In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the submicron scale. However, most published studies make a gray assumption and do not account for either dispersion or polarization. In this study, we propose a model based on the BTE, accounting for transverse acoustic and longitudinal acoustic phonons as well as optical phonons. 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, and accounting for phonon interaction rules, are used. In the present study, the BTE is numerically solved using a structured finite volume approach. For a problem involving a film with two boundaries at different temperatures, the numerical results match the analogous exact solutions from radiative transport literature for various acoustic thicknesses. For the same problem, the transient thermal response in the acoustically thick limit matches results from the solution to the parabolic Fourier diffusion equation. In the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model. Experimental in-plane thermal conductivity data for silicon thin films over a wide range of temperatures are also matched satisfactorily.

*Microscale Energy Transport*, Tien, C.-L., Majumdar, A., and Gerner, F. M., eds., Taylor and Francis, Washington, D.C., pp. 1–94.

*Solid State Physics*, Saunders, Philadelphia.

*Introduction to Solid State Physics*, Wiley, New York.

*Proceedings—ASME Summer Heat Transfer Conference, Las Vegas, NV*, Paper No. HT2003-47312.

*Solid State Physics*, Seitz, F. and Thurnbull, D., eds., Academic Press, New York, pp. 1–98.

*Thermal Conductivity*, Tye, R. P., ed., Academic Press, London, pp. 1–68.

*ASME International Mechanical Engineering Congress and Exposition, Washington, DC*, Paper No. IMECE2003-42447.

*Proceedings—ASME Heat Transfer/Fluids Engineering Summer Conference, Charlotte, NC*, Paper No. HT-FED2004-56252.

*Radiative Heat Transfer*, McGraw-Hill, New York.

*Thermophysical Properties of Matter*, IFI/Plenum, New York.

*Numerical Heat Transfer and Fluid Flow*, Taylor & Francis, London.