Spin-orbit splittings in Si/SiGe quantum wells

TL;DR

This paper models spin-orbit splittings in Si/SiGe quantum wells using effective-mass and tight-binding methods, revealing dominant Dresselhaus contributions and quantifying parameters as functions of electric field and well width.

Contribution

It introduces a combined effective-mass and tight-binding approach to accurately calculate spin-orbit splittings in Si/SiGe quantum wells, including parameter dependencies.

Findings

Dresselhaus terms dominate the spin-orbit splitting

Rashba parameter is linear in electric field

Splitting magnitude can reach up to 1 μeV

Abstract

We present a calculation of the wavevector-dependent subband level splitting from spin-orbit coupling in Si/SiGe quantum wells. We first use the effective-mass approach, where the splittings are parameterized by separating contributions from the Rashba and Dresselhaus terms. We then determine the parameters by fitting tight-binding numerical results obtained using the quantitative nanoelectronic modeling tool, NEMO-3D. We describe the relevant parameters as a function of applied electric field and well width in our numerical simulations. For a silicon membrane, we find the bulk Rashba parameter to be linear in field, $\alpha = \alpha^1E_z$ with $\alpha^1 \simeq 2\times$ 10 $^{-5}$nm$^{-2}$. The dominant contribution to the spin-orbit splitting is from Dresselhaus-type terms, and the magnitude for a typical flat SiGe/Si/SiGe quantum well can be as high as 1$\mu$eV.