### Abstract

A first-principles study of the frequency-dependent second-harmonic generation (SHG) coefficients of various SiC polytypes (2H, 4H, 15R, 6H, and 3C), a group spanning the complete range of "hexagonality," was carried out. It uses a recently developed computational approach based on the self-consistent linear muffin-tin orbital band-structure method, which is applied using the local-density approximation to density-functional theory with a simple a posteriori gap correction. The susceptibilies are obtained in the independent-panicle approximation, i.e., without local-field effects. The zero-frequency limits of the ratio χ_{333}
^{(2)}/χ_{311}
^{(2)} for the noncubic polytypes were found to be in excellent agreement with those obtained by the pseudopotential method (and in disagreement with simple geometric predictions), while the magnitudes of the individual components themselves were found to be smaller than the values earlier calculated. The spectral features of the full χ^{(2)} (-2ω,ω,ω) for 2H are found to differ markedly from those of the other polytypes. The spectra in the series of decreasing degree of hexagonality (4H, 15R, and 6H) gradually approach those for the zinc-blende (3C) form. The independent tensorial components appearing in the rhombohedral but not in the hexagonal forms are found to be about a factor 6 smaller than the other ones. An analysis of the SHG spectra in terms of ω and 2ω resonances and individual band-to-band contributions is presented. It is suggested that second-harmonic generation spectra have an advantage over linear optical spectra for probing the electronic structure, particularly for the region within a few eV of the band edges in that they exhibit more detailed fine structure. That results from the sign variations in the products of matrix elements occurring in the SHG.

Original language | English |
---|---|

Pages (from-to) | 9705-9715 |

Number of pages | 11 |

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

Volume | 57 |

Issue number | 16 |

Publication status | Published - 15 Apr 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*(16), 9705-9715.

**Second-harmonic generation in SiC polytypes.** / 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. 16, pp. 9705-9715.

}

TY - JOUR

T1 - Second-harmonic generation in SiC polytypes

AU - Rashkeev, Sergey

AU - Lambrecht, Walter R L

AU - Segall, Benjamin

PY - 1998/4/15

Y1 - 1998/4/15

N2 - A first-principles study of the frequency-dependent second-harmonic generation (SHG) coefficients of various SiC polytypes (2H, 4H, 15R, 6H, and 3C), a group spanning the complete range of "hexagonality," was carried out. It uses a recently developed computational approach based on the self-consistent linear muffin-tin orbital band-structure method, which is applied using the local-density approximation to density-functional theory with a simple a posteriori gap correction. The susceptibilies are obtained in the independent-panicle approximation, i.e., without local-field effects. The zero-frequency limits of the ratio χ333 (2)/χ311 (2) for the noncubic polytypes were found to be in excellent agreement with those obtained by the pseudopotential method (and in disagreement with simple geometric predictions), while the magnitudes of the individual components themselves were found to be smaller than the values earlier calculated. The spectral features of the full χ(2) (-2ω,ω,ω) for 2H are found to differ markedly from those of the other polytypes. The spectra in the series of decreasing degree of hexagonality (4H, 15R, and 6H) gradually approach those for the zinc-blende (3C) form. The independent tensorial components appearing in the rhombohedral but not in the hexagonal forms are found to be about a factor 6 smaller than the other ones. An analysis of the SHG spectra in terms of ω and 2ω resonances and individual band-to-band contributions is presented. It is suggested that second-harmonic generation spectra have an advantage over linear optical spectra for probing the electronic structure, particularly for the region within a few eV of the band edges in that they exhibit more detailed fine structure. That results from the sign variations in the products of matrix elements occurring in the SHG.

AB - A first-principles study of the frequency-dependent second-harmonic generation (SHG) coefficients of various SiC polytypes (2H, 4H, 15R, 6H, and 3C), a group spanning the complete range of "hexagonality," was carried out. It uses a recently developed computational approach based on the self-consistent linear muffin-tin orbital band-structure method, which is applied using the local-density approximation to density-functional theory with a simple a posteriori gap correction. The susceptibilies are obtained in the independent-panicle approximation, i.e., without local-field effects. The zero-frequency limits of the ratio χ333 (2)/χ311 (2) for the noncubic polytypes were found to be in excellent agreement with those obtained by the pseudopotential method (and in disagreement with simple geometric predictions), while the magnitudes of the individual components themselves were found to be smaller than the values earlier calculated. The spectral features of the full χ(2) (-2ω,ω,ω) for 2H are found to differ markedly from those of the other polytypes. The spectra in the series of decreasing degree of hexagonality (4H, 15R, and 6H) gradually approach those for the zinc-blende (3C) form. The independent tensorial components appearing in the rhombohedral but not in the hexagonal forms are found to be about a factor 6 smaller than the other ones. An analysis of the SHG spectra in terms of ω and 2ω resonances and individual band-to-band contributions is presented. It is suggested that second-harmonic generation spectra have an advantage over linear optical spectra for probing the electronic structure, particularly for the region within a few eV of the band edges in that they exhibit more detailed fine structure. That results from the sign variations in the products of matrix elements occurring in the SHG.

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M3 - Article

VL - 57

SP - 9705

EP - 9715

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 16

ER -