Heat transport in sub-micron conduction

In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the sub-micron scale. However, most published studies make a gray assumption (single average phonon mode with single group velocity and relaxation time) and do not account for either dispersion or polarization. Additionally, even under the gray assumption, mainly steady state problems have been considered in the literature.; A model, based on the BTE and accounting for transverse and longitudinal acoustic phonons, and optical phonons, is proposed. This model incorporates realistic phonon dispersion curves for silicon. The interactions among the different phonon branches and different phonon frequencies are considered, and the proposed model satisfies energy conservation. Frequency-dependent relaxation times, obtained from perturbation theory, are employed. The BTE is numerically solved by a structured finite volume approach. In the acoustically-thick limit, the bulk silicon thermal conductivity is recovered from the model. Also, the transient thermal response in the acoustically-thick limit matches results from the solution to the Fourier diffusion equation. Additionally, thermal conductivities of silicon sub-micron thin films are predicted, and a fair match is obtained between the results of the model and experimental data in the literature, thereby lending credibility to the proposed model.; The problem of heat generation in a sub-micron silicon-on-insulator (SOI) transistor is considered. The proposed model is used to make thermal predictions in the SOI structure. Results from this model are compared to those obtained from other simpler models found in literature, and considerable discrepancies are found.; Lastly, the problem of transient electrostatic discharge phenomena in sub-micron transistors is also considered. The proposed model is again used to predict thermal phenomena in a domain with transient energy dissipation and results are compared to those obtained from other models from literature. Large differences are found between the results. Overall, the present work aims at improving thermal modeling efforts in microelectronics and in the big picture, such models can ultimately be used for design purposes.