Phonon transport models for heat conduction in sub-micron geometries with application to microelectronics

Chunjian Ni, Purdue University

Abstract

In this dissertation, a new phonon Boltzmann transport equation (BTE) model, the anisotropic relaxation time phonon BTE model, is developed to address the simulation of sub-micron thermal transport. The full-scattering model directly computes three-phonon scattering interactions by enforcing energy and momentum conservation, and is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time phonon BTE model developed in this dissertation employs a single-mode relaxation time idea, but the relaxation time is a function of wave-vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior as well as relaxation times satisfying conservation rules. A critical issue in the model development is the accounting for the role of three-phonon N scattering processes. Direct inclusion of N processes into the anisotropic relaxation time model is not possible because such an inclusion would engender thermal resistance. Instead, following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted bulk thermal conductivities of silicon and silicon thin-film thermal conductivities with experimental measurements. Self-heating in a metal-oxide-semiconductor field-effect transistor (MOSFET) is simulated using the new phonon BTE model assuming a prescribed heat source, and its predictions are compared with the full-scattering phonon BTE model. The results obtained from the two models are close, and suggest that the relaxation-time BTE may be used for practical device simulations. Thermal transport in the MOSFET device due to electron-phonon scattering is simulated next, but now using phonon generation rates obtained from an electron Monte Carlo simulation of device by Aksamija. The Monte Carlo device simulation assumes that the electrons reside at the bottom of the conduction band. It uses the full phonon dispersion curves for 22 types of electron-phonon scattering events. Detailed profiles of phonon emission/absorption rates in the physical and momentum spaces are generated and are used in a MOSFET thermal transport simulation with the anisotropic relaxation time BTE model. At a source/drain voltage and a gate voltage of 1 V each, the total heat dissipation of the device from the electron Monte Carlo simulation is found to be 3197.9 W/m. The anisotropic relaxation time BTE simulation predicts a maximum temperature rise of 46.5 K; this is much higher than the Fourier prediction of the maximum temperature rise of 6.5 K. Heat fluxes leaving the boundaries associated with different phonon polarizations and frequencies are also examined to reveal the main modes responsible for transport. Parallel computation schemes are developed for both the full-scattering phonon BTE model and the anisotropic relaxation time phonon BTE model. Two strategies are explored: spatial domain decomposition and phonon band decomposition. The parallel computations are first validated by comparing parallel simulation results with those obtained from serial simulations. The computation and communication times for different cases are investigated. The parallel performance of the full-scattering phonon BTE model exceeds that of the anisotropic relaxation time phonon BTE model because of the high local computational load. For the full-scattering phonon BTE model, the spatial domain decomposition strategy achieves better performance than the phonon band decomposition strategy because of the long message length associated with the later partitioning strategy. For the anisotropic relaxation BTE model, the performance of both the strategies is similar for the modest problem size tested in this dissertation. (Abstract shortened by UMI.)

Degree

Ph.D.

Advisors

Murthy, Purdue University.

Subject Area

Mechanical engineering

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