Polaronic Effects in Wurtzite In_xGa_1-xN/GaN Parabolic Quantum Well

Abstract:

The energy levels of polaron in a wurtzite InxGa1-xN/GaN parabolic quantum well are investigated by adopting a modified Lee-Low-Pines variational method. The ground state energy, the transition energy and the contributions of different branches of optical phonon modes to the ground state energy as functions of the well width are given. The effects of the anisotropy of optical phonon modes and the spatial dependence effective mass, dielectric constant, phonon frequency on energy levels are considered in calculation. In order to compare, the corresponding results in zinc-blende parabolic quantum well are given. The results indicate that the contributions of the electron-optical phonon interaction to ground state energy of polaron in InxGa1-xN/GaN is very large, and make the energy of polaron reduces. For a narrower quantum well，the contributions of half-space optical phonon modes is large , while for a wider one, the contributions of the confined optical phonon modes are larger. The ground state energy and the transition energy of polaron in wurtzite InxGa1-xN/GaN are smaller than that of zinc-blende InxGa1-xN/GaN, and the contributions of the electron-optical phonon interaction to ground state energy of polaron in wurtzite InxGa1-xN/GaN are greater than that of zinc-blende InxGa1-xN/GaN. The contributions of the electron-optical phonon interaction to ground state energy of polaron in wurtzite InxGa1-xN/GaN (about from 22 to 32 meV) are greater than that of GaAs/AlxGa1-xAs parabolic quantum well (about from 1.8 to 3.2 meV). Therefore, the electron-optical phonon interaction should be considered for studying electron state in InxGa1-xN/GaN parabolic quantum well.

• Periodical: Advanced Materials Research (Volume 629)
• Pages: 145-151
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.629.145
• Online since: December 2012
• Authors: Ren Tu Ya Wu, Qi Zhao Feng
• Keywords: Electron-Optical Phonon Interaction, Nitride Parabolic Quantum Well, Polaron

References

[1] Perkins JD, Mascarenhas A, Zhang Y, Geisz JF. Friedman DJ, Olson JM, et al. Nitrogen-activated transition, level repulsion, and ban gap reduction in GaAs1-xNx with x<0. 03. Phys. Rev. Lett., 1999; 82: 3312-3315.

[2] Wang RM, Chen GD, Zhu YZ. Micro-Raman scattering study of hexagonal InGaN epitaxial layer. Acta Phys. Sin., 2006; 55: 914 -919.

DOI: 10.7498/aps.55.914

[3] Lee BC, Kim KW, Dutta M, Stroscio MA. Electron-optical-phonon scattering in wurtzite crystals. Phys. Rev. B, 1997; 56: 997-1000.

DOI: 10.1103/physrevb.56.997

[4] Lee BC, Kim KW, Stroscio MA, Dutta M. Optical-phonon confinement and scattering in wurtzite heterostructures. Phys. Rev. B, 1998; 58: 4860-4865.

DOI: 10.1103/physrevb.58.4860

[5] Komirenko SM, Kim KW, Stroscio MA, Dutta M. Energy-dependent electron scattering via interaction with optical phonons in wurtzite crystals and quantum wells. Phys. Rev. B, 2000; 61: 2034-(2040).

DOI: 10.1103/physrevb.61.2034

[6] Wang H, Farias GA, Freire VN. Iterface-related exciton-energy blueshift in GaN/AlxGa1-xN zinc-blende and wurtzite singale quantum wells. Phys. Rev. B, 1999; 60: 5705-5713.

[7] Shi JJ. Electron–interface-phonon interaction in wurtzite multilayer heterostructures. Solid State Commun., 2003; 127: 51-55.

DOI: 10.1016/s0038-1098(03)00256-4

[8] Shi JJ, Chu XL, Goldys EM. Propagating optical-phonon modes and their electron-phonon interactions in wurtzite GaN∕AlxGa1−xN quantum wells. Phys. Rev. B, 2004; 70: 115318-115326.

DOI: 10.1103/physrevb.68.165335

[9] Zhao FQ, Gong J. Energy of a polaron in a wurtzite nitride finite parabolic quantum well. Chin. Phys. Lett., 2007; 24: 1327-1331.

DOI: 10.1088/0256-307x/24/5/056

[10] Zhao FQ, Zhang M. Bound polarons in wurtzite GaN/AlxGa1-xN Quantum Well. Phys. Stat. Sol. C, 2011; 8: 62-65.

[11] Zhao FQ, Zhang M. Polaronic effect on the electron energy spectrum in a wurtzite InxGa1-xN/GaN Quantum Well. J. Phys. Soc. Jap., 2011; 80: 94713-1 - 94713-5.

[12] Zhao FQ, Zhang M. Polaronic effects in wurtzite GaN/AlxGa1-xN Quantum Well s. Int. J. Mod. Phys. B, 2011; 25: 2105-2114.

[13] Cai J, Shi JJ. Exciton state in wurtzite InGaN/GaN quantum wells: strong built-in electron field and interface optical-phonon effetcs. Solid State Commun., 2008; 145: 235.

DOI: 10.1016/j.ssc.2007.11.021

[14] Zhu YH, Shi JJ. Effects of built-in electric field on polarons in wurtzite GaN/AlN quantum wells. Physica E, 2009; 41: 746-752.

DOI: 10.1016/j.physe.2008.11.019

[15] Zhao HP, Tansu N. Optical gain characteristics of staggered InGaN quantum wells lasers. J. Appl. Phys., 2010; 107: 113110-113122.

DOI: 10.1063/1.3407564

[16] Lai KY, Lin GJ, Lai YL, Chen YF, He JH. Effect of indium fluctuation on the photovoltaic characteristics of InGaN/GaN multiple quantum well solar cells. Appl. Phys. Lett., 2010; 96: 081103-081106.

DOI: 10.1063/1.3327331

[17] Belabbes A, de Carvalho LC, Schleife A, Bechstedt F. Cubic inclusions in hexagonal AlN, GaN, and InN: Electronic states. Phys. Rev. B, 2011; 84: 125108-125117.

DOI: 10.1103/physrevb.84.125108

[18] Chang WL, A. John P. Radiative life time of an exciton confined in a strained GaN/Ga1-xAlxN cylindrical dot: built-in electric field effects. Chin. Phys. B, 2011; 20: 077104-1 – 077104-6.

DOI: 10.1088/1674-1056/20/7/077104

[19] Qi XH, Kong XY，Lin JY. Effects of a spatially dependent effective mass on the hydrogenic impurity binding energy in a finite parabolic quantum well. Phys. Rev. B, 1998; 58: 10578-10582.

DOI: 10.1103/physrevb.58.10578

[20] Goldhana R, Scheiner J, Shokhovets S, Frey T, Köhler U, As D J, Lischka K. Refractive index and gap energy of cubic InxGa1−xN. Appl. Phys. Lett., 2000; 76: 291-294.

DOI: 10.1063/1.125725

[21] Vurgaftman I, Melyer JR. Band parameters for nitrogen-containing semiconductors. J. Appl. Phys., 2003; 94: 3675-3697.

[22] Zhao FQ, Liang XX. Polarons with spatially dependent mass in a finite parabolic quantum well, Chin. Phys. Lett., 2002; 19: 974-977.

DOI: 10.1088/0256-307x/19/7/329