Diffusion of Hydrogen in Proton Implanted Silicon: Dependence on the Hydrogen Concentration

TL;DR

This paper investigates how hydrogen concentration affects its diffusion in proton-implanted silicon, revealing that higher concentrations lead to decreased activation energy parameters and proposing a defect saturation model to explain the diffusion behavior.

Contribution

It introduces a model linking defect saturation with hydrogen diffusion changes and analyzes the temperature dependence of diffusion across various studies.

Findings

Arrhenius parameters decrease with increasing hydrogen concentration

Defect saturation leads to hydrogen residing in less favorable lattice positions

Modified Arrhenius equation correlates diffusion behavior across studies

Abstract

The reported diffusion constants for hydrogen in silicon vary over six orders of magnitude. This spread in measured values is caused by the different concentrations of defects in the silicon that has been studied. Hydrogen diffusion is slowed down as it interacts with impurities. By changing the material properties such as the crystallinity, doping type and impurity concentrations, the diffusivity of hydrogen can be changed by several orders of magnitude. In this study the influence of the hydrogen concentration on the temperature dependence of the diffusion in high energy proton implanted silicon is investigated. We show that the Arrhenius parameters, which describe this temperature dependence decrease with increasing hydrogen concentration. We propose a model where the relevant defects that mediate hydrogen diffusion become saturated with hydrogen at high concentrations. When the defects that provide hydrogen with the lowest energy positions in the lattice are saturated, hydrogen resides at energetically less favorable positions and this increases the diffusion of hydrogen through the crystal. Furthermore, we present a survey of different studies on the diffusion of hydrogen. We observed a correlation of the Arrhenius parameters calculated in those studies, leading to a modification of the Arrhenius equation for the diffusion of hydrogen in silicon.