# Multiphonon Intracenter Relaxation of Boron Acceptor States in Diamond

## Abstract

The relaxation rates are calculated in the adiabatic approximation, in which the steady-state impurity states are taken to be electronic-vibrational (vibronic) states. The probabilities of transitions between these states with the emission (or absorption) of one or several phonons are calculated in first-order perturbation theory on the assumption that the transitions are a result of the violation of adiabaticity. The electron part of the wave function of the vibronic state is described by a simple Hamiltonian with an isotropic effective mass. The wave function of the ground state is determined by the quantum defect method. According to the calculations, a hole relaxes from the excited boron acceptor state, whose energy is 304 meV higher than the energy of the ground state, to the ground state with the emission of two optical phonons with a rate of ~10{sup 11} s{sup –1}. This value is an estimate from above, since the model of nondispersive optical phonons used in the study overestimates the number of phonon modes, whose participation in relaxation is allowed by the energy conservation law. However, despite the rough approximation, it can be concluded that the multiphonon relaxation of boron acceptor states in diamond is a fast process.

- Authors:

- Institute for Physics of Microstructures, Russian Academy of Sciences (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22749716

- Resource Type:
- Journal Article

- Journal Name:
- Semiconductors

- Additional Journal Information:
- Journal Volume: 52; Journal Issue: 11; Other Information: Copyright (c) 2018 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7826

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; ADIABATIC APPROXIMATION; BORON; DIAMONDS; EFFECTIVE MASS; GROUND STATES; MEV RANGE; PHONONS; RELAXATION; WAVE FUNCTIONS

### Citation Formats

```
Bekin, N. A., E-mail: nbekin@ipmras.ru.
```*Multiphonon Intracenter Relaxation of Boron Acceptor States in Diamond*. United States: N. p., 2018.
Web. doi:10.1134/S1063782618110040.

```
Bekin, N. A., E-mail: nbekin@ipmras.ru.
```*Multiphonon Intracenter Relaxation of Boron Acceptor States in Diamond*. United States. doi:10.1134/S1063782618110040.

```
Bekin, N. A., E-mail: nbekin@ipmras.ru. Thu .
"Multiphonon Intracenter Relaxation of Boron Acceptor States in Diamond". United States. doi:10.1134/S1063782618110040.
```

```
@article{osti_22749716,
```

title = {Multiphonon Intracenter Relaxation of Boron Acceptor States in Diamond},

author = {Bekin, N. A., E-mail: nbekin@ipmras.ru},

abstractNote = {The relaxation rates are calculated in the adiabatic approximation, in which the steady-state impurity states are taken to be electronic-vibrational (vibronic) states. The probabilities of transitions between these states with the emission (or absorption) of one or several phonons are calculated in first-order perturbation theory on the assumption that the transitions are a result of the violation of adiabaticity. The electron part of the wave function of the vibronic state is described by a simple Hamiltonian with an isotropic effective mass. The wave function of the ground state is determined by the quantum defect method. According to the calculations, a hole relaxes from the excited boron acceptor state, whose energy is 304 meV higher than the energy of the ground state, to the ground state with the emission of two optical phonons with a rate of ~10{sup 11} s{sup –1}. This value is an estimate from above, since the model of nondispersive optical phonons used in the study overestimates the number of phonon modes, whose participation in relaxation is allowed by the energy conservation law. However, despite the rough approximation, it can be concluded that the multiphonon relaxation of boron acceptor states in diamond is a fast process.},

doi = {10.1134/S1063782618110040},

journal = {Semiconductors},

issn = {1063-7826},

number = 11,

volume = 52,

place = {United States},

year = {2018},

month = {11}

}