BN - Boron Nitride

Band structure and carrier concentration

Basic Parameters
    for Zinc Blende crystal structure
    for Hexagonal crystal structure
    for Wurtzite crystal structure
Band structure
    for Zinc Blende crystal structure
    for Hexagonal crystal structure
    for Wurtzite crystal structure
Effective Density of States in the Conduction and Valence Band
Dependence on Hydrostatic Pressure
Effective Masses and Density of States
Donors and Acceptors

Basic Parameters for Zinc Blende crystal structure

    Remarks Referens
Energy gaps, Eg
 6.1...6.4 eV 300 K Rumyantsev et al. (2001)
Energy gaps, Eg ind
G15v-X1c		 6.4(5) eV 300 K, UV absorption;
other data in range 6...8eV		 Chrenko (1974)
  6.99 eV
8.6 eV		 calculated, Band structure
calculated, Band structure		 Huang & Ching (1985)
Prasad & Dubey (1984)
Energy gaps, Eg dir
G15v-G1c		 14.5 eV
10.86 eV
9.94 eV		 300 K, reflecsivity
calculated, Band structure
calculated, Band structure 		Philipp & Taft (1962)
Prasad & Dubey (1984)
Huang & Ching (1985)
Electron affinity 4.5 eV 300 K Rumyantsev et al. (2001)
Conduction band      
Energy separation EG 8.5-10 eV 300 K Rumyantsev et al. (2001)
Energy separation EL >12 eV 300 K  
Effective conduction banddensity of states 2.1·1019 cm-3 300 K  
Effective valence banddensity of states 2.6·1019 cm-3 300 K  

Basic Parameters for Hexagonal crystal structure

    Remarks Referens
Energy gaps, Eg 5.2(2) eV
3.2...5.8 eV		 300 K, reflectance
range of experimental data
temperature dependence of resistivity 		Hoffmann et al. (1984)
  4.0...5.8 eV 300 K Rumyantsev et al. (2001)
Energy gaps, Eg dir 7.1 eV
   Carpenter & Kirby (1982)
Electron affinity 4.5 eV 300 K Rumyantsev et al. (2001)
    Remarks Referens
Conduction band      
Energy separation EG 9 eV 300 K Rumyantsev et al. (2001)
Energy separation EM >12 eV 300 K  
Energy separation EL 10 eV 300 K  
Energy separation EA 10 eV 300 K  
Effective conduction banddensity of states 2.1x1019 cm-3 300 K  
Effective valence banddensity of states 2.1x1019 cm-3 300 K  

Basic Parameters for Wurtzite, Zinc Blende & Hexagonal crystal structure at 300 K

Crystal structure Wurtzite Zinc Blende Hexagonal
Energy gaps, Eg 4.5-5.5 eV 6.1...6.4 eV 4.0...5.8 eV
Conduction band      
Energy separation EG 8.5 eV 8.5-10 eV 9 eV
Energy separation EM 6.6 eV    
Energy separation EL   >12 eV  
Energy separation EA     10 eV
Effective conduction banddensity of states 1.5x1019 cm-3 2.1x1019 cm-3  
Effective valence banddensity of states 2.6x1019 cm-3 2.6x1019 cm-3  

 

Band structure for Zinc Blende BN

All band structure calculations lead to an indirect gap structure, the conduction band minima being situated at X.
BN, cubic. Band structure calculated with the LCAO-method, including ionicity and fitting of APW results at high symmetry points.
Prasad & Dubey (1984)
BN, cubic. Band structure calculated with the LCAO-method, ab intitio calculation.
Hoffmann et al. (1984)
BN, zinc blende(cubic). Band structure. Important minima of the conduction band and maxima of the valence band.
300K; Eg =6.1-6.4 eV; Ep= 8.5-10eV; EL > 12 eV
For details see Rodriguez-Hernandez et al. (1995) and Ferhatet al. (1998)

Brillouin zone of the face centered cubic lattice, the Bravais lattice of the diamond and zincblende structures.

Band structure for Hexagonal BN

BN, hexagonal (graphite-like). Band structure. Important minima of the conduction band and maxima of the valence band. The energy gaps between the top of the valence band and H, M, K, and L valleys of the conduction band are of the same order of magnitude. The energies of the valence band maxima are very close in the points K, H, and M of Brillouin zone.
300K; Eg =4.0-5.8 eV; EA= 10eV; EG = 9 eV
For details see Yong-Nian Xu and Ching (1991), Zunger al. (1976) and Taylor and Clarke (1997)
BN, Hexagonal(graphite-like). Band structure calculated with the tight binding method. Hoffmann et al. (1984)
A band structure calculation [Catellani et al. (1984)] taking into account interlayer interaction proposes an indirect gap of 3.9 eV between a valence band maximum at H and a conduction band minimum at M as well as additional interlayer conduction bands with minimum at the zone center
Brillouin zone of the hexagonal lattice.

Band structure for Wurtzite BN

BN, Wurtzite. Band structure. Important minima of the conduction band and maxima of the valence band.
300K; Eg =4.5-5.5 eV; EM= 6.6eV; EG = 8.5 eV
For details see Christersen and Gorczyca (1994) and Yong-Nian Xu and Ching(1991).


Effective Density of States in the Conduction Band, Nc

Only the calculated data available for the values of electron effective masses for all types of BN crystals (see Effective Masses ).
Wurtzite Nc ~= 4.82 x 1015 · (mcd/m0)3/2· T3/2 (cm-3) ~= 2.8 x 1015 x T3/2(cm-3)
Zinc blende Nc ~= 4.82 x 1015 · (mcd/m0)3/2· T3/2 (cm-3) ~= 4.1 x 1015 x T3/2(cm-3)

Effective Density of States in the Valence Band, Nv

Only the calculated data available for the values of hole effective masses for all types of BN crystals. These calculations are fairly inaccurate. As a crude estimate, the effective density of states in the valence band, Nv:
Nv ~= 5.0 x 1015 · T3/2 (cm-3)
could be used for all crystal modifications of BN (see Effective Masses ).

Dependence on Hydrostatic Pressure

Pressure dependence of the energy gap of zinc blende BN.
(Onodera et al., 1993)

  Referens
zinc blende BN dEg/dP = 3.0 meV/GPa Kim et al. (1996)
wurtzite BN dEg/dP = 3.8 meV/GPa Kim et al. (1996)

Effective Masses and Density of States:

Electrons

Effective Masses for Zinc Blende BN
The surface of equel energy are ellipsoids.
    Remarks Referens
Effective electron mass  ml 0.752 mo calculated from
band structure data		 Huang & Ching (1985)
Effective electron mass
      (longitudinal) ml
      (transversal) mt 		1.2mo
0.26mo		   Xu & Ching et al. (1991)
Effective mass of density of states in one valley of conduction band [Xu & Ching et al. (1991)]
mc=(ml·mt2)1/3=0.43mo
Effective mass of conductivity [Xu & Ching et al. (1991)] : mcc=3(1/ml+ 2/mt)-1 ~= 0.35mo
Effective mass of density of states for all valleys of conduction band [Xu & Ching et al. (1991)]: mcd ~= 0.9mo
Effective Masses for Hexagonal crystal BN
    Remarks Referens
Effective electron mass ml
     in the direction M G
     in the direction M L		 0.26mo
2.21mo		 300 K Xu & Ching et al. (1991)
Effective Masses for Wurtzite BN
The surface of equel energy are ellipsoids.
    Remarks Referens
Effective electron mass
      (longitudinal) ml
      (transversal) mt 		0.35mo
0.24mo		   Xu & Ching et al. (1991)
Effective mass of density of states in one valley of conduction band [Xu & Ching et al. (1991)]
mc=(ml·mt2)1/3=0.27mo
Effective mass of conductivity [Xu & Ching et al. (1991)] : mcc~=3(1/ml+ 2/mt)-1 ~= 0.27mo
Effective mass of density of states for all valleys of conduction band [Xu & Ching et al. (1991)]: mcd~=0.7mo

Holes

Effective Masses for Zinc Blende BN   Remarks Referens
Effective hole masses (heavy) mh 0.375 mo
0.962 mo 		|| [110]
|| [111]		 Madelung (1991)
Effective hole masses (heavy) mlp 0.150 mo
0.108 mo		 || [110]
|| [111] 		Madelung (1991)
Effective hole masses mh
     in the direction G K		 m1 ~= 3.16 mo
m2 ~= 0.64 mo
m3 ~= 0.44 mo		 300 K Xu & Ching et al. (1991)
     in the direction G X 0.55mo 300 K Xu & Ching et al. (1991)
     in the direction G L m1 ~= 0.36 mo
m2 ~= 1.20 mo 		300 K Xu & Ching et al. (1991)

Effective Masses for Hexagonal crystal BN   Remarks Referens
Effective hole masses mh
     in the direction K G
     in the direction M G
     in the direction M L 		0.47mo
0.50mo
1.33mo 		300 K Xu & Ching et al. (1991)

Effective Masses for Wurtzite BN   Remarks Referens
Effective hole masses mh
     in the direction G K
     in the direction G A
     in the direction G M 		0.88mo
1.08mo
1.02mo 		300 K Xu & Ching et al. (1991)

Donors and Acceptors

Zinc Blende (cubic) BN:

Ionization energies of donors   Si 
  C
  S
 0.24 eV
0.28-0.41eV
0.05 eV
 Wentorf (1957), Mishima et al. (1987), Taniguchi et al. (1993), Gubanov et al. (1997)
Ionization energies of acceptor   Be
 0.19 eV
 Wentorf (1957), Mishima et al. (1987), Taniguchi et al. (1993), Gubanov et al. (1997)

Hexagonal(graphite-like) BN:

Ionization energies of donors 0.7...1.5 eV
 Wentorf (1957), Mishima et al. (1987), Taniguchi et al. (1993), Gubanov et al. (1997)
Ionization energies of acceptor =< 1.5 eV
 Wentorf (1957), Mishima et al. (1987), Taniguchi et al. (1993), Gubanov et al. (1997)

Data on doping with Mg see Lu et al. (1996)