### Abstract

The wurtzite Al_{x}Ga_{1-x}N, In_{x}Ga _{1-x}N, and Al_{x}In_{1-x}N alloys are studied by numerical simulation based on first-principles calculations. For Al _{x}Ga_{1-x}N the Vegard's law deviation parameter is 0.018 ±0.001 A for the a lattice constant and -0.036 ± 0.005 Å for the c lattice constant. For In_{x}Ga_{1-x}N that is 0.047 ± 0.011 Å for the a lattice constant and -0.117 ± 0.026 Å for the c lattice constant. For Al_{x}In_{1-x}N that is 0.063 ± 0.014 Å for the a lattice constant and -0.160 ± 0.015 Å for the c lattice constant The results indicate that the band gap bowing parameters obtained with the equilibrium lattice constant and with the lattice constants derived from the Vegard's law are 0.341 ±0.035 eV and 0.351 ± 0.043 eV respectively for Al_{x}Ga_{1-x}N, 1.782 ± 0.076 eV and 1.916 ± 0.068 eV respectively for In _{x}Ga_{1-x}N, and 3.668 ± 0.147 eV and 3.457 ± 0.152 eV respectively for Al_{x}In_{1-x}N.

Original language | English |
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Article number | 54 |

Pages (from-to) | 296-305 |

Number of pages | 10 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 5628 |

DOIs | |

Publication status | Published - 2005 Jun 1 |

Event | Semiconductor Lasers and Applications II - Beijing, China Duration: 2004 Nov 8 → 2004 Nov 9 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*5628*, 296-305. [54]. https://doi.org/10.1117/12.575300

}

*Proceedings of SPIE - The International Society for Optical Engineering*, vol. 5628, 54, pp. 296-305. https://doi.org/10.1117/12.575300

**Vegard's law deviation in band gaps and bowing parameters of the wurtzite III-nitride ternary alloys.** / Liou, Bo Ting; Yen, Sheng Horng; Kuo, Yen Kuang.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Vegard's law deviation in band gaps and bowing parameters of the wurtzite III-nitride ternary alloys

AU - Liou, Bo Ting

AU - Yen, Sheng Horng

AU - Kuo, Yen Kuang

PY - 2005/6/1

Y1 - 2005/6/1

N2 - The wurtzite AlxGa1-xN, InxGa 1-xN, and AlxIn1-xN alloys are studied by numerical simulation based on first-principles calculations. For Al xGa1-xN the Vegard's law deviation parameter is 0.018 ±0.001 A for the a lattice constant and -0.036 ± 0.005 Å for the c lattice constant. For InxGa1-xN that is 0.047 ± 0.011 Å for the a lattice constant and -0.117 ± 0.026 Å for the c lattice constant. For AlxIn1-xN that is 0.063 ± 0.014 Å for the a lattice constant and -0.160 ± 0.015 Å for the c lattice constant The results indicate that the band gap bowing parameters obtained with the equilibrium lattice constant and with the lattice constants derived from the Vegard's law are 0.341 ±0.035 eV and 0.351 ± 0.043 eV respectively for AlxGa1-xN, 1.782 ± 0.076 eV and 1.916 ± 0.068 eV respectively for In xGa1-xN, and 3.668 ± 0.147 eV and 3.457 ± 0.152 eV respectively for AlxIn1-xN.

AB - The wurtzite AlxGa1-xN, InxGa 1-xN, and AlxIn1-xN alloys are studied by numerical simulation based on first-principles calculations. For Al xGa1-xN the Vegard's law deviation parameter is 0.018 ±0.001 A for the a lattice constant and -0.036 ± 0.005 Å for the c lattice constant. For InxGa1-xN that is 0.047 ± 0.011 Å for the a lattice constant and -0.117 ± 0.026 Å for the c lattice constant. For AlxIn1-xN that is 0.063 ± 0.014 Å for the a lattice constant and -0.160 ± 0.015 Å for the c lattice constant The results indicate that the band gap bowing parameters obtained with the equilibrium lattice constant and with the lattice constants derived from the Vegard's law are 0.341 ±0.035 eV and 0.351 ± 0.043 eV respectively for AlxGa1-xN, 1.782 ± 0.076 eV and 1.916 ± 0.068 eV respectively for In xGa1-xN, and 3.668 ± 0.147 eV and 3.457 ± 0.152 eV respectively for AlxIn1-xN.

UR - http://www.scopus.com/inward/record.url?scp=18944398444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18944398444&partnerID=8YFLogxK

U2 - 10.1117/12.575300

DO - 10.1117/12.575300

M3 - Conference article

AN - SCOPUS:18944398444

VL - 5628

SP - 296

EP - 305

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

SN - 0277-786X

M1 - 54

ER -