Draft:Gallium nitride (data page)

Gallium nitride (GaN) is a wide-band gap compound semiconductor of gallium and nitrogen. This page provides supplementary numerical data on its structural, electronic, mechanical, thermal, and optical properties, to accompany the main Gallium nitride article. Unless otherwise noted, all values refer to the ambient-pressure wurtzite polytype (α-GaN) at 300 K.

Structure and properties

Gallium nitride crystallizes in two structures, listed separately below: the stable wurtzite form, and a metastable cubic zinc blende form.

Wurtzite (α-GaN), stable phase

Basic structural and electronic parameters, wurtzite GaN, 300 K

Property	Value	Notes	Source
Crystal structure	Wurtzite	Space group C 6v4 –P63mc
Lattice constant, a	3.189 Å	300 K; reported range 3.160–3.190 Å across samples
Lattice constant, c	5.186 Å	300 K; also reported as 5.178 Å by Qian et al. (1996); broader range 5.125–5.190 Å across samples
Density	6.15 g cm−3	300 K
Number density of atoms	8.9×1022 cm−3
Molar mass	83.73 g mol−1	Ga (69.72) + N (14.01)
Debye temperature	600 K
Linear thermal expansion, αa	5.59×10−6 K−1	in-plane, a-axis
Linear thermal expansion, αc	3.17×10−6 K−1	c-axis

Zinc blende (β-GaN), metastable cubic phase

Basic structural parameters, zinc blende GaN, 300 K

Property	Value	Source
Space group	T 2d–F43m
Lattice constant, a	4.52 Å
Density	6.15 g cm−3
Debye temperature	600 K

Electronic and transport properties

This section lists gallium nitride's band gap, dielectric constants, effective carrier masses, and carrier mobilities.

Selected electronic parameters, 300 K

Property	Wurtzite	Zinc blende	Source
Direct band gap	≈3.4–3.44 eV	≈3.1–3.3 eV (direct, Γ point; agrees with absorption measurements on cubic GaN)
Static dielectric constant, ε(0)	8.9 (isotropic avg.); 9.5(3)–10.4(3) resolved E⊥c / E∥c	9.7
High-frequency dielectric constant, ε(∞)	5.35 (avg.); 5.35(20)–5.8(4) resolved	5.3
Electron affinity	4.1 eV	4.1 eV
Effective electron mass, me	0.20 m0	0.13 m0
Effective heavy-hole mass	1.1–1.6 m0 (mhhz = 1.1 along c; mhh = 1.4–1.6 in-plane)	0.8–1.7 m0 (m[100] = 0.8; mhh = 1.3; m[111] = 1.7)
Optical phonon energy	91.2 meV	87.3 meV
Breakdown field	≈5×106 V cm−1 (also reported 3.3×106 V cm−1)	≈5×106 V cm−1
Electron mobility (bulk, undoped, n ≈ 1017 cm−3)	≤1000 cm2 V−1 s−1; ≤440 cm2 V−1 s−1 in purest early material	≤1000 cm2 V−1 s−1
Hole mobility	≤200 cm2 V−1 s−1	≤350 cm2 V−1 s−1
Electron diffusion coefficient	25 cm2 s−1	25 cm2 s−1
Hole diffusion coefficient	5 cm2 s−1	9 cm2 s−1

Mechanical properties and elastic constants

This section lists gallium nitride's elastic constants and derived mechanical moduli.

Elastic constants, wurtzite GaN, 300 K (Voigt notation)

Constant	Value (GPa)	Source
C11	390 ± 15
C12	145 ± 20
C13	106 ± 20
C33	398 ± 20
C44	105 ± 10

Derived mechanical moduli, 300 K

Property	Wurtzite	Zinc blende	Source
Bulk modulus, Bs	210 ± 10 GPa	204 GPa
Shear modulus, C′	—	67 GPa
Young's modulus, Y0 ([100])	—	181 GPa
Poisson ratio, σ0	—	0.352
Anisotropy factor, A	—	0.43
Surface microhardness (Knoop)	1200–1700 kg mm−2	—

Acoustic wave velocities, wurtzite GaN, [100] and [001] directions, 300 K

Direction	Mode	Velocity (105 cm s−1)	Source
[100]	Longitudinal (VL)	7.96
[100]	Transverse, polarization ∥ [001]	4.13
[100]	Transverse, polarization ∥ [010]	6.31
[001]	Longitudinal (VL)	8.04

Thermal properties

This section lists gallium nitride's melting behavior, specific heat, and thermal conductivity.

Thermal properties, wurtzite/zinc blende GaN

Property	Value	Notes	Source
Melting point	≈2500 °C	Requires high N2 overpressure; at 1 atm, GaN decomposes well below this temperature rather than melting congruently, which is why bulk single crystals require pressurized growth
Specific heat, Cp (298–1773 K)	Cp = 38.1 + 8.96×10−3T (J mol−1 K−1)	T in kelvin
Specific heat (mass basis)	0.49 J g−1 °C−1	300 K
Thermal conductivity	1.3 W cm−1 °C−1	300 K, along c-axis; strongly sample/purity dependent
Thermal diffusivity	0.43 cm2 s−1	300 K
Bulk modulus	204 GPa (20.4×1011 dyn cm−2)

Thermochemical properties

This section lists the standard enthalpy of formation of gallium nitride.

Standard enthalpy of formation, Δ_fH°₂₉₈(GaN, s)

Value (kJ mol−1)	Method	Source
−110	Combustion calorimetry on an uncharacterized sample; the long-standard tabulated value
−156.8 ± 16.0	Oxide-melt solution calorimetry on characterized samples of varying stoichiometry, extrapolated to GaN
−157.7	Temperature dependence of the equilibrium N2 pressure over GaN
−126.8 (2007) / −129.3 (2009)	Refinement from vapor-pressure data
−165 (2008)	Experimental re-determination, same group as Ranade et al.
−112.49 (calculated)	DFT (ab initio) total-energy calculation, compared against the classic −110 kJ/mol value

Optical properties

This section lists gallium nitride's refractive index and vibrational (phonon) spectrum.

Refractive index (bulk, room temperature)

Values below are calculated from the Sellmeier equation for bulk wurtzite GaN (coefficients given below), evaluated across its validity range of 0.50–5.10 μm. GaN is uniaxial and positively birefringent (n_e > n_o) with the optic axis along c.

Refractive index of bulk wurtzite GaN vs. wavelength, 300 K (calculated from Sellmeier fit; accuracy ≈ ±0.002)

Wavelength (μm)	no (E ⊥ c)	ne (E ∥ c)
0.50	2.4051	2.4445
0.60	2.3634	2.4006
0.70	2.3396	2.3751
0.80	2.3244	2.3592
0.90	2.3141	2.3483
1.00	2.3065	2.3402
1.20	2.2960	2.3295
1.50	2.2867	2.3195
2.00	2.2762	2.3086
3.00	2.2578	2.2898
4.00	2.2352	2.2662
5.00	2.2052	2.2348

Sellmeier equation coefficients

Standard two-pole form: $n^{2}(\lambda )=1+{\dfrac {A_{1}\lambda ^{2}}{\lambda ^{2}-B_{1}^{2}}}+{\dfrac {A_{2}\lambda ^{2}}{\lambda ^{2}-B_{2}^{2}}}$, with λ in micrometres.

Sellmeier coefficients for bulk wurtzite GaN, 300 K

Coefficient	Ordinary wave (no)	Extraordinary wave (ne)
A1	4.199	4.347
A2	3.625	2.964
B1 (μm)	0.1753	0.1781
B2 (μm)	17.05	15.23

Valid 0.50–5.10 μm; standard deviations of the fit are 1.7–1.8×10⁻³. Linear temperature coefficients at 532 nm: dn_o/dT = (5.6 ± 0.1)×10⁻⁵ K⁻¹, dn_e/dT = (5.8 ± 0.1)×10⁻⁵ K⁻¹.

Phonon frequencies (wurtzite, Γ point, 300 K)

Zone-centre optical phonon wavenumbers

Mode	Wavenumber (cm−1)	Source
A1(TO)	533
E1(TO)	559
A1(LO)	744
E1(LO)	746
E2 (low)	143–146
E2 (high)	560–579

References

Category:Chemical data pages Category:Gallium compounds Category:Nitrides Category:Semiconductors