Statistical Model Applied To Ax By C1-x-y D Quaternary Alloys: Bond Lengths And Energy Gaps Of Alx Gay In1-x-y X (x=as, P, Or N) Systems

We extend the generalized quasichemical approach (GQCA) to describe the Ax By C1-x-y D quaternary alloys in the zinc-blende structure. Combining this model with ab initio ultrasoft pseudopotential calculations within density functional theory, the structural and electronic properties of Alx Gay In1-x-y X (X=As, P, or N) quaternary alloys are obtained, taking into account the disorder and composition effects. Results for the bond lengths show that the variation with the compositions is approximately linear and also does not deviate very much from the value of the corresponding binary compounds. The maximum variation observed amounts to 3.6% for the In-N bond length. For the variation of band gap, we obtain a bowing parameter b=0.26 eV for the (Ga0.47 In0.53 As)z (Al0.48 In0.52 As)1-z quaternary alloy lattice matched to InP, in very good agreement with experimental data. In the case of AlGaInN, we compare our results for the band gap to data for the wurtzite phase. We also obtained a good agreement despite all evidences for cluster formation in this alloy. Finally, a bowing parameter of 0.22 eV is obtained for zinc-blende AlGaInN lattice matched with GaN. © 2006 The American Physical Society.7323Li, J., Nam, K.B., Kim, K.H., Lin, J.Y., Jiang, H.X., (2001) Appl. Phys. Lett., 78, p. 61. , APPLAB 0003-6951 10.1063/1.1331087Adivarahan, V., Chitnis, A., Zhang, J.P., Shatalov, M., Yang, J.W., Simin, G., Asif Khan, M., Shur, M.S., (2001) Appl. Phys. Lett., 79, p. 4240. , APPLAB 0003-6951 10.1063/1.1425453Yasan, A., McClintock, R., Mayes, K., Darvish, S.R., Kung, P., Razegui, M., (2002) Appl. Phys. Lett., 81, p. 801. , APPLAB 0003-6951 10.1063/1.1497709Nagahama, S., Yanamoto, T., Sano, M., Mukai, T., (2001) Jpn. J. Appl. Phys., Part 1, 40, p. 788. , JAPNDE 0021-4922 10.1143/JJAP.40.L788Fujii, T., Nakata, Y., Sigiyama, Y., Hiyiamizu, S., (1986) Jpn. J. Appl. Phys., 25, p. 254. , JAPLD8 0021-4922Olego, D., Chang, T.Y., Silberg, E., Caridi, E.A., Pinczuk, A., (1982) Appl. Phys. Lett., 41, p. 476. , APPLAB 0003-6951 10.1063/1.93537Hirayama, H., Kinoshita, A., Yamabi, T., Enomoto, Y., Hirata, A., Araki, T., Nanishi, Y., Aoyagi, Y., (2002) Appl. Phys. Lett., 80, p. 207. , APPLAB 0003-6951 10.1063/1.1433162Takayama, T., Yuri, M., Itoh, K., Baba, T., Harris Jr., J.S., (2001) J. Cryst. Growth, 222, p. 29. , JCRGAE 0022-0248 10.1016/S0022-0248(00)00869-1Koukitu, A., Kumegai, Y., Seki, H., (2000) J. Cryst. Growth, 221, p. 743. , JCRGAE 0022-0248Feng, S.-W., Cheng, Y.-C., Chung, Y.-Y., Yang, C.C., Ma, K.-J., Yan, C.-C., Hsu, C., Jiang, H.X., (2003) Appl. Phys. Lett., 82, p. 1377. , APPLAB 0003-6951 10.1063/1.1556965Chen, C.H., Chen, Y.F., Lan, Z.H., Chen, L.C., Chen, K.H., Jiang, H.X., Lin, J.Y., (2004) Appl. Phys. Lett., 84, p. 1480. , APPLAB 0003-6951 10.1063/1.1650549Marques, M., Teles, L.K., Scolfaro, L.M.R., Ferreira, L.G., Leite, J.R., (2004) Phys. Rev. B, 70, p. 073202. , PRBMDO 0163-1829 10.1103/PhysRevB.70.073202Marques, M., Ferreira, L.G., Teles, L.K., Scolfaro, L.M.R., (2005) Phys. Rev. B, 71, p. 205204. , PRBMDO 0163-1829 10.1103/PhysRevB.71.205204Teles, L.K., Furthmüller, J., Scolfaro, L.M.R., Leite, J.R., Bechstedt, F., (2000) Phys. Rev. B, 62, p. 2475. , PRBMDO. 0163-1829. 10.1103/PhysRevB.62.2475Teles, L.K., Scolfaro, L.M.R., Leite, J.R., Furthmüller, J., Bechstedt, F., (2002) J. Appl. Phys., 92, p. 7109. , JAPIAU. 0021-8979. 10.1063/1.1518136Teles, L.K., Furthmüller, J., Scolfaro, L.M.R., Leite, J.R., Bechstedt, F., (2001) Phys. Rev. B, 63, p. 085204. , PRBMDO. 0163-1829. 10.1103/PhysRevB.63.085204Teles, L.K., Scolfaro, L.M.R., Leite, J.R., Furthmüller, J., Bechstedt, F., (2002) Appl. Phys. Lett., 80, p. 1177. , APPLAB. 0003-6951. 10.1063/1.1450261Tabata, A., Teles, L.K., Scolfaro, L.M.R., Leite, J.R., Kharchenko, A., Frey, T., As, D.J., Bechstedt, F., (2002) Appl. Phys. Lett., 80, p. 769. , APPLAB. 0003-6951. 10.1063/1.1436270Connolly, J.W.D., Williams, A.R., (1983) Phys. Rev. B, 27, p. 5169. , PRBMDO 0163-1829 10.1103/PhysRevB.27.5169Chen, A.-B., Sher, A., (1995) Semiconductor Alloys, , Plenum Press, New YorkKresse, G., Furthmüller, J., (1996) Comput. Mater. Sci., 6, p. 15. , CMMSEM. 0927-0256. 10.1016/0927-0256(96)00008-0Kresse, G., Furthmüller, J., (1996) Phys. Rev. B, 54, p. 11169. , PRBMDO. 0163-1829. 10.1103/PhysRevB.54.11169Hohenberg, P., Kohn, W., (1964) Phys. Rev., 136, p. 864. , PRVBAK 0096-8269 10.1103/PhysRev.136.B864Kohn, W., Sham, L.J., (1965) Phys. Rev., 140, p. 1133. , PRVAAH 0096-8250 10.1103/PhysRev.140.A1133Vanderbilt, D., (1990) Phys. Rev. B, 41, p. 7892. , PRBMDO 0163-1829 10.1103/PhysRevB.41.7892Perdew, J.P., Zunger, A., (1981) Phys. Rev. B, 23, p. 5048. , PRBMDO 0163-1829 10.1103/PhysRevB.23.5048Monkhorst, H.J., Pack, J.D., (1976) Phys. Rev. B, 13, p. 5188. , PLRBAQ 0556-2805 10.1103/PhysRevB.13.5188Marques, M., Teles, L.K., Scolfaro, L.M.R., Leite, J.R., Furthmüller, J., Bechstedt, F., (2003) Appl. Phys. Lett., 83, p. 890. , APPLAB. 0003-6951. 10.1063/1.1597986Jeffs, N.J., Blant, A.V., Cheng, T.S., Foxon, C.T., Bailey, C., Harrison, P.G., Mosselmans, J.F.W., Dent, A.J., (1998) Mater. Res. Soc. Symp. Proc., 512, p. 519. , MRSPDH 0272-9172Miyano, K.E., Woicik, J.C., Robins, L.H., Bouldin, C.E., Wickenden, D.K., (1997) Appl. Phys. Lett., 70, p. 2108. , APPLAB 0003-6951 10.1063/1.118963Saito, T., Arakawa, Y., (1999) Phys. Rev. B, 60, p. 1701. , PRBMDO 0163-1829 10.1103/PhysRevB.60.1701Sze, S.M., (1981) Physics of Semiconductor Devices, , Wiley, New YorkChen, S.-G., Fan, X.-Q., (1997) J. Phys.: Condens. Matter, 9, p. 3151. , JCOMEL 0953-8984 10.1088/0953-8984/9/15/008Sökeland, F., Rohlfing, M., Krüger, P., Pollmann, J., (2003) Phys. Rev. B, 68, p. 075203. , PRBMDO. 0163-1829. 10.1103/PhysRevB.68.075203Schörmann, J., Potthast, S., Schnietz, M., Li, S.F., As, D.J., Lischka, K., Phys. Status Solidi C, , ZZZZZZ. 1610-1634 (to be published)Yu. Davydov, V., Klochikhin, A.A., Seisyan, R.P., Emtsev, V.V., Ivanov, S.V., Bechstedt, F., Furthmüller, J., Graul, J., (2002) Phys. Status Solidi B, 229, p. 1. , PSSBBD. 0370-1972. 10.1002/1521-3951(200202)229:33.0.CO;2-OYu. Davydov, V., Klochikhin, A.A., Emtsev, V.V., Kurdyukov, D.A., Ivanov, S.V., Vekshin, V.A., Bechstedt, F., Haller, E.E., (2002) Phys. Status Solidi B, 234, p. 787. , PSSBBD. 0370-1972. 10.1002/1521-3951(200212)234:33.0.CO;2-HBechstedt, F., Furthmüller, J., Ferhat, M., Teles, L.K., Scolfaro, L.M.R., Leite, J.R., Yu. Davydov, V., Goldhahn, R., (2003) Phys. Status Solidi a, 195, p. 628. , PSSABA. 0031-8965. 10.1002/pssa.200306164(1998) Gallium Nitride (GaN) I and II, Semiconductors and Semimetals, 50. , edited by J. I. Pankove and T. D. Moustakas, Vol. Academic Press, New York(1999), 57. , ibid. Vol. Academic Press, New YorkNadja, S.P., Kean, A.H., Dawson, M.D., Duggan, G., (1995) J. Appl. Phys., 77, p. 3412. , JAPIAU 0021-8979 10.1063/1.358631McIntosh, F.G., Boutros, K.S., Roberts, J.C., Bedair, S.M., Piner, E.L., El-Masry, N.A., (1996) Appl. Phys. Lett., 68, p. 40. , APPLAB 0003-6951 10.1063/1.116749Ryu, M.-Y., Chen, C.Q., Kuokstis, E., Yang, J.W., Simin, G., Khan, M.A., W. Yu, S.P., (2002) Appl. Phys. Lett., 80, p. 3943. , APPLAB 0003-6951 10.1063/1.1482415Yamaguchi, S., Kariya, M., Nitta, S., Kato, H., Takeuchi, T., Wetzel, C., Amano, H., Akasaki, I., (1998) J. Cryst. Growth, 195, p. 309. , JCRGAE 0022-0248 10.1016/S0022-0248(98)00629-0Davies, J.I., Marshall, A.C., Scott, M.D., Griffiths, R.J.M., (1988) Appl. Phys. Lett., 53, p. 276. , APPLAB 0003-6951 10.1063/1.100593Kopf, R.F., Wei, H.P., Perley, A.P., Livescu, G., (1992) Appl. Phys. Lett., 60, p. 2386. , APPLAB 0003-6951 10.1063/1.107005Cury, L.A., Beerens, J., Praseuth, J.P., (1993) Appl. Phys. Lett., 63, p. 1804. , APPLAB 0003-6951 10.1063/1.110668Böhrer, J., Krost, A., Bimberg, D.B., (1993) Appl. Phys. Lett., 63, p. 1918. , APPLAB. 0003-6951. 10.1063/1.110648Fan, J.C., Chen, Y.F., (1996) J. Appl. Phys., 80, p. 1239. , JAPIAU 0021-8979 10.1063/1.362862Vurgaftman, I., Meyer, J.R., Ram-Mohan, L.R., (2001) J. Appl. Phys., 89, p. 5815. , JAPIAU 0021-8979 10.1063/1.1368156Han, J., Figiel, J.J., Petersen, G.A., Myers, S.M., Crawford, M.H., Banas, M.A., (2000) Jpn. J. Appl. Phys., Part 1, 39, p. 2372. , JAPNDE 0021-4922 10.1143/JJAP.39.2372Aumer, M.E., Leboeuf, S.F., McIntosh, F.G., Bedair, S.M., (1999) Appl. Phys. Lett., 75, p. 3315. , APPLAB 0003-6951 10.1063/1.12533

Magnetic Properties Of Gan Mnx Ga1-x N Digital Heterostructures: First-principles And Monte Carlo Calculations

The energetic and magnetic properties of wurtzite GaN Mnx Ga1-x N digital heterostructures are investigated by first-principles total energy calculations, within the spin density-functional theory, and Monte Carlo simulations. In a wurtzite GaN model sample, periodic in the c axis, we replace a GaN monolayer (a plane) by a plane with composition Mnx Ga1-x N, and study its properties for varying the GaN spacer layer thickness and Mn concentration x. The 100% MnN monolayer possesses an antiferromagnetic (AFM) ground state when, in the periodic sample, it is isolated from the other MnN monolayers by more than four GaN spacer layers. The case of submonolayers (x<1) is studied by Monte Carlo simulations based on an Ising Hamiltonian, whose parameters are obtained from ab initio calculations on five configurations. At 700°C, up to the concentration of 8% Mn, the two-dimensional (2D) alloy is stable. However, above this concentration, there is a strong tendency to the formation of MnN clusters with an AFM ground state defined by ferromagnetic Mn rows coupled antiferromagnetically with other Mn rows. The behavior of the magnetization with the temperature is completely different in these two concentration regimes, with the 2D MnN cluster being very stable, whereas the 2D alloy presents low magnetic transition temperatures. © 2006 The American Physical Society.7322Wolf, S.A., Awschalom, D.D., Buhrman, R.A., Daughton, J.M., Von Molnár, S., Roukes, M.L., Chtchelkanova, A.Y., Treger, D.M., (2001) Science, 294, p. 1488. , SCIEAS. 0036-8075. 10.1126/science.1065389Ohno, H., (1998) Science, 281, p. 951. , SCIEAS 0036-8075 10.1126/science.281.5379.951Ohno, H., Shen, A., Matsukura, F., Oiwa, A., Endo, A., Katsumoto, S., Iye, Y., (1996) Appl. Phys. Lett., 69, p. 363. , APPLAB 0003-6951 10.1063/1.118061Kawakami, R.K., Johnston-Halperin, E., Chen, L.F., Hanson, M., Guebels, N., Speck, J.S., Gossard, A.C., Awschalom, D.D., (2000) Appl. Phys. Lett., 77, p. 2379. , APPLAB 0003-6951 10.1063/1.1316775Sanvito, S., (2003) Phys. Rev. B, 68, p. 054425. , PRBMDO 0163-1829 10.1103/PhysRevB.68.054425Dietl, T., Ohno, H., Matsukura, F., Cibert, J., Ferrand, D., (2000) Science, 287, p. 1019. , SCIEAS 0036-8075 10.1126/science.287.5455.1019Bergqvist, L., Eriksson, O., Kudrnovský, J., Drchal, V., Korzhavyi, P., Turek, I., (2004) Phys. Rev. Lett., 93, p. 137202. , PRLTAO. 0031-9007. 10.1103/PhysRevLett.93.137202Sato, K., Dederichs, P.H., Katayama-Yoshida, H., (2005) J. Supercond., 18, p. 33. , JOUSEH 0896-1107 10.1007/s10948-005-2146-8Hori, H., Sonoda, S., Sasaki, T., Yamamoto, Y., Shimizu, S., Suga, K., Kindo, K., (2002) Physica B, 324, p. 142. , PHYBE3 0921-4526 10.1016/S0921-4526(02)01288-7Reed, M.L., El-Masry, N.A., Stadelmaier, H.H., Ritums, M.K., Reed, M.J., Parker, C.A., Roberts, J.C., Bedair, S.M., (2001) Appl. Phys. Lett., 79, p. 3473. , APPLAB 0003-6951 10.1063/1.1419231Overberg, M.E., Abernathy, C.R., Pearton, S.J., Theodoropoulou, N.A., McCarthy, K.T., Hebarb, A.F., (2001) Appl. Phys. Lett., 79, p. 1312. , APPLAB 0003-6951 10.1063/1.1397763Theodoropoulou, N.A., Hebarb, A.F., Overberg, M.E., Abernathy, C.R., Pearton, S.J., Chu, S.N.G., Wilson, R.G., (2001) Appl. Phys. Lett., 78, p. 3475. , APPLAB 0003-6951 10.1063/1.1376659Zajac, M., Gosk, J., Kaminska, M., Twardowski, A., Szyszko, T., Podsiadlo, S., (2001) Appl. Phys. Lett., 79, p. 2432. , APPLAB 0003-6951 10.1063/1.1406558Boselli, M.A., Da Cunha Lima, I.C., Leite, J.R., Troper, A., Ghazalli, A., (2004) Appl. Phys. Lett., 84, p. 1138. , APPLAB 0003-6951 10.1063/1.1646759Hohenberg, P., Kohn, W., (1964) Phys. Rev., 136, p. 864. , PRVBAK 0096-8269 10.1103/PhysRev.136.B864Kohn, W., Sham, L.J., (1965) Phys. Rev., 140, p. 1133. , PRVAAH 0096-8250 10.1103/PhysRev.140.A1133Wang, Y., Perdew, J.P., (1991) Phys. Rev. B, 43, p. 8911. , PRBMDO 0163-1829 10.1103/PhysRevB.43.8911Kresse, G., Furthmüller, J., (1996) Comput. Mater. Sci., 6, p. 15. , CMMSEM. 0927-0256. 10.1016/0927-0256(96)00008-0Kresse, G., Furthmüller, J., (1996) Phys. Rev. B, 54, p. 11169. , PRBMDO. 0163-1829. 10.1103/PhysRevB.54.11169Kresse, G., Joubert, D., (1999) Phys. Rev. B, 59, p. 1758. , PRBMDO 0163-1829 10.1103/PhysRevB.59.1758Monkhorst, H.J., Pack, J.D., (1974) Phys. Rev. B, 13, p. 5188. , PLRBAQ 0556-2805 10.1103/PhysRevB.13.5188Kronik, L., Jain, M., Chelikowsky, J.R., (2002) Phys. Rev. B, 66, p. 041203. , PRBMDO 0163-1829 10.1103/PhysRevB.66.041203Sanyal, B., Bengone, O., Mirbt, S., (2003) Phys. Rev. B, 68, p. 205210. , PRBMDO 0163-1829 10.1103/PhysRevB.68.205210Sanvito, S., Hill, N.A., (2001) Phys. Rev. Lett., 87, p. 267202. , PRLTAO 0031-9007 10.1103/PhysRevLett.87.267202Schmidt, G., Ferrand, D., Molenkamp, L.W., Filip, A.T., Van Wees, B.J., (2000) Phys. Rev. B, 62, p. 4790. , PRBMDO 0163-1829 10.1103/PhysRevB.62.R4790Pickett, W.E., Moodera, J.S., (2001) Phys. Today, 54, p. 39. , PHTOAD 0031-9228Marques, M., Teles, L.K., Scolfaro, L.M.R., Ferreira, L.G., Leite, J.R., (2004) Phys. Rev. B, 70, p. 073202. , PRBMDO 0163-1829 10.1103/PhysRevB.70.07320

Theoretical prediction of ferromagnetic MnN layers embedded in wurtzite GaN

We studied, using the spin density functional theory, the manganese mononitride (MnN) grown on GaN in the wurtzite phase, forming the GaN/MnN heterostructures. We obtained a ferromagnetic ground state with a higher magnetic moment than the hypothetical wurtzite bulk MnN. This behavior can be explained in terms of the high magnetization of the MnN interface monolayers that have longer first and second neighbors bond lengths due to structure relaxation. We suggest that this system can be applied to the new spintronics technology by being able to provide spin polarized carriers in the important wide-gap nitride systems.88

Effect of nanostructuration on compressibility of cubic BN

Compressibility of high-purity nanostructured cBN has been studied under quasi-hydrostatic conditions at 300 K up to 35 GPa using diamond anvil cell and angle-dispersive synchrotron X-ray powder diffraction. A data fit to the Vinet equation of state yields the values of the bulk modulus B0 of 375(4) GPa with its first pressure derivative B0' of 2.3(3). The nanometer grain size (\sim20 nm) results in decrease of the bulk modulus by ~9%

Electronic and Optical Properties of Small Metal Fluoride Clusters

We report a systematic investigation on the electronic and optical properties of the smallest stable clusters of alkaline-earth metal fluorides, namely, MgF2, CaF2, SrF2, and BaF2. For these clusters, we perform density functional theory (DFT) and time-dependent DFT (TDDFT) calculations with a localized Gaussian basis set. For each molecule ((MF2)n, n = 1-3, M = Mg, Ca, Sr, Ba), we determine a series of molecular properties, namely, ground-state energies, fragmentation energies, electron affinities, ionization energies, fundamental energy gaps, optical absorption spectra, and exciton binding energies. We compare electronic and optical properties between clusters of different sizes with the same metal atom and between clusters of the same size with different metal atoms. From this analysis, it turns out that MgF2 clusters have distinguished ground-state and excited-state properties with respect to the other fluoride molecules. Sizeable reductions of the optical onset energies and a consistent increase of excitonic effects are observed for all clusters under study with respect to the corresponding bulk systems. Possible consequences of the present results are discussed with respect to applied and fundamental research

Magnetic properties of GaN/MnxGa1-xN digital heterostructures: First-principles and Monte Carlo calculations

The energetic and magnetic properties of wurtzite GaN/MnxGa1-xN digital heterostructures are investigated by first-principles total energy calculations, within the spin density-functional theory, and Monte Carlo simulations. In a wurtzite GaN model sample, periodic in the c axis, we replace a GaN monolayer (a plane) by a plane with composition MnxGa1-xN, and study its properties for varying the GaN spacer layer thickness and Mn concentration x. The 100% MnN monolayer possesses an antiferromagnetic (AFM) ground state when, in the periodic sample, it is isolated from the other MnN monolayers by more than four GaN spacer layers. The case of submonolayers (x < 1) is studied by Monte Carlo simulations based on an Ising Hamiltonian, whose parameters are obtained from ab initio calculations on five configurations. At 700 degrees C, up to the concentration of 8% Mn, the two-dimensional (2D) alloy is stable. However, above this concentration, there is a strong tendency to the formation of MnN clusters with an AFM ground state defined by ferromagnetic Mn rows coupled antiferromagnetically with other Mn rows. The behavior of the magnetization with the temperature is completely different in these two concentration regimes, with the 2D MnN cluster being very stable, whereas the 2D alloy presents low magnetic transition temperatures.732

Magnetic properties of MnN: Influence of strain and crystal structure

For manganese mononitride (MnN), the total energy versus lattice constant is obtained using the spin density functional theory. Instead of the tetragonally distorted NaCl structure, we study the zinc blende and wurtzite structures in which AlN, GaN, and InN crystallize. The ground state with nonmagnetic, antiferromagnetic (AFM), or ferromagnetic (FM) arrangement of spins depends on the polymorph of MnN and on the lattice constant. At equilibrium lattice constants, in zinc blende it is AFM in [100] direction, and in wurtzite it is FM. The zinc blende polytype of MnN under hydrostatic pressure at the InN lattice constant presents FM ground state. For the wurtzite polytype at the GaN and AIN lattice constants, the AFM is the ground state, but goes back to a FM ground state for the InN lattice constants. For both, structures, the system presents a half-metallic state at InN lattice constants (with a total magnetic moment of 4 mu(B) per Mn atom) instead of the metallic state obtained for smaller lattice constants. Results indicate that the FM or the AFM state of Ga1-xMnxN and In1-xMnxN may be related to, relaxed, or strained, MnN incorporations or Mn-rich composition fluctuations. (c) 2005 American Institute of Physics.861

Statistical model applied to A(x)B(y)C(1-x-y)D quaternary alloys: Bond lengths and energy gaps of AlxGayIn1-x-yX (X=As, P, or N) systems

We extend the generalized quasichemical approach (GQCA) to describe the A(x)B(y)C(1-x-y)D quaternary alloys in the zinc-blende structure. Combining this model with ab initio ultrasoft pseudopotential calculations within density functional theory, the structural and electronic properties of AlxGayIn1-x-yX (X=As, P, or N) quaternary alloys are obtained, taking into account the disorder and composition effects. Results for the bond lengths show that the variation with the compositions is approximately linear and also does not deviate very much from the value of the corresponding binary compounds. The maximum variation observed amounts to 3.6% for the In-N bond length. For the variation of band gap, we obtain a bowing parameter b=0.26 eV for the (Ga0.47In0.53As)(z)(Al0.48In0.52As)(1-z) quaternary alloy lattice matched to InP, in very good agreement with experimental data. In the case of AlGaInN, we compare our results for the band gap to data for the wurtzite phase. We also obtained a good agreement despite all evidences for cluster formation in this alloy. Finally, a bowing parameter of 0.22 eV is obtained for zinc-blende AlGaInN lattice matched with GaN.732