Gas Rarefaction Effects Research Articles

Study on the Performance of Gas Journal Bearings for Power MEMS

Gas journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in Power MEMS deriving from the extremely shallow structures. With the reference Knudsen number being included, the modified Reynolds equation for gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The boundary condition for modified Reynolds equation is given. The numerical method is employed to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles of gas journal bearings for Power MEMS under different reference Knudsen numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with the reference Knudsen number increasing, and the attitude angle changes conversely. Moreover, when the eccentricity ratio is smaller, the effect of gas rarefaction on the attitude angle is less.

Characteristics of micro-gas journal bearings based on kinetic theory

According to Poiseuille and Couette flow rate correctors, Q ˜ p ( D , α 1 , α 2 ) and Q ˜ C ( D , α 1 , α 2 ) , the modified molecular gas lubrication (MMGL) equation is applied for the analysis of micro-gas journal bearings. The effects of gas rarefaction are considered for arbitrary inverse Knudsen numbers ( D) and non-symmetric accommodation coefficients (AC) conditions ( α 1≠ α 2). The combined effects of Q ˜ p ( D , α 1 , α 2 ) and Q ˜ C ( D , α 1 , α 2 ) on the performance of micro-gas journal bearings are firstly discussed. The results show that the surface property (AC) of moving surface affects the bearing performance more significantly than that of stationary surface does. The load carrying capacity increases as the AC of moving surface increases or the inverse Knudsen number increases.

Predicting microscale gas flows and rarefaction effects through extended Navier–Stokes–Fourier equations from phoretic transport considerations

We test an extended continuum-based approach for analyzing micro-scale gas flows over a wide range of Knudsen number and Mach number. In this approach, additional terms are invoked in the constitutive relations of Navier–Stokes–Fourier equations, which originate from the considerations of phoretic motion as triggered by strong local gradients of density and/or temperature. Such augmented considerations are shown to implicitly take care of the complexities in the flow physics in a thermo-physically consistent sense, so that no special boundary treatment becomes necessary to address phenomenon such as Knudsen paradox. The transition regime gas flows, which are otherwise to be addressed through computationally intensive molecular simulations, become well tractable within the extended quasi-continuum framework without necessitating the use of any fitting parameters. Rigorous comparisons with direct simulation Monte Carlo (DSMC) computations and experimental results support this conjecture for cases of isothermal pressure driven gas flows and high Mach number shock wave flows through rectangular microchannels.

Effects of rarefaction on the characteristics of micro gas journal bearings

Given the definition of the reference Knudsen number for micro gas journal bearings, the range in the number is related to the viscosity of air at different temperatures. A modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first-order slip boundary condition is proposed that takes into account the gas rarefaction effect. The finite difference method (FDM) is adopted to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles for micro gas journal bearings at different reference Knudsen numbers, bearing numbers and journal eccentricity ratios. Numerical analysis shows that pressure profiles and non-dimensional load capacities decrease markedly as gas rarefaction increases. Attitude angles change conversely, and when the eccentricity ratio is less than 0.6, the attitude angles rise slightly and the influence of the reference Knudsen number is not marked. In addition, the effect of gas rarefaction on the non-dimensional load capacity and attitude angle decreases with smaller bearing numbers.

Simulation of gas flow through tubes of finite length over the whole range of rarefaction for various pressure drop ratios

The rarefied gas flow through circular tubes of finite length has been investigated computationally by the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as functions of the gas rarefaction, the length-to-radius ratio, and the pressure ratio along the tube. The gas rarefaction, which is inversely proportional to the Knudsen number, is varied from 0 to 2000, i.e., the free-molecular, transitional, and hydrodynamic regimes are embraced. A wide range of the length-to-radius ratio, namely, from 0 corresponding to the orifice flow up to 10 representing a sufficiently long tube, has been considered. Several values of the pressure ratio between 0 and 0.7 have been regarded. This pressure range covers both gas flow into vacuum and into a background gas. It has been found that the rarefaction parameter has the most significant effect on the flowfield characteristics and patterns, followed by the pressure ratio drop, while the length-to-radius ratio has a rather modest impact. Several interesting findings have been reported including the behavior of the flow rate and other macroscopic quantities in terms of these three parameters. In addition, the effect of gas rarefaction on the choked flow and on the Mach disks at large pressure drops is discussed. Comparison of some of the present numerical results with available experimental data has shown a good agreement.

Linear Stability Analysis of the Herringbone Groove Journal Bearings in Microsystems: Consideration of Gas Rarefaction Effects

The dynamic performance of the herringbone groove journal bearings (HGJBs) with the effects of gas rarefaction taken into account is considered for applications in microsystems. Two important parameters (the Knudsen number Kn and the tangential momentum accommodation coefficients, TMACs or the accommodation coefficients, ACs) that affect gas rarefaction significantly are considered. Small variations in film thickness and pressure from the equilibrium state are substituted into the transient modified molecular gas lubrication (MMGL) equation, which considers effects of gas rarefactions with the Poiseuille and Couette flow rate correctors. The gas film in the rotor-bearing system is modeled as stiffness and damping elements with coefficients dependent on the exciting frequency. The dynamic coefficients are then obtained by solving the linearized MMGL equations. The equations of motion of the rotor as well as the dynamic coefficients are performed for the present linear stability analysis. Due to the exciting frequency-dependent nature of the dynamic coefficients, an iterative method with the golden section technique is introduced in the linear stability analysis of rotor-bearing systems. The critical mass parameters and the related threshold speed are computed and discussed. The results of this study prove that HGJBs in microsystems can operate at concentric conditions at very high speeds.

Property Analysis of the Rough Slider Bearings in Micromotors for MEMS Applications

Based on the kinetic theory of gases, a new slip model is applied for the gas-lubricated Rayleigh slider bearings beneath three bushings of a micromotor in microelectromechanical systems (MEMS). A modified Reynolds equation is established by taking into account of the coupling effects of gas rarefaction and roughness and then analytical solutions for pressure distribution, load-carrying capacity and its streamwise location, and velocity profile are obtained for various slider-bearing configurations. The new slip model is validated by comparisons with the results presented in other researcherspsila works. It is indicated that the present new slip model is of better accuracy in predicting the bearing properties than the first-order, second-order slip models, and modified molecular gas lubrication model and is a good approximation to variable hard sphere and variable soft sphere models. The solutions provided by the present new slip model match the solution obtained using the linearized Boltzmann equation very well. The results also show that the coupled effects of gas rarefaction and roughness are of great significance in the design of the bushings for slider bearings in micromotors.

Slip flow characteristics of compressible gaseous in microchannels

In this paper, a numerical model for three-dimensional compressible gaseous slip flow in microchannel was established. Gas viscosity is modified based on Knudsen number using Veijola’s model due to the increased rarefaction effects in microscale. By comparing with experimental data, the model used in the present paper for calculating is credible. The result shows that the gas viscosity needs to be modified in the calculation because it can improve the accuracy of the result. The influences of gas compressibility, rarefaction effect and size effect on flow characteristics are comprehensively described. For compressible flow, a new non-dimensional parameter relative slip length L s /D h is proposed to correlate fRe. The suggested correlation for fRe with L s /D h is validated by comparing with experimental data. This correlation can be used for both slip and non-slip flow, and for both compressible and incompressible flow.

Effect of gas rarefaction on the performance of submicron fins

High thermal conductivity and high surface to volume ratios of nanostructures such as carbon nanotubes and metallic nanowires make them great candidates as micro/nano-fins and thus a potential solution to the ever-increasing thermal management challenges in electronics and photonics. With sizes ranging in the order of a few hundred nanometers or less, the fluid flow through these structures fall in the transition, slip, and even molecular transport regimes. The effects of the velocity and temperature slips (gas rarefaction) could not be neglected. In this study, a simple analytical model has been developed to predict the effect of gas rarefaction on the heat transfer performance of submicron fins. It is shown that the effects of gas rarefaction should be taken into account when designing micro/nano-fins since such effects can significantly reduce the heat transfer enhancement postulated for micro/nano-fins.

Dynamic characteristics of grooved air bearings in microsystems

The performance of grooved air bearings in microsystems is analysed and discussed. The modified molecular gas lubrication (MMGL) equation is utilized as the governing equation for the gas film to include the effect of gas rarefaction. The gas rarefaction is significantly affected by two important parameters (Knudsen numbers ( Kn) and accommodation coefficients (ACs)). The Poiseuille and Couette flowrate correctors ( QP and QC) are introduced in the MMGL equation to extend the lubrication theory (compressible Reynolds equation) for arbitrary Kn and tangential momentum accommodation coefficients or ACs. At a specific operating condition, the transient MMGL equation is linearized by small variations in film thickness and pressure. The linearized MMGL equation is then solved by finite-element method to obtain the dynamic pressure distributions. Therefore, the dynamic coefficients (stiffness and damping coefficients) are obtained by integrating the dynamic pressure over the bearing surfaces.

Modelling of the reactive sputtering process with non-uniform discharge current density and different temperature conditions

The majority of current models of the reactive magnetron sputtering assume a uniform shape of the discharge current density and the same temperature near the target and the substrate. However, in the real experimental set-up, the presence of the magnetic field causes high density plasma to form in front of the cathode in the shape of a toroid. Consequently, the discharge current density is laterally non-uniform. In addition to this, the heating of the background gas by sputtered particles, which is usually referred to as the gas rarefaction, plays an important role. This paper presents an extended model of the reactive magnetron sputtering that assumes the non-uniform discharge current density and which accommodates the gas rarefaction effect. It is devoted mainly to the study of the behaviour of the reactive sputtering rather that to the prediction of the coating properties. Outputs of this model are compared with those that assume uniform discharge current density and uniform temperature profile in the deposition chamber. Particular attention is paid to the modelling of the radial variation of the target composition near transitions from the metallic to the compound mode and vice versa. A study of the target utilization in the metallic and compound mode is performed for two different discharge current density profiles corresponding to typical two pole and multipole magnetics available on the market now. Different shapes of the discharge current density were tested. Finally, hysteresis curves are plotted for various temperature conditions in the reactor.

Electrical Characterization of Microelectromechanical Silicon Carbide Resonators.

This manuscript describes the findings of a study to investigate the performance of SiC MEMS resonators with respect to resonant frequency and quality factor under a variety of testing conditions, including various ambient pressures, AC drive voltages, bias potentials and temperatures. The sample set included both single-crystal and polycrystalline 3C-SiC lateral resonators. The experimental results show that operation at reduced pressures increases the resonant frequency as damping due to the gas-rarefaction effect becomes significant. Both DC bias and AC drive voltages result in nonlinearities, but the AC drive voltage is more sensitive to noise. The AC voltage has a voltage coefficient of 1∼4ppm/V at a DC bias of 40V. The coefficient of DC bias is about -11ppm/V to - 21ppm/V for poly-SiC, which is more than a factor of two better than a similarly designed polysilicon resonator (-54 ppm/V). The effective stiffness of the resonator decreases (softens) as the bias potential is increased, but increases (hardens) as drive voltage increase when scan is from low to high frequency. The resonant frequency decreases slightly with increasing temperature, exhibiting a temperature coefficient of -22 ppm/°C, between 22°C and 60°C. The thermal expansion mismatch between the SiC device and the Si substrate could be a reason that thermal coefficient for these SiC resonators is about twofold higher than similar polysilicon resonators. However, the Qs appear to exhibit no temperature dependence in this range.

Analysis of viscous heating in a micro-rocket flow and performance

Micro-rockets for propulsion of small spacecrafts exhibit significant differences with regard to their macroscale counterparts, mainly caused by the role of the viscous dissipation and heat transfer processes in the micron-sized scale. The goal of this work is to simulate the transient operation of a micro-rocket to investigate the effects of viscous heating on the flow and performance for four configurations of the expanding gas and wafer material. The modelling follows a multiphysics approach that solves the fluid and solid regions fully coupled. A continuum-based description that incorporates the effects of gas rarefaction through the micro-nozzle, viscous dissipation and heat transfer at the solid-gas interface is presented. Non-equilibrium is addressed with the implementation of a 2nd-order slip-model for the velocity and temperature at the walls. The results stress that solid-fluid coupling exerts a strong influence on the flowfield and performance as well as the effect of the wafer during the first instants of the transient in micro-rockets made of low and high thermal conductivity materials.

Analytic determination of the effective thermal conductivity of PEM fuel cell gas diffusion layers

Accurate information on the temperature field and associated heat transfer rates are particularly important in devising appropriate heat and water management strategies in proton exchange membrane (PEM) fuel cells. An important parameter in fuel cell performance analysis is the effective thermal conductivity of the gas diffusion layer (GDL). Estimation of the effective thermal conductivity is complicated because of the random nature of the GDL micro structure. In the present study, a compact analytical model for evaluating the effective thermal conductivity of fibrous GDLs is developed. The model accounts for conduction in both the solid fibrous matrix and in the gas phase; the spreading resistance associated with the contact area between overlapping fibers; gas rarefaction effects in microgaps; and salient geometric and mechanical features including fiber orientation and compressive forces due to cell/stack clamping. The model predictions are in good agreement with existing experimental data over a wide range of porosities. Parametric studies are performed using the proposed model to investigate the effect of bipolar plate pressure, aspect ratio, fiber diameter, fiber angle, and operating temperature.

Squeeze film effects on dynamic performance of MEMS μ-mirrors-consideration of gas rarefaction and surface roughness

The squeeze film behavior of MEMS torsion mirrors is modeled, analyzed and discussed. Effects of gas rarefaction (first-order slip-flow model with non-symmetric accommodation coefficients, ACs) and surface roughness are considered simultaneously by using the average Reynolds type equation (ARTE). Based on the operating conditions with small variations in film thickness and pressure, the ARTE is linearized. A coordinate transformation, by stretching or contracting the axes by referring to the roughness flow factors, is proposed to transform the linearized ARTE into a diffusion type modal equation. The dynamic coefficients (stiffness and damping coefficients) are then derived and expressed in analytical form. The results show that the tilting frequency (or Γ0 squeeze number), roughness parameters (γ Peklenik numbers, σ standard deviation of composite roughness) and gas rarefaction parameters (D inverse Knudsen number, $$\alpha_{1}, \alpha_{2}:$$ ACs) are all important parameters on analyzing the dynamic performance of MEMS torsion mirrors.

Simulation and Characterization of IPVD System with External ICP Antenna

The experimental ionized physical vapor deposition (IPVD) system with an external antenna is described, and experimental characterization of the plasma was performed: plasma density was up to 5 × 1012 cm−3, the argon ionization ratio was ∼0.2–0.4%, and copper ionization ratio was ∼28% in bulk plasma, corresponding to ionized Cu+ flux ratio in range the 73–95%. To aid further development and IPVD technology extendibility to the future nanoscale fabrication, the 2D plasma fluid model for IPVD system was developed. The model comprised the Cu + Ar collisional mechanism including charge exchange and Penning ionization, considering gas rarefaction effect, variable ion mobility approach, and analytical approach in description of the thermalization of sputtered Cu. The simulation results were validated through experimental measurements of the plasma characteristics by electrical probe and provided reasonable results in 2 to 15 Pa pressure range. The implementation of the model for optimized design of scaled-up IPVD system was demonstrated.

Wafer Redeposition Impact on Etch Rate Uniformity in IPVD System

The liner and seed deposition and feature coverage in an ionized physical vapor deposition (IPVD) technique depends on the background gas pressure and an RF bias power applied to the substrate electrode. Under such conditions, a redeposition (RD) occurs at the increased pressures, and it has a noticeable impact on the actual feature coverage and performance nonuniformity (NU) across the wafer. An analytical 2-D plasma fluid model, combined with analytical thermalization model, and experimental validation were used to investigate the impact of the wafer RD on the intrinsic and apparent etch rates (ERs) and their NU in the IPVD system. The model comprised the Cu+Ar collisional mechanism, including charge exchange and Penning ionization, considering gas rarefaction effect and variable ion mobility approach. The analytical approach was implemented to describe the mechanism of the thermalization of sputtered Cu. The experiment encompassed pressure range from 0.6 to 8.7 Pa and the table power from 100 to 800 W, showing the dramatic effect of the RD on the ER uniformity. Depending on the pressure, the apparent ER NU (one with contribution of the RD) can vary from ~6% (min-max) to over 20% (min-max). An intrinsic ER NU (contribution of the RD is extracted) is from 5% (min-max) to over 16% (min-max), shifted with respect to the pressure. The most significant impact of the RD effect has been observed at the edge of a 300-mm wafer. The evaluation on Ta (TaN) liners exhibits similar trends in RD, but a shift in the performance curves shows that the key factor in RD uniformity is the mean free path of the etched material

Multiscale Monte Carlo Simulation of Circular DC Magnetron Sputtering: Influence of Magnetron Design on Target Erosion and Film Deposition

We present an experimental and computational study of the effect of magnetron design on the target erosion profile, wafer-level deposition uniformity, and feature-scale deposition topography in a circular DC magnetron sputtering system. We have conducted a multiscale Monte Carlo simulation consisting of a particle-in-cell Monte Carlo collision plasma simulation for target sputter erosion, a collisional transport simulation for film deposition, and a feature-scale deposition topography simulation. The entire simulation results for each step are verified in comparison with the experimental results for various process conditions. A new semiempirical calibration method, for converting an estimated ion current density distribution into a target erosion profile, is proposed with regard to the gas rarefaction effect due to sputtering wind. In conclusion, the whole performance indices of a circular DC magnetron sputtering system are substantially influenced by magnetron design, and the effectiveness of our multiscale Monte Carlo simulation methodology is validated.

Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects

Rarefied gas flows in micro-electro-mechanical systems (MEMS) devices, calculated from the linearized Bhatnagar-Gross-Krook model equation [P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954)], are studied in a wide range of Knudsen numbers. Both plane Poiseuille and Couette flows are investigated numerically by extending a finite difference technique first introduced by Cercignani and Daneri [J. Appl. Phys. 34, 3509 (1963)]. Moreover, a variational approach, applied to the integrodifferential form of the linearized Boltzmann equation [C. Cercignani, J. Stat. Phys. 1, 297 (1969)], is used to solve in a unified manner the plane Poiseuille-Couette problem by means of the computation of only one functional. General boundary conditions of Maxwell’s type have been considered, assuming both symmetric and nonsymmetric molecular interaction between gas-solid interfaces, in order to take into account possible differences in the accommodation coefficients on the walls of MEMS devices. Based on the analysis presented in this paper, an accurate database valid in the entire Knudsen regime can be created for the Poiseuille-Couette problem, to be used in micromechanical applications.

Stability of Hypersonic Boundary Layer on Porous Wall with Regular Microstructure

Theoretical and experimental studies of hypersonic boundary-layer stabilization using a passive porous coating of regular microstructure are discussed. Propagation of disturbances inside pores is simulated with linear acoustic theory including the gas rarefaction effect. This model provides boundary conditions for stability analysis of boundary-layer disturbances on the porous wall. Experiments were conducted in the Mach 6 wind tunnel on a 7-deg half-angle sharp cone whose longitudinal half-surface is solid and whose other half-surface is covered by a perforated sheet comprising equally spaced cylindrical blind microholes. Hot-wire measurements of natural disturbances and artificially excited wave packets are conducted on both solid and porous surfaces. Natural disturbance spectra indicate that the second mode is a dominant instability. The porous coating stabilizes the second mode and weakly affects the first mode. Measurements of artificially excited wave packets show that the porous coating leads to substantial decrease of the wave-packet growth. The experimental data on phase speeds and amplitudes of the second-mode disturbances are compared with theoretical predictions. Satisfactory agreement is obtained for both solid and porous surfaces. This study confirms the concept of hypersonic boundary-layer stabilization by passive porous coatings, which can be used for laminar flow control.