Lattice Phonon and Electron Temperatures in Silicon-Aluminum Thin Films Pair: Comparison of Boltzmann Equation and Modified Two-Equation Model

Phonon and carrier transport in silicon-aluminum film pairs is examined. The energy transport equation for electrons and lattice subsystems for aluminum film is derived from the Boltzmann equation. Equivalent equilibrium temperature for lattice phonons and electrons are computed across the silicon and aluminum film. Reflection and transmittance of phonons at the silicon interface are considered to account for the thermal boundary resistance. The influence of film thickness on equivalent equilibrium temperature is also examined. Electron and lattice phonon temperature predictions are compared with their counterparts obtained from the modified two-equation model for the aluminum film. It is found that the solution of Boltzmann equation predicts slightly higher temperature at the silicon interface than that of the modified two-equation model. The nonlinear behavior of lattice phonon temperature at the aluminum interface extends toward the aluminum film with increasing film thickness.