Quantum confinement in semiconductor random alloys: a case study on Si/SiGe/Si

Local composition fluctuations in random alloys become crucial when one or more dimensions are reduced to the nanoscale. Using extended H\"uckel theory, we study the semiconductor random alloy SiGe sandwiched between Si due to its relevance for transistor devices. We evaluate the effects of the alloy composition, layer thickness, and local fluctuations of the Ge concentration on the band alignment and the band gap. The results are compared with the finite quantum well model. That model captures the essential physics and can act as a computationally faster alternative.