A. Venkattraman

Direct measurements and numerical simulations of gas charging in microelectromechanical system capacitive switches

Gas breakdown in microelectromechanical system capacitive switches is demonstrated using high resolution current measurements and by particle-in-cell/Monte Carlo collision (PIC/MCC) simulations. Measurements show an electric current through a 3 μm air gap increasing exponentially with voltage, starting at 60 V. PIC/MCC simulations with Fowler-Nordheim [Proc. R. Soc. London, Ser. A 119, 173 (1928)] field emission reveal self-sustained discharges with significant ion enhancement and a positive space charge. The effective ion-enhanced field emission coefficient increases with voltage up to about 0.3 with an electron avalanche occurring at 159 V. The measurements and simulations demonstrate a charging mechanism for microswitches consistent with earlier observations of gas pressure and composition effects on lifetime.

Scaling law for direct current field emission-driven microscale gas breakdown

The effects of field emission on direct current breakdown in microscale gaps filled with an ambient neutral gas are studied numerically and analytically. Fundamental numerical experiments using the particle-in-cell/Monte Carlo collisions method are used to systematically quantify microscale ionization and space-charge enhancement of field emission. The numerical experiments are then used to validate a scaling law for the modified Paschen curve that bridges field emission-driven breakdown with the macroscale Paschen law. Analytical expressions are derived for the increase in cathode electric field, total steady state current density, and the ion-enhancement coefficient including a new breakdown criterion. It also includes the effect of all key parameters such as pressure, operating gas, and field-enhancement factor providing a better predictive capability than existing microscale breakdown models. The field-enhancement factor is shown to be the most sensitive parameter with its increase leading to a signif...

Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Abstract Non-equilibrium rarefied flows are encountered frequently in supersonic flight at high altitudes, vacuum technology and in microscale devices. Prediction of the onset of non-equilibrium is important for accurate numerical simulation of such flows. We formulate and apply the discrete version of Boltzmann’s H -theorem for analysis of non-equilibrium onset and accuracy of numerical modeling of rarefied gas flows. The numerical modeling approach is based on the deterministic solution of kinetic model equations. The numerical solution approach comprises the discrete velocity method in the velocity space and the finite volume method in the physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter and a third-order WENO schemes. The use of entropy considerations in rarefied flow simulations is illustrated for the normal shock, the Riemann and the two-dimensional shock tube problems. The entropy generation rate based on kinetic theory is shown to be a powerful indicator of the onset of non-equilibrium, accuracy of numerical solution as well as the compatibility of boundary conditions for both steady and unsteady problems.

A study of field emission process in electrostatically actuated MEMS switches

Abstract A study of field emission process in MEMS-based capacitor/switch-like geometries is presented. High resolution current–voltage characteristics up to breakdown have been obtained across micro-gaps in fixed–fixed Metal–Air–Metal and Metal–Air–Insulator–Metal structures. In metallic devices the I–V dependence reveals Fowler–Nordheim theory effects. In the presence of insulator the process is found to be limited by the film conductivity following Poole–Frenkel dependence. The data analysis reveals the major importance of surface asperities on the onset of the field emission process while it is also presented that charge transfer may occur between metal and insulator surfaces even in the presence of micrometer scale gaps.

Direct simulation Monte Carlo modeling of e-beam metal deposition

Three-dimensional direct simulation Monte Carlo (DSMC) method is applied here to model the electron-beam physical vapor deposition of copper thin films. Various molecular models for copper-copper interactions have been considered and a suitable molecular model has been determined based on comparisons of dimensional mass fluxes obtained from simulations and previous experiments. The variable hard sphere model that is determined for atomic copper vapor can be used in DSMC simulations for design and analysis of vacuum deposition systems, allowing for accurate prediction of growth rates, uniformity, and microstructure.

DSMC Collision Model for the Lennard-Jones Potential: Efficient Algorithm and Verification

An efficient algorithm to implement elastic scattering using the Lennard-Jones (LJ) in-termolecular potential in the direct simulation Monte Carlo (DSMC) method is presented. The exact elastic scattering angle for the LJ intermolecular potential obtained by numerical integration is used to construct a piecewise polynomial representation in terms of two collision parameters-the reduced impact parameter and the reduced relative energy. The 5 th degree polynomials representation is obtained using the Chebyshev basis. The implementation valid for reduced relative energies ranging from 0.001 to 10.0 is verified by DSMC simulations of subsonic and supersonic Couette flow of Argon at temperatures of 273 K and 40 K and is shown to accurately reproduce the viscosity variation with temperature that corresponds to the LJ intermolecular potential. The LJ collision model is formulated in non-dimensional coordinates and is applicable to arbitrary gas species. For the Couette flow problem, the algorithm is shown to have a computational cost comparable to the variable hard sphere (VHS) model that is widely used in DSMC simulations.

Near-Contact Gas Damping and Dynamic Response of High-g MEMS Accelerometer Beams

This paper introduces and experimentally validates a new model for near-contact gas damping of microbeams. The model is formulated based on numerical simulations of rarefied gas dynamics using the Boltzmann Ellipsoidal Statistical Bhatnagar-Gross-Krook (ES-BGK) equation. The result is compared with existing models by simulating the motion of beams under high-g acceleration. To experimentally validate the damping models, single crystal silicon MEMS g-switches with cantilever microbeams of various lengths were utilized. The experimental measurements of beam dynamics under peak accelerations of approximately 50,000 g and acceleration ramp rates from 600 to 3,000 g/μs are compared with simulations. Additionally, the damping coefficients are extracted from existing vibrational mode data, and the resulting values are compared to the various models. The new near-contact model was found to predict contact and release times within a root-mean-square deviation from experiment below 9 and 7 for contact and release events, respectively. The damping values for the vibrational modes away from contact were predicted within 33% error, showing a more consistent predictive capability than provided by earlier models.

Numerical evaluation of RF gas ionization effects in micro-and nano-scale devices

Micro- and nano-scale gaps are likely to occur in miniaturized and high frequency devices. Large electric fields (~10s V/μm) may result in such gaps even for relatively small voltages commonly found in existing electronics. These strong fields can potentially induce gas discharge, which may lead to performance degradation or even device failure. Gas discharge is due to generation and movement of charged species as a result of impact ionization, secondary electron emission, and field emission phenomena. In this paper, the importance of field emission in gas discharge in small gaps for both DC and RF regimes is investigated by using a numerical-based comparison technique.

Simulations of Impulsive Dynamics in RF MEMS Capacitive Switches

Radio Frequency Micro-Electro-Mechanical Systems (RF MEMS) have emerged as a promising enabling technology for low-cost and low-power switches, actuators, and sensors. However, the reliability of these devices, especially those involving repeated contacting events, remains a major stumbling block for their widespread adaptation. In this work we present dynamic simulations of RF MEMS switch response due to electrostatic actuation in the presence of gas damping and residual stress. The dynamics emerging from the interaction between the beam structure and gas environment shows generation of stress waves induced by contact. It has been observed that these impulsive effects could lead to transient stresses that are significantly greater than the steady state bending stress. S-N curves for LIGA Nickel are used to make predictions for the lifetime at various voltages and operating gas pressures that show pressure dependence consistent with earlier experimental observations.Copyright

Effects of Uncertainty in Gas‐Surface Interaction on DSMC Simulations of Hypersonic Flows

This study uses the non‐intrusive generalized polynomial chaos method to investigate the effects of uncertainties in the gas‐surface interaction model on the hypersonic boundary layer flow over a flat plate. In particular, the polynomial chaos method is applied to assess uncertainties in the surface shear, normal stress, heat flux, flowfield temperature and density resulting from uncertain surface temperature and accommodation coefficient. The polynomial chaos approach allows us to estimate probability density functions from fewer flowfield samples than the traditional random Monte Carlo sampling. The flowfield solutions are computed by the DSMC code SMILE. The analysis shows that surface fluxes and flowfields in the hypersonic boundary layer are more sensitive to the accommodation coefficient than surface temperature uncertainty.