AlN - Inllium Nitride

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

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 Γ1' state (see Band structure) lies slightly higher than the Γ6 state (transition E||c (Γ1'v-Γlc) at lower energy than transition E c (Γ6v - Γlc), 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  

 

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.


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)

Effective density of states in the conduction band: Nc

Wurtzite AlN
Nc ~= 4.82 x 1015 · (mΓ/mo)3/2 T3/2 (cm-3) ~= 1.2 x 1015 x T3/2 (cm-3)

Effective density of states in the valence band: Nv

Wurtzite AlN
Nv = 9.4 x 1016 x T3/2 (cm-3)

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 O5h; lattice parameter 4.04 A) takes place at the pressure of 17 GPa (~=173 kbar) [ Gorczyca & Christensen (1993)]

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)

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:   7.26mo 300 K  

Donors and Acceptors

Wurtzite AlN
Native donors:

Si, Mg (ionization energy ΔE ~= 1 eV)

Donors:

C, Ge, Se

Acceptors:

C, Hg
Ionization energies (Et-Ec)
    
d1 is the donor level of N vacancies (VN) 0.17 eV Tansley & Egan (1992);
Chu et al. (1967);
Francis and Worell (1976);
Jenkins and Dow (1989);
Mohammad et al. (1995);
Boguslawski et al. (1996);
Gorczyca et al. (1997)
d2 is the donor level of N vacancies (VN) 0.5 eV  
d3 is the donor level of N vacancies (VN)
  		0.8-1.0 eV
  		 
d4 is the donor levels of C in Al sites (CAl) 0.2 eV  
d5 is the donor levels of N in Al sites (NAl) 1.4-1.85 eV  
d6 is the donor levels of Al in N sites (AlN) 3.4-4.5 eV  

Ionization energies (Ev-Et)
    
a1 is the acceptor levels of Al vacancies (VAl) 0.5 eV
 Tansley & Egan (1992);
Chu et al. (1967);
Francis and Worell (1976);
Jenkins and Dow (1989);
Mohammad et al. (1995);
Boguslawski et al. (1996);
Gorczyca et al. (1997)
a2 is the acceptor levels of C in N sites (CN) 0.4 eV
  
a3 is the acceptor levels of Zn in Al sites (ZnAl) 0.2 eV
  
a4 is the acceptor levels of Mg in Al sites (MgAl) 0.1 eV
  
AlN, Wurtzite. Level positions in the forbidden gap of AlN.
Tansley & Egan (1992)