Electronic Energy Levels in Group-III Nitrides
D W Palmer, 2011
This article is a detailed review of the published information concerning the electronic energy levels created
within the valence-band to conduction-band energy gap of crystalline boron nitride, aluminum nitride, gallium nitride
and indium nitride by the presence of lattice defects and impurities. Theoretical and experimental data for the
zinc-blende and wurtzite structures are considered in detail, and certainties and uncertainties concerning the energy
levels and their tlikely impurity or defect identities are assessed.
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PROPERTY / MATERIAL . |
Cubic (Beta) AlN |
Hexagonal (Alpha) AlN |
Structure | Zinc Blende | Wurzite |
|
Space Group | F bar4 3m |
C46v ( = P63mc) |
Stability | Meta-stable | Stable |
Lattice Parameter(s) at 300K |
0.436 nm |
a0=0.3111 nm c0 = 0.4978 nm |
Density at 300K | 3.285 g.cm-3 |
3.255 g.cm-3 |
Elastic Moduli at 300 K | . . . | . . . |
Linear Therm. Expansion Coeff. at 300 K |
. . . |
Along a0: 5.3x10-6 K-1
Along c0: 4.2x10-6 K-1 |
Calculated Spontaneous Polarisations |
Not Applicable |
0.081 C m-2
Bernardini et al 1997 Bernardini & Fiorentini 1999
|
Calculated Piezo-electric Coefficients |
Not Applicable |
e33 = + 1.46 C m-2
e31 = 0.60 C m-2
Bernardini et al 1997 Bernardini & Fiorentini 1999
|
Phonon Energies |
. . . |
. . . |
Thermal Conductivity near 300K |
. . . |
Units: Wcm-1K-1
Tansley et al 1997b
3.0 to 3.3 for thick, free-standing AlN
Florescu et al, 2001
|
Melting Point |
. . . |
. . .. K |
Dielectric Constant at Lowish Frequency |
. . . |
Mean = 9.14 |
Refractive Index |
. . . |
2.15±0.05 at 3eV
Tansley et al 1997b
|
Nature of Energy Gap Eg |
Direct |
Direct |
Energy Gap Eg at 300 K |
. . . eV |
6.2 eV
Yoshida et al 1982 Vurgaftman et al (2001) |
Energy Gap Eg at 5 K |
. . . |
6.28 eV
Vurgaftman et al (2001) |
Intrinsic Carrier Conc. at 300 K |
. . . |
. . . |
Ionisation Energy of . . . Donor |
. . . . |
. . . |
Electron Mobility at 300 K for n= . . |
. . . |
. . . |
Electron Mobility at 77 K for n= . . |
. . . . |
. . . |
Ionisation Energy of . . . Acceptor |
. . . |
. . . |
Hole Mobility at 300 K for p= . . |
. . . . |
. . . . |
Hole Mobility at 77 K for p=. . . |
. . . . |
. . . |
. |
Cubic (Beta) AlN |
Hexagonal (Alpha) AlN |
|
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PROPERTY / MATERIAL .
|
Cubic (Beta) GaN .
|
Hexagonal (Alpha) GaN .
|
Structure |
Zinc Blende |
Wurzite |
|
Space Group |
F bar4 3m |
C46v ( = P63mc) |
Stability |
Meta-stable |
Stable |
Lattice Parameter(s) at 300K |
0.450 nm |
a0 = 0.3189 nm c0 = 0.5185 nm |
Density at 300K |
6.10 g.cm-3 |
6.095 g.cm-3 |
Elastic Moduli at 300 K |
. . . |
. . . |
Linear Thermal Expansion Coeff. at 300 K |
. . . |
Along a0: 5.59x10-6 K-1
Along c0: 7.75x10-6 K-1 |
Calculated Spontaneous Polarisations |
Not Applicable |
0.029 C m-2
Bernardini et al 1997 Bernardini & Fiorentini 1999
|
Calculated Piezo-electric Coefficients |
Not Applicable |
e33 = + 0.73 C m-2
e31 = 0.49 C m-2
Bernardini et al 1997 Bernardini & Fiorentini 1999
|
Phonon Energies |
TO: 68.9 meV LO: 91.8 meV |
A1(TO): 66.1 meV E1(TO): 69.6 meV E2: 70.7 meV
A1(LO): 91.2 meV E1(LO): 92.1 meV |
Debye Temperature |
|
600K (estimated)
Slack, 1973 |
Thermal Conductivity near 300K |
. . . |
Units: Wcm-1K-1
1.3,
Tansley et al 1997b
2.2±0.2 for thick, free-standing GaN
Vaudo et al, 2000
2.1 (0.5) for LEO material where few (many) dislocations
Florescu et al, 2000, 2001
circa 1.7 to 1.0
for n=1x1017 to 4x1018cm-3
in HVPE material
Florescu, Molnar et al, 2000
2.3 ± 0.1
in Fe-doped HVPE material
of ca. 2 x108 ohm-cm,
& dislocation density ca. 105 cm-2
(effects of T & dislocation density also given).
Mion et al, 2006a, 2006b
|
Melting Point |
. . . |
. . . |
Dielectric Constant at Low/Lowish Frequency |
. . . |
Along a0: 10.4 Along c0: 9.5 |
Refractive Index |
2.9 at 3eV
Tansley et al 1997b
|
2.67 at 3.38eV
Tansley et al 1997b
|
Nature of Energy Gap Eg |
Direct |
Direct |
Energy Gap Eg at 1237K |
|
2.73 eV
Ching-Hua Su et al, 2002
|
Energy Gap Eg at 293-1237 K |
|
3.556 - 9.9x10-4T2 / (T+600) eV
Ching-Hua Su et al, 2002
|
Energy Gap Eg at 300 K |
3.23 eV
Ramirez-Flores et al 1994
. 3.25 eV
Logothetidis et al 1994
|
3.44 eV
Monemar 1974
. 3.45 eV
Koide et al 1987
. 3.457 eV
Ching-Hua Su et al, 2002
|
Energy Gap Eg at ca. 0 K |
3.30 eV
Ramirez-Flores et al1994 Ploog et al 1995
|
3.50 eV
Dingle et al 1971 Monemar 1974
|
Intrinsic Carrier Conc. at 300 K |
. . . |
. . . |
Ionisation Energy of . . . Donor |
. . . . |
. . . |
Electron effective mass me* / m0 |
. . . |
0.22
Moore et al, 2002
|
Electron Mobility at 300 K
for n = 1x1017 cm-3:
for n = 1x1018 cm-3:
for n = 1x1019 cm-3: |
. . . |
. ca. 500 cm2V-1s-1
ca. 240 cm2V-1s-1
ca. 150 cm2V-1s-1
Rode & Gaskill, 1995 Tansley et al 1997a
|
Electron Mobility at 77 K for n = . . |
. . . . |
. . . |
Ionisation Energy of Acceptors | . . . |
Mg: 160 meV
Amano et al 1990
Mg: 171 meV
Zolper et al 1995
Ca: 169 meV
Zolper et al 1996
|
Hole Hall Mobility at 300 K for p= . . . |
. . . |
. . . . |
Hole Hall Mobility at 77 K for p= . . . |
. . . . |
. . . |
. |
Cubic (Beta) GaN |
Hexagonal (Alpha) GaN |
|
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Hexagonal (Alpha) InN .
|
Structure |
Zinc Blende |
Wurzite |
Space Group |
F bar4 3m |
C46v ( = P63mc) |
Stability |
Meta-stable |
Stable |
Lattice Parameter(s) at 300K |
0.498 nm |
a0 = 0.3544 nm c0 = 0.5718nm |
Density at 300K |
6.93 g.cm-3 |
6.81 g.cm-3 |
Elastic Moduli at 300 K |
. . . |
. . . |
Linear Therm. Expansion Coeff. at 300 K |
. . . |
ca. 4 x 10-6 K-1
Tansley et al 1997b
|
Calculated Spontaneous Polarisations |
Not Applicable |
0.032 C m-2
Bernardini et al 1997 Bernardini & Fiorentini 1999
|
Calculated Piezo-electric Coefficients |
Not Applicable |
e33 = + 0.97 C m-2
e31 = 0.57 C m-2
Bernardini et al 1997 Bernardini & Fiorentini 1999
|
Elastic Moduli at 300 K |
. . . |
. . . |
Phonon Energies |
. . . |
. . . |
Thermal Conductivity |
. . . |
0.8±0.2 Wcm-1K-1
Tansley et al 1997b
|
Melting Point |
. . . |
. . .. K |
Dielectric Constant at Low/Lowish Frequency |
. . . |
ca. 15
Tansley et al 1997b
|
Refractive Index |
. . . |
2.9-3.05
Tansley et al 1997b
|
Nature of Energy Gap Eg |
Direct |
Direct |
Energy Gap Eg at 300K. |
. . . | . . . |
Energy Gap Eg at 2K
Some Details of Publications that considered the InN band-gap.
|
. . . |
.
0.692±0.002eV
Arnaudov et al 2004
.
|
Intrinsic Carrier Conc. at 300 K |
. . . |
. . . |
Ionisation Energy of . . . Donor |
. . . |
. . . |
Electron Hall Mobility at 300 K for n= . . . |
. . . . |
. . . |
Electron Hall Mobility at 77 K for n= . . . |
. . . . |
. . . |
Ionisation Energy of . . . Acceptor |
. . . |
. . . |
Hole Hall Mobility at 300 K for p= . . . |
. . . . |
. . . . |
Hole Hall Mobility at 77 K for p= |
. . . . |
. . . |
. |
Cubic (Beta) InN |
Hexagonal (Alpha) InN |
|
INDIVIDUAL REFERENCES
Amano H, Kitoh M, Hiramatsu H & Akasaki I, 1990,
J.Electrochem.Soc. 137, 1639
Arnaudov B, Pashkova t, Paskov PP, Magnusson B, Valcheva E, Monemar B,
Lu H, Schaff WJ, Amano H and Akasaki I,
Phys. Rev. B 69 (March 2004) 115216
Bernardini F, Fiorentini V and Vanderbilt D, 1997, Phys. Rev. B 56, R10024
Bernardini F and Fiorentini V, 1999, phys. stat. sol. 216, 391
. . . . (Proc. Internat. Conf. on Nitride Semiconductors, 1999, Montpellier, France)
Ching-Hua Su et al, 2002, J. of Crystal Growth 235, 111-114
Dingle R, Sell DD, Stokowski SE and Ilegems M, 1971, Phys.Rev.B 4, 1211
Florescu D I et al, 2000, Appl.Phys.Lett. 77, 1464
Florescu D I, Molnar R J et al, 2000, J.Appl.Phys 88, 3295
Florescu D I, Asnin V M and Pollak F H, (2001)
Compound Semiconductor 7, 62 (a review)
Logothetidis S, Petals J, Cardona M and Moustakes TD, 1994,
Phys.Rev.B 50, 18017
Mion C, Muth J F, Preble E A & Hanser D, 2006a, Appl.Phys.Lett. 89, 092123
Mion C, Muth J F, Preble E A & Hanser D, 2006b, Superlattices
. . . . & Microstructures 40, 338
Monemar B, 1974, Phys.Rev.B 10, 676
Moore W J, Freitas J A Jnr, Lee S K, Paark S S and Han J Y, 2002,
. . . . . Phys Rev B 65, 081201
Ploog K H, Brandt O, Yang H, Menniger J and Klann R, 1995,
. . . . Proc. TWN-95 Conference, Nagoya, Japan, Sept 1995 :
published in Solid State Electronics.
Ramirez-Flores G, Navarro-Contreras H, Lastras-Martinez A, Powell RC and Greene J E,
. . . . 1974, Phys.Rev.B 50, 8433
Rode D L & Gaskill D K, 1995, Appl.Phys.Lett. 66, 1972
Slack G A, , 1973, J. Phys. Chem. Solids 34, 321
Vaudo R et al, International Workshop on Nitride Semiconductors, Japan, 2000
Vurgaftman I, Meyer J R and Ram-Mohan L R (2001), J.Appl.Phys. 89, 5815
Zopler J C, Hagerott-Crawford M, Pearton S J, Abernathy C R,
Vartuli C B, Yuan C & Stall R A, 1996,
. . . . J.Electron.Mat. 25, 839
Zopler J C, Wilson R G, Pearton S J & Stall R A, 1996,
. . . . Appl. Phys. Lett. 68, 1945
BOOKS
<
BR>A-B Chen and A Sher, "Semiconductor Alloys - Physics and Materials Engineering"
. . . (Plenum, 1995)
S Nakumura and G Fasol, "The Blue Laser Diode -
GaN Based Light Emitters and Lasers"
. . . (Springer, 1997)
S J Pearton (Ed.), "GaN and Related Materials" (Gordon and Breach, 1997)
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