2D-3D crossover in a dense electron liquid in silicon

TL;DR

This study investigates the electronic properties of a dense, disordered 2D array of phosphorus atoms in silicon, revealing a crossover from 2D to 3D behavior that aligns with weak localization theory and scaling concepts.

Contribution

It demonstrates the 2D-3D crossover in a dense silicon phosphorus electron system and shows the applicability of weak localization and scaling theories in describing its magnetotransport properties.

Findings

Magnetotransport is well described by weak localization theory.

A 2D-3D crossover occurs upon warming.

Scaling concepts explain the crossover except when fields are nearly parallel to planes.

Abstract

Doping of silicon via phosphene exposures alternating with molecular beam epitaxy overgrowth is a path to Si:P substrates for conventional microelectronics and quantum information technologies. The technique also provides a new and well-controlled material for systematic studies of two-dimensional lattices with a half-filled band. We show here that for a dense ($n_s=2.8\times 10^{14}$\,cm$^{-2}$) disordered two-dimensional array of P atoms, the full field angle-dependent magnetostransport is remarkably well described by classic weak localization theory with no corrections due to interaction effects. The two- to three-dimensional cross-over seen upon warming can also be interpreted using scaling concepts, developed for anistropic three-dimensional materials, which work remarkably except when the applied fields are nearly parallel to the conducting planes.