Strain Relaxation of Si/SiGe Heterostructures by a Geometric Monte Carlo Approach

Solid-state-based quantum technologies, such as electronic spin-qubits, constitute a leading approach to the realization of quantum computation. Electronic spin-qubits hosted in semiconductor heterostructures demand the highest crystalline quality, specifically with respect to the structure and formation of in-plane misfit dislocations (MDs). Here, the formation mechanisms of MD networks in such Si/SiGe heterostructures are investigated. For this purpose, strained Si layers on relaxed Si0.7Ge0.3 with thicknesses above the critical thickness are grown by molecular beam epitaxy to allow for the formation of MDs. MDs are mapped out by electron channeling contrast imaging and the experimental results are compared to MD networks calculated by Monte Carlo simulations. The simulations show that the ratio between the threading dislocation density (TDD) and the average length of MDs is a constant for a given set of parameters, here 2.9 for sufficiently large dislocation statistics and simultaneous extension of MDs. Further, the fractal dimension of the MD network determined by the box-counting method as an alternative quantity to characterize MD networks is introduced. This allows to infer the formation mechanism of MDs in real devices and hence the quantification of resulting average relaxation within the Si-quantum well.