# Spin-orbit effects in the hydrogenic impurity levels of wurtzite semiconductors

## TL;DR

This paper calculates how spin-orbit interactions affect hydrogenic impurity energy levels in wurtzite semiconductors, comparing intrinsic and extrinsic effects using perturbation theory and Kane model for specific materials.

## Contribution

It introduces a first-order perturbation approach to quantify spin-orbit effects on impurity levels in wurtzite semiconductors, including a renormalized extrinsic interaction from Kane theory.

## Key findings

- Intrinsic and extrinsic spin-orbit effects vary among materials.
- The extrinsic Rashba interaction is comparable to the intrinsic Dresselhaus effect.
- Quantitative estimates provided for GaN, ZnO, InN, and AlN.

## Abstract

The corrections to the $E_2^*$ energy level of hydrogenic impurities in semiconductors with wurtzite crystal structure are calculated using first-order perturbation theory in the envelope-function approximation. We consider the intrinsic (Dresselhaus) spin-orbit effective Hamiltonian in the conduction band and compare its effects to the renormalized extrinsic (Rashba) spin-orbit interaction which is analogous to the spin-orbit interaction in the bare hydrogen atom. In order to evaluate the extrinsic spin-orbit interaction we obtain the renormalized coupling constant $\lambda^*$ for wurtzite semiconductors from 8-band Kane theory. We apply our theory to four representative binary semiconductors with wurtzite crystal structure, namely, GaN, ZnO, InN and AlN, and discuss the relative strength of the effects of the intrinsic and extrinsic spin-orbit contributions.