Modeling of phonon transport in semiconductor alloys: Application to SiGe and InGaAs thermal conductivity calculations

In this work, we develop a modeling framework to describe heat transport in SiGe and InGaAs semiconductor alloys. The approach extends the classical Callaway–Debye formalism, originally developed for pristine crystals, incorporating the virtual crystal approximation. Anharmonic phonon–phonon interactions are modeled using expressions dependent on the Grüneisen parameter, while alloy-related scattering is treated within a perturbative framework that accounts for both mass disorder and stress field fluctuations induced by lattice mismatch. One of the major contributions of this work lies in the introduction of the Monte Carlo calculations a spatially explicit description of disorder in the alloy, enabling a correction of its relaxation time. Furthermore, this approach departs from the commonly accepted isotropic scattering approximation through the implementation of a frequency dependent scattering phase function formalism to describe accurately phonon transport in alloyed compounds. This new model is implemented in a Monte Carlo framework, and thermal conductivity is evaluated using the Green–Kubo formalism based on the autocorrelation functions of the phonon heat flux. The approach is applied to SiGe and InGaAs alloys over a wide range of temperatures and compositions. The results obtained show excellent agreement with experimental data taken from the literature, demonstrating the relevance of the proposed modeling strategy and highlighting the importance of taking into account both spatial correlations and directional effects in scattering within the alloy.