### Abstract

A first-principles study of the frequency-dependent second-harmonic generation (SHG) coefficients of various SiC polytypes (Formula presented), (Formula presented), (Formula presented), (Formula presented), and (Formula presented), 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-particle approximation, i.e., without local-field effects. The zero-frequency limits of the ratio (Formula presented) 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 (Formula presented) for (Formula presented) are found to differ markedly from those of the other polytypes. The spectra in the series of decreasing degree of hexagonality (Formula presented), (Formula presented), and (Formula presented) gradually approach those for the zinc-blende (Formula presented) 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 (Formula presented) and (Formula presented) 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 |
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Pages (from-to) | 9705-9715 |

Number of pages | 11 |

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

Volume | 57 |

Issue number | 16 |

DOIs | |

Publication status | Published - 1 Jan 1998 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

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

*57*(16), 9705-9715. https://doi.org/10.1103/PhysRevB.57.9705