In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semicondutors at sub-micron scales. Most studies make a gray assumption and do not account for phonon dispersion or polarization in any detail. In this study, the problem of heat generation in a sub-micron silicon-on-insulator (SOI) transistor is addressed. A model, based on the solution to the BTE incorporating full phonon dispersion effects, is presented and used to study the SOI self-heating problem. A structured finite volume approach is used to solve the BTE. The results from the full phonon dispersion model are compared to predictions using the Fourier diffusion equation and also to predictions from the solution to the BTE using a semi-gray model which appears in literature. Significant differences are found between the models and confirm the need for an accounting for phonon dispersion and polarization effects.

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