Imaging the Oblique Propagation of Electrons in Germanium Crystals at Low Temperature and Low Electric Field

TL;DR

This study visualizes how electrons in germanium crystals move obliquely due to anisotropic effective masses at low temperatures and fields, revealing detailed propagation patterns and valley transitions.

Contribution

First full two-dimensional imaging of oblique electron and hole propagation and valley transitions in germanium at cryogenic temperatures and low electric fields.

Findings

Electrons exhibit oblique trajectories due to anisotropic mass tensors.

Charge density patterns match Monte Carlo simulations.

Electrons transition between valleys during drift.

Abstract

Excited electrons in the conduction band of germanium collect into four energy minima, or valleys, in momentum space. These local minima have highly anisotropic mass tensors which cause the electrons to travel in directions which are oblique to an applied electric field at sub-Kelvin temperatures and low electric fields, in contrast to the more isotropic behavior of the holes. This experiment produces, for the first time, a full two-dimensional image of the oblique electron and hole propagation and the quantum transitions of electrons between valleys for electric fields oriented along the [0,0,1] direction. Charge carriers are excited with a focused laser pulse on one face of a germanium crystal and then drifted through the crystal by a uniform electric field of strength between 0.5 and 6 V/cm. The pattern of charge density arriving on the opposite face is used to reconstruct the trajectories of the carriers. Measurements of the two-dimensional pattern of charge density are compared in detail with Monte Carlo simulations developed for the Cryogenic Dark Matter Search (CDMS) to model the transport of charge carriers in high-purity germanium detectors.