Sandip Mazumder

Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization

The Boltzmann Transport Equation (BTE) for phonons best describes the heat flow in solid nonmetallic thin films. The BTE, in its most general form, however, is difficult to solve analytically or even numerically using deterministic approaches. Past research has enabled its solution by neglecting important effects such as dispersion and interactions between the longitudinal and transverse polarizations of phonon propagation. In this article, a comprehensive Monte Carlo solution technique of the BTE is presented. The method accounts for dual polarizations of phonon propagation, and non-linear dispersion relationships. Scattering by various mechanisms is treated individually. Transition between the two polarization branches, and creation and destruction of phonons due to scattering is taken into account. The code has been verified and evaluated by close examination of its ability or failure to capture various regimes of phonon transport ranging from diffusive to the ballistic limit. Validation results show close agreement with experimental data for silicon thin films with and without doping. Simulation results show that above 100 K, transverse acoustic phonons are the primary carriers of energy in silicon.

Rigorous 3-D Mathematical Modeling of PEM Fuel Cells II. Model Predictions with Liquid Water Transport

In this part of the paper, we present a model to treat formation and transport of liquid water in proton exchange membrane ~PEM! fuel cells ~FCs! in three-dimensional ~3-D! geometry. The performance of modern-day PEM FCs at high current density are largely dictated by the effective management of liquid water. In the first part of this paper, a rigorous model was presented to model PEM FCs using a computational fluid dynamic technique. It was found that under the assumption of no liquid water formation, the model consistently overpredicted measured polarization behavior. In the model presented here, the phase change process is modeled as an equilibrium process, while the transport of liquid water is governed by pressure, surface tension, gravity and electro-osmotic drag. Results show that the inclusion of liquid water transport greatly enhances the predictive capability of the model and is necessary to match experimental data at high current density.

A probability density function approach to modeling turbulence-radiation interactions in nonluminous flames

Abstract The interactions between turbulence and radiation, although acknowledged and qualitatively understood over the last several decades, are extremely difficult to model. Traditional Eulerian turbulence models are incapable of addressing the closure problem for any realistic reactive flow situation, on account of the large number of unknown turbulent moments. A novel approach, based on the velocity-composition joint probability density function (PDF) method, has been used to attain closure. The ability of this method to accurately determine any one-point scalar correlation makes it a suitable candidate for modeling turbulence–radiation interactions (TRI) . Results presented for a bluff-body-stabilized methane–air diffusion flame demonstrate the importance of turbulence–radiation interactions in flame calculations.

Monte Carlo Study of Phonon Heat Conduction in Silicon Thin Films Including Contributions of Optical Phonons

The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures T200 K, longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50‐200 K) and to increase it at high temperature 200 K, especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures. DOI: 10.1115/1.4000447

A FAST MONTE CARLO SCHEME FOR THERMAL RADIATION IN SEMICONDUCTOR PROCESSING APPLICATIONS

Thermal radiation is the most effective way for rapid thermal processing (RTP) and rapid thermal chemical vapor deposition (RTCVD) of wafers. It is well known in the semiconductor equipment design community that the Monte Carlo method for radiation is the only method that can accurately model radiative transport in RTP and RTCVD reactors. However, it has often been argued that it is expensive and difficult to use as a commercial design tool. In this article, a fast Monte Carlo scheme is presented. The basic algorithm is the classical surface-to-surface ray-tracing algorithm. In addition, a modified form of the binary spatial partitioning (BSP) algorithm is implemented to speed up ray tracing by at least a factor of 3. The results demonstrate a high level of accuracy with fairly low computational cost.

Sub-grid scale modeling of heterogeneous chemical reactions and transport in full-scale catalytic converters

This article presents a novel approach to treat heterogeneous catalytic reactions occurring in porous or honeycomb monoliths. The approach allows accurate modeling of full-scale catalytic converters with low computational cost. In this approach, the entire catalytic monolith is treated as an anisotropic porous medium, and sub-grid scale models are employed to represent the heterogeneous chemical reactions occurring at the solid-fluid interfaces within the monolith. Full coupling between fluid flow, heat transfer, species transport, and heterogeneous chemical reactions is achieved through flux balance of species and energy at the solid-fluid interfaces. The model allows for unlimited number of finite-rate reaction steps and species, including surface-adsorbed species and site coverage effects. The model was validated for hydrogen-assisted combustion of methane-air mixtures over platinum catalyst clusters in a full-scale catalytic converter. Validation against experimental data exhibits excellent match for ignition temperature for various methane and/or hydrogen inlet concentrations. Transient calculations show that the time constant for ignition matches well with previously reported results. Because the model is based on a sub-grid scale approach, it is orders of magnitude more efficient for modeling full-scale catalytic converters than conventional approaches where each channel within the catalytic monolith has to be represented by a computational grid.

Application of the full spectrum correlated-k distribution approach to modeling non-gray radiation in combustion gases

The treatment of radiative transport through combustion gases is rendered extremely difficult by the strong spectral variation of the absorption coefficients of molecular gases. In the full spectrum correlated-k distribution (FSCK) approach, a transformation is invoked, whereby the radiative transfer equation (RTE) is transformed from wavenumber to non-dimensional Planck-weighted wavenumber space after reordering of the spectrum. The reordering results in a relatively smooth spectrum, allowing accurate spectral integration with very few quadrature points. The numerical procedures, required to use the FSCK model for full-scale combustion applications, have been outlined in this article. The FSCK model was first coupled with the Discrete Ordinates Method (DOM) for solution of the transformed RTE. The accuracy of the model was then examined for a variety of cases ranging from homogeneous one-dimensional media to inhomogeneous multi-dimensional media with simultaneous variations in both temperature and concentrations. Comparison with line-by-line calculations shows that the FSCK model is exact for homogeneous media, and that its accuracy in inhomogeneous media is limited by the accuracy of the scaling approximation. Several approaches for effective scaling of the absorption coefficient are examined. The model is finally used for radiation calculations in a full-scale combustor, with full coupling to fluid flow, heat transfer and multi-species chemistry. The computational savings resulting from use of the FSCK model is found to be more than four orders of magnitude when compared with line-by-line calculations.

Turbulence-Radiation Interactions in Nonreactive Flow of Combustion Gases

A nonreactive hot mixture of radiatively participating species, typically carbon dioxide and water vapor, may be found in the exhaust sections of almost all combustors. Since the scalar fluctuations in such nonreactive flows are substantially smaller than in flames, it is commonly believed that the effects of turbulence-radiation interactions (TRI) on altering wall heat fluxes in nonreactive flows are negligible. Such belief, however, has not been substantiated by evidence to date. The purpose of this note is to investigate the conditions under which turbulence-radiation interactions may be important in nonreactive flows. The final outcome was found to be largely dependent on how the scalar fluctuations correlate, rather than the magnitude of the fluctuations themselves. It was found that for most situations of practical interest, TRI effects are indeed negligible.

The importance of predicting rate-limited growth for accurate modeling of commercial MOCVD reactors

Over-heating of semitransparent fused silica (quartz) pieces within metalorganic chemical vapor deposition (MOCVD) reactors may result in parasitic deposition on reactor walls, leading to loss of precursors. Although growth on the substrate (epitaxial growth) is diffusion-limited, parasitic deposition on reactor walls occurs at colder temperatures and is therefore, rate-limited. The modeling of low-temperature deposition requires complex chemical mechanisms, which account not only for the kinetics of decomposition, but also the kinetics of adsorption and desorption at the surfaces. In this article, the role of parasitic deposition and rate-limited growth has been demonstrated for growth of gallium arsenide in a commercial horizontal MOCVD reactor (Crystal Specialties 425). Numerical computations were performed for a wide range of operating conditions. Comparison of numerical predictions with experimental data clearly indicates the need for the development and use of detailed surface chemistry mechanisms in modeling parasitic rate-limited deposition in order to accurately predict the growth rate on the target surfaces in commercial MOCVD reactors.

A New Numerical Procedure for Coupling Radiation in Participating Media With Other Modes of Heat Transfer

Traditionally, radiation in participating media is coupled to other modes of heat transfer using an iterative procedure in which the overall energy equation (EE) and the radiative transfer equation (RTE) are solved sequentially and repeatedly until both equations converge. Although this explicit coupling approach is convenient from the point of view of computer code development, it is not necessarily the best approach for stability and convergence. A new numerical procedure is presented in which the EE and RTE are implicitly coupled and solved simultaneously, rather than as segregated equations