Deformation slip and twinning in bulk and nanocrystalline semiconductors

Yielding and twinning in bulk and nanocrystalline semiconductors are considered based on the activation of perfect or partial dislocation loops. Assuming that the yield stress of the crystal is proportional to the critical stress necessary for the activation of a perfect Frank-Read source, it is shown that for a range of crystal orientations with respect to the applied shear stress, the Hall-Petch relationship for a silicon polycrystal fails when the average grain diameter is of the order of 3 nm or less. It is further shown that, assuming the double-cross-slip mechanism of twin formation in silicon, twinning is easier than slip for a range of crystal orientations in nanocrystals.