Fine control of plastic and elastic relaxation in Ge/Si vertical heterostructures

We present a theoretical investigation of plasticity onset and strain relaxation in Ge on Si pillar-like, vertical heterostructures (VHEs). By means of linear elasticity theory solved by Finite Element Methods, we determine the critical thickness h(c) for the insertion of a 60 degrees dislocation in Si1-xGex/Si VHEs as a function of their lateral extension. Then, we quantify the effect of inserting one or more buffer layers in further delaying plasticity when growing a Ge-pure layer on top of the VHEs. The presence of intermediate layers of suitable Ge content allows for the formation of fully coherent structures up to the micron scale. The optimal thickness of one or multiple buffers to avoid dislocations is also discussed.