## GaN

Gallium Nitride (GaN) is a very hard, mechanically stable, wide bandgap semiconductor. GaN is used in light emitting diodes, lasers, sensors, high-power transistors, and high-frequency transistors. Gallium Nitride forms the wurtzite and zincblende crystal structures.

 Crystal structure: Wurtzite Bravais lattice: hexagonal Space group: P63mc = 186 Point group: 6mm = C6v Molecular Weight $83.73$ g/mol Molecular density $n_{atoms}=8.9 \times 10^{22}$ 1/cm³  Density $\rho= 6.15$ g/cm³

The primitive GaN wurtzite unit cell contains 4 atoms.

The N atoms are positioned at $[\frac{1}{3}, \frac{2}{3}, 0]$ and $[\frac{2}{3}, \frac{1}{3}, \frac{1}{2}]$ while the Ga atoms are positioned at $[\frac{1}{3}, \frac{2}{3}, \frac{3}{8}]$ and $[\frac{2}{3}, \frac{1}{3}, \frac{7}{8}]$.

The lattice parameters of the conventional unit cell are:

$$a = 0.3180\, \text{nm}, \, b = 0.3180 \,\text{nm}, \, c = 0.5166 \,\text{nm}, \, \alpha = 90^{\circ} , \,\beta = 90^{\circ} ,\,\gamma = 120^{\circ}.$$

### Wurtzite and Zincblende comparison

 Properties Wurtzite Zincblende Bandgap Eg 3.4 eV (direct) 3.2 eV (direct) Effective density of states in conduction band (300 K) Nc 2.3 × 1024 m-3 1.2 × 1024 m-3 Effective density of states in valence band (300 K) Nv 4.6 × 1025 m-3 4.1 × 1025 m-3 Effective mass electrons m*/m0 m* = 0.20 m* = 0.13 Effective mass holes m*/m0 mlh* = 0.3 mhh* =1.4 mlh* = 0.19 mhh* = 1.3 Electric Breakdown Field 3.3 × 106 V/cm

### Electrical Band Structure (Wurtzite)

GaN is a direct bandgap semiconductor.