The choice on the bandgap energies for GaN is based on a publication [139]. The particular setup for the masses has negligible impact within the available range, thus an average value [140] is chosen.

An interesting result of the literature search is the fact that in almost all MC simulations the piezoelectric scattering mechanisms were modeled assuming a cubic crystal structure. This is a correct approach to most of the technologically significant semiconductors, whereas for wurtzites the hexagonal structure has to be accounted for in the relevant piezoelectric scattering model.

The role of piezoelectric interaction in bulk wurtzite GaN has been
analyzed by Kokolakis *et al.* [141]. In particular,
the effect of acoustic piezoelectric scattering is taken in
consideration, and the scattering rates have been calculated including
the effect of screening. In accordance with their simulations, present
results show that the piezoacoustic rates are higher in the wurtzite
phase than in the cubic phase, and they are very sensitive to the
background doping of the sample. Since nitrides exhibit the largest
piezoelectric constants among all of the III-V semiconductors, an
accurate modeling of piezoelectric scattering is especially
important. In this work a piezoelectric scattering model similar to
[142,141] is used, assuming equipartition, valid at
temperatures over one Kelvin and considering non-parabolicity and
screening in terms of the Thomas-Fermi inverse length .

Bandgap energy | Electron mass | Non-parabolicity | Scattering models | Ref. | |||||||||||

U | ADP | ||||||||||||||

eV | eV | eV | m | m | m | 1/eV | 1/eV | 1/eV | eV | meV | meV | g/cm | - | - | |

3.5 | - | - | 0.19 | - | - | 0.187 | - | - | 12.0 | - | 99.5 | 6.1 | 9.5 | 5.35 | [143] |

3.5 | 5.00 | - | 0.19 | 1.00 | - | 0.187 | - | - | 12.0 | - | 92.0 | 6.1 | 9.5 | 5.35 | [144] |

3.5 | 5.00 | - | 0.19 | 0.7 | - | 0.187 | - | - | 12.0 | - | 92.0 | 6.1 | 9.5 | 5.35 | [145] |

3.4 | 5.50 | 5.60 | 0.19 | - | - | - | - | - | 10.1 | - | 92.0 | 6.095 | 9.5 | 5.35 | [146] |

3.5 | 5.50 | 5.60 | 0.20 | 0.40 | 0.60 | 0.183 | 0.065 | 0.029 | 8.3 | 92.9 | 92.9 | 6.1 | 8.9 | 5.35 | [147] |

3.5 | 5.5 | 5.6 | 0.19 | 0.4 | 0.6 | 0.187 | 0.065 | 0.029 | 12.0 | - | 92.0 | 6.1 | 9.5 | 5.35 | [148] |

3.39 | 5.39 | 5.59 | 0.20 | 0.40 | 0.60 | 0.189 | 0.067 | 0.029 | 8.3 | 91.2 | 91.2 | 6.15 | 8.9 | 5.35 | [149] |

3.5 | 4.99 | 5.25 | 0.20 | 0.24 | 0.40 | 0.19 | 0.17 | 0 | 7.8 | 65.0 | 92.0 | 6.095 | 9.5 | 5.35 | [110] |

3.39 | 5.49 | 5.29 | 0.20 | 1.00 | 1.00 | 0.189 | 0 | 0 | 8.3 | 91.2 | 91.2 | 6.15 | 8.9 | 5.35 | [150] |

3.5 | 5.50 | 5.60 | 0.19 | 0.40 | 0.60 | 0.183 | 0.065 | 0.029 | 10.1 | 92.0 | 92.0 | 6.1 | 8.9 | 5.35 | [151] |

3.5 | 5.45 | 5.60 | 0.21 | 0.25 | 0.40 | 0.19 | 0.1 | 0 | 8.0 | 65.0 | 92.0 | 6.095 | 9.5 | 5.35 | [140] |

3.36 | - | - | 0.20 | - | - | - | - | - | 10.1 | - | 92.0 | 6.095 | 9.5 | 5.35 | [152] |

3.52 | 5.77 | 5.87 | 0.212 | - | - | 0.37 | - | - | 8.3 | 65.8 | 90.88 | 6.087 | 9.7 | 5.28 | [153] |

3.5 | 4.5 | 4.6 | 0.186 | 0.40 | 0.60 | 0.189 | 0.065 | 0.029 | 8.3 | - | 99.5 | 6.15 | 9.5 | 5.35 | [116] |

3.52 | 5.77 | 5.87 | 0.212 | 0.493 | 0.412 | - | - | - | 8.3 | - | 90.88 | 6.087 | 9.7 | 5.28 | [154] |

3.5 | 5.60 | 3.90 | 0.20 | 0.60 | 0.22 | 0.183 | 0.029 | 0.065 | 8.3 | 80.0 | 92.2 | 6.15 | 9.95 | 5.35 | [155] |

3.39 | 5.49 | 5.29 | 0.21 | 1.00 | 1.0 | 0.189 | 0 | 0 | 8.3 | 92.0 | 92.0 | 6.15 | 8.9 | 5.35 | [139] |

3.39 | 5.49 | 5.29 | 0.2 | 1.0 | 1.0 | 0.189 | 0 | 0 | 8.3 | 91.2 | 91.2 | 6.15 | 8.9 | 5.35 | [156] |

3.39 | 5.49 | 5.29 | 0.2 | 1.0 | 1.0 | 0.189 | 0 | 0 | 8.3 | 92.0 | 92.0 | 6.15 | 8.9 | 5.35 | [157] |

3.39 | 5.29 | 5.49 | 0.20 | 0.30 | 0.40 | 0.189 | 0 | 0 | 8.3 | 91.0 | 92.0 | 6.1 | 8.9 | 5.35 |

Material parameters as used by different group are given in Table 3.1, while Table 3.2 summarizes the experimental and theoretical values of the elastic constants , , and , available for wurtzite GaN in the literature. From these the corresponding values for , , , and are calculated. The latest experimental values for GaN [158] are adopted in the MC simulation [159].

Data | Refs. | |||||||

GPa | GPa | GPa | GPa | GPa | m/s | m/s | ||

296 | 120 | 24 | exp. | [160] | 245 | 50 | 6342 | 2855 |

374 | 106 | 101 | exp. | [161] | 348 | 114 | 7557 | 4331 |

390 | 145 | 105 | exp. | [162] | 376 | 112 | 7859 | 4290 |

377 | 160 | 81 | exp. | [163] | 355 | 92 | 7637 | 3888 |

365 | 135 | 109 | exp. | [164] | 360 | 111 | 7693 | 4278 |

370 | 145 | 90 | exp. | [165] | 364 | 108 | 7733 | 4212 |

373 | 141 | 94 | exp. | [158] | 355 | 103 | 7641 | 4110 |

369 | 94 | 118 | calc. | [166] | 353 | 126 | 7620 | 4546 |

396 | 144 | 91 | calc. | [167] | 368 | 105 | 7775 | 4153 |

367 | 135 | 95 | calc. | [168] | 350 | 103 | 7585 | 4122 |

350 | 140 | 101 | calc. | [169] | 347 | 103 | 7548 | 4106 |

Table 3.3 summarizes the experimental and theoretical values of the piezoelectric coefficients , , and , available for GaN in the literature. In cases, where is not available, is assumed. From these, the corresponding and are calculated, which are necessary to obtain the coupling coefficient taking into account the wurtzite structure [159].

Data | Refs. | |||||

C/m | C/m | C/m | Data | Refs. | C/m | C/m |

-0.30 | -0.36 | 1.00 | exp. | [170] | 0.103 | 0.123 |

- | -0.55 | 1.12 | exp. | [171] | 0.175 | 0.234 |

- | -0.33 | 0.65 | calc. | [143] | 0.061 | 0.082 |

- | -0.49 | 0.73 | calc. | [172] | 0.118 | 0.149 |

-0.22 | -0.22 | 0.43 | calc. | [173] | 0.027 | 0.036 |

- | -0.32 | 0.63 | calc. | [169] | 0.058 | 0.077 |

- | -0.44 | 0.86 | calc. | [174] | 0.109 | 0.145 |

S. Vitanov: Simulation of High Electron Mobility Transistors