Michael Shur

A more detailed (but less up to date) parameter list for GaN, AlN, InN, BN, SiC, and SiGe can be found in

M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, Editors, John Wiley and Sons, 2001 “Properties of Advanced Semiconductor Materials: GaN, AlN, InN, BN, and SiGe“

Basic GaN, AlN, and InN Parameters

Home

Wide Band Gap Research

Our research

Table I: Nitride Parameters (many data in Table 1 are courtesy of Brian Foutz, Cornell University, with some corrections and additions).

	Units	GaN	AlN	InN
Crystal Structure		Wurtzite	Wurtzite	Wurtzite
Density	g/cm	6.15 [1]	3.23 [1]	6.81 [1]
Longitudinal Constant (Cl)	dyn/cm^2	4.42 x 10^11 [1]	4.42 x 10^11 [1]	4.42 x 10^11 [1]
Transverse Constant (Ct)	dyn/cm^2	2.65 x 10^11 [1]	2.65 x 10^11 [1]	2.65 x 10^11 [1]
Transverse Sound Velocity	cm/s	2.68 x 10^5 [2]	3.70 x 10^5 [2]	2.55 x 10^5 [2]
Longitudinal Sound Velocity	cm/s	6.56 x 10^5 [2]	9.06 x 10^5 [2]	6.24 x 10^5 [2]
Static Dielectric Constant		8.9 [3]	8.5 [1]	15.3 [3]
High Frequency Dielectric Constant		5.35 [3] and [22]	4.77 [1]	8.4 [3]
Energy Gap (G Valley)	eV	3.39 [19]	6.2 [20]	1.89 [21]
Effective Mass (G Valley)	me	0.20 [3] and [22] 0.19 (transverse) [27] 0.23 (longitudinal) [27]	0.48 [1] 0.33 (transverse) [28] 0.32 (longitudinal) [28]	0.11 [3]
Deformation Potential	eV	8.3 [1]	9.5 [1]	7.1 [1]
Polar Optical Phonon Energy	meV	91.2 [1]	99.2 [1]	89.0 [1]
Piezoelectric Constant e14	C/m^2	0.375 [1]	0.92 [4]	0.375 [1]
Piezoelectric Constant e15	C/m^2		-0.58 [5]
Piezoelectric Constant e31	C/m^2		-0.48 [5]
Piezoelectric Constant e33	C/m^2		1.55 [5]
Intervalley Coupling Coefficient	eV	91.2 [6]	99.2 [6]	89.0 [6]
Intervalley Deformation Potential	eV/cm	1 x 10^9 [7]	1 x 10^9 [7]	1 x 10^9 [7]
Lattice Constant, a	Angstr.	3.189 [13]	3.11 [13]	3.54 [13]
Lattice Constant, c	Angstr.	5.185 [13]	4.98 [13]	5.70 [13]
Electron mobility	cm^2/Vs	1000 [14]	135 [15]	3200 [16]
Hole mobility	cm^2/Vs	30 [13]	14 [13]
Saturation velocity	cm/s	2.5 x 10^7 [14]	1.4 x 10^7 [15]	2.5 x 10^7 [16]
Peak velocity	cm/s	3.1 x 10^7 [14]	1.7 x 10^7 [15]	4.3 x 10^7 [16]
Peak velocity field	kV/cm	150 [14]	450 [15]	67 [16]
Breakdown field	V/cm	> 2.5 x 10^6 [29]
Heavy hole mass (transverse and longitudinal)	me	Longitudinal: mhhl = 2.04 [27] mhhl = 2.09 [28] Transverse (in basal plane) mhht = 1.81 [27] mhht = 0.37 [28]	Transverse mhht = 0.73 [28] Longitudinal: mhhl = 3.52
Light hole mass	me	Longitudinal: mlhl = 2.04 [27] mlhl = 0.74 [28] Transverse mass: mlht = 0.19 [27] mlht = 0.39 [28]	0.471 [13]
Thermal Conductivity	W/cmK	1.3 [24]	2.85 [23]
Melting Temperature	^oC	>1700 [13]	3000 [13]	1100 [13]

Except for the data in the table below, the zinc-blende GaN parameters are taken equal to the wurtzite GaN parameters.

Table II: Zinc-blende Nitride Data

	Units	GaN (Zinc-blende)	AlN (Zinc-blende)
Lattice Constant, a	Angstr.	4.52 [10]
Electron Mobility	cm^2/Vs	1500 [18]
Saturation velocity	cm/s	2.5 x 10^7 [18]
Peak velocity	cm/s	3.5 x 10^7 [18]
Peak velocity field	kV/cm	110 [18]
Light hole effective mass	me	0.16 [26]
Heavy hole effective mass	me	0.8 [25] 0.84 [26]	Zinc-Blende AlN: mhh = 1.43 [26] mlh = 0.29 [26]
Peak electron velocity field	kV/cm	110 [18]

Table III: Conduction Band Structure Data

		Units	GaN (Cubic)	GaN (Wurtzite)	AlN (Wurtzite)	InN (Wurtzite)
Gamma Valley	Energy Gap	eV	3.2 [10]	3.39 [19]	6.2 [20]	1.89 [21]
	Effective Mass	me	0.15 [11] 0.19 [26][27]	0.20 [3] and [22] me = 0.23 (0.19) [27]	0.48 [1] Transverse met = 0.33 Longitudinal mel =0.32 [28]	0.11 [3]
	Nonparabolicity	eV^-1	0.213 [12]	0.189	0.044	0.419
Second Valley	Energy Gap	eV	4.7	5.29	6.9	4.09
	Effective Mass	me	1.00	1.00	1.00	1.00
	Degeneracy		3 (X)	1 (G')	6 (L-M)	1 (A)
	Nonparabolicity	eV^-1	0.00	0.00	0.00	0.00
Third Valley	Energy Gap	eV	6.0	5.49	7.2	4.49
	Effective Mass	me	1.00	1.00	1.00	1.00
	Degeneracy		4 (L)	6 (L-M)	2 (K)	1 (K)
	Nonparabolicity	eV^-1	0.00	0.00	0.00	0.00

The energy gaps of the second and third valleys were obtained by taking the differences between the upper valley conduction band minimums and the gamma valley minimum (taken from Ref. [9]) and adding them to the energy gap of the gamma valley. The degeneracy of the upper valleys was obtained from Ref. [9] also. Due to variations in band structure calculations, the effective mass of the upper valleys is set to the mass of the free electron and the nonparabolicity of the upper valleys is set to zero. The nonparabolicity of the gamma valley is calculated using the Kane model [12].

Table IV. Piezoelectric constants.

(Data taken partially from (Bykhovski et al., 1997), InN constants estimated from ab initio calculations

(Bernardini and Fiorentini, 1997) and using optic phonon frequencies of InN.

elm (C/m^2)	e33	e31	e15	e14
GaN (electromechanical coefficients)	1	-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
SiC	0.2		0.08
ZnO	1.32	-0.57	-0.48
GaAs	-0.185	0.093	0.093	-0.16

Table V. [After G. D. O'Clock, Jr. and M. T. Duffy, Acoustic surface wave properties of epitaxially grown aluminum nitride and gallium nitride on sapphire, APL, 23(2), 55-56 (1973)],

The electromechanical coupling coefficient, k², depends on GaN thickness, t, to wavelength ratio, l, and on the surface orientation. The data are for GaN grown on sapphire

Orientation	t/l	k^2 (%)
(0001) GaN on (0001) sapphire	0.017	0.015
(11-20) GaN on (1-120) sapphire	0.017	0.007
(11-20) GaN on (1-120) sapphire	0.063	0.04

References

[1] V. W. L. Chin, T. L. Tansley, and T. Osotchan, J. Appl. Phys. 75, 7365 (1994).

[2] The transverse sound velocity is calculated from the transverse constant and the density:

V_t = (C_t/r)^1/2

Similarly the longitudinal sound velocity is calculated from the longitudinal constant:

V_l = Sqrt(C_l/r).

[3] S. N. Mohammad and H. Morkoc, Prog. Quant. Electron. 20, 361 (1996).

[4] This value is calculated as an effective value for the zinc-blende structure based on the measured wurtzite piezoelectric constants (see [5]).

[5] John G. Gualtieri, John A. Kosinski, and Arthur Ballato, IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control 41, 53 (1994).

[6] The intervalley coupling constant is assumed to be the same energy as the polar optical phonon energy, an approximation that holds for GaAs [8].

[7] The intervalley deformation potential assumed to be the same as GaAs [8].

[8] M. A. Littlejohn, J. R. Hauser, and T. H. Glisson, J. Appl. Phys. 48, 4587 (1977).

[9] W. R. L. Lambrecht and B. Segall, in Properties of Group III Nitrides, No. 11 EMIS Datareviews Series, edited by J. H. Edgar ( Inspec, London, 1994 ), Chapter 4. 

[10] T. Lei, T. D. Moustakas, R. J. Graham, Y. He, and S. J. Berkowitz, J. Appl. Phys. 71, 4933 (1992).

[11] M. Fanciulli, T. Lei, and T. D. Moustakas, Phys. Rev. B. 48, 15144 (1993).

[12] The nonparabolicity is calculated from the Kane Model. The energy of the G valley is assumed to be non-parabolic, spherical, and of the form

h²k²/2m* = E(1 + aE),

where k denotes the wave vector, E represents the energy, m* is the effective mass, and the non-parabolicity coefficient, a, is given by

a = (1 - m*/m_e)²/E_g ,

where m_e and E_g denote the bare electron mass and the energy gap, respectively.

[13] Michael S. Shur and M. Asif Khan, MRS. Bull. 22 (2), 44 (1997).

[14] U. V. Bhapkar and M. S. Shur, J. Appl. Phys., 82 (4), 1649 (1997).

[15] S. K. O'Leary, B. E. Foutz, M. S. Shur, U. V. Bhapkar, and L. F. Eastman, Solid State Comm. 105, 621 (1998).

[16] S. K. O'Leary, B. E. Foutz, M. S. Shur, U. V. Bhapkar, and L. F. Eastman, J. Appl. Phys. 83, 826 (1998).

[17] Jan Kolnik, Ismail H. Oguzman, Kevin F. Brennan, Rongping Wang, P. Paul Ruden, and Yang Wang, J. Appl. Phys. 78, 1033 (1995).

[18] Unpublished. For means of comparison GaN zinc-blende transport data were calculated using the same Monte Carlo program used to calculate the transport data from Refs. [14-16].

[19] H. P. Maruska and J. J. Tietjen, Appl. Phys. Lett. 15, 327 (1969).

[20] W. M. Yim, E. J. Stofko, P. J. Zanzucchi, J. I. Pankove, M. Ettenburg, and S. L. Gilbert, J. Appl. Phys. 44, 292 (1973).

[21] T. L. Tansley and C. P. Foley, J. Appl. Phys. 59, 3241 (1986).

[22] A. S. Barker, Jr. and M. Ilegems, Phys. Rev. B 7, 743 (1973).

[23] G.A. Slack, R.A. Tanzilli, R.O. Pohl, J.W. Vandersande, J. Phys. Chem. Solids, vol. 48, 641 (1987)]

[24] E.K. Sichel, J.I. Pankove [J. Phys. Chem. Solids, vol. 38, 330 (1977)]

[25] D. J. As, A. Ruther, M. Lubbers, J. Mimkes, K. Lischka and D. Schikora. P-type conductivity with a high hole mobility in cubic GaN/GaAs epilayers. Mat. Res. Soc. Symp. Proc. 449, 615-620 (1997).

[26] Z.-J. Tian, M. W. C. Dharma-Wardana, and L. J. Lewis. Electronic structures of wide band-gap (AlN)m(GaN)n [001] superlattices. Mat. Res. Soc. Symp. Proc. 395, 473-478 (1996).

[27] W. R. L. Lambrecht, K. Kim, S. N. Rashkeev, and B. Segall. Electronic and optical properties of the group-III nitrides, their heterostructures and alloys. Mat. Res. Soc. Symp. Proc. 395, 455-466 (1996).

[28] J. A. Majewski, M. Stadele, and P. Vogl. Electronic structure of biaxially strained wurtzite crystals GaN and AlN. Mat. Res. Soc. Symp. Proc. 449, 887-892 (1997).

Home

Wide Band Gap Research

Our research

Revised 2/5/02