Energy-Gap Values for Indium Gallium Nitride and Indium Nitride

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ENERGY-GAP VALUES FOR HEXAGONAL In_xGa_1-xN and InN Author - d.w.palmer@semiconductors.co.uk
When quoting data from here, please state the reference as
D W Palmer, www.semiconductors.co.uk, 2004.

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Shubina et al 2004
New Experimental Data that Indicate an Energy Band-gap of close to 1.4eV for InN
This paper reports experimental data, obtained by photo-luminescence, cathodo-luminescence, transmission electron microscopy and thermally detected optical absorption (TDOA) on MBE-grown and MOCVD-grown hexagaonal InN, that are interpreted as indicating that the well known PL emission from InN at about 0.7eV is due to a transition at an electronic state at the interface between metallic indium inclusions and the InN matrix, and that the actual energy band-gap of hexagaonal InN, as determined from their TDOA data, is close to 1.4eV.

Matsuoka et al 2002
In(x)Ga(1-x)N at Room Temperature for x = 1.0, ie for InN
In experimental studies at room temperature on MOVPE-grown wurzite InN, Matsuoka et al, 2002, have found strong photo-luminescence at 0.76 eV and definite optical absorption at 0.7-1.0 eV; they deduce that the energy gap of wurzite InN is in the range 0.7-1.0 eV, that conclusion being consistent with the 0.7-0.8 eV value proposed by Wu et al 2002 (see below).

Wu et al 2002
In(x)Ga(1-x)N at 77-300 K for x = 1.0, ie for InN
Using the measurement techniques of optical absorption, photo-luminescence and photo-modulated reflectance applied to MBE-grown wurzite InN at 77K and 300K, Wu et al 2002 have deduced an energy gap of 0.7-0.8eV for this semiconductor. That new experimental result is unexpected and surprising since previous studies (see below) have indicated an energy gap of 1.9-2.0 eV for wurzite-structure InN.

O'Donnell et al 2000, and Associated Papers

In(x)Ga(1-x)N at Low Temperature for 0 < x < 0.4
Detailed experimental data on the low temperature (10K) energy-gap values E_g(x) (measured by optical absorption spectroscopy) and dominant photo- luminescence (PL) band peak energies E_p(x) for MOCVD-grown hexagonal (wurzite-structure) In_xGa_1-xN for x between 0.00 and 0.40 have been reported by O'Donnell et al 2000, which includes reference to related information in O'Donnell et al 1999, Martin et al 1999 and O'Donnell et al 1999/2000. The indium contents x of the samples were measured by RBS, EDX, EXAFS and EPMA (electron-probe micro-analysis), including point-to-point composition mapping. A summary of their results is given here.

It is important to note that, because the PL emission is associated with the presence of small indium-rich regions acting probably as quantum dots, E_p(x) is significantly smaller than E_g(x).

O'Donnell et al find that their experimental data for E_g(x) for their In(x)Ga(1-x)N material at or near 10K can be well fitted
both by a function quadratic in x of the form

E_g(x) = (1-x)*E_g(GaN) + x*E_g(InN) - b*x*(1-x)

where b is the "bowing parameter" of the Eg(x) curve,

and by a function linear in x, having a slope m, of the form

E_g(x) = E_g(GaN) + m*x ,

in which, for 10K, the best-fit parameters have values as follows:

E_g(GaN) = 3.50 eV, E_g(InN) = 1.95 eV, b = 2.5 eV, m = - 3.2 eV .

They find, in addition, that E_p(x) is linearly related to E_g(x). The E_p and E_g scales in Fig. 1 of O'Donnell et al 2000 correspond to a relationship for In(x)Ga(1-x)N at 10K that is as follows:

E_p(x) = 1.429*E_g(x) - 1.50 .

The formulae above give the following data for E_g(x) and E_p(x),
and for the corresponding photon wavelengths Lamda,
for In(x)Ga(1-x)N at or near 10K.

.	..	Quadratic Formula for E_g(x)		..	Linear Formula for E_g(x)
Indium Content x	..	E_g(x) (Lamda) eV (nm)	E_p(x) (Lamda) eV (nm)	..	E_g(x) (Lamda) eV (nm)	E_p(x) (Lamda) eV (nm)
.	..	.	.	..	.	.
0.000	..	3.50 (354)	3.50 (354)	..	3.50 (354)	3.50 (354)
0.050	..	3.30 (375)	3.22 (385)	..	3.34 (371)	3.27 (379)
0.100	..	3.12 (397)	2.96 (419)	..	3.18 (390)	3.04 (407)
.	..	..	.	..	.	.
0.150	..	2.95 (420.5)	2.71 (457)	..	3.02 (411)	2.82 (440)
0.200	..	2.79 (444)	2.49 (499)	..	2.86 (434)	2.59 (479)
0.250	..	2.64 (469)	2.28 (544)	..	2.70 (459)	2.36 (526)
.	..	.	.	..	.	.
0.300	..	2.51 (494)	2.09 (594)	..	2.54 (488)	2.13 (582)
0.350	..	2.39 (519)	2.00 (621)	..	2.38 (521)	1.90 (652)
0.400	..	2.28 (544)	1.76 (705)	..	2.22 (559)	1.67 (741)
.	..	.	.	..	.	.

In(x)Ga(1-x)N at 293K for 0 < x < 0.4

O'Donnell et al 1999/2000 reported that their experimental E_g(x) data for In(x)Ga(1-x)N at room temperature for x between 0.00 and 0.40 could be fitted by a linear-in-x formula,

E_g(x) = E_g(GaN) + m*x , as above for low temperature, but with

E_g(GaN) = 3.44 eV (which is not significantly different from the value of 3.45 eV reported by Koide et 1987),
and m = - 3.0 eV .

Concerning E_p, their equations (3) and (4) in that paper lead to an E_p(E_g) relationship that is as follows:

E_p(x) = 1.433*E_g(x) - 1.491 eV .

The formulae above give the following data for E_g(x) and E_p(x),
and for the corresponding photon wavelengths Lamda,
for In(x)Ga(1-x)N at room temperature.

Indium Content x	E_g(x) (Lamda) eV (nm)	E_p(x) (Lamda) eV (nm)
.	.	.
0.000	3.44 (360)	3.44 (360)
0.050	3.29 (377)	3.22 (385)
0.100	3.14 (395)	3.01 (412)
.	.	.
0.150	2.99 (415)	2.79 (444)
0.200	2.84 (437)	2.58 (481)
0.250	2.69 (461)	2.36 (525)
.	.	.
0.300	2.54 (488)	2.15 (577)
0.350	2.39 (519)	1.93 (641)
0.400	2.24 (554)	1.72 (721>
.	.	.

Osamura et al 1975, Nakamura 1994, Nakamura and Fasol 1997

In_xGa_1-xN at 300K for 0 < x < 1.0
Energy-gap values E_g(x) for hexagonal In_xGa_1-xN at 300K are shown in the Table below as calculated by an expression, that was found as the best fit to experimental data for x between 0 and 1 (Osamura et al 1975, Nakamura 1994, Nakamura and Fasol 1997), of the quadratic form

E_g(x) = (1-x)*E_g(GaN) + x*E_g(InN) - b*x*(1-x)

where b is the "bowing parameter" of the Eg(x) curve. The value of x for each In_xGa_1-xN sample was determined in the experimental work by x-ray diffraction measurement of the sample lattice parameters and application of Vegard's Law.

The evaluation here sets E_g(GaN) and E_g(InN) as 3.437eV (Monemar 1974) and 1.950eV (Nakamura 1994) respectively,
and b as 1.00 eV (Nakamura 1994).

The formulae above give the following data for E_g(x) and E_p(x),
and for the corresponding photon wavelengths,
for In(x)Ga(1-x)N at room temperature.

Indium Content x	Energy Gap E_g eV	Corresponding Optical Wavelength nm
.	.	.
0.000	3.437	360.8
0.050	3.315	374
0.100	3.20	388
0.150	3.09	402
0.200	2.98	416
.	.	.
0.250	2.88	431
0.300	2.78	446
0.350	2.69	461
0.400	2.60	476.5
0.450	2.52	492
.	.	.
0.500	2.44	507.5
0.550	2.37	523
0.600	2.305	538
0.650	2.24	553
0.700	2.19	567
.	.	.
0.750	2.13	581
0.800	2.09	594
0.850	2.05	606
0.900	2.01	617
0.950	1.98	627
.	.	.
1.000	1.950	635.9

REFERENCES:

Koide Y, Itoh H, Khan MRH, Hiramatsu K, Sawaki N and Akasaki I, 1987, J. Appl. Phys. 61, 4540
Martin R W, O'Donnell K P, Middleton P G and Van der Stricht W, 1999, Appl. Phys. Lett. 74, 263
Matsuoka T et al, Appl.Phys.Lett. 81 (2002) 1246-1248
Monemar B, 1974, Phys.Rev.B 10, 676
Nakamura S, 1994, Microelec.J. 25, 651
Nakumura S and Fasol G, 1997,"The Blue Laser Diode - GaN Based Light Emitters and Lasers" (Springer)
O'Donnell K P, Martin R W, Middleton P G, 1999, Phys. Rev. Lett. 82, 237
O'Donnell K P, Martin R W , White M E, Jacobs K, Van der Stricht W, Demeester P, Vantomme A,
Wu M F and Mosselmans J F W, 1999/2000,
MRS Fall Meeting 1999: Mat. Res. Soc. Symp. Vol.595 (2000), W 11.26
O'Donnell K P, Martin R W, Trager-Cowan C, White M E, Esona K, Deatcher C, Middleton P G,
Jacobs K, Van der Stricht W, Merlet C, Gil B, Vantomme A and Mosselmans J F W, 2000,
E-MRS Spring Meeting 2000, Strasbourg: to be published in Mat. Sci. Eng. B
Osamura K, Naka S and Murakami Y, J.Appl.Phys. 46 (1975) 3432
Shubina T V, Ivanov S V, Jmerik V N, Solnyshkov D D, Veshkin V A, Kop'ev P S, Vasson A,
. . . . Leymarie J, Kavokin A, Amano H, Shimono K, Kasic A and Monemar B
. . . . 2004, Phys. Rev. Lett. 92 (19 March 2004) 117407-1 to 117407-4
Tansley T L, Goldys E M, Godlewski M, Zhou B and Zuo H Y, 1997a,
. . . . in "GaN and Related Materials", S J Pearton (Ed.), (Gordon and Breach, 1997) p.233
Wu J, Appl.Phys.Lett. 80 (2002) 3967-3969

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