L W Wang, Some recent advances in ab initio calculations of nonradiative decay rates of point defects in semiconductors[J]. J. Semicond., 2019, 40(9): 091101. doi: 10.1088/1674-4926/40/9/091101.

**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.

**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.

**References:**

[1] |
Peka S I. Theory of F-centers. Zh Eksp Theor Fiz, 1950, 20, 510 |

[2] |
Huang K. Theory of light absorption and non-radiative transitions in F-centres. Phys Proc Roy Soc A, 1950, 204(22), 406 |

[3] |
Kovaskiy V A. Theory of nonradiative transitions in noncondon approximation: Low temperatures. Phys Solid State, 1962, 4, 1635 |

[4] |
Kovarskiy V A, Tchaikovskiy I A, Sinyavskiy E P. Quantum kinetic equations for processes with nonradiative recombination. Phys Solid State, 1964, 8, 2129 |

[5] |
Passler R. Description of nonradiative multiphonon transitions in the static coupling scheme. Czecho J Phys, 1974, 24(3), 322 |

[6] |
Passler R. Description of nonradiative multiphonon transitions in the static coupling scheme II. Approximations. Czecho J Phys, 1975, 25, 219 |

[7] |
Freed K F, Jortner J. Multiphonon processes in the nonradiative decay of large molecules. J Chem Phys, 1970, 52, 6272 |

[8] |
Huang K. Adiabatic approximation theory and static coupling theory of nonradiative transitons. Scientia Sinica, 1981, 24, 27 |

[9] |
Huang K. Lattice relaxation and theory of multiphonon transitions. Prog Phys, 1981, 1, 31 |

[10] |
Landau L, Litshitz E M. Quantum mechanics: Nonrelativistic theory. New York: Pergamon, 1977 |

[11] |
Zener C. Non-adiabatic crossing of energy levels. Proc Roy Soc A, 1932, 137, 696 |

[12] |
Marcus R A. Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys, 1993, 65, 599 |

[13] |
Henry C H, Lang D V. Nonradiative capture and recombination by multiphonon emission in GaAs and GaP. Phys Rev B, 1977, 15, 989 |

[14] |
Alkauskas A, Yan Q, Van de Walle C G. First-principles theory of nonradiative carrier capture via multiphonon emission. Phys Rev B, 2014, 90, 075202 |

[15] |
Shi L, Wang L W. |

[16] |
Shi L, Xu K, Wang L W. Reply to " Comment on ‘Comparative study of |

[17] |
Liu Y Y, Zheng F, Jiang X, et al. |

[18] |
Nalbach P, Thorwart M. Landau-Zener transitions in a dissipative environment: numerically exact results. Phys Rev Lett, 2009, 103, 220401 |

[19] |
Zhang S S, Gao W, Cheng H, et al. Symmetry-breaking assisted Landau-Zener transitions in Rydberg atoms. Phys Rev Lett, 2018, 120, 063203 |

[20] |
Wei S W. Overcoming the doping bottleneck in semiconductors. Comput Mater Sci, 2004, 30, 337 |

[21] |
Lany S, Zunger A. Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs. Phys Rev B, 2008, 78, 235104 |

[22] |
Freysoldt C, Grabowski B, Hickel T, et al. First-principles calculations for point defects in solids. Rev Mod Phys, 2014, 86, 253 |

[23] |
Heyd J, Scuseria G E, Ernerhof M. Hybrid functionals based on a screened Coulomb potential. J Chem Phys, 2003, 118, 8207 |

[24] |
Lyons J L, Van de Walle C G. Computationally predicted energies and properties of defects in GaN. npj Comput Mat, 2017, 3, 12 |

[25] |
Shuai Z, Wang L, Song C. Theory of charge transport in carbon electronic materials. Springer Science & Business Media, 2012 |

[26] |
Ferrer F J A, Cerezo J, Soto J, et al. First-principle computation of absorption and fluorescence spectra in solution accounting for vibronic structure, temperature effects and solvent inhomogenous broadening. Comput Theor Chem, 2014, 1040, 328 |

[27] |
Baiardi A, Bloino J, Barone V. General time dependent approach to vibronic spectroscopy including Franck–Condon, Herzberg–Teller, and Duschinsky effects. J Chem Theory Comput, 2013, 9, 4097 |

[28] |
Borrelli R, Capobianco A, Peluso A. Generating function approach to the calculation of spectral band shapes of free-base Chlorin including Duschinsky and Herzberg-Teller effects. J Phys Chem A, 2012, 116, 9934 |

[29] |
Lin S H. Rate of interconversion of electronic and vibrational energy. J Chem Phys, 1966, 44, 3759 |

[30] |
http://www.pwmat.com |

[31] |
Shi L, Xu K, Wang L W. Comparative study of |

[32] |
Aratat Y, Mohammedy F M, Hassan M M S. Optical and other measurement techniques of carrier lifetime in semiconductors. Int J Optoelectron Eng, 2012, 2, 5 |

[33] |
Kim S, Hood S N, Wash A. Anharmonic lattice relaxation during nonradiative carrier capture. Phys Rev B, 2019, 100, 041202 |

[34] |
Yang J H, Shi L, Wang L W, et al. Non-radiative carrier recombination enhanced by two-level process: a first-principles study . Sci Rep, 2016, 6, 21712 |

[35] |
Wang Z, Li S S, Wang L W. Efficient real-time time-dependent density functional theory method and its application to a collision of an ion with a 2D material. Phys Rev Lett, 2015, 114, 063004 |

[36] |
Kang J, Wang L W. Nonadiabatic molecular dynamics with decoherence and detailed balance under a density matrix ensemble formalism. Phys Rev B, 2019, 99, 224303 |

[1] |
Peka S I. Theory of F-centers. Zh Eksp Theor Fiz, 1950, 20, 510 |

[2] |
Huang K. Theory of light absorption and non-radiative transitions in F-centres. Phys Proc Roy Soc A, 1950, 204(22), 406 |

[3] |
Kovaskiy V A. Theory of nonradiative transitions in noncondon approximation: Low temperatures. Phys Solid State, 1962, 4, 1635 |

[4] |
Kovarskiy V A, Tchaikovskiy I A, Sinyavskiy E P. Quantum kinetic equations for processes with nonradiative recombination. Phys Solid State, 1964, 8, 2129 |

[5] |
Passler R. Description of nonradiative multiphonon transitions in the static coupling scheme. Czecho J Phys, 1974, 24(3), 322 |

[6] |
Passler R. Description of nonradiative multiphonon transitions in the static coupling scheme II. Approximations. Czecho J Phys, 1975, 25, 219 |

[7] |
Freed K F, Jortner J. Multiphonon processes in the nonradiative decay of large molecules. J Chem Phys, 1970, 52, 6272 |

[8] |
Huang K. Adiabatic approximation theory and static coupling theory of nonradiative transitons. Scientia Sinica, 1981, 24, 27 |

[9] |
Huang K. Lattice relaxation and theory of multiphonon transitions. Prog Phys, 1981, 1, 31 |

[10] |
Landau L, Litshitz E M. Quantum mechanics: Nonrelativistic theory. New York: Pergamon, 1977 |

[11] |
Zener C. Non-adiabatic crossing of energy levels. Proc Roy Soc A, 1932, 137, 696 |

[12] |
Marcus R A. Electron transfer reactions in chemistry. Theory and experiment. Rev Mod Phys, 1993, 65, 599 |

[13] |
Henry C H, Lang D V. Nonradiative capture and recombination by multiphonon emission in GaAs and GaP. Phys Rev B, 1977, 15, 989 |

[14] |
Alkauskas A, Yan Q, Van de Walle C G. First-principles theory of nonradiative carrier capture via multiphonon emission. Phys Rev B, 2014, 90, 075202 |

[15] |
Shi L, Wang L W. |

[16] |
Shi L, Xu K, Wang L W. Reply to " Comment on ‘Comparative study of |

[17] |
Liu Y Y, Zheng F, Jiang X, et al. |

[18] |
Nalbach P, Thorwart M. Landau-Zener transitions in a dissipative environment: numerically exact results. Phys Rev Lett, 2009, 103, 220401 |

[19] |
Zhang S S, Gao W, Cheng H, et al. Symmetry-breaking assisted Landau-Zener transitions in Rydberg atoms. Phys Rev Lett, 2018, 120, 063203 |

[20] |
Wei S W. Overcoming the doping bottleneck in semiconductors. Comput Mater Sci, 2004, 30, 337 |

[21] |
Lany S, Zunger A. Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs. Phys Rev B, 2008, 78, 235104 |

[22] |
Freysoldt C, Grabowski B, Hickel T, et al. First-principles calculations for point defects in solids. Rev Mod Phys, 2014, 86, 253 |

[23] |
Heyd J, Scuseria G E, Ernerhof M. Hybrid functionals based on a screened Coulomb potential. J Chem Phys, 2003, 118, 8207 |

[24] |
Lyons J L, Van de Walle C G. Computationally predicted energies and properties of defects in GaN. npj Comput Mat, 2017, 3, 12 |

[25] |
Shuai Z, Wang L, Song C. Theory of charge transport in carbon electronic materials. Springer Science & Business Media, 2012 |

[26] |
Ferrer F J A, Cerezo J, Soto J, et al. First-principle computation of absorption and fluorescence spectra in solution accounting for vibronic structure, temperature effects and solvent inhomogenous broadening. Comput Theor Chem, 2014, 1040, 328 |

[27] |
Baiardi A, Bloino J, Barone V. General time dependent approach to vibronic spectroscopy including Franck–Condon, Herzberg–Teller, and Duschinsky effects. J Chem Theory Comput, 2013, 9, 4097 |

[28] |
Borrelli R, Capobianco A, Peluso A. Generating function approach to the calculation of spectral band shapes of free-base Chlorin including Duschinsky and Herzberg-Teller effects. J Phys Chem A, 2012, 116, 9934 |

[29] |
Lin S H. Rate of interconversion of electronic and vibrational energy. J Chem Phys, 1966, 44, 3759 |

[30] |
http://www.pwmat.com |

[31] |
Shi L, Xu K, Wang L W. Comparative study of |

[32] |
Aratat Y, Mohammedy F M, Hassan M M S. Optical and other measurement techniques of carrier lifetime in semiconductors. Int J Optoelectron Eng, 2012, 2, 5 |

[33] |
Kim S, Hood S N, Wash A. Anharmonic lattice relaxation during nonradiative carrier capture. Phys Rev B, 2019, 100, 041202 |

[34] |
Yang J H, Shi L, Wang L W, et al. Non-radiative carrier recombination enhanced by two-level process: a first-principles study . Sci Rep, 2016, 6, 21712 |

[35] |
Wang Z, Li S S, Wang L W. Efficient real-time time-dependent density functional theory method and its application to a collision of an ion with a 2D material. Phys Rev Lett, 2015, 114, 063004 |

[36] |
Kang J, Wang L W. Nonadiabatic molecular dynamics with decoherence and detailed balance under a density matrix ensemble formalism. Phys Rev B, 2019, 99, 224303 |

L W Wang, Some recent advances in ab initio calculations of nonradiative decay rates of point defects in semiconductors[J]. J. Semicond., 2019, 40(9): 091101. doi: 10.1088/1674-4926/40/9/091101.

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Manuscript received: 18 August 2019 Manuscript revised: Online: Accepted Manuscript: 21 August 2019 Uncorrected proof: 26 August 2019 Published: 01 September 2019

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