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:

• Lattice Constants
• Elastic Constants
• Piezoelectric Tensor, Spontaneous Polarization, and Dielectric Constant
• Energy Gap and Valence Band Splitting
• Band Offsets and Electron Affinity
• Effective Masses of Electrons and Holes
• Ionization Energies of Impurities
• Frequency-dependent dielectric constant

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 x_i are the species concentrations satisfying the relation

, (2)

f_i are the values of the property f for pure materials, and f_ik 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)
	AlN	GaN	InN	AlN	GaN	InN
[1]	0.3111	0.3182	0.3540	0.4980	0.5185	0.5705
[2]	0.3112	0.3189	0.3540	0.4982	0.5185	0.5705
[3]		0.3188			0.5186
[4]	0.3091	0.3160	0.3528	0.4952	0.5138	0.5684

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]	345	396	374	367	190	223
	[4]	345, 411	398	391	396		271
	[5]	345, 411	398	365, 377, 390	350
C12	[2]	125	137	106	135	104	115
	[4]	125, 149	140	143	144		124
	[5]	125, 149	142	135, 160, 135	140
C13	[2]	120	108	70	103	121	92
	[1]	120		114		94
	[4]	120, 99	127	108	100		94
	[5]	120, 99	112	114, 106	104
C33	[2]	395	373	379	405	182	224
	[1]	395		381		200
	[4]	395, 389	382	399	392		200
	[5]	395, 389	383	381, 398	376
C44	[2]	118	116	101	95	10	48
	[4]	118, 125	96	103	91		46
	[5]	118, 125	127	109, 81, 105	101

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

 

	AlN	GaN	InN
C11 (GPa)	395	375	225
C12 (GPa)	140	140	110
C13 (GPa)	115	105	95
C33 (GPa)	385	395	200
C44 (GPa)	120	100	45
ν=C13/(C13+C33)	0.23	0.21	0.32

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

Piezoelectric Tensor, Spontaneous Polarization, and Dielectric Constant

 

	e33	e31	e15	e14
GaN (electromechanical coefficients)	1.0	-0.36	-0.3
GaN (mobility)	0.44	-0.22	-0.22	0.375
GaN (from optical phonons)	0.65	-0.33	-0.33	0.56
GaN (ab initio)	0.73	-0.49
InN (from optical phonons)	0.43	-0.22	-0.22	0.37
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].

 

	AlN	GaN	InN
Spontaneous polarization Pzs (C/m2)	-0.081	-0.029	-0.032
Piezoelectric tensor e33 (C/m2)	1.55	0.65	0.43
Piezoelectric tensor e31 (C/m2)	-0.58	-0.33	-0.22
Piezoelectric tensor e15 (C/m2)	-0.48	-0.33	-0.22
Dielectric constant ε33	8.5	8.9	15.3

Table 5 Polarization parameters and dielectric constants of binary nitrides.

The general approximation of the bandgap of a multi-component nitride alloy In_xAl_yGa_1-x-yN as a function of composition is

, (3)

 

	AlN	GaN	InN
Bandgap EG at T=0 (eV)	6.25	3.51	0.69
Varshni parameter a (meV/K)	1.799	0.909	0.404
Varshni parameter b (K)	1462	830	454
Crystal field splitting (eV)	-93.2	22.3	37.3
Spin-orbital splitting (eV)	11.1	11.1	11.1
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.

 

	AlN		GaN		InN
	⊥	||	⊥	||	⊥	||
mn	0.25	0.25	0.2	0.2	0.1	0.1
mlh	1.95	0.25	1.1	0.15	1.35	0.1
mhh	1.95	2.58	1.1	1.65	1.35	1.45
mso	0.23	1.93	0.15	1.1	0.09	1.54

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

 

Material		E0 (eV)	A1	Γ1 (eV)	E1 (eV)	ε∞	A0	Γ0 (eV)
AlN	ordinary	6.05	1.4	0.8	8.05	2.8	2.6	0.55
	extraordinary		1.6
InN	ordinary	0.7	1.6	1.2	5.39	5.7	2.5	0.85
	extraordinary		2.0	0.85		5.6	3.3	1.35
GaN	ordinary	3.6	1.1	0.9	7	4.1	1.2	1.1
	extraordinary		1.25

Table 8 Optical parameters of binary nitrides at 300 K.

 

Material		E0 (eV)	A1	Γ1 (eV)	E1 (eV)	ε∞	A0	Γ0 (eV)
Al2O3	ordinary	0.00	2.075	0.00	13.3	1.00	0.00	0.00
	extraordinary		2.045
6H-SiC	ordinary	4.80	5.50	1.10	7.10	1.00	0.00	0.40
	extraordinary		4.00			2.80	2.7
4H-SiC	ordinary	5.40	5.30	1.10	7.30	1.00	1.10	0.40
	extraordinary		1.00		7.00	5.70	7.50	0.95

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).