Spin-lattice relaxation times of single donors and donor clusters in silicon

TL;DR

This paper introduces an atomistic method to calculate spin-lattice relaxation times ($T_1$) in silicon nanostructures, accounting for full band structure and spin-orbit interaction, matching experimental results without adjustable parameters.

Contribution

The paper presents a novel atomistic approach to compute $T_1$ times in silicon, incorporating full band structure and strain effects, enabling accurate predictions for donors and clusters.

Findings

$T_1$ varies as $B^5$ in magnetic fields, matching experiments.

Relaxation times can be engineered by modifying electronic wavefunctions.

The method accurately predicts $T_1$ for single donors and clusters without adjustable parameters.

Abstract

An atomistic method of calculating the spin-lattice relaxation times ($T_1$) is presented for donors in silicon nanostructures comprising of millions of atoms. The method takes into account the full band structure of silicon including the spin-orbit interaction. The electron-phonon Hamiltonian, and hence the deformation potential, is directly evaluated from the strain-dependent tight-binding Hamiltonian. The technique is applied to single donors and donor clusters in silicon, and explains the variation of $T_1$ with the number of donors and electrons, as well as donor locations. Without any adjustable parameters, the relaxation rates in a magnetic field for both systems are found to vary as $B^5$ in excellent quantitative agreement with experimental measurements. The results also show that by engineering electronic wavefunctions in nanostructures, $T_1$ times can be varied by orders of magnitude.