Nonequilibrium cross-plane energy transport in aluminum–silicon–aluminum wafer

Abstract

Transient phonon transport across cross-planes of aluminum–silicon–aluminum combined films is investigated and the Boltzmann transport equation is incorporated to formulate the energy transport in the combined films. Since electrons and phonons thermally separate in the thin aluminum film during heating, the Boltzmann equation is used separately in the electron and lattice subsystems to account for the energy transport in the aluminum film. Electron–phonon coupling is incorporated for the energy exchange between electron and lattice subsystems in the film. Thermal boundary resistance (TBR) is introduced at the interfaces of the silicon–aluminum films. In order to examine the ballistic contribution of phonons on the phonon intensity distribution in the silicon film, frequency-dependent solution of the Boltzmann equation is used in the silicon film and the film thickness is varied to investigate the size effect on the thermal conductivity in the film. It is found that equivalent equilibrium temperature of phonons remains high at silicon–aluminum interface because of the ballistic contribution of the phonons. Equivalent equilibrium temperature for the electron subsystem becomes higher than that corresponding to phonon temperature at the aluminum–silicon interface.