Some recent advances in ab initio calculations of nonradiative decay rates of point defects in semiconductors

Linwang Wang

doi:10.1088/1674-4926/40/9/091101

Journals >Journal of Semiconductors >Volume 40 >Issue 9 >Page 091101 > Article

Journal of Semiconductors
Vol. 40, Issue 9, 091101 (2019)

Some recent advances in ab initio calculations of nonradiative decay rates of point defects in semiconductors

Linwang Wang

Author Affiliations

Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States

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DOI: 10.1088/1674-4926/40/9/091101 Cite this Article

Linwang Wang. Some recent advances in ab initio calculations of nonradiative decay rates of point defects in semiconductors[J]. Journal of Semiconductors, 2019, 40(9): 091101 Copy Citation Text

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Abstract

In this short review, we discuss a few recent advances in calculating the nonradiative decay rates for point defects in semiconductors. We briefly review the debates and connections of using different formalisms to calculate the multi-phonon processes. We connect Dr. Huang’s formula with Marcus theory formula in the high temperature limit, and point out that Huang’s formula provide an analytical expression for the phonon induced electron coupling constant in the Marcus theory formula. We also discussed the validity of 1D formula in dealing with the electron transition processes, and practical ways to correct the anharmonic effects.

$ H(r,R) \psi_i(r,R) = \epsilon_i(R) \psi_i(r,R) . $

(1)

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$ \bigg[ \sum\limits_R {-{1\over 2 M_{ R}} \nabla_{ R}^2 + \epsilon_i(R)} \bigg] \phi_{i,n}(R) = E_{i,n} \phi_{i,n}(R). $

(2)

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$ C(i,j,R) = {{\rm d} F_{R,\alpha} \over {\rm d} \alpha } . $

(3)

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$ {\hat P} \psi_k = \alpha \int [\psi_i(r) \psi_j^*(r')+\psi_j(r) \psi_i^*(r')] f(|r-r'|) \psi_k(r'){\rm d}^3r', $

(4)

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$ \delta(\omega) = {1\over 2{\text{π}}} \int_{-\infty}^{\infty} {\rm e}^{i \omega t} {\rm d}t . $

(5)

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$ W_{ij} = {2{\text{π}}}\sum\limits_{k_1,k_2} C_{i,j}^{k_1} C_{i,j}^{k_2} A_{ij}^{k_1,k_2} , $

(6)

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$ A_{ij}^{k_1,k_2} = {1\over 2{\text{π}} Z} \int_{-\infty}^{\infty} \chi_{ij}^{k_1,k_2}(t,T) {\rm e}^{-i (E_i-E_j) t} {\rm d}t, $

(7)

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$ \begin{split} W_{ij} =\; & {2{\text{π}}}\!\!\int_{-\infty}^{\infty}\!\!\bigg\{ \Big[\!\sum\limits_k \! C_{i,j}^k \Delta Q_{ij}^k \big( {\rm{cos}}(\omega_k t) + i{\rm{coth}}(\beta \omega_k/2) {\rm{sin}}(\omega_k t)\big)\!\Big]^2\\ & {+\, {1\over2} \sum\limits_k |C_{i,j}^k|^2 {1\over \omega_k} \big( {\rm{coth}}(\beta \omega_k/2) {\rm{cos}}(\omega_k t)+i {\rm{sin}}(\omega_k t)\big) \bigg\} }\\ & \times {1\over 2{\text{π}}} {\rm{exp}}\big[-i t (E_j-E_i) - \sum\limits_s {\omega_s\over2} |\text{Δ} Q_{ij}^s|^2\big( {\rm{coth}}(\beta \omega_s/2)\\ & \times(1-{\rm{cos}}(\omega_s t)-i {\rm{sin}}(\omega_s t)\big) \big] {\rm d}t. \end{split}$

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Linwang Wang. Some recent advances in ab initio calculations of nonradiative decay rates of point defects in semiconductors[J]. Journal of Semiconductors, 2019, 40(9): 091101

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