Propiedades del nitruro de boro de wurtzita

Estructura cristalina del nitruro de boro de wurtzita en comparación con las estructuras cristalinas del nitruro de boro cúbico y del nitruro de boro hexagonal

Resumen ejecutivo

1. La expansión térmica del nitruro de boro de wurtzita es de aprox. 1,5 menor que el del nitruro de boro hexagonal. Lo que significa una mayor estabilidad de la capa de recubrimiento de nitruro de boro de wurtzita a altas temperaturas (<2000 °C = 3632 °F);
2. Las conductividades térmicas del cristal de wurtzita, paralelas y perpendiculares al eje, son idénticas. Lo que significa una mayor estabilidad de las propiedades térmicas en comparación con otros materiales resistentes al calor, incluidas formas de nitruro de boro como hexagonal y cúbico (blenda de zinc).
3. El nitruro de boro de Wurtzita tiene una banda prohibida más amplia, una mayor conductividad térmica y una mayor polarización espontánea, lo que representa un potencial para la fabricación de dispositivos electrónicos avanzados, por ejemplo. en ingeniería de tensiones y desarrollo de emisores UV profundos.

La investigación

El nitruro de boro es un compuesto refractario de boro y nitrógeno resistente térmica y químicamente con la fórmula química BN. Tiene las siguientes 4 estructuras cristalinas:

- BNw (estructura wurtzita), similar a la lonsdaleita, un raro polimorfo hexagonal de carbono, pero ligeramente más blando que la forma cúbica;
- BNcub (BN cúbico, estructura blenda de zinc), más blando que el diamante, pero su estabilidad térmica y química es superior;
- BNhex (BN hexagonal), el más estable y suave entre los polimorfos de BN, por lo que se utiliza como lubricante y aditivo en productos cosméticos;
- romboédrico.

A continuación se presenta la investigación de las propiedades de las primeras 3 estructuras cristalinas.

BNhex es estable en condiciones normales. BNhex (Hexagonal, también conocido como a-BN) con una estructura similar al grafito se conoce desde hace más de un siglo. Muchas propiedades del BN hexagonal son altamente anisotrópicas y dependen del método de crecimiento. En muchos casos, los diferentes valores de los parámetros físicos de BNhex dados reflejan las diferencias en las propiedades del material del BN hexagonal cultivado mediante diferentes métodos.

BNcub es metaestable en condiciones normales. BNcub (modificación de blenda de zinc, también conocida como cúbica o esfalerita o b-BN) se sintetizó por primera vez en 1957 utilizando una técnica similar a la utilizada para el crecimiento de diamantes. Ahora se encuentran disponibles comercialmente polvos de nitruro de boro cúbico.

La fase BNw es metaestable en todas las condiciones. La BNw (estructura de wurtzita, también conocida como g-BN) se sintetizó por primera vez en 1963. Normalmente, los cristales de BN con simetría de wurtzita son muy pequeños (fracción de micras), muy defectuosos y contienen otras fases.
BNw (nitruro de boro de wurtzita) y BNcub (nitruro de boro cúbico) tienen una longitud de unión, módulos elásticos y resistencia ideal a la tracción y al corte similares, lo que sugiere que los dos demostrarían resistencias a la indentación similares, alrededor de 50 GPa; el diamante es de 70 a 150 GPa.
Tradicionalmente, el nitruro de boro de wurtzita (BNw) se produce transformando nitruro de boro hexagonal (BNhex), la forma cristalina más estable de nitruro de boro. Puede comprar polvo de nitruro de boro de wurtzita, obtenido por compresión por choque (explosión) de nitruro de boro hexagonal, aquí.
El nitruro de boro de wurtzita es un material prometedor de banda prohibida ancha del grupo III-V para dispositivos electrónicos avanzados porque tiene muchas propiedades superiores al nitruro de galio (GaN) y al nitruro de aluminio (AlN), como una banda prohibida más amplia, mayor conductividad térmica, y una mayor polarización espontánea.

Parámetros básicos para la estructura cristalina cúbica/zinc Blende

  RemarksReferens
Crystal structureZinc Blende  
Group of symmetryT2d — F43m  
Number of atoms in 1 cm3  
Debye temperature1700 K  
Density3.4870 g cm-3
3.450 g cm-3		X-ray
Soma et al. (1974)
Rumyantsev et al. (2001)
Lattice constant, a3.6157(10) A X-raySohno et al. (1974)
Melting point, Tm2973° CWentorf (1957)
Bulk modulus400 GPa300 K 
Hardness9.5on the Mohs scale 
Surface hardness4500 kg mm-2300 K 
Second order elactic moduli, c117.120 ·1012 dyn cm-2300 K, interpolated from
measured values of other
III-IV compound		Steigmeier (1963)
Phonon wevenumber vLO1305(1) cm-1300 K, RamanSanjurjo et al. (1983)
Phonon wevenumber vTO1054.7(6) cm-1300 K, RamanSanjurjo et al. (1983)

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

  RemarksReferens
Energy gaps, Eg
6.1÷6.4 eV300 KRumyantsev et al. (2001)
Energy gaps, Egind
G15v-X1c		6.4(5) eV300 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)
Effective electron mass  ml0.752 mocalculated from
band structure data		Huang & Ching (1985)
Effective electron mass
      (longitudinal) ml
      (transversal) mt		0.35mo
0.24mo		1.2mo
0.26mo		Xu & Ching et al. (1991)
Effective hole masses (heavy) mh0.375 mo
0.962 mo		|| [100]
|| [111]		Madelung (1991)
Effective hole masses (heavy) mlp0.150 mo
0.108 mo		|| [100]
|| [111]		Madelung (1991)
Effective hole masses mh
     in the direction G  K		m1 ~=3.16
m2 ~=0.64
m3 ~=0.44		300 K Xu & Ching et al. (1991)
     in the direction G  X0.55mo300 KXu & Ching et al. (1991)
     in the direction G  Lm1 ~=0.36
m2 ~=1.20		300 KXu & Ching et al. (1991)
Electron affinity4.5 eV300 KRumyantsev et al. (2001)


  RemarksReferens
Dielectric constant (static)7.1300 K, infrared reflectivityGielisse et al.(1967)
Dielectric constant (high frequency)4.5
4.46		300 K, infrared reflectivity Gielisse et al.(1967)
Rumyantsev et al. (2001)
Refractive index, n2.17 300 K,
wavelegth 0.589mm		Gielisse et al.(1967)
Optical phonon energy~130 meV300 K
Rumyantsev et al. (2001)
Bulk modulus400 GPa  
Debye temperature1700 K  
Melting point, Tm2973° Calso see Thermal properties.
Phase diagrams.		Wentorf (1957)
Specific heat~0.6 J g-1°C -1  
Thermal conductivity
    experimentally achieved
7.4 W cm-1 °C -1
  
    theoretically estimated~13 W cm-1 °C -1  
Thermal expansion, linear
1.2·10-6 °C -1  


  RemarksReferens
carrier concentration
and mobility:		   
n
µ		1015 cm-3
0.2 cm2/Vs		500 K, polycrystalline material, type of carrier not determinedBam et al.(1976)
n
µ		1014 cm-3
4 cm2/Vs		900 K, mobility increases exponentially with rising temperature between 500 K and  Bam et al.(1976)

Basic Parameters for Hexagonal crystal structure

  RemarksReferens
Crystal structureHexagonal  
Group of symmetryD6c-P63mmc  
Number of atoms in 1 cm3  
Debye temperature400 K  
Density2.18 g cm-3
2.0-2.28 g cm-3		 Madelung (1991)
Rumyantsev et al. (2001)
Lattice constant, a2.5040 A
2.5-2.9 A		297 K
300 K		Lynch et al. (1966)
Rumyantsev et al. (2001)
Lattice constant, c6.6612 A
6.66 A		297 K
300 K		Lynch et al. (1966)
Rumyantsev et al. (2001)
Decomposition temperature, Tdec2600(100) KJanaf Thermochemical
Tables (1965)
Bulk modulus36.5 GPa300 K 
Hardness1.5on the Mohs scale 
Phonon wevenumber, v49 cm-1
E2g, zone center Raman modeHoffman et al. (1966)
770 cm-1
A2u, infrared active mode 
1367 cm-1
E2g, zone center Raman mode 
1383 cm-1
E1u, infrared active mode 

Brillouin zone of the hexagonal lattice.

  RemarksReferens
Energy gaps, Eg5.2(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 eV300 KRumyantsev et al. (2001)
Energy gaps, Eg dir7.1 eV
 Carpenter & Kirby (1982)
Effective electron mass ml
     in the direction M   G
     in the direction M  L		0.26mo
2.21mo		300 KXu & Ching et al. (1991)
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 KXu & Ching et al. (1991)
Electron affinity4.5 eV300 KRumyantsev et al. (2001)


  RemarksReferens
Dielectric constant (static) =5.06
=6.85		|| to c axis
_ to c axis		Geick et al.(1966)
Dielectric constant (high frequency)4.10
4.95		parallel to c axis
perpendicular to c axis
for 300 K;
see also Optical properties.
Dielectric functions		Geick et al.(1966)
  = 2.2;
=4.3		300 KRumyantsev et al. (2001)
Dielectric constant (static)7.1300 K, infrared reflectivityGielisse et al.(1967)
Dielectric constant (high frequency)4.5
4.46		300 K, infrared reflectivity Gielisse et al.(1967)
Rumyantsev et al. (2001)
Refractive index, n1.65
1.65
2.13		BN- film
perpendicular to c axis
parallel to c axis
Takahashi et al.(1981)
Ishii et al. (1983)
Ishii et al. (1983)
Debye temperature400 K  
Bulk modulus36.5 GPa  
Melting point see Termal properties.
Phase diagrams.		 
Decomposition temperature, Tdec2600(100) KJanaf Thermochemical Tables (1965)
Specific heat~0.8 J g-1°C -1  
Thermal conductivity
   parallel to the c axis
    perpendicular to the c axis
=<0.3 W cm-1 °C -1
=<6 W cm-1 °C -1		 Rumyantsev et al. (2001)
Thermal expansion, linear
    parallel to the c axis
    perpendicular to the c axis
38·10-6 °C -1
-2.7·10-6 °C -1		  

Parámetros básicos de Wurtzita, Blende de zinc y estructura cristalina hexagonal a 300 K

Crystal structureWurtziteZinc BlendeHexagonal
Group of symmetryC46v-P63mcT2d-F43mD6c-P63mmc
Density3.4870 g cm-33.450 g cm-32.0-2.28 g cm-3
Bulk modulus400 GPa400 GPa36.5 GPa
Debye temperature1400 K1700 K400 K
Melting point 
see Thermal properties.
Phase diagrams.
Specific heat~0.75 J g-1°C -1~0.6 J g-1°C -1~0.8 J g-1°C -1
Density3.4870 g cm-33.450 g cm-32.0-2.28 g cm-3
Hardness on the Mohs scale 9.51.5
Surface hardness3400 kg mm-24500 kg mm-2 
Dielectric constant (static)=6.8 ; =5.1 7.1=6.85 ; =5.06 
Dielectric constant (high frequency) ~=  = 4.2-4.5 4.46=4.3;  = 2.2
Infrared refractive index2.052.11.8
Lattice constant, a2.55 A 3.615 A 2.5-2.9 A 
Lattice constant, c4.17 A 6.66
Effective electron mass
      (longitudinal) ml
      (transversal) mt		0.35mo
0.24mo		1.2mo
0.26mo
     (in the direction M   G)
     (in the direction M  L)		0.26mo
2.21mo
Effective hole masses mh
     in the direction G  K		0.88mom1 ~=3.16
m2 ~=0.64
m3 ~=0.44		 
     in the direction G  A
     in the direction G  M		1.08mo
1.02mo		  
     in the direction G  X 0.55mo 
     in the direction G  L m1 ~=0.36
m2 ~=1.20		 
     in the direction K   G
     in the direction M   G
     in the direction M  L		  0.47mo
0.50mo
1.33mo
Effective hole massesof dencity of states mv~=1.0mo  
Electron affinity4.5 eV4.5 eV4.5 eV
Thermal conductivity
    experimentally achieved
    theoretically estimated
 7.4 W cm-1 °C -1
~13 W cm-1 °C -1		 
    parallel to the c axis
    perpendicular to the c axis
  =<0.3 W cm-1 °C -1
=<6 W cm-1 °C -1
Thermal expansion, linear
 1.2·10-6 °C -1 
Thermal expansion, linear
    parallel to the c axis
    perpendicular to the c axis
2.7·10-6 °C -1
2.3·10-6 °C -1		 38·10-6 °C -1
-2.7·10-6 °C -1
Optical phonon energy~130 meV~130 meV


Crystal structureWurtziteZinc BlendeHexagonal
Energy gaps, Eg4.5-5.5 eV6.1...6.4 eV4.0...5.8 eV
Conduction band   
Energy separation EG 8.5 eV8.5-10 eV9 eV
Energy separation EM6.6 eV  
Energy separation EL >12 eV 
Energy separation EA  10 eV
Effective conduction banddensity of states1.5x1019 cm-32.1x1019 cm-3 
Effective valence banddensity of states2.6x1019 cm-32.6x1019 cm-3 
Breakdown field (2...6)x 106 V cm-1(1...3)x 106 V cm-1
Mobility electrons =<200 cm2 V-1 s-1 
Mobility holes =<500 cm2 V-1 s-1 
Diffusion coefficient electrons =<5 cm2 s-1 
Diffusion coefficient holes =<12 cm2 s-1 
Effective valence banddensity of states2.6x1019 cm-32.6x1019 cm-3 


Propiedades termales

Parametros basicos

Zinc Blende crystal structure
  RemarksReferens
Bulk modulus400 GPa  
Debye temperature1700 K  
Melting point, Tm2973° Calso see Phase diagrams for BN.Wentorf (1957)
Specific heat~0.6 J g-1°C -1  
Thermal conductivity
    experimentally achieved
    theoretically estimated		7.4 W cm-1 °C -1
~13 W cm-1 °C -1		  
Thermal expansion, linear1.2·10-6 °C -1  

Propiedades térmicas de la estructura cristalina hexagonal.

  RemarksReferens
Debye temperature400 K  
Bulk modulus36.5 GPa  
Melting point see Phase diagrams for BN.Solozhenko (1994) and Solozhenko et al.(1998)
Decomposition temperature, Tdec2600(100) KJanaf Thermochemical Tables (1965)
Specific heat~0.8 J g-1°C -1  
Thermal conductivity     parallel to the c axis
    perpendicular to the c axis		=<0.3 W cm-1 °C -1
=<6 W cm-1 °C -1		 Rumyantsev et al. (2001)
Thermal expansion, linear
    parallel to the c axis
    perpendicular to the c axis		38·10-6 °C -1
-2.7·10-6 °C -1		  

Wurtzite, Zinc Blende & Hexagonal crystal structure at 300 K

Crystal structureWurtziteZinc BlendeHexagonal
Bulk modulus400 GPa400 GPa36.5 GPa
Melting point 
Specific heat~0.75 J g-1°C -1~0.6 J g-1°C -1~0.8 J g-1°C -1
Thermal conductivity
    experimentally achieved
    theoretically estimated		 7.4 W cm-1 °C -1
~13 W cm-1 °C -1		 
    parallel to the c axis
    perpendicular to the c axis		  <0.3 W cm-1 °C -1
<6 W cm-1 °C -1
Thermal expansion, linear 1.2·10-6 °C -1 
Thermal expansion, linear
    parallel to the c axis
    perpendicular to the c axis		2.7·10-6 °C -1
2.3·10-6 °C -1		 38·10-6 °C -1
-2.7·10-6 °C -1

Thermal conductivity

BN, Zinc Blende. Temperature dependence of thermal conductivity for different samples.
Slack (1973), Makedon et al. (1972)
BN, Zinc Blende. Temperature dependences of the thermal conductivity of undoped and Se doped before and after annealing at 900-1000 K.
1- undoped Zinc blende BN;
2-4 - Se doped Zinc blende BN
Selenium concentration:
  2 -- 2.4 x 1018 cm-3, before annealing;
  3 -- 2.4 x 1018 cm-3, annealed;
  4 -- 1019 cm-3, annealed
Shipilo et al. (1986)


The highest thermal conductivity achieved for single-crystal zinc blende BN is 7.4 W cm-1 K-1 [Novikov et al. (1983)].

BN, Hexagonal. Thermal conductivity perpendicular to the c axis versus temperature of three samples deposited at different temperatures.
Duclaux et al. (1992)
BN, Hexagonal. Thermal conductivity perpendicular to the c axis versus temperature of highly oriented samples.
Sichel et al. (1976)

BN, Hexagonal. Thermal conductivity perpendicular to the c axis as a function of temperature for two samples.
Simpson & Stuckes (1971)

BN, Hexagonal. Thermal conductivity parallel to the c axis as a function of temperature for two samples.
Simpson & Stuckes (1971)

Temperature dependence of the specific heat

Wurtzite BN . Temperature dependence of the specific heat.

BN, Wurtzite. Temperature dependence of the specific heat.
Gorbunov et al. (1988); see also Sirota & Kofman (1976) and Inaba & Yoshiasa (1997).
The abnormality with extremum at 21 K is caused by the presence of the ordered point defects system in the lattice for two samples. Solozhenko (1994)

At 420 K < T < 980 K, the specific heat Cp of Wurtzite BN can be approximated as
Cp= 48.35x (T2 ·(T2- 8.37xT+ 68306)-1)2 (J/Kmol) Solozhenko (1994).

Zinc Blende BN . Temperature dependence of the specific heat.

BN, Zinc Blende. Temperature dependence of the specific heat at low temperatures (single crystal).
Solozhenko et al. (1987); see also Sirota & Kofman (1976).

BN, Zinc Blende. Temperature dependence of high temperature specific heat according to different authors.
Lyusternik and Solozhenko (1992).

At 300 < T < 1100 K, the specific heat Cp of Zinc Blende BN can be approximated as
Cp= 48.4x (T2 · (T2- 9.71xT+ 60590)-1)2 (J/Kmol) Lyusternik and Solozhenko (1992).

Hexagonal BN . Temperature dependence of the specific heat.

BN, Hexagonal. Temperature dependence of specific heat.
Gorbunov et al. (1988); see also Sichel et al. (1976)

At 1300 < T < 2200 K, the specific heat Cp of can be approximated as
Cp= 52.48 - 9.42·10-4 x T - 64877 x T-2 (J/Kmol) Solozhenko (1994).

Linear thermal expansion coefficient.

BN, Wurtzite. Linear thermal expansion coefficient of parallel (curve 1) and perpendicular (curve 2) to c axis.
Kolupayeva et al. (1986).
BN, Hexagonal. Linear thermal expansion coefficient.
Slack & Bartram (1975).
BN, Zinc Blende. Linear thermal expansion coefficient
Top curve, in a direction parallel to the c axis; bottom curve, in a direction perpendicular to the c axis.
Yates et al. (1975). See also Belenkii et al. (1985).

Thermal expansion at different pressure

BN, Hexagonal. Thermal expansion at different pressure:
circles, 1.6 GPa; squares, 5.0 GPa; triangles, 7.1 GPa. Solid and open symbols are used for the directions parallel and perpendicular to c axis, respectively.
Solozhenko & Peun (1997).

Phase diagrams

Phase diagrams for BN.
1, Bundy-Wentorf's diagram; 2, Equilibrium diagram; , h-BN <=> c-BN boundary line.
Solozhenko (1994)
Equilibrium phase diagram of BN.
1 is hexagonal-zinc blende BN liquid triple point; 2 is hexagonal-wurtzite BN liquid metastable triple point;
a) line of hexagonal-wurtzite BN metastable equilibrium; b) metastable beam of hexagonal BN melting curve; c) line of wurtzite BN metastable melting .
Solozhenko et al.(1998)

Band structure and carrier concentration


All band structure calculations lead to an indirect gap structure, the conduction band minima being situated at X.

Basic Parameters for Zinc Blende crystal structure

  RemarksReferens
Energy gaps, Eg
6.1...6.4 eV300 KRumyantsev et al. (2001)
Energy gaps, Eg ind
G15v-X1c		6.4(5) eV300 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 affinity4.5 eV300 KRumyantsev et al. (2001)
Conduction band   
Energy separation EG 8.5-10 eV300 KRumyantsev et al. (2001)
Energy separation EL>12 eV300 K 
Effective conduction banddensity of states2.1·1019 cm-3300 K 
Effective valence banddensity of states2.6·1019 cm-3300 K 

Basic Parameters for Hexagonal crystal structure

  RemarksReferens
Energy gaps, Eg5.2(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 eV300 KRumyantsev et al. (2001)
Energy gaps, Eg dir7.1 eV
 Carpenter & Kirby (1982)
Electron affinity4.5 eV300 KRumyantsev et al. (2001)
  RemarksReferens
Conduction band   
Energy separation EG 9 eV300 KRumyantsev et al. (2001)
Energy separation EM>12 eV300 K 
Energy separation EL10 eV300 K 
Energy separation EA10 eV300 K 
Effective conduction banddensity of states2.1x1019 cm-3300 K 
Effective valence banddensity of states2.1x1019 cm-3300 K 

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

Crystal structureWurtziteZinc BlendeHexagonal
Energy gaps, Eg4.5-5.5 eV6.1...6.4 eV4.0...5.8 eV
Conduction band   
Energy separation EG 8.5 eV8.5-10 eV9 eV
Energy separation EM6.6 eV  
Energy separation EL >12 eV 
Energy separation EA  10 eV
Effective conduction banddensity of states1.5x1019 cm-32.1x1019 cm-3 
Effective valence banddensity of states2.6x1019 cm-32.6x1019 cm-3 

 

Band structure for Zinc Blende BN

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 ).
WurtziteNc ~= 4.82 x 1015 · (mcd/m0)3/2· T3/2 (cm-3) ~= 2.8 x 1015 x T3/2(cm-3)
Zinc blendeNc ~= 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 BNdEg/dP = 3.0 meV/GPaKim et al. (1996)
wurtzite BNdEg/dP = 3.8 meV/GPaKim et al. (1996)

Effective Masses and Density of States:

Electrons

Effective Masses for Zinc Blende BN
The surface of equel energy are ellipsoids.
  RemarksReferens
Effective electron mass  ml0.752 mocalculated 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
  RemarksReferens
Effective electron mass ml
     in the direction M G
     in the direction M L		0.26mo
2.21mo		300 KXu & Ching et al. (1991)
Effective Masses for Wurtzite BN
The surface of equel energy are ellipsoids.
  RemarksReferens
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 RemarksReferens
Effective hole masses (heavy) mh0.375 mo
0.962 mo		|| [110]
|| [111]		Madelung (1991)
Effective hole masses (heavy) mlp0.150 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 X0.55mo300 KXu & Ching et al. (1991)
     in the direction G Lm1 ~= 0.36 mo
m2 ~= 1.20 mo		300 KXu & Ching et al. (1991)

Effective Masses for Hexagonal crystal BN  RemarksReferens
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 KXu & Ching et al. (1991)

Effective Masses for Wurtzite BN  RemarksReferens
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 KXu & 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 donors0.7...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)

Optical properties

Zinc Blende crystal structure
  RemarksReferens
Dielectric constant (static)7.1300 K, infrared reflectivityGielisse et al.(1967)
Dielectric constant (high frequency)4.5
4.46		300 K, infrared reflectivity Gielisse et al.(1967)
Rumyantsev et al. (2001)
Refractive index, n2.17300 K, wavelegth 0.589mmGielisse et al.(1967)
Infrared refractive index~=2.1300 K, InfraredRumyantsev et al. (2001)
Optical phonon energy~130 meV300 K
Rumyantsev et al. (2001)

Hexagonal crystal structure
  RemarksReferens
Dielectric constant (static) =5.06
=6.85		|| to c axis
 perp. to c axis		Geick et al.(1966)
Dielectric constant (high frequency)4.10
4.95		parallel to c axis
perpendicular to c axis
for 300 K;
see also Dielectric functions		Geick et al.(1966)
  = 2.2;
=4.3		300 KRumyantsev et al. (2001)
Dielectric constant (static)7.1300 K, infrared reflectivityGielisse et al.(1967)
Dielectric constant (high frequency)4.5
4.46		300 K, infrared reflectivity Gielisse et al.(1967)
Rumyantsev et al. (2001)
Refractive index, n1.65
1.65
2.13		BN- film
perpendicular to c axis
parallel to c axis
Takahashi et al.(1981)
Ishii et al. (1983)
Ishii et al. (1983)
Infrared refractive index~=1.8300 K, InfraredRumyantsev et al. (2001)
 BN, hexagonal. Ordinary and extraordinary dielectric functions e2 vs. wavelength and photon energy in the range 13---30eV (b).
Mamy et al. (1983)

Wurtzite, Zinc Blende & Hexagonal crystal structure at 300 K
Crystal structureWurtziteZinc BlendeHexagonal
Infrared refractive index~=2.05~=2.1~=1.8

Optical properties of Wurtzite, Zinc Blende & Hexagonal crystal

BN, hexagonal. Ordinary and extraordinary dielectric functions e2 vs. wavelength and photon energy in the range 5--9eV
Mamy et al. (1981)
BN, hexagonal. Ordinary and extraordinary dielectric functions e2 vs. wavelength and photon energy in the range 13--30eV
Mamy et al. (1981)
BN, zinc blende. Refractive index n versus photon energy
Miyata et al. (1989)
BN. Refractive index n versus wavenumber.
1 -- Zinc blende
2 -- Hexagonal BN.
Stenzel et al. (1996)
BN, Wurtzite. Reflectance R as a function of photon energy for two samples.
1, 500oC annealed;
2, 100o C annealed (nanoscale powder compacted into dense solid under high pressure).
Yixi et al. (1994)
BN, Zinc Blende. Reflectance R as a function of photon energy.
Miyata et al. (1989)
BN, Hexagonal. Reflectance R as a function of wavelength .
Zunger et al. (1976)
BN, Hexagonal. Reflectance R as a function of wavelength .
Hoffman et al. (1984)
BN, Wurtzite. The absorption coefficient as a function of photon energy for two samples.
1, 500oC annealed;
2, 100oC annealed (nanoscale powder compacted into dense solid under high pressure).
Yixi et al. (1994)
BN, Zinc Blende. The absorption coefficient versus photon energy.
Miyata et al. (1989)
BN, Zinc Blende. The absorption coefficient versus photon energy at different hydrostatic pressures. The energies shown by arrows are defined as indirect band gaps.
Onodera et al. (1993)
BN, Zinc Blende. The absorption coefficient versus wavenumber in the infrared.
Chrenko et al. (1974)
BN, Hexagonal. The absorption coefficient versus wavelength. 300K.
Zunger et al. (1976)
BN, Hexagonal. The absorption coefficient versus wavelength at 4.2 K and 600 K.
Zunger et al. (1976)



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