Intrinsic lattice thermal conductivity of Si/Ge and GaAs/AlAs superlattices

Abstract

We present a theory of the intrinsic lattice thermal conductivity in Si/Ge-based and GaAs/AlAs quantum well superlattices using an exact iterative solution of the inelastic phonon Boltzmann equation. An adiabatic bond charge model is employed to accurately represent the phonon dispersions and the empirical anharmonic force constants are introduced yielding the measured values for bulk thermal conductivities. We show that the kinematic constraints of the superlattice decrease the phonon-phonon scattering, resulting in higher intrinsic lattice thermal conductivities than those calculated from constant relaxation-time approximations and simple model phonon dispersions. The role of mini-umklapp processes, produced as a result of zone-folding in superlattices, is also addressed. Finally, we find larger calculated intrinsic lattice thermal conductivities of GaAs/AlAs superlattices than those predicted from a relaxation-time approach, implying that interface scattering plays a more important role than previously documented. These findings are consistent with experimental measurements for short-period GaAs/AlAs structures.