GaNWurtzite crystalCrystal structure WurtziteGroup of symmetry C4

6v-P63mcNumber of atoms in 1 cm3 8.9·1022

Debye temperature 600 KDensity 6.15 g cm-3 300 KDielectric constant (static) 8.9 300 K Bougrov et al. (2001)

10.4(3)9.5(3)

E||c

E c

Barker et al.(1973)

Dielectric constant (high frequency) 5.35 300 K Bougrov et al. (2001)5.8(4)5.35(20)

300 K, E||c

300 K, E c

Manchon et al.(1970)Barker et al.(1973)

Effective mass of density of state mv 1.5 m0 Leszczynski et al. (1996), Fan et al. (1996)Effective electron mass me 0.20 mo 300 K Bougrov et al. (2001)

0.27 (6) mo 300K; Faraday rotation Rheinlander & Neumann (1974)

Effective electron mass me0.20(2) mo 300K; fit of reflectance spectrum Bloom et al.(1973)

Effective electron mass me|| 0.20(6) mo

Effective hole masses 0.8 (2) mo 300 K, experimental Pankove et al.(1975)Effective hole masses (heavy) mhh mhh = 1.4 mo

mhhz = 1.1 mo

mhh = 1.6 mo

300 K; calculated values Leszczynski et al. (1996),Fan et al. (1996)

Effective hole masses (light) mlh = 0.3 mo mlhz = 1.1 mo

mlh = 0.15 mo

300 K; calculated values Leszczynski et al. (1996),Fan et al. (1996)

Effective hole masses (split-off band) ms

msh = 0.6 mo mshz = 0.15 mo

msh = 1.1 mo

300 K; calculated values Leszczynski et al. (1996),Fan et al. (1996)

Electron affinity 4.1 eV 300 K Bougrov et al. (2001)Lattice constant, a 3.160 ÷ 3.190 A Lagerstedt et al. (1979)

3.189 A 300 K Qian et al. (1996)Lattice constant, c 5.125 ÷ 5.190 A Lagerstedt et al. (1979)

5.186 A 300 K Bougrov et al. (2001)5.178 A 300 K Qian et al. (1996)

Optical phonon energy 91.2 meV 300 K Bougrov et al. (2001)Thermal expansion coefficient, a 5.59x10-6 K-1 Qian et al. (1996)Thermal expansion coefficient, c 3.17x10-6 K-1 Qian et al. (1996

Zinc Blende crystal structureCrystal structure Zinc Blende

Group of symmetry T2d-F43m

Number of atoms in 1 cm3 8.9·1022

Debye temperature 600 K

Density 6.15 g cm-3

Dielectric constant (static) 9.7 300 K Bougrov et al. (2001)

Dielectric constant (high frequency) 5.3 300 KEffective mass of density of state mv 1.4 mo

Effective electron mass me 0.13 mo 300 KEffective hole masses (heavy) mh mhh = 1.3 mo

m[100] = 0.8 mo

m[111] = 1.7 mo

300 K Leszczynski et al. (1996),Fan et al. (1996)

Effective hole masses (light) mlp mlh = 0.19mo m[100] = 0.21 mo

m[111] = 0.18 mo

300 K

Effective hole masses (split-off band) ms msh = 0.33 mo m[100] = 0.33 mo

m[111] = 0.33 mo

300 K

Electron affinity 4.1 eV 300 K Bougrov et al. (2001)Lattice constant, a 4.52 A 300 K

Optical phonon energy 87.3 meV 300 K

Basic Band StructureZinc Blende crystal structure

RemarksReferensEnergy gaps, Eg 3.28 eV 0 K Bougrov et al. (2001)Energy gaps, Eg 3.2 eV 300 KElectron affinity 4.1 eV 300 KConduction bandEnergy separation between Γ valley and X valleys EΓ1.4 eV 300 K Bougrov et al. (2001)Energy separation between Γ valley and L valleys EL 1.6 ÷ 1.9 eV 300 KEffective conduction band density of states 1.2 x 1018 cm-3 300 KValence bandEnergy of spin-orbital splitting Eso 0.02 eV 300 KEffective valence band density of states 4.1 x 1019 cm-3 300 K

Wurtzite crystal structureRemarks References

Energy gaps, Eg 3.47 eV 0 K Bougrov et al. (2001)3.39 eV 300 K Chow & Ghezzo (1996)

Energy gaps, Eg,dir 3.503 (2) eV 1.6 K; photoluminescence,from excitonic gap adding the excitonbinding energy

Monemar (1974)

3.4751(5) eV 1.6 K; A-exciton (transition from Γ9v)3.4815(10) eV

1.6 K; B-exciton (transition from upper Γ7v)

3.493 (5) eV 1.6 K; C-exciton (transition from lower Γ7v)3.44 eV 300K; temperature dependence below 295 K given by:

Eg(T) - Eg(0) = - 5.08 x 10-4 T2/(996 - T), (T in K) .see also Figure "Band gap energy and exciton energies vs. temperature"

Madelung (1991)

Electron affinity 4.1 eV 300 K Bougrov et al. (2001)

Remarks ReferencesConduction bandEnergy separation between Γ valley and M-L valleys 1.1 ÷ 1.9 eV 300 K Bougrov et al. (2001)

Energy separation between M-L-valleys degeneracy 6 eV 300 KEnergy separation between Γ valley and A valleys 1.3 ÷ 2.1 eV 300 KEnergy separation between A-valley degeneracy 1 eV 300 Kalso The energy separations between the Γ9 state and the two Γ 7 states can be calculated from the energy separations of the A-, B-, C-excitons.

Madelung (1991)

Effective conduction band density of states 2.3 x 1018 cm-3 300 KValence bandEnergy of spin-orbital splitting Eso 0.008 eV 300 K Bougrov et al. (2001)

Energy of spin-orbital splitting Eso 11(+5,-2) meV 300 K; calculated from the values of energy gap Eg,dir

(given above)

Dingle & Ilegems (1971)

Energy of crystal-field splitting Ecr 0.04 eV 300 K Bougrov et al. (2001)Energy of crystal-field splitting Ecr 22 (2) meV 300 K;

calculated from the values of energy gap Eg,dir

(given above)

Dingle & Ilegems (1971)

Effective valence band density of states 4.6 x 1019 cm-3 300 K

Band structureZinc Blende GaN

Band structure of zinc blende(cubic) GaN. Important minima of the conduction band and maxima of the valence band. 300K; Eg =3.2 eV eV; EX= 4.6 eV; EL= 4.8-5.1 eV; Eso = 0.02 eVFor details see Suzuki, Uenoyama & Yanase (1995) .

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

Wurtzite GaN

GaN, Wurtzite. Band structure. Important minima of the conduction band and maxima of the valence band. Valence band 3 splitted bands. This splitting results from spin-orbit interaction and from crystal symmetry.300K; Eg =3.39 eV eV; EM-L= 4.5-5.3 eV; EA= 4.7-5.5 eV; Eso = 0.008 eV; Ecr = 0.04 eVFor details see Suzuki, Uenoyama & Yanase (1995) .

Brillouin zone of the hexagonal lattice.

GaN, Wurtzite. Band structure calculated with an empirical pseudopotential methodThe band structure differs only slightly from other spin-neglecting calculations. Introduction of spin-orbit interaction leads to a splitting of the uppermost valence band at Γ from Γ1 + Γ6 , into Γ9 + Γ7 + Γ7 . The energy differences between these terms can be described by two parameters - the spin-orbit splitting energy Eso (Δso) and the crystal field splitting energy Ecr(Δcr). Bloom et al.(1974)

Temperature dependencesThe energy gap versus temperature:Bougrov et al. (2001) :Eg = Eg(0) - 7.7·10-4x T2/(T + 600) (eV)

Eg(0) = 3.47 eV (wurtzite)Eg(0) = 3.28 eV (zinc blende)

Guo & Yoshida (1994) Teisseyre al. (1994) :Eg = Eg(0) - 9.39 x 10-4 x T2/(T + 772) (eV)

Eg (0 K) = 3.427 eVwhere T is temperature in degrees K

Varshni expression: Guo & Yoshida (1994), Teisseyre al. (1994) :Eg = Eg(0) - 9.39·10-4x T2/(T + 772) (eV)where Eg(0) = 3.427 eV and T is temperature in degrees K

GaN, Wurtzite. Band gap energy and exciton energies vs. Temperature Monemar (1974). Temperature dependence below 295 K given by: Eg(T) - Eg(0) = - 5.08 x 10-4 T2/(996 - T), (T in K). Eg(300K) =3.44 eV

GaN, Wurtzite. Band gap energy versus temperature. GaN samples were grown on different substrates using different techniques. Experimental data are taken from four different works. Bougrov et al. (2001)

GaN, Zinc Blende(cubic). The Band gap energy versus temperature. GaN films were grown on Si (100) substrates. The dependences were extracted from pseudodielectric-function spectrum using two different theoretical models. Petalas et al. (1995)

GaN, Zinc Blende(cubic). The Band gap energy versus temperature. GaN films were grown on MgO (1x1) substrates.Ramirez-Flores et al. (1994)

GaN, Wurtzite & Zinc Blende. The intrinsic carrier concentration vs. temperature. Bougrov et al. (2001)

Intrinsic carrier concentrationni = (Nc·Nv)1/2exp(-Eg/(2kBT))

Effective density of states in conduction band: NcNc ~= 4.82 x 1015 · (mΓ/m0)3/2T3/2 (cm-3) ~= 4.3 x 1014 x T3/2 (cm-3) (Wurtzite)Nc ~= 4.82 x 1015 · (mΓ/m0)3/2T3/2 (cm-3) ~= 2.3 x 1014 x T3/2 (cm-3) (Zinc Blende)

Effective density of states in valence band: NvNv = 8.9 x 1015 x T3/2 (cm-3) (Wurtzite)Nv = 8.0 x 1015 x T3/2 (cm-3) (Zinc Blende BN)

Dependence on hydrostatic pressureWurtziteEg = Eg(0) + 4.2 x 10-3P-1.8x 10-5P2 (eV)Where P is pressure in kbar. Morkoc et al. (1994), Akasaki & Amano (1994a).

Band discontinuities at HeterointerfacesWurtzite GaN AlN/GaN (0001) Martin et al. (1996)Conduction band discontinuity ΔEc = 2.0 eVValence band discontinuity ΔEv = 0.7 eVInN/GaNConduction band discontinuity ΔEc = 0.43 eVValence band discontinuity ΔEv = 1.0 eV

Zinc Blende BN (cubic)GaAs/GaNValence band discontinuity Ding et al. (1997)ΔEv = 1.84 eV

Effective Masses and density of states:ElectronsFor wurtzite crystal structure the surfaces of equal energy in Γ valley should be ellipsoids, but effective masses in z direction and perpendicular directions are estimated to be approximately the same:Zinc Blendeme =0.13 mo 300 K Bougrov et al. (2001) Wurtziteme =0.20 mo 300 K Bougrov et al. (2001) me =0.27 mo (6) 300 K, Faraday rotation Rheinlander & Neumann (1974)me =0.20 mo (2) 300 K, fit of reflectance spectrum Bloom et al.(1973) me||=0.20 mo (6)

HolesFor zinc blende crystals, only calculated data are available.Effective mass of density of state mv mv = 1.4 mo

Effective hole masses (heavy) mhh mhh = 1.3 mo 300 K Leszczynski et al. (1996), Fan et al. (1996)m[100] = 0.8 mo

m[111] = 1.7 mo

Effective hole masses (light) mlp mlh = 0.19 mo 300 Km[100] = 0.21 mo

m[111] = 0.18 mo

Effective hole masses (split-off band) ms msh = 0.33 mo 300 Km[100] = 0.33 mo

m[111] = 0.33 mo

Experimental data for wurtzite crystals give the value of hole effective mass about 1.0 m0. This value is less than the calculated one.Effective mass of density of state mv mv = 1.5 mo Leszczynski et al. (1996), Fan et al. (1996)Effective hole masses 0.8 (2) mo 300 K experimental Pankove et al.(1975) Effective hole masses (heavy) mhh mhh = 1.4 mo 300 K Calc.: Leszczynski et al. (1996), Fan et al. (1996)

mhhz = 1.1 mo

mhh = 1.6 mo

Effective hole masses (light) mlp 0.259 mo 300 K, calculatedEffective hole masses (light) mlh = 0.3 mo 300 K, calculated Leszczynski et al. (1996), Fan et al. (1996)

mlhz = 1.1 mo

mlh = 0.15 mo

Effective hole masses (split-off band) ms msh = 0.6 mo 300 K, calculated Leszczynski et al. (1996), Fan et al. (1996)mshz = 0.15 mo

msh = 1.1 mo

Donors and acceptorsZinc Blende (cubic) GaNFor cubic GaN, only calculated data are available. [see Neugebauer & Van de Walle (1994), Boguslawski et al. (1995), Mattila et al. (1996) , Boguslawski & Bernholc (1996), Gorczyca et al. (1997)].

Wurtzite GaNIonizaton energies of Shallow donorsSi 0.12-0.02 eV Bougrov et al. (2001) Native defect level VN 0.03 eVIonizaton energies of Shallow acceptorsMg 0.14-0.21 eV Strite & Morkoc (1992), Akasaki & Amano (1994b)Zn 0.21eVNative defect level VGa 0.14eV

Most important levels in Wurtzite GaN

Donors, Ionization Energy (Et - Ec)Impurity or Defect Ga Site N Site Referens Si 0.12-0.02 eV Bougrov et al.

(2001) VN (vacancy) 0.03; 0.1 eV C 0.11-0.14 eV Mg 0.26; 0.6 eV

Acceptors, lonization Energy (Ev - Et) Impurity or Defect Ga Site N Site ReferencesVGa (vacancy) 0.14 Bougrov et al.

(2001) Mg 0.14-0.21 eV Si 0.19 eV Zn 0.21-0.34 eV Hg 0.41 eV Cd 0.55 eV Be 0.7 eV Li 0.75 eV C 0.89 eV Ga 0.59-1.09 eV

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diffusion, or coevaporation of Mg, Appl. Phys. Lett. 64(1) (1994), 64-66 . Savastenko, VA, Sheleg, A.U., Phys. Status Solidi (a) 48 (1978) K135. Sheleg, A.U, Savastenko, V.A.,: Vesti Akad. Nauk BSSR, Ser. Fiz. Mat. Nauk 3 (1976) 126. Shur, M.S., B. Gelmont, A. Khan, J. Electronic Mater. 25, 777-785 (1996). Shur M.S. M.A. Khan, Mat. Res. Bull. 22, 2 (1997) 44. Sichel, E.K., Pankove J.I., Phys. Chem. Solids 38, Thermal conductivity of GaN. 25-360 K. J. Phys. Chem. Solids 38, 3 (1977), 330. Siegle, H., G. Kaczmarczyk, L. Filippidis, L. Litvinchuk, A. Hoffmann, C. Thornsen, Zone-boundary phonons in hexagonal and cubic GaN, Phys. Rev. B 55,

11 (1997), 7000-7004 . Strite, S, H. Morkoc, J. Vac. Sci. Technol. B 10, 4 (1992), 1237-1266. Suzuki, M, T. Uenoyama, A. Yanase, First-principles calculations of effective-mass parameters of AlN and GaN, Phys. Rev. B 52, 11 (1995), 8132-8139 . Szweda, R. Gallium Nitride & Related Wide Bandgap Materials & Devices: A Market & Technology Overview 1996-2001 , Elsevier Trends Division,

Oxford, 1997. Teisseyre H., Perlin P., Suski T., Grzegory I., Porowski S., Jun J., Pietraszko A., Moustakas T.D. Temperature dependence of the energy gap in GaN bulk

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fundamental absorption edge (0.78-4.77 eV) by spectroscopic ellipsometry and the optical transmission method, Appl. Phys. Lett. 70, 24 (1997), 3209- 3211.

Zi, J., X. Wan, G. Wei, K. Zhang, X. Xie, J. Phys. Condens. Matter 8 (1996), 6323-6328. Gallium, Aluminum and Indium Nitrides. 4th International Workshop" September 18-19, 2000 St Petersburg, Russia. Abs., Proc.(pdf 2.1MB, in russian)

AlNBasic ParametersWurtzite crystal structure

Remarks ReferencesGroup of symmetry C4

6v-P63mcNumber of atoms in 1 cm3 9.58·1022

Debye temperature 1150 KMelting point 3273 K MacChesney et al. (1970)Density 3.255 g cm-3

3.23 g cm-3

X-ray Slack (1973)Goldberg (2001)

Dielectric constant (static) 9.148.5

300 K, reflectivity300K

Collins et al. (1967)

Dielectric constant (high frequency) 4.844.64.77

300 K, reflectivity300 K

Collins et al. (1967)Goldberg (2001)

Infrared refractive index 2.1 - 2.21.9 - 2.11.8 - 1.9

300 K, Epitaxial films and monocrystals300 K, Polycrystalline films300 K, Amorphous films

Meng, (1994)

Effective electron mass me 0.4 mo 300 K Xu and Ching (1993)Effective hole masses (heavy) for kz direction mhz for kx direction mhx

3.53 mo 10.42 mo

300 KSuzuki & 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

0.25mo 3.81mo

300 K

Effective mass of density of state mv: 7.26mo 300 KElectron affinity 0.6 eV 300 K Goldberg (2001)Lattice constant, a 3.11(1) A 300 K; X-ray diffraction on ultrafine powder Iwama, et al. (1971);

Qian et al. (1996)3.112 A 300 K Goldberg (2001)

Lattice constant, c 4.98(1) A 300 K; X-ray diffraction on ultrafine powder Iwama, et al. (1971)4.982 A 300 K Goldberg (2001)4.979 A 300 K Qian et al. (1996)

Thermal diffusivity 1.47 cm2 s-1

Thermal conductivity 2.85 W cm-1 °C -1 300 K. experiment Slack et al. (1987)Thermal expansion coefficient, linear αort = αc = 5.27 x10-6 K-1

α|| = αa =4.15 x10-6 K-1

T=20...800 °C. X-ray, epitaxial layers Sirota & Golodushko (1974)also see Qian et al. (1996)

Radiative recombination coefficient 0.4 x 10-10 cm-1 s-1 300 KOptical phonon energy 99.2 meV 300 K

Basic Electrical propertiesBreakdown field 1.2 ÷ 1.8 x 106 V cm-1 300 KMobility electrons 300 cm2 V-1 s-1 300 KMobility holes 14 cm2 V-1 s-1 300 KDiffusion coefficient electrons 7 cm2 s-1 300 KDiffusion coefficient holes 0.3 cm2 s-1 300 KElectron thermal velocity 1.85 x 105 m s-1 300 KHole thermal velocity 0.41 x 105 m s-1 300 K

Mobility and Hall effectOwing to the large bandgap, transport is always extrinsic

Conductivity σ 10-3 ÷ 10-5 Ω-1 cm-1 290 K ; doped (Al2OC) single p-type crystals (blue) Edwards et al. (1965)10-11 ÷ 10-13 Ω-1 cm-1 300 K ; undoped single crystals (colorless or pale yellow)

Electron drift mobility μn ~= 300 cm2 V-1 s-1 300 K ; calculated Chin et al. (1994)Phonon-limited electron drift mobility μn

~= 2000 cm2 V-1 s-1 77 K ; calculated for very weak doped AlN

Mobility holes μp 14 cm2 V-1 s-1 290 K ; doped single crystal, the authors point out that this result must be viewed with some caution

Edwards et al. (1965)

AlN, Wurtzite. Electron mobility vs. electron concentration at 300 K. Wongchotiqul et al. (1996)

AlN, Wurtzite. The temperature dependence of phonon limited electron drift mobility calculated for two values of electron effective mass m*.1 - m*/mo = 0.42;2 - m*/mo = 0.52Chin et al. (1994)

Recombination parametersRemarks Reference

Radiative recombination coefficient 0.4 x 10-10 cm3 s-1. 300 K Walker et al. (1997)Effective majority carrier (electrons) lifetime (effective lifetime of holes on the traps)

>= 35 ms 300 K

Only calculated data are available

AlN. Radiative recombination coefficient B versus temperature. Dmitriev & Oruzheinikov (1996)

Band structure and carrier concentrationEnergy gaps in wurtzite (Hexagonal) crystal structureEg remark References6.026 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)

Goldberg (2001) all 300K:

Conduction band

Energy separation between Γ valley and M-L valleys ~0.7 eV

Energy separation between M-L valleys degeneracy 6 eV

Energy separation between Γ valley and K valleys ~1.0 eV

Energy separation between K valley degeneracy 2 eV

Valence band

Energy of spin-orbital splitting Eso 0.019 eV

Effective conduction band density of states 6.3 x 1018 cm-3

Effective valence band density of states 4.8 x 1020 cm-3

AlN, Wurtzite. Band structure. Important minima of the conduction band and maxima of the valence band. For details see Christensen & Gorczyca (1994) 300K; Eg=6.2 eV; EM-L= 6.9 eV; Eso = 0.019 eV; Ek= 7.2 eV

AlN, Wurtzite. Band structure calculated with an a semi-empirical tight binding method. Kobayashi et al. (1983)

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.

Energies of symmetry points of the band structure (relative to the top of the valence band)calculated values, see Band structure sect and Kobayashi et al. (1983) . Data in brackets from Huang & Ching (1985).

Energies of symmetry pointsE (Γ1v) -18.40 (-14.43) eVE (Γ3v) -7.10 (-4.68) eVE (Γ5v) -1.22(-0.60) eVE (Γ6v , Γ1'v) 0.00 eVE (Γ1c) 6.2 (6.25) eVE (Γ3c) 8.92 (9.38) eVE (Γ6c , Γ1'c) 13.0 eVE (Γ1'3'v) -7.52 (-4.26) eVE (Γ24v) -1.97 (-1.06) eVE (Γ13v) -1.87 (-1.03) eVE (Γ13c) 9.99 (9.40) eVE (Γ1'3'c) 13.53 eV

Thermal propertiesBasic parameters

Wurtzite crystal structure Remarks ReferensBulk modulus 21 x 1011 dyn cm -2 Goldberg (2001)Debye temperature 1150 KMelting point 3273 K MacChesney et al. (1970)

3023 K (between 100 and 500 atm of nitrogen) Goldberg (2001)

Specific heat 0.6 J g-1°C -1

Thermal diffusivity 1.47 cm2 s-1

Thermal conductivity 2.85 W cm-1 °C -1 300 K. experiment Slack et al. (1987)Thermal expansion coefficient, linear

αort = αc = 5.27 x10-6 K-1 T=20...800 °C. X-ray, epitaxial layers Sirota & Golodushko (1974)also see Qian et al. (1996) α|| = αa = 4.15 x10-6 K-1

Thermal conductivity

AlN, Wurtzite sructure. The thermal conductivity K vs. temperature. 1 -- AlN single crystal with no oxygen and a sample diameter of 0.54 cm (estimate); 2 -- AlN single crystal containing N0 ~= 4.2 x 1019 cm-3 oxygen atoms (measure); 3 -- N0 ~= 3 x 1020 cm-3 oxygen atoms. Slack et al. (1987)

AlN, Wurtzite sructure. Conductivity vs. reciprocal temperature for hot-pressed material. EA: activation energy for conductivity. Francis & Worrell (1976)

At 0.4 < T < 3 K: K ~ T2.54 At 500 < T < 1800 K: K ~ T-1.25 Maximal measured value of thermal conductivity at 300 K is 2.85 W cm-1 K-1 [Slack et al. (1987)].

Specific HeatThe specific heat Cp of AlN at constant pressure (Koshchenko et al. (1984)) :At 300< T< 1800K, Cp = 45.94 + 3.347 x 10-3 x T -14.98 x 105 x T -2 (J mol-1 K) At 1800 < T < 2700 K, Cp = 37.34 + 7.866 x 10-3 x T (J mol-1 K)

AlN. The specific heat vs. temperature at constant pressure. Koshchenko et al. (1984)

Thermal expansion(Slack and Bartram (1975), Touloukian at al. (1977), Meng (1994), Morkoc et al. (1994) Qian et al. (1996) )For the direction along the c-axis: At 300 : αc = 5.3 x 10-6 K-1

At 293 < T < 1700 K, Δc/c300 = -7.006 x 10-2 + 1.583 x 10-4 x T + 2.719 x 10-7 x T2 - 5.834 x 10-11 x T3 For the perpendiculardiraection: At 300 : αa = 4.2 x 10-6 K-1

At 293 < T < 1700 K, Δa/a300 = -8.679 x 10-2 + 1.929 x 10-4 x T + 3.400 x 10-7 x T2 -7.969 x 10-11 x T3

AlN. The linear expansion coefficient α vs. temperature for ceramic AlN samples. α = 1/3 (Δc/c + 2Δa/a)Slack & Bartram (1975)

Calculated vapor pressure of Al and N2 in equilibrium with solid AlN and liquid Al. Meng (1994)

Temperature dependenceTemperature dependence of energy gap: (Guo & Yoshida (1994) Teisseyre al. (1994))Eg = Eg(0) - 1.799 x 10-3 x T2/(T + 1462) eV Eg (300 K) = 6.026 eV0 < T < 300 K, where T is temperature in degrees K.

Effective density of statesConduction Band:Nc ~= 4.82 x 1015 · (mΓ/mo)3/2 T3/2 (cm-3) ~= 1.2 x 1015 x T3/2 (cm-3)Valence Band :Nv = 9.4 x 1016 x T3/2 (cm-3)

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

Mechanical Properties, Elastic Constants, Lattice VibrationsBasic parameters

Remarks ReferensDensity 3.255 g cm-3

3.23 g cm-3X-ray Slack (1973)

Goldberg (2001)

Surface microhardnesson basal plane (0001)

800 kg mm-2 300 K, using Knoop's pyramid test Nikolaev et al. (1998) see also Drory et al. (1996)

Elastic constants at 300 K.Wurtzite AlN. Elastic constants at 300 K. C11 410 ± 10 GPa McNeil (1993)

see also Wright (1997)C12 149 ± 10 GPaC13 99 ± 4 GPaC33 389 ± 10 GPaC44 125 ± 5 GPaWurtzite AlN. Bulk modulus (compressibility-1) For T = 300 KBs = [ C33(C11 + C11) - 2(C13)2] x [C11+ C12-4C13+ 2C33 ]-1 Bs = 210 GPaYoung modulus, Y0 308 GPa Gerlich et al. (1986)Poisson ratio, σ0 along the different crystallographic directions {0001}, c-plane 0.287 Thokala & Chaudhuri (1995) {1120}, r-plane (l = <0001>, m = <1100>) 0 {1120}, r-plane (l = <1100>, m = <0001>) 0.216The sound velocities and related elastic module(experimental data) The velocity of the longitudinal waves, vl 10,127 m s-1 Gerlich et al. (1986) The velocity of the shear waves, vs 6,333 m s-1

The longitudinal elastic modulus, CL 334 GPa The shear elastic modulus, Cs 131 GPa

Temperature derivatives of the elastic module dlnCL / dT = -0.37 x 10-4 K-1;dlnCs / dT = -0.57 x 10-4 K-1;dlnBs / dT = -0.43 x 10-4 K-1

Acoustic Wave SpeedsWurtzite crystal structureWave propagation direction Wave character Expression for wave speed Wave speed (in units of 105 cm/s)[100] VL (longitudinal) (C11/ρ )1/2 11.27

VT (transverse, polarization along [001]) (C44/ρ )1/2 6.22VT (transverse, polarization along [010]) ((C11-C12)/2ρ )1/2 6.36

[001] VL (longitudinal) (C33/ρ )1/2 10.97VT(transverse ) (C44/ρ )1/2 6.22

Phonon frequencies Wurtzite crystal structurephonon wavenumbers: Remarks ReferencesνTO(E1) 895(2) cm-1 RT. Raman scattering Sanjurjo et al. (1983)νLO(E1) 671.6(8) cm-1

νTO(A1) 888(2) cm-1

νLO(A1) 659.3(6) cm-1

ν(E2) 303 cm-1 Raman scattering, tentative assignment Carlone, et al. (1984)ν(E2) 426 cm-1

νTO(A1) 514 cm-1

νTO(E1) 614 cm-1

νLO(A1) 663 cm-1

νLO(E1) 821 cm-1

νLO(E1) 821 cm-1

nTO (E1) 657-673 cm-1 Collins et al. (1967);Collins et al. (1967);MacMillan et al. (1993);

nTO (A1) 607-614 cm-1

or 659-667 cm-1

Perlin et al. (1993);Meng (1994)

nLO (E1) 895-924 cm-1

nLO (A1) 888-910 cm-1

n(1) (E2) 241-252 cm-1

n(2) (E2) 655-660 cm-1

AlN, Wurtzite. Pressure dependences of the phonon frequencies.Perlin et al. (1993)

AlN. Calculated phonon dispersion curves and phonon DOS function for bulk AlN. The solid and dashed lines correspond to the Λ1 (or T1) and Λ2 (or T2) irreps, respectively. Davydov et al. (1998)

Dependence on Hydrostatic pressureHydrostatic Pressure versus the energy gap (Gorczyca & Christensen (1993))dEg/dP = 3.6 x 10-3 (eV/kbar)

Conduction band first- and second-order pressure derivatives (Van Camp et al. (1993)):Eg = Eg(0) + 3.6 x 10-3 P - 1.7 x 10-6 P2

Ek = Ek(0) + 6.3 x 10-4 P + 1.7 x 10-6 P2

EL = EL(0) + 8.0 x 10-4 P + 6.9 x 10-7 P2 EM = EM(0) + 7.5 x 10-4 P + 1.0 x 10-6 P2 In 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)]

Piezoelectric constantse15 -0.48 C m-2 Xinjiao et al. (1986)

e31 -0.58 C m-2

e33 1.55 C m-2

Band discontinuities at Heterointerfaces for wurtzite AlN:InN/AlN(0001) ReferencesConduction band discontinuity ΔEc = 2.7 eV Martin et al. (1996)Valence band discontinuity ΔEv = 1.8 eVGaN/AlN (0001)Conduction band discontinuity ΔEc = 2.0 eV Martin et al. (1996)Valence band discontinuity ΔEv = 0.7 eVSiC/AlN (0001)Valence band discontinuity ΔEv = 1.4 eV King et al. (1996)

Effective Masses and Density of States: ElectronsFor wurtzite crystal structure theoretical estimations of the electron effective mass anisotropy in Γ valley: Wurtzite AlN Remarks ReferensEffective 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)

HolesWurtzite AlN Remarks References

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 AcceptorsWurtzite AlNNative donors: Si, Mg (ionization energy ΔE ~= 1 eV)Donors: C, Ge, SeAcceptors: C, Hg

Ionization Energies :Tansley & Egan (1991); Chu et al. (1967); Francis and Worell (1976); Jenkins and Dow (1989); Mohammad et al. (1995); Boguslawski et al. (1996); Gorczyca et al. (1997)d1 is the donor level of N vacancies (VN) 0.17 eVd2 is the donor level of N vacancies (VN) 0.5 eVd3 is the donor level of N vacancies (VN) 0.8-1.0 eVd4 is the donor levels of C in Al sites (CAl) 0.2 eVd5 is the donor levels of N in Al sites (NAl) 1.4-1.85 eVd6 is the donor levels of Al in N sites (AlN) 3.4-4.5 eV

Ionization energies (Ev-Et) :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)a1 is the acceptor levels of Al vacancies (VAl) 0.5 eVa2 is the acceptor levels of C in N sites (CN) 0.4 eVa3 is the acceptor levels of Zn in Al sites (ZnAl) 0.2 eVa4 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)

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