Three-dimensional SiGe/Si heterostructures: Switching the dislocation sign by substrate under-etching

We present a joint theoretical and experimental analysis of the dislocation distribution in graded epitaxial SiGe crystals grown on under-etched Si pillars by low-energy plasma-enhanced chemical vapor deposition. Dislocation dynamics simulations are used to investigate preferential positioning of 60. dislocations introduced in the system to release the lattice misfit strain. Coupling to a finite-element solver is exploited to allow for the exact numerical treatment of the stress fields in the presence of a complex distribution of free surfaces. The results show that, by suitably under-etching the Si pillars, it is possible to reverse the sign of the Burgers vector of the dislocations. This helps explaining differences in the experimentally observed distribution of dislocations in SiGe crystals grown on vertical and under-etched pillars, leading to a strong reduction of defects in the latter case. The agreement between simulations and experiments is not simply qualitative: the predicted number of defects generated by multiplication processes in tall crystals is indeed fully consistent with the measured one