Nitride Parameters

K 6 U ] $ Nitride Parameters%6Physical Constants for Transport Studies of the Group III-Nitrides

Table I: Nitride Parameters
?B%###8&(((3<HHHC2NNNE2NNN9$NNN;$NNN:&=;>B&]<=P"@;@G-]<>5";;;;#<<<E/C==E/&=&E/&=&E/&<&@">>>A%LLL3'>==3'>==11@FG-1;;&3$PQW-$PQQ3%?@?/$L&&/->>&4%<:&,->==
Units GaN AlN InN
Crystal Structure Wurtzite Wurtzite Wurtzite
Density g/cm³ 6.15 [1] 3.23 [1] 6.81 [1]
Transverse Constant (C_t) dyn/cm² 4.42 x 10¹¹ [1] 4.42 x 10¹¹ [1] 4.42 x 10¹¹ [1]
Longitudinal Constant (C_l) dyn/cm² 2.65 x 10¹² [1] 2.65 x 10¹² [1] 2.65 x 10¹² [1]
Transverse Sound Velocity cm/s 2.68 x 10⁵ [2] 3.70 x 10⁵ [2] 2.55 x 10⁵ [2]
Longitudinal Sound Velocity cm/s 6.56 x 10⁵ [2] 9.06 x 10⁵ [2] 6.24 x 10⁵ [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 (GValley) m_e 0.20 [3] and [22] 0.48 [1] 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/m² 0.375 [1] 0.92 [4] 0.375 [1]
Piezoelectric Constant e₁₅ C/m² -0.58 [5]
Piezoelectric Constant e₃₁ C/m² -0.48 [5]
Piezoelectric Constant e₃₃ C/m² 1.55 [5]
Intervalley Coupling Coefficient eV 91.2 [6] 99.2 [6] 89.0 [6]
Intervalley Deformation Potential eV/cm 1 x 10⁹ [7] 1 x 10⁹ [7] 1 x 10⁹ [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 cm²/Vs 1000 [14] 135 [15] 3200 [16]
Hole mobility cm²/Vs 30 [13] 14 [13]
Saturation velocity cm/s 2.5 x 10⁷ [14] 1.4 x 10⁷ [15] 2.5 x 10⁷ [16]
Peak velocity cm/s 3.1 x 10⁷ [14] 1.7 x 10⁷ [15] 4.3 x 10⁷ [16]
Peak velocity field kV/cm 150 [14] 450 [15] 67 [16]
Breakdown field V/cm >5 x 10⁶ [13]
Light hole mass m_e 0.259 [13] 0.471 [13]
Thermal Conductivity W/cmK 1.5 [13] 2 [13]
Melting Temp ^oC >1700 [13] 3000 [13] 1100 [13]
FExcept for the data in the table below, the zinc-blende GaN parameters/are taken equal to the wurtzite GaN parameters.

Table II: Zinc-blende Specific Data
>&%1:'<11?3$O-$O3%>
Units GaN (Zinc-blende)
Lattice Constant, a Angstr. 4.52 [10]
Electron Mobility cm²/Vs 1500 [18]
Saturation velocity cm/s 2.5 x 10⁷ [18]
Peak velocity cm/s 3.5 x 10⁷ [18]
Peak velocity field kV/cm 110 [18]
!

Table III: Band Structure Data
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Units GaN (Cubic) GaN (Wurtz) AlN InN
Gamma Valley Energy Gap eV 3.2 [10] 3.39 [19] 6.2 [20] 1.89 [21]
Effective Mass m_e 0.15 [11] 0.20 [3] and [22] 0.48 [1] 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 m_e 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 m_e 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
GThe energy gaps of the second and third valleys were obtained by takingIthe differences between the upper valley conduction band minimums and theIgamma valley minimum (taken from Ref. [9]) and addingGthem to the energy gap of the gamma valley. The degeneracy of the upperOvalleys were obtained from Ref. [9] also. Due to variationsGin band structure calculations, the effective mass of the upper valleysFis set to the mass of the free electron and the nonparabolicity of theHupper valleys is set to zero. The nonparabolicity of the gamma valley is9calculated using the Kane model [12].C

References]H

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

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

V_t = Sqrt(C_t/r)"P

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

V_l = Sqrt(C_l/r).F

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

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

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

[6] The intervalley coupling constant is assumedJto be the same energy as the polar optical phonon energy, an approximationwhich holds for GaAs [8]. I

[7] The intervalley deformation potential assumedsto be the same as GaAs [8].)N

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

[9] W. R. L. Lambrecht and B. Segall, in PropertiesHof Group III Nitrides, No. 11 EMIS Datareviews Series, edited3by J. H. Edgar ( Inspec, London, 1994 ), Chapter 4.AG

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

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

[12] The nonparabolicity is calculated from the KaneGModel. The energy of the G valley is assumedH/to be non-parabolic, spherical, and of the formII

h²k²/2m* = E(1/*+ aE),O

where k denotes the wavevector, E represents the energy, m* is the effectiveNImass, and the non-parabolicity coefficient, a,is given by W

a = (1 - m*/m_e)²/E_g/ ,F

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

[13] Michael S. Shur and M. Asif Khan, Mat. Res.Bull. 22 (2), 44 (1997)."K

[14] U. V. Bhapkar and M. S. Shur, J. Appl. Phys.,r82 (4), 1649 (1997).NF

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

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

[17] Jan Kolnik, Ismail H. Oguzman, Kevin F. Brennan,9FRongping Wang, P. Paul Ruden, and Yang Wang, J. Appl. Phys. 78,1033 (1995).Q

[18] Unpublished. For means of comparison GaN Zinc-blende Htransport data was calculated using the same Monte Carlo program used toGcalculate the transport data from Refs. [14-16].DJ

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

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

[21] T. L. Tansley and C. P. Foley, J. Appl. Phys.1

	Units	GaN	AlN	InN
Crystal Structure		Wurtzite	Wurtzite	Wurtzite
Density	g/cm³	6.15 [1]	3.23 [1]	6.81 [1]
Transverse Constant (C_t)	dyn/cm²	4.42 x 10¹¹ [1]	4.42 x 10¹¹ [1]	4.42 x 10¹¹ [1]
Longitudinal Constant (C_l)	dyn/cm²	2.65 x 10¹² [1]	2.65 x 10¹² [1]	2.65 x 10¹² [1]
Transverse Sound Velocity	cm/s	2.68 x 10⁵ [2]	3.70 x 10⁵ [2]	2.55 x 10⁵ [2]
Longitudinal Sound Velocity	cm/s	6.56 x 10⁵ [2]	9.06 x 10⁵ [2]	6.24 x 10⁵ [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 (GValley)	m_e	0.20 [3] and [22]	0.48 [1]	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/m²	0.375 [1]	0.92 [4]	0.375 [1]
Piezoelectric Constant e₁₅	C/m²		-0.58 [5]
Piezoelectric Constant e₃₁	C/m²		-0.48 [5]
Piezoelectric Constant e₃₃	C/m²		1.55 [5]
Intervalley Coupling Coefficient	eV	91.2 [6]	99.2 [6]	89.0 [6]
Intervalley Deformation Potential	eV/cm	1 x 10⁹ [7]	1 x 10⁹ [7]	1 x 10⁹ [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	cm²/Vs	1000 [14]	135 [15]	3200 [16]
Hole mobility	cm²/Vs	30 [13]	14 [13]
Saturation velocity	cm/s	2.5 x 10⁷ [14]	1.4 x 10⁷ [15]	2.5 x 10⁷ [16]
Peak velocity	cm/s	3.1 x 10⁷ [14]	1.7 x 10⁷ [15]	4.3 x 10⁷ [16]
Peak velocity field	kV/cm	150 [14]	450 [15]	67 [16]
Breakdown field	V/cm	>5 x 10⁶ [13]
Light hole mass	m_e	0.259 [13]	0.471 [13]
Thermal Conductivity	W/cmK	1.5 [13]	2 [13]
Melting Temp	^oC	>1700 [13]	3000 [13]	1100 [13]

	Units	GaN (Zinc-blende)
Lattice Constant, a	Angstr.	4.52 [10]
Electron Mobility	cm²/Vs	1500 [18]
Saturation velocity	cm/s	2.5 x 10⁷ [18]
Peak velocity	cm/s	3.5 x 10⁷ [18]
Peak velocity field	kV/cm	110 [18]

		Units	GaN (Cubic)	GaN (Wurtz)	AlN	InN
Gamma Valley	Energy Gap	eV	3.2 [10]	3.39 [19]	6.2 [20]	1.89 [21]
	Effective Mass	m_e	0.15 [11]	0.20 [3] and [22]	0.48 [1]	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	m_e	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	m_e	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