New Semiconductor Materials. Biology systems.
Characteristics and Properties

NSM Archive - Indium Nitride (InN) - Band structure

Band structure and carrier concentration

Basic Parameters
Band structure
Intrinsic carrier concentration
Effective Density of States in the Conduction and Valence Band
Temperature Dependences
Dependences on Hydrostatic Pressure
Band Discontinuities at Heterointerfaces
Effective Masses and Density of States
Donors and Acceptors

---

Basic Parameters

Wurtzite(hexagonal) crystal structure		Remarks	Referens
Energy gaps, Eg	1.970 eV	300 K	Guo & Yoshida (1994), Teisseyre al. (1994)
	1.9-2.05 eV	300 K	Zubrilov (2001)
	2.05 (1) eV	300K; absorption edge	Tyagai et al. (1977)
	2.11 eV	78 K	Osamura et al. (1975)
	1.89 eV	RT	Foley & Tansley (1986)

Conduction band		Remarks	Referens
Energy separation between  Γ valley and M-L valleys	2.9 ÷ 3.9 eV	300 K	Zubrilov (2001)
Energy separation between  M-L valleys degeneracy	6 eV	300 K
Energy separation between Γ valley and A valleys	0.7÷ 2.7eV	300 K
Energy separation between A valley degeneracy	1 eV	300 K
Energy separation between Γ valley and Γ1 valleys	1.1÷ 2.6eV	300 K
Energy separation between Γ1 valley degeneracy	1 eV	300 K
Valence band
Energy of spin-orbital splitting Eso	0.003 eV	300 K	Zubrilov (2001)
Energy of crystal-field splitting Ecr	0.017 eV	300 K
Effective conduction band density of states	9 x 1017 cm-3	300 K
Effective valence band density of states	5.3 x 1019 cm-3	300 K

---

Band structure

InN, Wurtzite. Band structure. Important minima of the conduction band and maxima of the valence band. This splitting results from spin-orbit interaction and from crystal symmetry.   300K;     Eg = 1.9 - 2.05 eV;       EΓ1 = 3.0 - 4.5 eV;     EM-L = 4.8 - 5.8 eV;   EA = 2.6 - 4.7 eV;     Eso = 0.003 eV;        Ecr = 0.017 eV For details see Christensen & Gorczyca (1994), Jenkins (1994), Yeo et al. (1998), Pugh et al. (1999)

InN, Wurtzite. Band structure calculated with an empirical pseudopotential method The band structure shows a direct gap at Γ, closely similar to that of GaN. Foley &Tansley (1986)

Brillouin zone of the hexagonal lattice.

---

Temperature Dependences

Temperature dependence of energy gap:

Varshni expression:
Eg = Eg(0) - 2.45 x 10-4 x T2/(T + 624)   Eg(300K) = 1.970 eV	(eV)	Guo & Yoshida (1994), Teisseyre al. (1994)   see also   Osamura et al. (1975)
Bose-Einstein expression:
Eg = Eg(0) - 4.39 x 10-2 x 2/(exp(466/T) - 1)	(eV)

0 < T < 300 K, where T is temperature in degrees K.

InN, Wurtzite. The temperature dependences band gap. Broken line represents approximation (see above Varshni expression of Temperature dependence of energy gap ) with Eg (0) = 1.994 eV. Solid line represents approximation (see above Bose-Einstein expression of Temperature dependence of energy gap ) with Eg(0) = 1.994 eV Guo & Yoshida (1994)

---

Intrinsic carrier concentration:

n_i = (N_c·N_v)^1/2exp(-E_g/(2k_BT))

InN, Wurtzite. The temperature dependences of the intrinsic carrier concentration calculated for Eg magnitudes interval 1.9 ÷ 2.05 eV Zubrilov (2001)

Effective density of states in the conduction band N_c

Wurtzite InN

N_c ~= 4.82 x 10¹⁵ · (m_Γ/m₀)^3/2T^3/2 (cm^-3) ~= 1.76 x 10¹⁴ x T^3/2 (cm^-3)

Effective density of states in the valence band N_v

Wurtzite InN

N_v = 10¹⁶ x T^3/2 (cm^-3)

---

Dependence on Hydrostatic Pressure

Wurtzite InN

E_g = E_g(0) + 3.3 x 10^-2P      (eV)
where P is pressure in GPa. Christensen & Gorczyca (1994), Perlin et al. (1997).

---

Band Discontinuities at Heterointerfaces

Wurtzite InN

InN/AlN(0001)		Referens
Conduction band discontinuity	ΔEc = 2.7 eV	Martin et al. (1996), see also Wei & Zunger (1996)
Valence band discontinuity	ΔEv = 1.8 eV
InN/GaN
Conduction band discontinuity	ΔEc = 0.45 eV	Martin et al. (1996)
Valence band discontinuity	ΔEv = 1.05 eV

---

Effective Masses and Density of States:

Electrons

For wurtzite crystal structure the surfaces of equal energy in Γ valley should be ellipsoids, but effective masses in z-direction and perpendicular directions are estimated to be approximately the same:

Wurtzite InN		Remarks	Referens
Effective electron mass me	0.11mo	300 K	Lambrecht & Segall (1993)
	0.12mo	Calculated effective electron mass	Foley & Tansley (1986)
	0.11mo	300 K, plasma edge	Tyagai et al. (1977)

Holes

Wurtzite InN		Remarks	Referens
Effective hole masses (heavy)mh	1.63 mo	300 K	Xu & Ching (1993), Yeo et al. (1998), Pugh et al. (1999)
	0.5 mo	calculated	Foley & Tansley (1986)
Effective hole masses (light) mlp	0.27 mo	300 K	Xu & Ching (1993), Yeo et al. (1998), Pugh et al. (1999)
	0.17 mo	calculated	Foley & Tansley (1986)
Effective hole masses (split-off band) ms	0.65 mo	300 K	Xu & Ching (1993), Yeo et al. (1998), Pugh et al. (1999)
Effective mass of density of state mv   Statistics