbation equations are then obtained on the basis of the linear small perturbation method. In the converted spiral-curve-coordinates system, the finite-volume-method (FVM) is employed to discrete the surface domain of micro bearing. The results show, compared with the continuum-flow model, that under the slip-flow regime, the decrease in the pressure and stiffness become obvious with the increasing of the compressibility number. Moreover, with the decrease of the relative gas-film-thickness, the deviations of dynamic coefficients between slip-flow-model and continuum-flow-model are increasing.

Pressure effects on HiPIMS deposition of hafnium films

High power impulse magnetron sputtering (HiPIMS) was studied during the growth of hafnium films at argon pressures ranging from 0.80 to 5.33Pa with a fixed pulse length (50μs) and frequency (200Hz). The effect of inert gas pressure on the plasma conditions and film structure was investigated. The peak target current increased with pressure, but its sensitivity decreased above 2.00Pa, which corresponded to an increased ratio of ions to neutrals in the plasma. A comparison of plasma characteristics between Hf and Ti HiPIMS growth was made. In addition to pressure, the target currents were affected by the physical properties of the target material, particularly the secondary ionization energy and atomic mass. Sputtering gas rarefaction phenomena were found to be more pronounced for Hf, and as a result, the process characteristics and film properties had a strong interdependence on argon pressure discussed in this study. The microstructure of the hafnium films was analyzed with scanning electron microscopy and X-ray diffraction. When compared to Hf films deposited by dc magnetron sputtering, the HiPIMS process resulted in a decreased grain size and promoted the growth of the (100) orientation in the Hf films. These results demonstrate that Hf HiPIMS sputtering regimes have much stronger dependence on the working gas pressure compared to titanium, and these need to be taken into account to ensure that films are dense and have the desired morphology and crystallographic orientation.

Argon metastables in HiPIMS: time-resolved tunable diode-laser diagnostics

Time-resolved tunable diode-laser absorption spectroscopy measurements were performed on the argon metastable (Arm) level 3s23p54s excited at 801.478 nm, in the dense plasma region in front of the magnetron target in a high power impulse magnetron sputtering (HiPIMS) discharge. From the Doppler profile the evolution of the temperature and density was derived during the pulse as well as during the plasma decay, i.e. in the afterglow. It is shown that the Arm density sharply increases at the beginning of the discharge pulse, followed by a severe Arm depletion along with increasing gas temperature around the peak of the HiPIMS discharge current. The strong dynamics of these parameters involve many elementary processes such as electron-impact excitation, electron-impact de-excitation and ionization of Arm, gas rarefaction, electron temperature increase at the end of the pulse and gas diffusion. These phenomena are discussed with respect to several parameters: distance from the target, peak discharge current during the pulse, pulse length, and gas pressure.

Simulations of pressure-driven flows through channels and pipes with unified flow solver

The aim of this paper is to demonstrate the benefits of direct methods of solving kinetic equations and adaptive kinetic-fluid solvers for vacuum science and technology. We consider pressure-driven flows through short channels for a wide range of gas rarefaction degrees. Our Unified Flow Solver combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic and fluid solvers in different parts of computational domain. The discrete velocity method is used for direct numerical solution of Boltzmann and model kinetic equations. The advantages of adaptive hybrid method are demonstrated for compressible flows at large pressure gradients. For small pressure drops, direct solutions of the Boltzmann equation provide accurate solutions of rarefied flows not achievable by the traditional direct simulation Monte Carlo methods.

Rarefied gas flow through a zigzag channel

A rarefied gas flow through a channel of zigzag shape is calculated over the wide range of the gas rarefaction and for several values of the aspect ratio applying the linearized kinetic equation. In the hydrodynamic flow regime, the kinetic solution is compared with that obtained from the Stokes equation. An approach to calculate a flow rate through a chain composed from an arbitrary number of zigzags is proposed. It was found that in some situations, the flow rate through a zigzag channel is higher than that trough a straight channel of the same length.

Aerothermodynamics of Satellite During Atmospheric Reentry for the Whole Range of Gas Rarefaction: Influence of Inelastic Intermolecular Collisions

The aerothermodynamic characteristics of the Brazilian satellite Satelite de Reentrada Atmosferica were calculated for orbital-flight and atmospheric-reentry conditions with the direct simulation Monte Carlo method for a diatomic gas. The internal modes of molecule energy in the intermolecular interaction, such as the rotational energy, were taken into account. The numerical calculations cover a range of gas rarefactions wide enough to embrace the free-molecule and hydrodynamic regimes. Two Mach numbers were considered: 10 and 20. Numerical results include the drag force of the satellite, the energy flux, pressure coefficient, and skin friction coefficient over the satellite surface, the density and temperature distributions, and streamlines of the gas flow around the satellite. The influence of the satellite temperature upon these characteristics was evaluated at different satellite temperatures.

Pressure-driven flow of rarefied gas through a slit at a various pressure ratios

This paper numerically studies a pressure-driven flow of rarefied gas through a slit using a direct simulation Monte Carlo method. A gas mass flow rate through a slit and a gas flow field were calculated. The calculations were carried out for various values of the pressure ratio over a wide range of gas rarefaction. The dependency of the mass flow rate and the flow field characteristics on the pressure ratio value and gas rarefaction degree was determined. In addition, the paper presents a discussion on the existence of the shock waves within a flow field in a hydrodynamic regime of the gas flow.

Transient flow of rarefied gas through an orifice

A transient rarefied gas flow through a thin orifice is studied on the basis of the direct simulation Monte Carlo method. The mass flow rate and flow field are calculated as a function of the time in the transitional and hydrodynamic regimes with respect to the gas rarefaction. Two values of the pressure ratio, i.e., 0.1 and 0.5, are considered. A characteristic time equal to that needed to cross the orifice radius with the most probable molecular speed is introduced. It is found that it takes about ten characteristic times in order the flow rate to reach its steady value. The flow field past the orifice reaches the steady state during the same time in the transitional regime and it takes a longer time in the hydrodynamic regime.

An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage

By just applying a temperature difference to a micro-system filled with rarefied gas, it is possible to engender a displacement or a compression of the gas in the temperature gradient direction. This is the Thermal Transpiration phenomenon. In the present work, thermal transpiration has been studied both through an experimental approach, which exploits an original measuring system, and through a numerical approach, which is modeled on the basis of the Shakhov model kinetic equation. In both studies, a circular cross section glass micro-tube is submitted to a temperature gradient. The obtained results for Helium, such as the thermal molecular pressure difference, the thermal molecular pressure ratio and the thermal molecular pressure exponent at the final zero-flow stage, are analyzed in the case of a tube submitted to a temperature difference of 51 K. Finally, the obtained thermal molecular pressure ratio results are also compared to the semi-empirical formulas of Liang (1951) and Takaishi and Sensui (1963). These semi-empirical formulas are still in use nowadays to introduce correction factors for pressure measurements done when the pressure gauge functions at different temperatures in respect to the temperature of the operating gas. For the here working pressure conditions and the used tube dimensions the gas rarefaction conditions go from near free molecular to slip regime.

Effects of microfabrication defects on the performance of gas bearings with High aspect ratio in microengine

The Molecular Gas-film Lubrication model is combined with the tapered gas film thickness equation so that both the gas rarefaction effects and the taper effects are introduced simultaneously to study the steady-state performance and the stability charts of micro bearings. The results indicate that gas rarefaction effects lessen the load capacity and stiffness coefficients, decrease the damping coefficients at lower bearing numbers but increase them at higher bearing numbers. Meanwhile, compared with the ideal bearing with the same minimum clearance, the taper effects weaken the load capacity, increase the required stable minimum eccentricity and narrow the stable static load region.

Analysis of fluid-structure interaction for predicting resonant frequencies and quality factors of a microcantilever on a squeeze-film

The dynamic behavior of a flexible microcantilever vibrating above a substrate such as the cantilever-based structure of a radio frequency microelectromechanical switch is strongly affected by the motion of gas between the microcantilever and the substrate. In this paper, parameter studies to investigate the effects of geometry, material properties of a microcantilever, and ambient pressure on the resonant frequencies and quality factors of the microcantilever are described. A Reynolds-equation-based continuum model is used to derive the gas force reflecting the gas rarefaction effect due to the size effect of MEMS packed at low ambient pressure. The frequency response function of an inertially-excited microcantilever is developed using the mode superposition method. One interaction parameter, including information on geometry, material properties of a microcantilever, and ambient pressure, is defined to investigate the fluidstructure interaction in a microcantilever vibrating on a squeeze-film. The quality factors of the first three bending modes increase with the decreasing interaction parameter. The changing trend of associated resonant frequencies depends on the order of the bending mode.

Numerical modelling of rarefied gas flow through a slit at arbitrary pressure ratio based on the kinetic equation

A rarefied gas flow through a thin slit at an arbitrary gas pressure ratio is calculated on the basis of the kinetic model equations (BGK and S-model) applying the discrete velocity method. The calculations are carried out for the whole range of the gas rarefaction from the free-molecular regime to the hydrodynamic one. Numerical data on the flow rate and distributions of density, bulk velocity and temperature are reported. Comparisons of the present results with those based on the direct simulation Monte Carlo method and on the linearized BGK kinetic equation are performed. The conditions of applicability of the linearized theory are discussed.

An ionization region model for high-power impulse magnetron sputtering discharges

A time-dependent plasma discharge model has been developed for the ionization region in a high-power impulse magnetron sputtering (HiPIMS) discharge. It provides a flexible modeling tool to explore, e.g., the temporal variations of the ionized fractions of the working gas and the sputtered vapor, the electron density and temperature, and the gas rarefaction and refill processes. A separation is made between aspects that can be followed with a certain precision, based on known data, such as excitation rates, sputtering and secondary emission yield, and aspects that need to be treated as uncertain and defined by assumptions. The input parameters in the model can be changed to fit different specific applications. Examples of such changes are the gas and target material, the electric pulse forms of current and voltage, and the device geometry. A basic version, ionization region model I, using a thermal electron population, singly charged ions, and ion losses by isotropic diffusion is described here. It is fitted to the experimental data from a HiPIMS discharge in argon operated with 100 µs long pulses and a 15 cm diameter aluminum target. Already this basic version gives a close fit to the experimentally observed current waveform, and values of electron density ne, the electron temperature Te, the degree of gas rarefaction, and the degree of ionization of the sputtered metal that are consistent with experimental data. We take some selected examples to illustrate how the model can be used to throw light on the internal workings of these discharges: the effect of varying power efficiency, the gas rarefaction and refill during a HiPIMS pulse, and the mechanisms determining the electron temperature.