Sub-continuum simulations of heat conduction in silicon-on-insulator transistors

The temperature rise in sub-micrometer silicon devices is predicted at pres ent by solving the hear diffusion equation based an the Fourier law. The ac curacy of this approach needs to be carefully examined for semiconductor de vices in which the channel length is comparable with or smaller than the ph onon mean free path. The phonon mean free path in silicon at room temperatu re is near 300 nm and exceeds the channel length of contemporary transistor s. This work numerically integrates the two-dimensional phonon Boltzmann tr ansport equation (BTE) within the silicon region of a silicon-on-insulator (SOI) transistor. The BTE is solved together with the classical heat diffus ion equation in the silicon dioxide layer beneath the transistor. The predi cted peak temperature rise is nearly 160 percent larger than a prediction u sing the heat diffusion equation for the entire domain. The disparity resul ts both from phonon-boundary scattering and from the small dimensions of th e region of strongest electron-phonon energy transfer. This work clearly sh ows the importance of sub-continuum heat conduction In modem transistors an d will facilitate the development of simpler calculation strategies, which are appropriate for commercial device simulators.