The role of crystal diameter and impurity hardening on the threshold for dislocation formation in LEC GaAs.

We have calculated explicitly the dependence of the dislocation density on crystal radius and ambient temperature gradient in GaAs grown by the LEC technique. In addition, the effects of "impurity hardening" via in-alloying were investigated by varying systematically the critical resolved shear stress threshold according to estimated bounds given by Ehrenreich and Hirth. We show that for standard LEC growth conditions, it is not possible to grow dislocation-free crystals for diameters beyond ~ 1 cm. Furthermore, in extremely low gradients impurity hardening is not essential to produce low defect density crystals of diameters in the range 4-8cm. However, to achieve stable growth of such crystals a compromise between the effects of a moderate thermal gradient and the addition of a small amount of hardening agent is recommended. The predictions are in remarkably good agreement with LEC growth experiments and are also applicable to Bridgman methods.