Analysis of phonon-induced spin relaxation processes in silicon

TL;DR

This paper provides a comprehensive theoretical analysis of phonon-induced spin relaxation in silicon's conduction electrons, deriving detailed matrix elements and comparing them with empirical models to validate the findings.

Contribution

It introduces a detailed group theory and $k extit{ extperiodcentered}p$ perturbation approach to derive matrix elements for spin-flip transitions in silicon's conduction band, advancing understanding of spin relaxation mechanisms.

Findings

Derived explicit matrix element expressions for spin-flip transitions.

Found excellent agreement between analytical models and empirical pseudopotential calculations.

Identified key dependencies of scattering angles on electron and phonon properties.

Abstract

We study all of the leading-order contributions to spin relaxation of \textit{conduction} electrons in silicon due to the electron-phonon interaction. Using group theory, $k\cdot p$ perturbation method and rigid-ion model, we derive an extensive set of matrix element expressions for all of the important spin-flip transitions in the multi-valley conduction band. The scattering angle has an explicit dependence on the electron wavevectors, phonon polarization, valley position and spin orientation of the electron. Comparison of the derived analytical expressions with results of empirical pseudopotential and adiabatic band charge models shows excellent agreement.