Thermal conductivity of group-IV semiconductors from a kinetic-collective model

The thermal conductivity of group-IV semiconductors (silicon, germanium, diamond and grey tin) with several isotopic compositions has been calculated from a kinetic-collective model. From this approach, significantly different to Callaway-like models in its physical interpretation, the thermal conductivity expression accounts for a transition from a kinetic (individual phonon transport) to a collective (hydrodynamic phonon transport) behaviour of the phonon field. Within the model, we confirm the theoretical proportionality between the phonon-phonon relaxation times of the group-IV semiconductors. This proportionality depends on some materials properties and it allows us to predict the thermal conductivity of the whole group of materials without the need to fit each material individually. The predictions on thermal conductivities are in good agreement with experimental data over a wide temperature range.