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 = C_6v
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 *E_g*	3.4 eV (direct)	3.2 eV (direct)
Effective density of states in conduction band (300 K) *N_c*	2.3 × 10²⁴ m^-3	1.2 × 10²⁴ m^-3
Effective density of states in valence band (300 K) *N_v*	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**	m_lh^* = 0.3 m_hh^* =1.4	m_lh^* = 0.19 m_hh^* = 1.3
Electric Breakdown Field	3.3 × 10⁶ V/cm

Electrical Band Structure (Wurtzite)

GaN is a direct bandgap semiconductor.

Source: Rheinlander, A., Neumann, H. Plasma Faraday Rotation in n-Type GaN. Phys. Status Solidi (b) 64 (1974) K123. https://onlinelibrary.wiley.com/toc/15213951/64/2 (1 August 1974) Accessed: 01-02-2021