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Material Properties of AlInGaN Alloys

Here we suggest for you attention our database of material properties for AlInGaN alloys. The material properties presented below are used in the software package SimuLED, the engineering tool for LED and laser diode design and optimization. The section will be gradually expanding and eventually is going to cover the following subjects:

All the data in this section are provided free and in good faith. We strive to keep the materials in this section accurate and up to date, however, STR Group can not guarantee the accuracy and can not be held responsible for any possible inaccuracies or misuse of the materials.

If you have any questions regarding software for LED and laser diode design and optimization or would like to contribute to this database, please, contact us at mark.ramm@str-soft.com

Generally, these materials can be divided into two types:

  • materials of fixed chemical composition and structural modification (GaN, AlN, etc.);
  • alloys (AlInGaN, MgZnO, etc.).
For each material the user might need to specify some properties like energy gap, lattice constant, etc. Alloys are described on the basis of existing materials by a list of included materials and so called “bowing parameters”. Generally, each property of alloy including n species, is calculated as:
, (1)

where xi are the species concentrations satisfying the relation
, (2)

fi are the values of the property f for pure materials, and fik are the bowing parameters. One can use zero bowing parameters to describe linear variation of the property f with the alloy composition, so called Vegard law.

By default all properties except for the energy gap and electron affinity are assumed to have a linear dependence on the composition. In this section we discuss the data on materials properties available in literature in order to justify the choice of the parameters used. The data obtained for binary nitrides and the approximations applied for evaluation of the parameters of multi-component nitride compounds are both discussed.

Lattice Constants

Lattice constants of the multi-component nitride compounds are assumed to obey the Vegard law. The data on the lattice constants of binary nitrides are collected in Table 1. It is seen that the experimental data [1] - [3] agree well with each other. The ab initio calculations [4] provide underestimated constants. Therefore, the most reliable data are a = 0.3540 nm, a = 0.3188 nm, a = 0.3112 nm, c = 0.5705 nm, c = 0.5186 nm, and c = 0.4982 nm (the chosen values are shadowed in Table 1).

Ref.a(nm)c(nm)
AlNGaNInNAlNGaNInN
[1]0.31110.31820.35400.49800.51850.5705
[2]0.31120.31890.35400.49820.51850.5705
[3] 0.3188  0.5186 
[4]0.30910.31600.35280.49520.51380.5684

Table 1 Lattice constants of binary nitrides at 300 K.

Elastic Constants

The published data on the stiffness elastic constants of binary group-III nitrides are collected in Table 2. At the moment, there is no reliable information on the elastic constants of ternary and quaternary nitrides. Therefore, the linear approximation is normally used in to estimate the elastic constants. The most reliable stiffness constants and the respective Poisson coefficient ν are given in Table 3.

Cij
(GPa)
Ref. AlN GaN InN
exp.calc. exp.calc. exp.calc.
C11 [2] 345396 374367 190223
[4] 345, 411398 391396  271
[5] 345, 411398 365, 377, 390350   
C12 [2] 125137 106135 104115
[4] 125, 149140 143144  124
[5] 125, 149142 135, 160, 135140   
C13 [2] 120108 70103 12192
[1] 120  114  94 
[4] 120, 99127 108100  94
[5] 120, 99112 114, 106104   
C33 [2] 395373 379405 182224
[1] 395  381  200 
[4] 395, 389382 399392  200
[5] 395, 389383 381, 398376   
C44 [2] 118116 10195 1048
[4] 118, 12596 10391  46
[5] 118, 125127 109, 81, 105101   

Table 2 Stiffness constants of binary nitrides at 300 K(GPa).

 
 AlNGaNInN
C11 (GPa)395375225
C12 (GPa)140140110
C13 (GPa)11510595
C33 (GPa)385395200
C44 (GPa)12010045
ν=C13/(C13+C33)0.230.210.32

Table 3 Most reliable stiffness constants of binary nitrides at 300 K (GPa).

Piezoelectric Tensor, Spontaneous Polarization, and Dielectric Constant

 
 e33e31e15e14
GaN (electromechanical coefficients)1.0-0.36-0.3 
GaN (mobility)0.44-0.22-0.220.375
GaN (from optical phonons)0.65-0.33-0.330.56
GaN (ab initio)0.73-0.49  
InN (from optical phonons)0.43-0.22-0.220.37
InN (ab initio)0.97-0.57  
AlN (surface acoustic waves)1.55-0.58-0.48 
AlN (ab initio)1.46-0.60  

Table 4 Data on the piezoelectric tensor of binary nitrides (C/m2) [6].

 
 AlNGaNInN
Spontaneous polarization Pzs (C/m2)-0.081-0.029-0.032
Piezoelectric tensor e33 (C/m2)1.550.650.43
Piezoelectric tensor e31 (C/m2)-0.58-0.33-0.22
Piezoelectric tensor e15 (C/m2)-0.48-0.33-0.22
Dielectric constant ε338.58.915.3

Table 5 Polarization parameters and dielectric constants of binary nitrides.

Energy Gap and Valence Band Splitting

The general approximation of the bandgap of a multi-component nitride alloy InxAlyGa1-x-yN as a function of composition is
, (3)

 
 AlNGaNInN
Bandgap EG at T=0 (eV)6.253.510.69
Varshni parameter a (meV/K)1.7990.9090.404
Varshni parameter b (K)1462830454
Crystal field splitting (eV)-93.222.337.3
Spin-orbital splitting (eV)11.111.111.1
InGaN bowing parameter (eV)1.2
AlGaN bowing parameter (eV)1.0
AlInN bowing parameter (eV)4.5

Table 6 Band structure and deformation potential parameters of binary nitrides.

Band Offsets and Electron Affinity
For information, please, contact mark.ramm@str-soft.com
Effective Masses of Electrons and Holes

 
  AlN GaN InN
|| || ||
mn 0.250.25 0.20.2 0.10.1
mlh 1.950.25 1.10.15 1.350.1
mhh 1.952.58 1.11.65 1.351.45
mso 0.231.93 0.151.1 0.091.54

Table 7 Effective masses of electrons and holes in binary nitrides at 300 K.

Ionization Energies of Impurities
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Frequency-Dependent Dielectric Constants

 
MaterialE0 (eV) A1Γ1 (eV)E1 (eV) εA0Γ0 (eV)
AlNordinary6.05 1.40.88.05 2.82.60.55
extraordinary 1.6
InNordinary0.7 1.61.25.39 5.72.50.85
extraordinary 2.00.85 5.63.31.35
GaNordinary3.6 1.10.97 4.11.21.1
extraordinary 1.25

Table 8 Optical parameters of binary nitrides at 300 K.

 
MaterialE0 (eV) A1Γ1 (eV)E1 (eV) εA0Γ0 (eV)
Al2O3ordinary0.00 2.0750.0013.3 1.000.000.00
extraordinary 2.045
6H-SiCordinary4.80 5.501.107.10 1.000.000.40
extraordinary 4.00 2.802.7
4H-SiCordinary5.40 5.301.107.30 1.001.100.40
extraordinary 1.00 7.00 5.707.500.95

Table 9 Optical parameters for sapphire and silicon carbide at 300 K.

References

[1] I. Akasaki, H. Amano, “Crystal Growth and Conductivity Control of Group III Nitride Semiconductors and Their Application to Short Wavelength Light Emitters”, Jpn.J.Appl.Phys. 36, Pt.1 (1997) 5393.
[2] O. Ambacher, “Growth and applications of Group III-nitrides”, J. Phys. D 31 (1998) 2653.
[3] M. Leszcynski, T. Suski, H. Teisseyre, P. Perlin, I. Grzegory, J. Jun, S. Porowski, T.D. Moustakas, “Thermal expansion of gallium nitride”, J.Appl.Phys. 76 (1994) 4909.
[4] M. van Schilfgaarde, A. Sher, A.-B. Chen, “Theory of AlN, GaN, InN and their alloys”, J.Cryst.Growth 178 (1997) 8.
[5] K. Shimada, T. Sota, K. Suzuki, “First-principles study on electronic and elastic properties of BN, AlN, and GaN”, J.Appl.Phys. 84 (1998) 4951.
[6] www.iiiv.cornell.edu/
[7] J.A. Garrido, J.L. Sánchez-Rojas, A. Jimnénez, E. Muñoz, F. Omnes, P. Gibart, “Polarization fields determination in AlGaN/GaN heterostructure field-effect transistors from charge control analysis”, App.Phys.Lett. 75 (1999) 2407.
[8] D. Cherns, J. Barnard, F.A. Ponce, “Measurement of the piezoelectric field across strained InGaN/GhaN layers by electron holography”, Sol.St.Commun. 111 (1999) 281.
[9] V.W.L. Chin, T.L. Tansley, T. Osotchan, “Electron mobilities in gallium, indium, and aluminum nitrides”, J.Appl.Phys. 75 (1994) 7365.
[10] S.N. Mohammad, H. Morkoc, “Progress and prospects of group-III nitride semiconductors”, Prog. Quant. Electron. 20 (1996) 361.
[11] V.Fiorentini, F.Bernardini, and O.Ambacher, “Evidence for nonlinear polarization in III-V nitride alloy heterostructures”, Appl.Phys.Lett. 80 (2002) 1204.
[12] Eds. M.E. Levinshtein, S.L. Rumyantsev, M.S. Shur, “Properties of advanced semiconductor materials. GaN, AlN, InN, BN, SiC, SiGe”, Wiley-Interscience publications, J. Wiley & Sons, Inc., NY, 2001.
[13] I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors”, J. Appl. Phys. 94, 3675 (2003).
[14] J. Wu and W. Walukiewicz, “Band gaps of InN and group III nitride alloys”, Superlattices and Microstructures 34, 63 (2003).

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