Two-Dimensional Nanoscale Heat Conduction Using Ballistic-Diffusive Equations

Abstract It is well recognized that heat conduction in micro- and nanoscale and in ultrafast processes may deviate from the predictions of the Fourier law, due to boundary and interface scattering and the finite relaxation time of heat carriers. The Boltzmann equation is often used with the relaxation time approximation to study classical size effect. However, the solution of Boltzmann equation has been limited to few simple geometrical configurations such as thin films and superlattices. In this paper, we apply the transient ballistic-diffusive equation (BDE) to study the two-dimensional nonlocal phonon transport phenomena. The numerical calculation strategies developed in this paper can be promising for incorporating into commercial device simulator.