# Electron spin relaxation of single phosphorus donors in metal-oxide-semiconductor nanoscale devices

## TL;DR

This study investigates electron spin relaxation mechanisms of single phosphorus donors in MOS silicon devices at very low temperatures, revealing environmental effects like strain and noise sources that influence spin lifetime, with implications for quantum computing.

## Contribution

It identifies and characterizes different spin relaxation mechanisms in MOS devices, highlighting the roles of lattice strain and evanescent-wave Johnson noise, and explores their impact on spin qubit performance.

## Key findings

- Relaxation rate follows $B_0^5$ dependence at high fields, typical of bulk donors.
- Variations in relaxation rates are linked to lattice strain differences.
- At low fields, relaxation is dominated by evanescent-wave Johnson noise.

## Abstract

We analyze the electron spin relaxation rate $1/T_1$ of individual ion-implanted $^{31}$P donors, in a large set of metal-oxide-semiconductor (MOS) silicon nanoscale devices, with the aim of identifying spin relaxation mechanisms peculiar to the environment of the spins. The measurements are conducted at low temperatures ($T\approx 100$~mK), as a function of external magnetic field $B_0$ and donor electrochemical potential $\mu_{\rm D}$. We observe a magnetic field dependence of the form $1/T_1\propto B_0^5$ for $B_0\gtrsim 3\,$ T, corresponding to the phonon-induced relaxation typical of donors in the bulk. However, the relaxation rate varies by up to two orders of magnitude between different devices. We attribute these differences to variations in lattice strain at the location of the donor. For $B_0\lesssim 3\,$T, the relaxation rate changes to $1/T_1\propto B_0$ for two devices. This is consistent with relaxation induced by evanescent-wave Johnson noise created by the metal structures fabricated above the donors. At such low fields, where $T_1>1\,$s, we also observe and quantify the spurious increase of $1/T_1$ when the electrochemical potential of the spin excited state $|\uparrow\rangle$ comes in proximity to empty states in the charge reservoir, leading to spin-dependent tunneling that resets the spin to $|\downarrow\rangle$. These results give precious insights into the microscopic phenomena that affect spin relaxation in MOS nanoscale devices, and provide strategies for engineering spin qubits with improved spin lifetimes.