### Abstract

The development of a method for calculating the frequency-dependent second harmonic generation coefficient of insulators and semiconductors based on the self-consistent linearized muffin-tin orbitals band structure method is reported. The calculations are at the independent particle level and are based on the formulation introduced by A versa and Sipe [Phys. Rev. B 52, 14 636 (1995)]. The terms are rearranged in such a way as to exhibit explicitly all required symmetries including the Kleinman symmetry in the static limit. Computational details and convergence tests are presented. The calculated frequency-dependent X^{(2)}(-2ω,ω,ω) for the zinc-blende materials GaAs, GaP and wurtzite GaN and AlN are found to be in excellent agreement with that obtained by other first-principles calculations when corrections to the local density approximation are implemented in the same manner, namely, using the "scissors" approach. Similar agreement is found for the static values of x^{(2)} for zinc-blende GaN, AlN, BN, and SiC. The strict validity of the usual "scissors" operator implementation is, however, questioned. We show that better agreement with experiment is obtained when the corrections to the low-lying conduction bands are applied at the level of the Hamiltonian, which guarantees that eigenvectors are consistent with the eigenvalues. Results are presented for the frequency-dependent X^{(2)}( -2ω,ω,ω) for 3C-SiC. The approach is found to be very efficient and flexible, which indicates that it will be useful for a wide variety of material systems including those with many atoms in the unit cell.

Original language | English |
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Pages (from-to) | 3905-3919 |

Number of pages | 15 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 57 |

Issue number | 7 |

Publication status | Published - 15 Feb 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*57*(7), 3905-3919.

**Efficient ab initio method for the calculation of frequency-dependent second-order optical response in semiconductors.** / Rashkeev, Sergey; Lambrecht, Walter R L; Segall, Benjamin.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 57, no. 7, pp. 3905-3919.

}

TY - JOUR

T1 - Efficient ab initio method for the calculation of frequency-dependent second-order optical response in semiconductors

AU - Rashkeev, Sergey

AU - Lambrecht, Walter R L

AU - Segall, Benjamin

PY - 1998/2/15

Y1 - 1998/2/15

N2 - The development of a method for calculating the frequency-dependent second harmonic generation coefficient of insulators and semiconductors based on the self-consistent linearized muffin-tin orbitals band structure method is reported. The calculations are at the independent particle level and are based on the formulation introduced by A versa and Sipe [Phys. Rev. B 52, 14 636 (1995)]. The terms are rearranged in such a way as to exhibit explicitly all required symmetries including the Kleinman symmetry in the static limit. Computational details and convergence tests are presented. The calculated frequency-dependent X(2)(-2ω,ω,ω) for the zinc-blende materials GaAs, GaP and wurtzite GaN and AlN are found to be in excellent agreement with that obtained by other first-principles calculations when corrections to the local density approximation are implemented in the same manner, namely, using the "scissors" approach. Similar agreement is found for the static values of x(2) for zinc-blende GaN, AlN, BN, and SiC. The strict validity of the usual "scissors" operator implementation is, however, questioned. We show that better agreement with experiment is obtained when the corrections to the low-lying conduction bands are applied at the level of the Hamiltonian, which guarantees that eigenvectors are consistent with the eigenvalues. Results are presented for the frequency-dependent X(2)( -2ω,ω,ω) for 3C-SiC. The approach is found to be very efficient and flexible, which indicates that it will be useful for a wide variety of material systems including those with many atoms in the unit cell.

AB - The development of a method for calculating the frequency-dependent second harmonic generation coefficient of insulators and semiconductors based on the self-consistent linearized muffin-tin orbitals band structure method is reported. The calculations are at the independent particle level and are based on the formulation introduced by A versa and Sipe [Phys. Rev. B 52, 14 636 (1995)]. The terms are rearranged in such a way as to exhibit explicitly all required symmetries including the Kleinman symmetry in the static limit. Computational details and convergence tests are presented. The calculated frequency-dependent X(2)(-2ω,ω,ω) for the zinc-blende materials GaAs, GaP and wurtzite GaN and AlN are found to be in excellent agreement with that obtained by other first-principles calculations when corrections to the local density approximation are implemented in the same manner, namely, using the "scissors" approach. Similar agreement is found for the static values of x(2) for zinc-blende GaN, AlN, BN, and SiC. The strict validity of the usual "scissors" operator implementation is, however, questioned. We show that better agreement with experiment is obtained when the corrections to the low-lying conduction bands are applied at the level of the Hamiltonian, which guarantees that eigenvectors are consistent with the eigenvalues. Results are presented for the frequency-dependent X(2)( -2ω,ω,ω) for 3C-SiC. The approach is found to be very efficient and flexible, which indicates that it will be useful for a wide variety of material systems including those with many atoms in the unit cell.

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M3 - Article

VL - 57

SP - 3905

EP - 3919

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 7

ER -