Anderson Localization of Electrons in Silicon Donor Chains

TL;DR

This paper models electron localization in silicon donor chains, revealing how valley interference and positional disorder influence Anderson localization, with implications for nanoscale dopant-based devices.

Contribution

It introduces a multi-valley effective mass theory model for donor chains, incorporating positional disorder and valley interference effects, to analyze localization properties.

Findings

Localization length increases with chain length.

Positional accuracy significantly affects localization onset.

Valley interference modifies tunneling and localization behavior.

Abstract

We construct a model to study the localization properties of nanowires of dopants in silicon (Si) fabricated by precise ionic implantation or STM lithography. Experiments have shown that Ohm's law holds in some cases, in apparent defiance to the Anderson localization theory in one dimension. We investigate how valley interference affects the traditional theory of electronic structure of disordered systems. Each isolated donor orbital is realistically described by multi-valley effective mass theory (MV-EMT). We extend this model to describe chains of donors as a linear combination of dopant orbitals. Disorder in donor positioning is taken into account, leading to an intricate disorder distribution of hoppings between nearest neighbor donor sites (donor-donor tunnel coupling) -- an effect of valley interference. The localization length is obtained for phosphorous (P) donor chains from a transfer matrix approach and is further compared with the chain length. We quantitatively determine the impact of uncertainties $\delta R$ in the implantation position relative to a target and also compare our results with those obtained without valley interference. We analyse systematically the aimed inter-donor separation dependence ($R_0$) and show that fairly diluted donor chains ($R_0=7.7$ nm) may be as long as 100 nm before the effective onset of Anderson localization, as long as the positioning error is under a lattice parameter ($\delta R <0.543$ nm).