Thermal excitation of flexoelectricity in silicon

TL;DR

This study investigates the temperature-dependent flexoelectricity in silicon and germanium, revealing fundamental relationships with doping, bandgap, and temperature, which could advance silicon-based electromechanical devices.

Contribution

It provides the first comprehensive measurement of silicon's flexoelectricity across temperatures and establishes a quantitative relationship with bandgap and temperature, highlighting universality in semiconductors.

Findings

Flexoelectric coefficient in doped silicon is temperature-insensitive (~2.6 μC/m).

In intrinsic silicon, flexoelectricity varies significantly with temperature, from 15.2 nC/m to 1.8 μC/m.

The relationship between flexoelectricity, temperature, and bandgap is universal across silicon and germanium.

Abstract

Flexoelectricity, an electromechanical coupling between strain gradient and polarization, offers a promising dimension to enrich silicon-based devices. Although the flexoelectricity of silicon is known, some fundamental aspects remain ambiguous, such as the discrepancy between experimental results and theoretical predictions, the influence of doping concentration, and the role of the bandgap. Here, we measured the flexoelectricity of intrinsic and heavily doped Si over the temperature range of 223 -473 K. The flexoelectric coefficient is of 2.6 {\mu}C/m and barely varies with temperature in doped silicon, while in intrinsic silicon it varies by nearly two orders of magnitude from 15.2 nC/m to 1.8 {\mu}C/m as temperature increases. We show that their different temperature dependencies correspond to the temperature-insensitive donor ionization in doped silicon and the temperature-sensitive intrinsic excitation in intrinsic silicon, with the latter captured by a quantitative relationship between flexoelectricity, temperature and bandgap. Furthermore, similar experimental results on germanium (Ge) suggest the universality of this relationship in first-generation semiconductors. These findings would offer valuable reference for developing Si-based electromechanical devices, as well as understanding the strain-gradient effects on semiconductor band structures (flexoelectronics).