Spatial Imaging of Charge Transport in Silicon at Low Temperature

TL;DR

This study provides direct imaging of charge transport in high purity silicon at cryogenic temperatures, revealing insights into electron intervalley scattering and hole mass anisotropy influenced by temperature and electric field.

Contribution

It introduces a novel imaging approach to measure charge transport properties and models intervalley scattering and valence band warping effects in silicon at low temperatures.

Findings

Constant electron scattering rate at low voltages and cryogenic temperatures.

Temperature and electric field dependence of hole effective mass anisotropy.

Validation of a phenomenological model for intervalley scattering.

Abstract

We present direct imaging measurements of charge transport across a 1 cm$\times$ 1 cm$\times$ 4 mm crystal of high purity silicon ($\sim$20 k$\Omega$cm) at temperatures between 500 mK and and 5 K. We use these data to determine the intervalley scattering rate of electrons as a function of the electric field applied along the $\langle 111 \rangle$ crystal axis, and we present a phenomenological model of intervalley scattering that explains the constant scattering rate seen at low-voltage for cryogenic temperatures. We also demonstrate direct imaging measurements of effective hole mass anisotropy, which is strongly dependent on both temperature and electric field strength. The observed effects can be explained by a warping of the valence bands for carrier energies near the spin-orbit splitting energy in silicon.