Defect Phonon Renormalization during Nonradiative Multiphonon Transitions in Semiconductors

TL;DR

This paper demonstrates that phonon renormalization significantly impacts defect transition rates in semiconductors and introduces an improved method that accounts for mode changes, leading to more accurate calculations aligned with experimental data.

Contribution

The paper introduces a method that incorporates phonon mode changes and cross-mode interactions to improve the accuracy of defect transition rate calculations in semiconductors.

Findings

Phonon renormalization can cause errors of orders of magnitude in transition rate calculations.

Including Duschinsky matrix and off-diagonal terms improves agreement with experiments.

The new method enhances the accuracy of multiphonon transition rate predictions.

Abstract

As a typical nonradiative multiphonon transition in semiconductors, carrier capture at defects is critical to the performance of semiconductor devices. Its transition rate is usually calculated using the equal-mode approximation, which assumes that phonon modes and frequencies remain unchanged before and after the transition. Using the carbon substitutional defect ($\text{C}_\text{N}$) in GaN as a benchmark, here we demonstrate that the phonon renormalization can be significant during defect relaxation, which causes errors as large as orders of magnitude in the approximation. To address this issue, we consider (i) Duschinsky matrix connecting the initial-state and final-state phonons, which accounts for the changes in phonon modes and frequencies; and (ii) the off-diagonal contributions in total transition matrix element, which incorporates the cross terms of electron-phonon interactions between different modes. With this improvement, the calculated transition rates show agreements with experimental results within an order of magnitude. We believe the present method makes one step forward for the accurate calculation of multiphonon transition rate, especially in cases with large defect relaxations.