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 significant drop in the threshold breakdown electric field and also to a gradual merging with the Paschen law. The proposed scaling law is also shown to agree well with two independent sets of experimental data for microscale breakdown in air. The ability to accurately describe not just the breakdown voltage but the entire pre-breakdown process for given operating conditions makes the proposed model a suitable candidate for the design and analysis of electrostatic microscale devices

Simulations and Measurements of Gas-Droplet Flows in Supersonic Jets Expanding into Vacuum

Simulations and measurements of gas-droplet multiphase flows in application to supersonic expansions into vacuum have been considered and compared with each other. The experiments involved exposing a control surface to a supersonic plume from two different nozzles and measuring the size distribution of droplets at various locations. The simulations are based on the direct simulation Monte Carlo modeling of vapor-phase flow with a one-way coupling of droplet momentum and energy. The droplet trajectories are computed for the experimental conditions for droplets originating at the throat and lip of two different nozzles. The maximum droplet radius reaching the control surface and the variation of droplet size with angle predicted by the trajectory computations agree well with the measurements using Optical Microscopy

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 copperthin 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

Molecular Models for DSMC Simulations of Metal Vapor Deposition

The direct simulation Monte Carlo (DSMC) method is applied here to model the electron‐beam (e‐beam) physical vapor deposition of copper thin films. A suitable molecular model for copper‐copper interactions have been determined based on comparisons with experiments for a 2D slit source. The model for atomic copper vapor is then used in axi‐symmetric DSMC simulations for analysis of a typical e‐beam metal deposition system with a cup crucible. The dimensional and non‐dimensional mass fluxes obtained are compared for two different deposition configurations with non‐uniformity as high as 40% predicted from the simulations

Visualizing Non-Equilibrium Flow Simulations using 3-D Velocity Distribution Functions

Scientific visualization techniques have been used to probe and understand better the physics of non-equilibrium flows. A visualization methodology for nonequilibrium flow simulations using 3-D velocity distribution functions (VDFs) is illustrated in application to various non-equilibrium flow problems. A one-dimensional normal shock wave problem is considered for two different upstream Mach numbers corresponding to weak and strong non-equilibrium flow conditions. The iso-surfaces of 3-D VDFs inside the shock wave obtainedusing various solution techniques including the ES-BGK method, DSMC technique, Mott-Smith solution, and the Navier-Stokes (NS) distribution functions using Chapman-Enskog theory are compared and contrasted. The visualization technique is extended to two-dimensional hypersonic flow at M-19 past a flat plate with sharp leading edge by comparing the isosurfaces of 3-D NS VDFs obtained at three different locations in the flowfield. The visualization of 3-D VDFs is shown to provide valuable information about the degree and direction of non-equilibrium for both 1-D and 2-D flows

Lyo Calculator – the Calculator of Primary Freeze-Drying

Freeze-drying (lyophilization) is an important process of a pharmaceutical solution state transformation for storage. Due to complexities of the process and costs related to experiments, numerical simulations of freeze-drying become more useful and cost-efficient for research and development of the process and the hardware. Many numerical models have been created to model separate steps of the drying process. However, these models are not available for any user. This work presents an open-source model of primary drying in a vial. Pseudo steady- state heat and mass transfer model was used to compute vapor pressure, drying time, product temperature, and percent of fluid dried as functions of time. To verify the numerical model, results were compared to experimental data of a mannitol (5%) solution and a numerical model created by M.J. Pikal. Results show accuracy within 20% at low chamber pressures and shelf temperatures. Simulations and analysis showed that the tool can be successfully used as a basic approximation of drying results for a single vial and constant chamber pressure and shelf temperature

Implications of Rarefied Gas Damping for RF MEMS Reliability

Capacitive and ohmic RF MEMS switches are based on micron‐sized structures moving under electrostatic force in a gaseous environment. Recent experimental measurements [4, 5] point to a critical role of gas‐phase effects on the lifetime of RF MEMS switches. In this paper, we analyze rarefied flow effects on the gas‐damping behavior of typical capacitive switches. Several damping models based on Reynolds equation [7, 8] and on Boltzmann kinetic equation [9, 6] are applied to quantify the effects of uncertainties in fabrication and operating conditions on the impact velocity of switch contact surfaces for various switch configurations. Implications of rarefied flow effects in the gas damping for design and analysis of RF MEMS devices are discussed. It has been demonstrated that although all damping models considered predict a similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability‐related parameters such as the pull‐in voltage, closing time and impact velocity are also discussed

Model Uncertainties in a Sharp Leading-Edge Hypersonic Boundary Layer

The effects of uncertainties in the gas-surface interaction and intermolecular interaction models on the hypersonic boundary layer development are investigated using the nonintrusive generalized polynomial chaos method. In particular, uncertainties in the surface shear stress, normal stress, heat flux, flowfield temperature and density resulting from uncertain viscosity exponent, surface temperature and accommodation coefficient are considered. The polynomial chaos expansion approach is used to reconstruct the probability density function, calculate mean, standard deviation and skewness of the dependent variables from the DSMC calculations. The uncertainty analysis shows that surface fluxes and flowfields in the hypersonic boundary layer are more sensitive to the accommodation coefficient than surface temperature or viscosity exponent uncertainty

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

A Lennard-Jones (LJ) binary interaction model for dilute gases is obtained by representing the exact scattering angle as a polynomial expansion in non-dimensional collision variables. Rigorous theoretical verification of the model is performed by comparison with exact values of diffusion and viscosity cross sections and related collision integrals. The collision quantities given by the polynomial approximation model agree within 3.5% with those of the exact LJ scattering. The proposed model is compared in detail with the generalized soft sphere (GSS) model which is the closest in terms of fidelity among existing direct simulation Monte Carlo collision models. The GSS model\u27s performance for the collision integral used in the first approximate of viscosity coefficient is comparable to the proposed model for most reduced temperatures. However, other collision integrals deviate significantly, even at moderate reduced temperatures. The high fidelity of the proposed model at low reduced temperatures enables non-equilibrium simulations of gases with deep LJ potential well such as metallic vapors. The model is based on the scattering angle as opposed to viscosity or diffusion coefficients and provides a direct link to molecular dynamics simulations