Spin and valley-orbit splittings inSiGe∕Siheterostructures

Abstract

Spin and valley-orbit splittings are calculated in symmetric $\mathrm{Si}\mathrm{Ge}∕\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ quantum wells (QWs) by using the tight-binding approach. In accordance with the symmetry considerations an existence of spin splitting of electronic states in perfect QWs with an odd number of Si atomic planes is microscopically demonstrated. The spin splitting oscillates with QW width and these oscillations related to the intervalley reflection of an electron wave from the interfaces. It is shown that the splittings under study can efficiently be described by an extended envelope-function approach taking into account the spin- and valley-dependent interface mixing. The obtained results provide a theoretical base to the experimentally observed electron spin relaxation times in $\mathrm{Si}\mathrm{Ge}∕\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ QWs.