Cooling rate dependence of dislocation density in InP/Si from growth temperature to room temperature

We model the dislocation generation in InP/Si in the cooling stage, from growth temperature to room temperature (RT), in the presence of the thermal stress inherent in hetero-epitaxy. The calculations are based on simplified models of dislocation reactions; i.e., the generation of dislocations when the thermal stress exceeds the critical stress for dislocation formation, the stress relaxation resulting from the dislocation formation and from the movement of dislocations, and the annihilation of dislocations by the coalescence of two dislocations and by sweeping out to the edge of the wafer. The results show that the dislocation density at RT depends on the cooling rate. For the high cooling rates normally used for sample cooling, the dislocation density shows a small dependence on the cooling rate, and its value is in good agreement with that obtained experimentally. Conversely for low cooling rates, the dislocation density shows a strong dependence on the cooling rate. This means that high-quality and low-dislocation-density InP/Si hetero-wafers can be obtained by reducing the cooling rate.