A Two-Temperature Model of Narrow-Body Silicon Transistors Under Steady State and Transient Operation

We present a simple theory of diffusive phonon heat transport in silicon thin films using the Two-Temperature Model (TTM). In silicon thin films, boundary scattering reduces the lifetime and hence, the mean free path of acoustic phonons. As acoustic phonons are responsible for heat transport in silicon, the latter effect leads to a reduction in the lattice thermal conductivity. However, optical phonons are unaffected by boundary scattering. As the boundary scattering rate exceeds the inverse lifetime of acoustic phonons and the energy relaxation rate between optical and acoustic phonons, it results in an energy transfer bottleneck. The reduced lattice thermal conductivity from boundary scattering and the energy transfer bottleneck are taken into account in the TTM. We apply the TTM to find the steady temperature distribution in a 2D model of a silicon-on-insulator (SOI) device. The numerical results are in good agreement with those obtained from the more sophisticated full dispersion model of the Boltzmann Transport Equation (BTE). We apply the TTM to calculate the steady state and transient temperature distributions in a simplified 1D model of a SOI device.