Multiscale thermal device modeling using diffusion in the Boltzmann Transport Equation

Thermal modeling of some nano-scale devices requires attention to multiple length scales and physical phenomena, ranging from continuum level heat diffusion to atomic-scale interactions and phonon confinement. At the nanometer-scale, thermal phenomena such as ballistic phonon transport may be important. The present paper uses a multiscale thermal modeling approach including diffusion in the Boltzmann Transport Equation (BTE) to study heat transport in several applications like Silicon on Insulator transistors, Si thin films with heat pulse, a Si thin film sandwiched between two bulk layers of Silicon dioxide as in solar cells. Analytical solutions of both a multilayered Fourier model and a simple gray BTE with and without a diffusion term in the steady state are computed. Thermal modeling and analysis of some of these applications is performed using the COMSOL Multiphysics finite element software package. The BTE model with and without diffusion for multilayers is discussed for interface conditions involving reflectance and transmittance of phonons. The results obtained from the models are compared to existing published results for Si/Si, Si/Diamond layers and are found to be in good agreement.