Thermal transport through Ge-rich Ge/Si superlattices grown on Ge(001)

The cross-plane thermal conductivities of Ge-rich Si/Ge superlattices have been measured using both time-domain thermoreflectance and the differential 3 omega method. The superlattices were grown by molecular beam epitaxy on Ge(0 0 1) substrates. Crystal quality and structural information were investigated by x-ray diffractometry and transmission electron microscopy. The influence of segregation during growth on the composition profiles was modeled using the experimental growth temperatures and deposition rates. Those profiles were then employed to obtain parameter-free theoretical estimates of the thermal conductivity by combining firstprinciples calculations, Boltzmann transport theory and phonon Green's functions. Good agreement between theory and experiment is observed. The thermal conductivity shows a strong dependence on the composition and the thickness of the samples. Moreover, the importance of the composition profile is reflected in the fact that the thermal conductivity of the superlattices is considerably lower than predicted values for alloys with the same average composition and thickness. Measurement on different samples with the same Si layer thickness and number of periods, but different Ge layer thickness, show that the thermal resistance is only weakly dependent on the Ge layers. We analyze this phenomenon based on the first-principles mode, and build an approximate parametrization showing that, in this regime, the resistivity of a SL is roughly linear on the amount of Si.