InN-Indium Nitride

Band structure and carrier concentration

Wurtzite(hexagonal) crystal  structure   Remarks
Energy gaps,    Eg 1.970 eV  300 K
    1.9-2.05 eV 300 K 
    2.05 (1) eV  300K; absorption edge
    2.11   eV  78 K
    1.89     eV RT
Conduction band
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 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

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

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.
	Brillouin zone for wurtzite crystal.
	Rectangular coordinates for hexagonal crystal

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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)

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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)

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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).

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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

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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═	1.65 mo	300 K	Xu & Ching (1993), Yeo et al. (1998), Pugh et al. (1999)

Donors and Acceptors

Wurtzite InN

Ionization energies of Shallow Donors
Native defect level VN	<40-50 eV	Tansley & Egan (1992); Jenkins & Dow (1989)

InN, Wurtzite. Level positions in the forbidden gap of InN. I - experimental data that fall into five groups A-E. II - the calculated energies of point defects Tansley & Egan (1992)

Jorge L. Polentino U.
EES

http://www.ioffe.ru/SVA/NSM/Semicond/InN/bandstr.html

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