MSA  Vol.6 No.7 , July 2015
First Principles Study of the Structural and Electronic Properties of the ZnO/Cu2O Heterojunction
ABSTRACT
Many materials have been used in nanostructured devices; the goal of attaining high-efficiency thin-film solar cells in such a way has yet to be achieved. Heterojunctions based on ZnO/Cu2O oxides have recently emerged as promising materials for high-efficiency nanostructured devices. In this work, we are interested in the characterization of the surface and interface through nano-scale modeling based on ab initio (Density Functional Theory (DFT), Local Density Approximation (LDA), Generalized Gradient Approximation (GGA-PBE), and Pseudopotential (PP)). This study aims also to build a supercell containing a ZnO/Cu2O heterojunction and study the structural properties and the discontinuity of the valence band (band offset) from a semiconductor to an-other. We investigate crystal terminations of ZnO (0001) and Cu2O (0001). We calculate the energies of the polar surfaces and the work function in the c-axis for both oxides. We built a zinc oxide layer in the wurtzite structure along the [0001] direction, on which we placed a copper oxide layer in the hexagonal structure (CdI2-type). We choose the method of Van de Walle and Martin to calcu-late the energy offset. This approach fits well with the DFT. Our calculations give us a value that corresponds to other experimental and theoretical values.

Cite this paper
Zemzemi, M. and Alaya, S. (2015) First Principles Study of the Structural and Electronic Properties of the ZnO/Cu2O Heterojunction. Materials Sciences and Applications, 6, 661-675. doi: 10.4236/msa.2015.67068.
References
[1]   O’Regan, B. and Grätzel, M. (1991) A Low-Cost, High-Efficiency Solar Cell Based on Dye-Sensitized Colloidal TiO2 Films. Nature, 353,737-740.
http://dx.doi.org/10.1038/353737a0

[2]   Graetzel, M., Janssen, R.A., Mitzi, D.B. and Sargent, E.H. (2012) Materials Interface Engineering for Solution-Processed Photovoltaics. Nature, 488, 304-312.
http://dx.doi.org/10.1038/nature11476

[3]   Parida, B., Iniyan, S. and Goic, R. (2011) A Review of Solar Photovoltaic Technologies. Renewable and Sustainable Energy Reviews, 15, 1625-1636.
http://dx.doi.org/10.1016/j.rser.2010.11.032

[4]   Shevaleevskiy, O. (2008) The Future of Solar Photovoltaics, a New Challenge for Chemical Physics. Pure and Applied Chemistry, 80, 2079-2089.
http://dx.doi.org/10.1351/pac200880102079

[5]   Zunger, A., Wagner, S. and Petroff, P. (1993) New Materials and Structures for Photovoltaics. Journal of Electronic Materials, 22, 3-16.
http://dx.doi.org/10.1007/BF02665719

[6]   Surek, T. (2005) Crystal Growth and Materials Research in Photovoltaics, Progress and Challenges. Journal of Crystal Growth, 275, 292-304.
http://dx.doi.org/10.1016/j.jcrysgro.2004.10.093

[7]   Loferski, J.J. (1956) Theoretical Considerations Governing the Choice of the Optimum Semiconductor for Photovoltaic Solar Energy Conversion. Journal of Applied Physics, 27, 777-784.
http://dx.doi.org/10.1063/1.1722483

[8]   Nickel, N.H. and Terukov, E. (2005) Zinc Oxide—A Material for Micro- and Optoelectronic Applications. Springer, Berlin.
http://dx.doi.org/10.1007/1-4020-3475-X

[9]   Zemzemi, M. and Alaya, S. (2014) Structural, Electronic, and Fermi Surface Evolution in Zinc Oxide under High Pressure. Journal of Optoelectronics and Advanced Materials, 16, 471-475.

[10]   Look, D.C. (2001) Recent Advances in ZnO Materials and Devices. Materials Science and Engineering: B, 80, 383-387.
http://dx.doi.org/10.1016/S0921-5107(00)00604-8

[11]   Özgür, ü., Alivov, Y.I., Liu, C., Teke, A., Reshchikov, M.A., Dogan, S., Avrutin, V., Cho, S.J. and Morkoç, H. (2005) A Comprehensive Review of ZnO Materials and Devices. Journal of Applied Physics, 98, Article ID: 041301.
http://dx.doi.org/10.1063/1.1992666

[12]   Rai, B.P. (1998) Cu2O Solar Cells: A Review. Solar Cells, 25, 265-272.
http://dx.doi.org/10.1016/0379-6787(88)90065-8

[13]   Briskman, R.N. (1992) A Study of Electrodeposited Cuprous Oxide Photovoltaic Cells. Solar Energy Materials and Solar Cells, 27, 361-368.
http://dx.doi.org/10.1016/0927-0248(92)90097-9

[14]   Herion, J., Niekisch, E.A. and Scharl, G. (1980) Investigation of Metal Oxide/Cuprous Oxide Heterojunction Solar Cells. Solar Energy Materials, 4, 101-112.
http://dx.doi.org/10.1016/0165-1633(80)90022-2

[15]   Zemzemi, M., Alaya, S. and Ben Ayadi, Z. (2014) Ab Initio Study of Heterojunction Discontinuities in the ZnO/Cu2O System. Journal of Experimental and Theoretical Physics, 118, 945-950.
http://dx.doi.org/10.1134/S1063776114050185

[16]   Minami, T., Nishi, Y., Miyata, T. and Nomoto, J. (2011) High-Efficiency Oxide Solar Cells with ZnO/Cu2O Heterojunction Fabricated on Thermally Oxidized Cu2O Sheets. Applied Physics Express, 4, Article ID: 062301.
http://dx.doi.org/10.1143/APEX.4.062301

[17]   Kramm, B., Laufer, A., Reppin, D., Kronenberger, A., Hering, P., Polity, A. and Meyer, B.K. (2012) The Band Alignment of Cu2O/ZnO and Cu2O/GaN Heterostructures. Applied Physics Letters, 100, Article ID: 094102.
http://dx.doi.org/10.1063/1.3685719

[18]   Jeong, S.S., Mittiga, A., Salza, E., Masci, A. and Passerini, S. (2008) Electrodeposited ZnO/Cu2O Heterojunction Solar Cells. Electrochimica Acta, 53, 2226-2231.
http://dx.doi.org/10.1016/j.electacta.2007.09.030

[19]   Ichimura, M. and Song, Y. (2011) Band Alignment at the Cu2O/ZnO Heterojunction. Japanese Journal of Applied Physics, 50, Article ID: 051002.
http://dx.doi.org/10.7567/JJAP.50.051002

[20]   Noda, S., Shima, H. and Akinaga, H. (2013) Cu2O/ZnO Heterojunction Solar Cells Fabricated by Magnetron-Sputter Deposition Method Films Using Sintered Ceramics Targets. Journal of Physics: Conference Series, 433, Article ID: 012027.
http://dx.doi.org/10.1088/1742-6596/433/1/012027

[21]   Akimoto, K., Ishizuka, S., Yanagita, M., Nawa, N., Paul, G.K. and Sakurai, T. (2006) Thin Film Deposition of Cu2O and Application for Solar Cells. Solar Energy, 80, 715-722.
http://dx.doi.org/10.1016/j.solener.2005.10.012

[22]   Ozawa, K., Oba, Y. and Adamoto, K. (2009) Formation and Characterization of the Cu2O Overlayer on Zn-Terminated ZnO (0001). Surface Science, 603, 2163-2170.
http://dx.doi.org/10.1016/j.susc.2009.04.027

[23]   Machon, D., Sinitsyn, V.V., Dmitriev, V.P., Bdikin, I.K., Dubrovinsky, L., Kuleshov, I.V., Ponyatovsky, G. and Weber, H.P. (2003) Structural Transitions in Cu2O at Pressures up to 11 GPa. Journal of Physics: Condensed Matter, 15, 7227-7235.
http://dx.doi.org/10.1088/0953-8984/15/43/007

[24]   Bechstedt, F. (2003) Principles of Surface Physics. Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-642-55466-7

[25]   Holec, D. and Mayrhofer, P.H. (2012) Surface Energies of AlN Allotropes from First Principles. Scripta Materialia, 67, 760-762.
http://dx.doi.org/10.1016/j.scriptamat.2012.07.027

[26]   Meyer, B. and Marx, D. (2003) Density Functional Study of the Structure and Stability of ZnO Surfaces. Physical Review B, 67, Article ID: 035403.
http://dx.doi.org/10.1103/PhysRevB.67.035403

[27]   Soon, A., Sohnel, T. and Idriss, H. (2005) Plane-Wave Pseudopotential Density Functional Theory Periodic Slab Calculations of CO Adsorption on Cu2O (111) Surface. Surface Science, 579, 131-140.
http://dx.doi.org/10.1016/j.susc.2005.01.038

[28]   Duan, Y., Zhang, K.M. and Xie, X.D. (1994) Theoretical Studies of CO and NO on CuO and Cu2O (110) Surfaces. Surface Science, 321, 249-254.
http://dx.doi.org/10.1016/0039-6028(94)90183-X

[29]   Bredow, T. and Pacchioni, G. (1997) Comparative Periodic and Cluster Ab Initio Study on Cu2O (111)/CO. Surface Science, 373, 21-32.
http://dx.doi.org/10.1016/S0039-6028(96)01147-8

[30]   Yang, Y., Schlepütz, C.M., Bellucci, F., Allen, M.W., Durbin, S.M. and Clarke, R. (2013) Structural Investigation of ZnO-Polar (000-1) Surfaces and Schottky Interfacs. Surface Science, 610, 22-26.
http://dx.doi.org/10.1016/j.susc.2012.12.018

[31]   Schulz, K.H. and Cox, D.F. (1991) Photoemission and Low-Energy-Electron-Diffraction Study of Clean and Oxygen-Dosed Cu2O (111) and (100) Surfaces. Physical Review B, 43, 1610-1621.
http://dx.doi.org/10.1103/PhysRevB.43.1610

[32]   Soltys, J., Piechota, J., Lopuszyński, M. and Krukowski, S. (2013) Density Functional Theory (DFT) Study of Zn, O2 and O Adsorption on Polar ZnO (0001) and ZnO (000-1) Surfaces. Journal of Crystal Growth, 374, 53-59.
http://dx.doi.org/10.1016/j.jcrysgro.2013.03.048

[33]   Islam, M.M., Diawara, B., Maurice, V. and Marcus, P. (2009) First Principles Investigation on the Stabilization Mechanisms of the Polar Copper Terminated Cu2O (1 1 1) Surface. Surface Science, 603, 2087-2095.
http://dx.doi.org/10.1016/j.susc.2009.04.005

[34]   Cortona, P. and Mebarki, M. (2011) Cu2O Behavior under Pressure, an Ab Initio Study. Journal of Physics: Condensed Matter, 23, Article ID: 045502.
http://dx.doi.org/10.1088/0953-8984/23/4/045502

[35]   Bernardini, F. and Fiorentini, V. (1998) Macroscopic Polarization and Band Offsets at Nitride Heterojunctions. Physical Review B, 57, 9427-9430.
http://dx.doi.org/10.1103/PhysRevB.57.R9427

[36]   Wei, S.-H. and Zunger, A. (1998) Calculated Natural Band Offsets of All II-VI and III-V Semiconductors, Chemical Trends and the Role of Cation d Orbitals. Applied Physics Letters, 72, 2011.
http://dx.doi.org/10.1063/1.121249

[37]   Franciosi, A. and Van de Walle, C.G. (1996) Heterojunction Band Offset Engineering. Surface Science Reports, 25, 1-140.
http://dx.doi.org/10.1016/0167-5729(95)00008-9

[38]   Wilk, G.D., Wallace, R.M. and Anthony, J.M. (2001) High-κ Gate Dielectrics, Current Status and Materials Properties Considerations. Journal of Applied Physics, 89, 5243.
http://dx.doi.org/10.1063/1.1361065

[39]   Morteani, A.C., Sreearunothai, P., Hertz, L.M., Friend, R.H. and Silva, C. (2004) Exciton Regeneration at Polymeric Semiconductor Heterojunctions. Physical Review Letters, 92, Article ID: 247402.
http://dx.doi.org/10.1103/PhysRevLett.92.247402

[40]   Li, J. and Wang, L. (2004) Deformation Potentials of CdSe Quantum Dots. Applied Physics Letters, 85, 2929.
http://dx.doi.org/10.1063/1.1800288

[41]   Zhang, S.B., Wei, S.H. and Zunger, A. (2000) Microscopic Origin of the Phenomenological Equilibrium “Doping Limit Rule” in N-Type III-V Semiconductors. Physical Review Letters, 84, 1232.
http://dx.doi.org/10.1103/PhysRevLett.84.1232

[42]   Kavan, L., Graetzel, M., Gilbert, S.E., Klemenz, C. and Scheel, H.J. (1996) Electrochemical and Photoelectrochemical Investigation of Single-Crystal Anatase. Journal of the American Chemical Society, 118, 6716-6723.
http://dx.doi.org/10.1021/ja954172l

[43]   Shaltaf, R., Rignanese, G.M., Gonze, X., Giustino, F. and Pasquarello, A. (2008) Band Offsets at the Si/SiO2 Interface from Many-Body Perturbation Theory. Physical Review Letters, 100, Article ID: 186401.
http://dx.doi.org/10.1103/PhysRevLett.100.186401

[44]   Tersoff, J. (1984) Theory of Semiconductor Heterojunctions, The Role of Quantum Dipoles. Physical Review B, 30, 4874-4877.
http://dx.doi.org/10.1103/PhysRevB.30.4874

[45]   Cordona, M. and Christensen, N.E. (1987) Acoustic Deformation Potentials and Heterostructure Band Offsets in Semiconductors. Physical Review B, 35, 6182-6194.
http://dx.doi.org/10.1103/PhysRevB.35.6182

[46]   Hybertsen, M.S. (1990) Role of Interface Strain in a Lattice-Matched Heterostructure. Physical Review Letters, 64, 555-558.
http://dx.doi.org/10.1103/PhysRevLett.64.555

[47]   Van de Walle, C.G. and Martin, R.M. (1986) Theoretical Calculations of Heterojunction Discontinuities in the Si/Ge System. Physical Review B, 34, 5621-5634.
http://dx.doi.org/10.1103/PhysRevB.34.5621

[48]   Wong, L.M., Chiam, S.Y., Huang, J.Q., Wang, S.J., Pan, J.S. and Chim, W.K. (2010) Growth of Cu2O on Ga-Doped ZnO and Their Interface Energy Alignment for Thin Film Solar Cells. Journal of Applied Physics, 108, Article ID: 033702.
http://dx.doi.org/10.1063/1.3465445

[49]   Hohenberg, P. and Kohn, W. (1964) Inhomogeneous Electron Gas. Physical Review, 136, B864.

[50]   Kohn, W. and Sham, L.J. (1965) Quantum Density Oscillations in an Inhomogeneous Electron Gas. Physical Review, 140, A1133-A1138.
http://dx.doi.org/10.1103/PhysRev.140.A1133

[51]   Sharia, O., Demkov, A.A., Bersuker, G. and Lee, B.H. (2007) Theoretical Study of the Insulator/Insulator Interface, Band Alignment at the SiO2/HfO2 Junction. Physical Review B, 75, Article ID: 035306.
http://dx.doi.org/10.1103/PhysRevB.75.035306

[52]   52Gonze, X., Beuken, J.-M., Caracas, R., Detraux, F., Fuchs, M., Rignanese, G.-M., et al. (2002) First-Principles Computation of Material Properties: The ABINIT Software Project. Computational Materials Science, 25, 478-492. http,//www.abinit.org
http://dx.doi.org/10.1016/S0927-0256(02)00325-7


[53]   Gonze, X., Amadon, B., Anglade, P.-M., Beuken, J.-M., Bottin, F., Boulanger, P., et al. (2009) ABINIT: First-Principles Approach to Material and Nanosystem Properties. Computer Physics Communications, 180, 2582-2615.
http://dx.doi.org/10.1016/j.cpc.2009.07.007

[54]   Troullier, N. and Martins, J.L. (1991) Efficient Pseudopotentials for Plane-Wave Calculations. Physical Review B, 43, 1993-2006.
http://dx.doi.org/10.1103/PhysRevB.43.1993

[55]   Fuchs, M. and Scheffler, M. (1999) Ab Initio Pseudopotentials for Electronic Structure Calculations of Poly-Atomic Systems Using Density-Functional Theory. Computer Physics Communications, 119, 67-98.
http://dx.doi.org/10.1016/S0010-4655(98)00201-X

[56]   Perdew, J.P. and Wang, Y. (1992) Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Physical Review B, 45, 13244-13249.
http://dx.doi.org/10.1103/PhysRevB.45.13244

[57]   Ceperley, D.M. and Alder, B.J. (1980) Ground State of the Electron Gas by a Stochastic Method. Physical Review Letters, 45, 566-569.
http://dx.doi.org/10.1103/PhysRevLett.45.566

[58]   Perdew, J.P., Burke, K. and Ernzerhof, M. (1996) Generalized Gradient Approximation Made Simple. Physical Review Letters, 77, 3865-3868.
http://dx.doi.org/10.1103/PhysRevLett.77.3865

[59]   Monkhorst, H.J. and Pack, J.D. (1976) Special Points for Brillouin-Zone Integrations. Physical Review B, 13, 5188-5192.
http://dx.doi.org/10.1103/PhysRevB.13.5188

[60]   Jeong, S.H. and Aydil, E.S. (2009) Heteroepitaxial Growth of Cu2O Thin Film on ZnO by Metal Organic Chemical Vapor Deposition. Journal of Crystal Growth, 311, 4188-4192.
http://dx.doi.org/10.1016/j.jcrysgro.2009.07.020

[61]   Fariza, B.M., Sasano, J., Shinagawa, T., Watase, S. and Izaki, M. (2012) Light-Assisted Electrochemical Construction of (111)Cu2O/(0001)ZnO Heterojunction. Thin Solid Films, 520, 2261-2264.
http://dx.doi.org/10.1016/j.tsf.2011.09.022

[62]   Yang, M.J., Zhu, L.P., Li, Y.G., Cao, L. and Guo, Y.M. (2013) Asymmetric Interface Band Alignments of Cu2O/ZnO and ZnO/Cu2O Heterojunctions. Journal of Alloys and Compounds, 578, 143-147.
http://dx.doi.org/10.1016/j.jallcom.2013.05.033

[63]   Akimoto, K., Ishizuka, S., Yanagita, M., Nawa, N., Paul, G.K. and Sakurai, T. (2000) Thin Film Deposition of Cu2O and Application for Solar Cells. Solar Energy, 80, 715-722.
http://dx.doi.org/10.1016/j.solener.2005.10.012

[64]   Pearson, W.B. (1958) Handbook of Lattice Spacings and Structures of Metals and Alloys. Pergamon Press, Belfast.

[65]   Zemzemi, M., ElGhoul, N., Khirouni, K. and Alaya, S. (2014) First-Principle Study of the Structural, Electronic, and Thermodynamic Properties of Cuprous Oxide under Pressure. Journal of Experimental and Theoretical Physics, 118, 235-241.
http://dx.doi.org/10.1134/S1063776114020228

[66]   Werner, A. and Hochheimer, H.D. (1982) High Pressure X-Ray Study of Cu2O and Ag2O. Physical Review B, 25, 5929-5934.
http://dx.doi.org/10.1103/PhysRevB.25.5929

[67]   Onsten, A., Mansson, M., Muro, T., Matsushita, T., Nakamura, T., Kinoshita, T., Karlsson, O.U. and Tjernberg, O. (2009) Probing the Valence Band Structure of Cu2O Using High-Energy Angle-Resolved Photoelectron Spectroscopy. Physical Review B, 76, 115-127.
http://dx.doi.org/10.1103/PhysRevB.76.115127

[68]   Cox, D. and Schulz, K.H. (1991) H2O Adsorption on Cu2O (100). Surface Science, 256, 67-76.
http://dx.doi.org/10.1016/0039-6028(91)91200-H

[69]   Soon, A., Todorova, M., Delly, B. and Stampfl, C. (2006) Oxygen Adsorption and Stability of Surface Oxides on Cu (111): A First-Principles Investigation. Physical Review B, 73, Article ID: 165424.
http://dx.doi.org/10.1103/PhysRevB.73.165424

[70]   Altarawneh, M., Radney, M., Smith, P.V., Mackie, J.C., Kennedy, E.M., Dlugogorski, B.Z., Soon, A. and Stampfl, C. (2009) A First-Principles Density Functional Study of Chlorophenol Adsorption on Cu2O (110), CuO. The Journal of Chemical Physics, 130, Article ID: 184505.
http://dx.doi.org/10.1063/1.3123534

[71]   Kuo, F.L., Li, Y., Solomon, M., Du, J. and Shepherd, N.D. (2012) Workfunction Tuning of Zinc Oxide Films by Argon Sputtering and Oxygen Plasma: An Experimental and Computational Study. Journal of Physics D: Applied Physics, 45, Article ID: 065301.
http://dx.doi.org/10.1088/0022-3727/45/6/065301

[72]   Kim, T., Yoshitake, M., Yagyu, S., Nemsák, S., Nagata, T. and Chikyow, T. (2010) XPS Study on Band Alignment at Pt-O-Terminated ZnO (000-1) Interface. Surface and Interface Analysis, 42, 1528-1531.
http://dx.doi.org/10.1002/sia.3601

[73]   Jacobi, K., Zwicker, G. and Gutmann, A. (1984) Work Function, Electron Affinity and Band Bending of Zinc Oxide Surfaces. Surface Science, 141, 109-125.
http://dx.doi.org/10.1016/0039-6028(84)90199-7

[74]   Schlesinger, R., Xu, Y., Hofmann, O.T., Winkler, S., Frisch, J., Niederhausen, J., Vollmer, A., Blumstengel, S., Henneberger, F., Rinke, P., Scheffler, M. and Koch, N. (2013) Controlling the Work Function of ZnO and the Energy-Level Alignment at the Interface to Organic Semiconductors with a Molecular Electron Acceptor. Physical Review B, 87, Article ID: 155311.
http://dx.doi.org/10.1103/PhysRevB.87.155311

[75]   Marien, J. (1976) Field Emission Study of the Specificity of Zinc Oxide Polar Surfaces (0001) and (0001). Work Function and Hydrogen Adsorption. Physica Status Solidi (a), 38, 513-522.
http://dx.doi.org/10.1002/pssa.2210380211

[76]   Wander, A., Schedin, F., Steadman, P., Norris, A., McGrath, R., Turner, T.S., Thornton, G. and Harrison, N.M. (2001) Stability of Polar Oxide Surfaces. Physical Review Letters, 86, 3811-3814.
http://dx.doi.org/10.1103/PhysRevLett.86.3811

[77]   Na, S.-H. and Park, C.-H. (2010) First-Principles Study of the Surface Energy and Atom Cohesion of Wurtzite ZnO and ZnS-Implications for Nanostructure Formation. Journal of the Korean Physical Society, 56, 498-502.
http://dx.doi.org/10.3938/jkps.56.498

[78]   Soon, A., Todorova, M., Delly, B. and Stampfl, C. (2007) Thermodynamic Stability and Structure of Copper Oxide Surfaces: A First-Principles Investigation. Physical Review B, 75, Article ID: 125420.
http://dx.doi.org/10.1103/PhysRevB.75.125420

[79]   Yang, W.Y. and Rhee, S.W. (2007) Effect of Electrode Material on the Resistance Switching of Cu2O Film. Applied Physics Letters, 91, Article ID: 232907.
http://dx.doi.org/10.1063/1.2822403

[80]   Soon, A., Sohnel, T. and Idriss, H. (2005) Plane-Wave Pseudopotential Density Functional Theory Periodic Slab Calculations of CO Adsorption on Cu2O (111) Surface. Surface Science, 579, 131-140.
http://dx.doi.org/10.1016/j.susc.2005.01.038

[81]   Heimel, G., Romaner, L., Bredas, J.L. and Zojer, E. (2006) Interface Energetics and Level Alignment at Covalent Metal-Molecule Junctions: Π-Conjugated Thiols on Gold. Physical Review Letters, 96, Article ID: 196806.
http://dx.doi.org/10.1103/PhysRevLett.96.196806

[82]   Lang, N.D. and Kohn, W. (1971) Theory of Metal Surfaces: Work Function. Physical Review B, 3, 1215-1223.
http://dx.doi.org/10.1103/PhysRevB.3.1215

[83]   Feibelman, P.J. and Hamann, D.R. (1984) Quantum-Size Effects in Work Functions of Free-Standing and Adsorbed Thin Metal Films. Physical Review B, 29, 6463-6467.
http://dx.doi.org/10.1103/PhysRevB.29.6463

[84]   Ciraci, S. and Batra, I.P. (1986) Theory of the Quantum Size Effect in Simple Metals. Physical Review B, 33, 4294-4297.
http://dx.doi.org/10.1103/PhysRevB.33.4294

[85]   Fall, C., Binggeli, N. and Baldereschi, A. (1999) Deriving Accurate Work Functions from Thin-Slab Calculations. Journal of Physics: Condensed Matter, 11, 2689-2696.
http://dx.doi.org/10.1088/0953-8984/11/13/006

[86]   Desgreniers, S. (1998) High-Density Phases of ZnO: Structural and Compressive Parameters. Physical Review B, 58, 14102-14105.
http://dx.doi.org/10.1103/PhysRevB.58.14102

[87]   Zhang, D.K., Liu, Y.C., Liu, Y.L. and Yang, H. (2004) The Electrical Properties and the Interfaces of Cu2O/ZnO/ITO p-i-n Heterojunction. Physica B, 351, 178-183.
http://dx.doi.org/10.1016/j.physb.2004.06.003

[88]   Murnaghan, F. (1944) The Compressibility of Media under Extreme Pressures. Proceedings of the National Academy of Sciences of the United States of America, 30, 244-247.
http://dx.doi.org/10.1073/pnas.30.9.244

[89]   Hebbache, M. and Zemzemi, M. (2004) Ab Initio Study of High-Pressure Behavior of a Low Compressibility Metal and a Hard Material, Osmium and Diamond. Physical Review B, 70, Article ID: 224107.
http://dx.doi.org/10.1103/PhysRevB.70.224107

[90]   Lee, H. and Martin, R.M. (1997) Applications of the Generalized-Gradient Approximation to Atoms, Clusters, and Solids. Physical Review B, 56, 7197-7205.
http://dx.doi.org/10.1103/PhysRevB.56.7197

[91]   Gillen, R. and Robertson, J. (2013) Accurate Screened Exchange Band Structures for the Transition Metal Monoxides MnO, FeO, CoO and NiO. Journal of Physics: Condensed Matter, 25, Article ID: 165502.
http://dx.doi.org/10.1088/0953-8984/25/16/165502

[92]   Kümmel, S. and Kronik, L. (2008) Orbital-Dependent Density Functionals: Theory and Applications. Reviews of Modern Physics, 80, 3-60.
http://dx.doi.org/10.1103/RevModPhys.80.3

 
 
Top