Spin and valley-orbit splittings in SiGe/Si heterostructures

TL;DR

This paper calculates spin and valley-orbit splittings in SiGe/Si heterostructures using tight-binding and envelope-function methods, revealing oscillatory behavior and interface effects relevant for spin relaxation.

Contribution

It demonstrates the microscopic origin of spin splitting in perfect quantum wells with odd Si atomic layers and extends the envelope-function approach to include spin- and valley-dependent interface mixing.

Findings

Spin splitting exists in perfect QWs with odd Si layers.

Spin splitting oscillates with quantum well width.

Theoretical results align with experimental spin relaxation times.

Abstract

Spin and valley-orbit splittings are calculated in SiGe/Si/SiGe 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 inter-valley 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 SiGe/Si/SiGe QWs.