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Characteristics and Properties

NSM Archive - Aluminium Nitride (AlN) - Band structure

Band structure and carrier concentration

Basic Parameters
Band structure
Energies of symmetry points
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

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Basic Parameters

Wurtzite(hexagonal) crystal structure		Remarks	Referens
Energy gaps, Eg	6.026 eV	300 K	Guo & Yoshida (1994) Teisseyre al. (1994)
	6.2 eV	300 K, absorption (excitonic contribution near direct edge)	Yamashita et al. (1979)
	6.23 eV	77 K, absorption (excitonic contribution near direct edge)	Yamashita et al. (1979)
	6.28 eV	300 K, from excitonic edge assuming exciton binding energy of 75meV	Roskovcova & Pastrnak (1980)

From the dichroism of the absorption edge follows that the Γ_1' state (see Band structure) lies slightly higher than the Γ₆ state (transition E||c (Γ_1'v-Γ_lc) at lower energy than transition E c (Γ_6v - Γ_lc), both states being split by crystal field interaction . Yamashita et al. (1979)

Conduction band		Remarks	Referens
Energy separation between  Γ valley and M-L valleys	~0.7 eV	300 K	Goldberg (2001)
Energy separation between  M-L valleys degeneracy	6 eV	300 K
Energy separation between Γ valley and K valleys	~1.0 eV	300 K
Energy separation between K valley degeneracy	2 eV	300 K
Valence band
Energy of spin-orbital splitting Eso	0.019 eV	300 K	Goldberg (2001)
Effective conduction band density of states	6.3 x 1018 cm-3	300 K
Effective valence band density of states	4.8 x 1020 cm-3	300 K

 

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Band structure

AlN is a semiconductor with a large direct gap. Since it crystallizes in the wurtzite lattice the band structure differs from that of the most other III-V compounds.

	AlN, Wurtzite. Band structure. Important minima of the conduction band and maxima of the valence band.   300K;     Eg=6.2 eV;     EM-L= 6.9 eV;     Eso = 0.019 eV;     Ek= 7.2 eV For details see Christensen & Gorczyca (1994)
	AlN, Wurtzite. Band structure calculated with an a semi-empirical tight binding method. Kobayashi et al. (1983)

Energies of symmetry points of the band structure (relative to the top of the valence band)

Energies of symmetry points		Remarks	Referens
E (Γ1v)	-18.40 (-14.43) eV	calculated , see Band structure. Data in brackets Huang & Ching (1985)	zKobayashi et al. (1983)
E (Γ3v)	-7.10 (-4.68) eV
E (Γ5v)	-1.22(-0.60) eV
E (Γ6v , Γ1'v)	0.00 eV
E (Γ1c)	6.2 (6.25) eV
E (Γ3c)	8.92 (9.38) eV
E (Γ6c , Γ1'c)	13.0 eV
E (Γ1'3'v)	-7.52 (-4.26) eV
E (Γ24v)	-1.97 (-1.06) eV
E (Γ13v)	-1.87 (-1.03) eV
E (Γ13c)	9.99 (9.40) eV
E (Γ1'3'c)	13.53 eV

Brillouin zone of the hexagonal lattice.

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Temperature Dependences

Temperature dependence of energy gap:

Eg = Eg(0) - 1.799 x 10-3 x T2/(T + 1462)	(eV)	Guo & Yoshida (1994) Teisseyre al. (1994)
Eg (300 K) = 6.026 eV

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

AlN, Wurtzite. Optical band gap versus temperature. Guo & Yoshida (1994)

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Effective density of states in the conduction band: N_c

Wurtzite AlN

N_c ~= 4.82 x 10¹⁵ · (m_Γ/m_o)^3/2 T^3/2 (cm^-3) ~= 1.2 x 10¹⁵ x T^3/2 (cm^-3)

Effective density of states in the valence band: N_v

Wurtzite AlN

N_v = 9.4 x 10¹⁶ x T^3/2 (cm^-3)

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Dependence on Hydrostatic Pressure

Wurtzite AlN

Hydrostatic Pressure versus the energy gap

dEg/dP = 3.6 x 10-3         (eV kbar-1)

Gorczyca & Christensen (1993)

Conduction band first- and second-order pressure derivatives:

Eg = Eg(0) + 3.6 x 10-3 P - 1.7 x  10-6 P2      (eV)	Van Camp et al. (1993)
EM = EM(0) + 7.5 x 10-4 P + 1.0 x  10-6 P2      (eV)
EL = EL(0) + 8.0 x 10-4 P + 6.9 x  10-7 P2      (eV)
Ek = Ek(0) + 6.3 x 10-4 P + 1.7 x  10-6 P2      (eV)

where P is pressure in kbar.
Phase transition from the wurtzite phase to the rocksalt structure (space group O⁵_h; lattice parameter 4.04 A) takes place at the pressure of 17 GPa (~=173 kbar) [ Gorczyca & Christensen (1993)]

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Band Discontinuities at Heterointerfaces

Wurtzite AlN

InN/AlN(0001)		Referens
Conduction band discontinuity	ΔEc = 2.7 eV	Martin et al. (1996)
Valence band discontinuity	ΔEv = 1.8 eV
GaN/AlN (0001)
Conduction band discontinuity	ΔEc = 2.0 eV	Martin et al. (1996)
Valence band discontinuity	ΔEv = 0.7 eV
SiC/AlN (0001)
Valence band discontinuity	ΔEv = 1.4 eV	King et al. (1996)

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Effective Masses and Density of States:

Electrons

For wurtzite crystal structure theoretical estimations of the electron effective mass anisotropy in Γ valley:

Wurtzite AlN		Remarks	Referens
Effective electron mass of density of states for Γ valley me	0.40 mo	300 K, Teoretical estimations of the electron effective mass anisotropy	Xu and Ching (1993)

Holes

Wurtzite AlN		Remarks	Referens
Effective hole masses (heavy)     for kz direction mhz     for kx direction mhx	3.53 mo 10.42 mo	300 K	Suzuki & Uenoyama (1996)
Effective hole masses (light)     for kz direction mlz     for kx direction mlx	3.53 mo 0.24 mo	300 K
Effective hole masses (split-off band)     for kz direction msoz     for kx direction msox	0.25 mo 3.81 mo	300 K
Effective mass of density of state mv:   Statistics