J. Semicond. > Volume 35 > Issue 7 > Article Number: 073004

Strain effects on band structure of wurtzite ZnO: a GGA + U study

Liping Qiao 1, 2, , , Changchun Chai 1, , Yintang Yang 1, , Xinhai Yu 1, and Chunlei Shi 1,

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Abstract: Band structures in wurtzite bulk ZnO/Zn1-xMgxO are calculated using first-principles based on the framework of generalized gradient approximation to density functional theory with the introduction of the on-site Coulomb interaction. Strain effects on band gap, splitting energies of valence bands, electron and hole effective masses in strained bulk ZnO are discussed. According to the results, the band gap increases gradually with increasing stress in strained ZnO as an Mg content of Zn1-xMgxO substrate less than 0.3, which is consistent with the experimental results. It is further demonstrated that electron mass of conduction band (CB) under stress increases slightly. There are almost no changes in effective masses of light hole band (LHB) and heavy hole band (HHB) along[00k] and[k00] directions under stress, and stress leads to an obvious decrease in effective masses of crystal splitting band (CSB) along the same directions.

Key words: GGA + Uband gapsplitting energieselectron mass

Abstract: Band structures in wurtzite bulk ZnO/Zn1-xMgxO are calculated using first-principles based on the framework of generalized gradient approximation to density functional theory with the introduction of the on-site Coulomb interaction. Strain effects on band gap, splitting energies of valence bands, electron and hole effective masses in strained bulk ZnO are discussed. According to the results, the band gap increases gradually with increasing stress in strained ZnO as an Mg content of Zn1-xMgxO substrate less than 0.3, which is consistent with the experimental results. It is further demonstrated that electron mass of conduction band (CB) under stress increases slightly. There are almost no changes in effective masses of light hole band (LHB) and heavy hole band (HHB) along[00k] and[k00] directions under stress, and stress leads to an obvious decrease in effective masses of crystal splitting band (CSB) along the same directions.

Key words: GGA + Uband gapsplitting energieselectron mass



References:

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[14]

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[16]

Hung C C, ANAS M, John Z. Room-temperature quantum cascade laser: ZnO/Zn1-xMgxO versus GaN/AlxGa1-xN[J]. J Electron Mater, 2013, 42(5): 882. doi: 10.1007/s11664-013-2548-5

[17]

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[19]

Fan X F, Sun H D, Shen Z X. A first-principle analysis an the phase stabilities, chemical bonds and band gaps of wurtzite structure AxZn1-x alloys (A = Ca, Cd, Mg)[J]. J Phys: Condensed Matter, 2008, 20(23): 235221. doi: 10.1088/0953-8984/20/23/235221

[20]

Lai L N, Lian J S, Jiang Q. Optical and electronic properties of wurtzite structure MgxZn1-xO alloys[J]. Chin Phys Lett, 2011, 28(11): 117101. doi: 10.1088/0256-307X/28/11/117101

[21]

Zitouni K, Kadri A. Effects of lattice-mismatch induced built-in strain on the valence band properties of wurtzite ZnO/MgxZn1-xO quantum well heterostructures[J]. Phys Status Solidi, 2007, 4(1): 208. doi: 10.1002/(ISSN)1610-1642

[22]

Zhou G C, Sun X Z, Zhong X L. First-principle study on bonding mechanism of ZnO by LDA + U method[J]. Phys Lett A, 2007, 368(1): 112.

[23]

Janotti A, Van de Walle C G. LDA + U and hybrid functional calculations for defects in ZnO, SnO2, and TiO2[J]. Phys Status Solidi B, 2011, 248(4): 799. doi: 10.1002/pssb.v248.4

[24]

Sheetz R M, Richter E, Antonis N. Defect-induced optical absorption in the visible range in ZnO nanowires[J]. Phys Rev B, 2009, 80(19): 195314. doi: 10.1103/PhysRevB.80.195314

[25]

Wang Q B, Zhou C, Wu J. A GGA + U study of the optical properties of vanadium doped ZnO with and without single intrinsic vacancy[J]. Opt Commun, 2013, 297: 79. doi: 10.1016/j.optcom.2013.01.073

[26]

Wang L, Maxisch T, Ceder G. A first-principles approach to studying the thermal stability of oxide cathode materials[J]. Phys Rev B: Condensed Matter, 2006, 73: 195107. doi: 10.1103/PhysRevB.73.195107

[27]

Gai Y Q, Yao B, Lu Y M. Electronic and optical properties of ZnO thin film under in-plane biaxial strains: ab initio calculation[J]. Phys Lett A, 2007, 372: 72. doi: 10.1016/j.physleta.2007.07.001

[28]

Li Y F, Yao B, Lu Y M. Biaxial stress-dependent optical band gap, crystalline, and electronic structure in wurtzite ZnO: experimental and ab initio study[J]. J Appl Phys, 2008, 104(8): 083516. doi: 10.1063/1.3000601

[29]

Alahmed Z, Fu H X. Polar semiconductor ZnO under inplane tensile strain[J]. Phys Rev B, 2008, 77(4): 045213. doi: 10.1103/PhysRevB.77.045213

[1]

Stölzel M, Kupper J, Brandt M. Electronic and optical properties of ZnO/(Mg, Zn)O quantum wells with and without a distinct quantum-confined Stark effect[J]. J Appl Phys, 2012, 111(6): 063701. doi: 10.1063/1.3693555

[2]

Xu L Z, Liu Y L, Zhou H B. Ideal strengths, structure transitions, and bonding properties of a ZnO single crystal under tension[J]. J Phys: Condensed Matter, 2009, 21(49): 495402. doi: 10.1088/0953-8984/21/49/495402

[3]

Xiong W, Li S S. The electronic structure of strained ZnO/MgxZn1-xO superlattices and the influence of polarization[J]. Physica E, 2009, 41(3): 506. doi: 10.1016/j.physe.2008.09.013

[4]

Chauveau J M, Teisseire M, Chauveau H K. Anisotropic strain effects on the photoluminescence emission from heteroepitaxial and homoepitaxial nonpolar (Zn, Mg)O/ZnO quantum wells[J]. J Appl Phys, 2011, 109(10): 102420. doi: 10.1063/1.3578636

[5]

Aoumeur-Benkabou F Z, Ameri M, Kadoun A. Theoretical study on the origins of the gap bowing in MgxZn1-xO alloys[J]. Modeling and Numerical Simulation of Material Science, 2012, 2: 60. doi: 10.4236/mnsms.2012.23007

[6]

Nakano M, Tsukazaki A, Ueno K. Spatial distribution of two-dimensional electron gas in a ZnO/Mg0.2Zn0.8O heterostructure probed with a conducting polymer Schottky contact[J]. Appl Phys Lett, 2010, 96(5): 052116. doi: 10.1063/1.3309699

[7]

Fan W J, Abiyasa A P, Tan S T. Electronic structures of wurtzite ZnO and ZnO/MgxZn1-xO quantum wells[J]. J Cryst Growth, 2006, 287(1): 28. doi: 10.1016/j.jcrysgro.2005.10.037

[8]

Zitouni K, Kadri A. Effects of lattice-mismatch induced built-in strain on the valence band properties of wurtzite ZnO/MgxZn1-xO quantum well heterostructures[J]. Phys Status Solidi, 2007, 4(1): 208. doi: 10.1002/(ISSN)1610-1642

[9]

Fan W J, Xia J B, Agus P A. Band parameters and electronic structure of wurtzite ZnO and Zno/MgZnO quantum wells[J]. J Appl Phys, 2006, 99(1): 013702. doi: 10.1063/1.2150266

[10]

Saniz, Xu, Matsubara. A simplified approach to the band gap correction of defect formation energies: Al, Ga, and In-doped ZnO[J]. J Phys Chem Solids, 2013, 74(1): 45. doi: 10.1016/j.jpcs.2012.07.017

[11]

Andrei M, David V. First-principles study of polarization in Zn1-xMgxO[J]. Phys Rev B, 2007, 75: 045106. doi: 10.1103/PhysRevB.75.045106

[12]

Lin H X, Jing S, Yu L C. Optical and structural properties of ZnO/ZnMgO composite thin films prepared by sol-gel technique[J]. J Alloys Compounds, 2013, 548: 155. doi: 10.1016/j.jallcom.2012.09.043

[13]

Sua S C, Ling C C, Lu Y M. The optical properties of high quality ZnO/ZnMgO quantum wells on Si(111) substrates[J]. Solid State Commun, 2012, 152(4): 311. doi: 10.1016/j.ssc.2011.11.022

[14]

Su S C, Lv Y M. Ultraviolet electroluminescence of ZnMgO/n-ZnO/ZnMgO/p-GaN heterojunction light emitting diode[J]. Chinese Journal of Luminescence, 2011, 32(8): 821. doi: 10.3788/fgxb

[15]

Hao L, Guo J F, Song Z L. A ZnO/ZnMgO multiple-quantum-well ultraviolet random laser diode[J]. IEEE Electron Device Lett, 2011, 32(1): 54. doi: 10.1109/LED.2010.2089424

[16]

Hung C C, ANAS M, John Z. Room-temperature quantum cascade laser: ZnO/Zn1-xMgxO versus GaN/AlxGa1-xN[J]. J Electron Mater, 2013, 42(5): 882. doi: 10.1007/s11664-013-2548-5

[17]

Huang G Y, Wang C Y, Wang J T. Detailed check of the LDA + U and GGA + U corrected method for defect calculations in wurtzite ZnO[J]. Computer Phys Commun, 2012, 183(8): 1749. doi: 10.1016/j.cpc.2012.03.017

[18]

Karazhanova S Z, Ravindrana B P, Kjekhusa A. Electronic structure and band parameters for ZnX (X = O, S, Se, Te)[J]. J Cryst Growth, 2006, 287: 162. doi: 10.1016/j.jcrysgro.2005.10.061

[19]

Fan X F, Sun H D, Shen Z X. A first-principle analysis an the phase stabilities, chemical bonds and band gaps of wurtzite structure AxZn1-x alloys (A = Ca, Cd, Mg)[J]. J Phys: Condensed Matter, 2008, 20(23): 235221. doi: 10.1088/0953-8984/20/23/235221

[20]

Lai L N, Lian J S, Jiang Q. Optical and electronic properties of wurtzite structure MgxZn1-xO alloys[J]. Chin Phys Lett, 2011, 28(11): 117101. doi: 10.1088/0256-307X/28/11/117101

[21]

Zitouni K, Kadri A. Effects of lattice-mismatch induced built-in strain on the valence band properties of wurtzite ZnO/MgxZn1-xO quantum well heterostructures[J]. Phys Status Solidi, 2007, 4(1): 208. doi: 10.1002/(ISSN)1610-1642

[22]

Zhou G C, Sun X Z, Zhong X L. First-principle study on bonding mechanism of ZnO by LDA + U method[J]. Phys Lett A, 2007, 368(1): 112.

[23]

Janotti A, Van de Walle C G. LDA + U and hybrid functional calculations for defects in ZnO, SnO2, and TiO2[J]. Phys Status Solidi B, 2011, 248(4): 799. doi: 10.1002/pssb.v248.4

[24]

Sheetz R M, Richter E, Antonis N. Defect-induced optical absorption in the visible range in ZnO nanowires[J]. Phys Rev B, 2009, 80(19): 195314. doi: 10.1103/PhysRevB.80.195314

[25]

Wang Q B, Zhou C, Wu J. A GGA + U study of the optical properties of vanadium doped ZnO with and without single intrinsic vacancy[J]. Opt Commun, 2013, 297: 79. doi: 10.1016/j.optcom.2013.01.073

[26]

Wang L, Maxisch T, Ceder G. A first-principles approach to studying the thermal stability of oxide cathode materials[J]. Phys Rev B: Condensed Matter, 2006, 73: 195107. doi: 10.1103/PhysRevB.73.195107

[27]

Gai Y Q, Yao B, Lu Y M. Electronic and optical properties of ZnO thin film under in-plane biaxial strains: ab initio calculation[J]. Phys Lett A, 2007, 372: 72. doi: 10.1016/j.physleta.2007.07.001

[28]

Li Y F, Yao B, Lu Y M. Biaxial stress-dependent optical band gap, crystalline, and electronic structure in wurtzite ZnO: experimental and ab initio study[J]. J Appl Phys, 2008, 104(8): 083516. doi: 10.1063/1.3000601

[29]

Alahmed Z, Fu H X. Polar semiconductor ZnO under inplane tensile strain[J]. Phys Rev B, 2008, 77(4): 045213. doi: 10.1103/PhysRevB.77.045213

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L P Qiao, C C Chai, Y T Yang, X H Yu, C L Shi. Strain effects on band structure of wurtzite ZnO: a GGA + U study[J]. J. Semicond., 2014, 35(7): 073004. doi: 10.1088/1674-4926/35/7/073004.

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Manuscript received: 13 December 2013 Manuscript revised: 02 February 2014 Online: Published: 01 July 2014

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