Donor-driven spin relaxation in multi-valley semiconductors

TL;DR

This paper develops a theory explaining how impurity-driven short-range scattering causes spin relaxation in silicon, accounting for multivalley conduction band effects and impurity identity, crucial for silicon spintronics.

Contribution

It introduces the first comprehensive model quantifying impurity identity effects on spin relaxation in multi-valley silicon.

Findings

$f$-processes dominate spin relaxation at all temperatures

Impurity central-cell scattering is key at low temperatures

The theory accurately matches empirical impurity dependence

Abstract

We present a theory for spin relaxation of electrons due to scattering off the central-cell potential of impurities in silicon. Taking into account the multivalley nature of the conduction band and the violation of translation symmetry, the spin-flip amplitude is dominated by this short-range impurity scattering after which the electron is transferred to a valley on a different axis in $k$-space (the so called $f$-process). These $f$-processes dominate the spin relaxation at all temperatures, where scattering off the impurity central-cell dominate at low temperatures, and scattering with $\Sigma$-axis phonons at elevated temperatures. To the best of our knowledge, the theory is the first to explain and accurately quantify the empirically-found dependence of spin relaxation on the impurity identity. Accordingly, the new formalism fills a longstanding gap in the spin relaxation theory of $n$-type silicon, and it is valuable for characterization of silicon-based spintronic devices.