ZnO晶体的弹性模量和外压下电子结构的密度泛函理论计算
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摘要
ZnO晶体具有良好的光电性、透明导电性、压电性、气敏性、压敏性,且易与多种半导体材料实现集成化,形成复合材料。由于ZnO晶体具有这些优异的性质,使其具有广泛和潜在的用途。对于ZnO晶体的应用和相关器件的开发都依赖于对ZnO晶体的力学性能和电学性能的深入了解。本文“ZnO晶体的弹性模量和外压下电子结构的密度泛函理论计算”,旨在进一步研究ZnO晶体的力学性能及其电子结构,因此本学位论文选题具有重要的理论价值和实际指导意义。
本文论推导了六角密集晶体的体变弹性模量;采用基于密度泛函理论第一性原理理论下的平面波赝势方法,并采用局域密度近似(LDA)理论、广义梯度近似(GGA)和ABINIT软件对ZnO晶体的体变弹性模量进行了计算;得到了ZnO晶体的弹性模量为1.402Pa。
在研究ZnO晶体的能带结构中,从ZnO的固体物理学原胞基底矢量出发,得到了倒格子原胞的基底矢量,确定了简约布里渊区。在该区域内计算得到了截断能、k点取值等曲线,由此确定了合适的计算参数并且计算出了ZnO晶体的能带结构。在此基础上,采用局域密度近似(LDA)理论计算了ZnO晶体在不同压力下的能带结构和态密度。随着ZnO晶体的压缩,从能带结构中可以看出:当晶格常数压缩了5%时,在价带中出现了能量禁带,禁带宽度为0 .24eV;当晶格常数压缩了10%时,能量禁带已经非常明显,禁带宽度为0 .74eV。并且能量禁带在图像中向高能量区域迁移。在态密度图中,发现了同样的能量禁带。并且随着晶格常数不断被压缩,态密度也逐渐降低。
本文中得到的研究结果,对研究ZnO晶体的力学性能和电子结构提供了有益的理论参考。
ZnO crystal has good properties of photoelectricity, transparent conductivity, pressure sensibility, gas sensibility and piezoelectricity, and it’s easy to implement the integration with many kinds of semiconductor material. Because of its excellent physical properties, ZnO has the potential use of a wide range. The application of ZnO and the development of its relevant devices rely on the deep comprehension of the mechanics and electrical properties of ZnO crystal. This paper with the title of“Density Functional Theory Calculation of the Elastic Modulus and Electrical Structure in External Pressure of ZnO Crystal”is to further study the mechanics properties and electrical structure of ZnO crystal. This paper has important theoretic value and practical significance.
The analytical expression of crystal elastic modulus of hexagonal close packing construction is deduced in this paper. Elastic modulus of ZnO crystal is calculated via abinit package by planewave and pseduopotential based on the density functional theory (DTF) and first principles, and two different pseudopotentials of local density approximation (LDA) and generalized gradient approximation (GGA). The number of the elastic modulus is 1.402 Pa .
In the study on the band structure of ZnO crystal, the basis vectors of reciprocal lattice are determined by the basis vectors of solid state physics lattice of ZnO, therefore the first Brillouin zone is confirmed. In this region, the curves of cut off energy and the number of k points are calculated, and then the appropriate parameters are determined. On these bases, the band structure and density of states (DOS) in different external pressure are calculated by LDA. The conclusion is abtained from the band structure along with external pressure. The energy gap is appeared in the valence band when the lattice constant is compressed by 5%, and the width of energy gap is 0 .24eV. The energy gap is obvious very much when the lattice constant is compressed by 10%, and the width of energy gap is 0 .74eV. And the energy gap move to high energy zone in the graph. The same energy gap is discovered in the DOS graph. The DOS is decreased when the lattice constant is compressed.
The results required on this paper provide beneficial theoretical reference for the study on the mechanics properties and electric structure of ZnO crystal.
本文论推导了六角密集晶体的体变弹性模量;采用基于密度泛函理论第一性原理理论下的平面波赝势方法,并采用局域密度近似(LDA)理论、广义梯度近似(GGA)和ABINIT软件对ZnO晶体的体变弹性模量进行了计算;得到了ZnO晶体的弹性模量为1.402Pa。
在研究ZnO晶体的能带结构中,从ZnO的固体物理学原胞基底矢量出发,得到了倒格子原胞的基底矢量,确定了简约布里渊区。在该区域内计算得到了截断能、k点取值等曲线,由此确定了合适的计算参数并且计算出了ZnO晶体的能带结构。在此基础上,采用局域密度近似(LDA)理论计算了ZnO晶体在不同压力下的能带结构和态密度。随着ZnO晶体的压缩,从能带结构中可以看出:当晶格常数压缩了5%时,在价带中出现了能量禁带,禁带宽度为0 .24eV;当晶格常数压缩了10%时,能量禁带已经非常明显,禁带宽度为0 .74eV。并且能量禁带在图像中向高能量区域迁移。在态密度图中,发现了同样的能量禁带。并且随着晶格常数不断被压缩,态密度也逐渐降低。
本文中得到的研究结果,对研究ZnO晶体的力学性能和电子结构提供了有益的理论参考。
ZnO crystal has good properties of photoelectricity, transparent conductivity, pressure sensibility, gas sensibility and piezoelectricity, and it’s easy to implement the integration with many kinds of semiconductor material. Because of its excellent physical properties, ZnO has the potential use of a wide range. The application of ZnO and the development of its relevant devices rely on the deep comprehension of the mechanics and electrical properties of ZnO crystal. This paper with the title of“Density Functional Theory Calculation of the Elastic Modulus and Electrical Structure in External Pressure of ZnO Crystal”is to further study the mechanics properties and electrical structure of ZnO crystal. This paper has important theoretic value and practical significance.
The analytical expression of crystal elastic modulus of hexagonal close packing construction is deduced in this paper. Elastic modulus of ZnO crystal is calculated via abinit package by planewave and pseduopotential based on the density functional theory (DTF) and first principles, and two different pseudopotentials of local density approximation (LDA) and generalized gradient approximation (GGA). The number of the elastic modulus is 1.402 Pa .
In the study on the band structure of ZnO crystal, the basis vectors of reciprocal lattice are determined by the basis vectors of solid state physics lattice of ZnO, therefore the first Brillouin zone is confirmed. In this region, the curves of cut off energy and the number of k points are calculated, and then the appropriate parameters are determined. On these bases, the band structure and density of states (DOS) in different external pressure are calculated by LDA. The conclusion is abtained from the band structure along with external pressure. The energy gap is appeared in the valence band when the lattice constant is compressed by 5%, and the width of energy gap is 0 .24eV. The energy gap is obvious very much when the lattice constant is compressed by 10%, and the width of energy gap is 0 .74eV. And the energy gap move to high energy zone in the graph. The same energy gap is discovered in the DOS graph. The DOS is decreased when the lattice constant is compressed.
The results required on this paper provide beneficial theoretical reference for the study on the mechanics properties and electric structure of ZnO crystal.
引文
[1] Yu P, Tang Z K, Wong G K L, et al. Room temperature stimulated emission from ZnO quantum dot films.23rd Int Conf on the Physics of Semiconductors, Singapore, 1996: 1452-1456.
[2] Robert F., Will UV Lasers Beat the Blues, Science, 1997, 276: 895.
[3] Heo Y. W., Varadarjan V., Kaufman M.,Ren F., et al. Site-specific growth of Zno nanorods using catalysis-driven molecular-beam epitaxy, Appl. Phys. Lett., 2002, 81: 3046-3048.
[4] Tang Z. K., Wang G. K., Yu P., et al. Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films, Appl. Phys. Lett., 1998, 72: 3270-3272.
[5] Hideki Tanaka, Kazuhiko Ihara, Toshihiro Miyata, et al, Low resistivity polycrystalline ZnO:Al thin films prepared by pulsed laser deposition, J. Vac. Sci. Technol, 2004, A22: 1757-1762.
[6] Ohta H., Kawamura K., Orita M., et al. Current injection emission from a transparent p–n junction composed of p-SrCu2O2/n-ZnO, Appl. Phys. Lett., 2000, 77: 475-477.
[7] Zayer N. K.,et al., In situ monitoring of sputtered zinc oxide films for piezoelectric transducers, Thin Solid Films, 1999, 352: 179-184.
[8] Kim H. J., Lee H. N., Park J. C., et. al.,The Mechanism of Improvement of Contact Resistivity in TFT-LCDs between IZO Layers and Al-based Metal Lines by Diffusion of Mo Atoms, Curr. Appl. Phys., 2002, 2(6): 451-454.
[9] Wacogne B., Roe M. P., Pattinson T. J., et al., Effective Piezoelectric Activity of Zinc Oxide Films Grown by Radio-frequency Planar Magnetron Sputtering, Appl. Phys. Lett., 1995, 67(12): 1674-1676.
[10] Coutts T. J., Mason T. O., Perkins J. D.,et. al., Uniformity in Large Area ZnO: Al Films Prepared by Reactive Mid Frequency Magnetron Sputtering, Proc. Electrochem Soc., 1999, 11(2): 274-278.
[11] Dayan J. N., Sainkar S. R., Formulation and Characterization of ZnO: Sb Thick-films Gas Sensors, Thin Solid Films, 1998, 325(1-2):254-258.
[12] Makino T, Chia C H, Tuan N T, Segawa Y, Kawasaki M, Ohtomo A , Tamura K. Radiative and nonradiative recombination processes in lattice-matched (Cd,Zn)O/(Mg,Zn)O multiquantum wells, Appl. Phys. Lett. 2000, 77: 1632-1634.
[13] Ma D W, Ye Z Z, Chen L L, Dependence of structural and optical properties of Zn1-xCdxO films on the Cd composition, Phys. Status Solidi. A 2004, 201: 2929-2932.
[14] Sakurai K, Takagi T, Tanabe T, Takasu H, Fujita S Studies of the Growth Mechanism of Polycrystalline Cuinse2 Thin Films Prepared by a Sequential Process, Cryst. Growth 2002,514:237-239.
[15]蔡少华,黄坤耀,张玉容.元素无机化学,广州:中山大学出版社,1995.
[16]徐采栋,林蓉,汪大成.锌冶金物理化学,上海:上海科学技术出版社,1979.
[17]曹惠民,包文滁,安家驹.无机化合物合成手册,北京:化学工业出版社,1983.
[18]叶志镇,陈汉鸿,刘榕等.直流磁控溅射氧化锌薄膜的结构和室温PL谱,半导体学报, 2001, 22 (8): 1015-1018.
[19]梅光贵,王德润,周敬元等.湿法炼锌学,长沙:中南大学出版社,2001.
[20] Xu D H, Deng Z B, Xu Y, et al. An anode with aluminum doped on zinc oxide thin films for organic light emitting devices, Physics Letters A, 2005, 346 (1-3): 148-152.
[21]王丽玉,谢家纯,林碧霞,等. n-ZnO/p-Si异质结UV增强型光电探测器的研究,电子元件与材料, 2004, 23 (1) :42- 44.
[22] Tajahashi Y., Kanamori M, Kondoh A, et al. Photoconductivity of ultra-thin zinc oxide films. Jpn., Appl Phys, 1994, 33:6611-6615.
[23] Zhang D. H., Brodie D. E., Photoresponse of polycrystalline ZnO films deposited by r. f. bias sputtering, Thin Solid Films, 1995, 261:334-339.
[24] Zhang D. H., Fast photoresponse and the related change of crystallite barriers for ZnO films deposited by RF sputtering, Phys D, 1995, 28:1273-1277.
[25] Fabricius H., Skettrup T., Bisgaard P., Ultraviolet detectors in thin sputtered ZnO films, Appl Optics, 1986, 25:2764-2767.
[26] Liu Y., Gorla C. R., Liang S., et al. Ultraviolet detectors based on epitaxial ZnO films grown by MOCVD, Elec Mater, 2000, 29:69-74.
[27] Liang S., Sheng H., Liu Y, et al. ZnO Schottky ultraviolet photodetectors, Cryst Growth,2001, 225:110-113.
[28] Puyane R. Applications and product development in varistor tech-nology. J Mater Proc Tech, 1995, 55(3-4):268-277.
[29] Horio N, Hiramatsu M, Nawata M, et al. Preparation of zinc oxide/metal oxide multilayered thin films for low-voltage varistors. Vacuum, 1998, 51(4):719-722.
[30] Born M, Huang K. Dynamical Theory of Crystal Lattices. London:Oxford University Press, 1954. 166-212.
[31]谢希德,陆栋.固体能带理论.上海:复旦大学出版社,1998.66-139.
[32] Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys. Rev., 1964, 136(3B):864-871.
[33] Kohn W, Sham L J. Self-consistent Equations including exchange and correlation effects. Phys. Rev., 1965, 140(4A): 1133-1138.
[34]黄美纯.密度泛函理论的若干进展.物理学进展,2000,20(3), 199-219.
[35]肖慎修,王崇愚,陈天朗.密度泛函理论的离散变分方法在化学和材料物理学中的应用.北京:科学出版, 1998.10-11.
[36] Troullier , Martins J L. Pseudopotential plane-wave calculations for ZnS. Phys. Rev. B, 1991, 43(3):2213-2217.
[37] Troullier N, Martins J L. Straightforward method for generating soft transferable pseudopotentials. Solid State Communications, 1990, 74(7):613-616.
[38] Hartwigsen C, Goedecker S, Hutter J. Relativistic separable dual-space Gaussian pseudopotentials from H to Rn. Phys. Rev. B., 1998, 58(7):3641-3662.
[39] Goedecker S, Teter M, Hutter J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B., 1996, 54(3): 1703-1996.
[40] Fuchs M, Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Comput. Phys. Commun, 1999, 119(1):67-98.
[41] Perdew J P, Zunger A. Self-interaction correction to density functional approximations for many-electron systems. Phys. Rev. B, 1981, 23(10): 5048-5079.
[42] Perdew J P, Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B, 1992, 45(23):13244-13249.
[43] Perdew J P, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett, 1996, 77(18):3865-3868.
[44] Line D R, Handbook of Chemistry and Physics, CRC Press, 2003-2004.
[45]基泰尔,固体物理导论(原著第八版),化学工业出版社,2005.
[46] Chelikowsky J R. An oxygen pseudopotential:Application to the electronic structure of ZnO. Solid.State.Comm, 1977, 22(6): 351-354.
[47] Ivanov I, Pollmann J. Electronic structure of ideal and relaxed surfaces of ZnO: A prototype ionic wurtzite semiconductor and its surface properties. Phys. Rev. B, 1981, 24(12): 7275-7296.
[48] Schroer P, Kruger P, Pollmann J. First-principles calculation of the electronic structure of the wurtzite semiconductors ZnO and ZnS. Phys. Rev. B, 1993, 47(12): 6971-6980.
[49] Yang C K, Dy K S. Band structure of ZnO using the LMTO method. Solid State Comm, 1993,88(6): 491-494.
[50] Massidda S, Resta R, Posternak M et al. Polarization and dynamical charge of ZnO within different one-particle schemes. Phys. Rev. B, 1995, 52(24): R16977-R16980.
[51] Oshikiri M, Aryasetiawan F. Band gaps and quasiparticle energy calculations on ZnO, ZnS, and ZnSe in the zinc-blende structure by the GW approximation. Phys. Rev. B, 1999, 60(15): 10754-10757.
[52] Anderson Janotti, Chris G, Van de Walle. New insights into the role of native point defects in ZnO. Journal of Crystal Growth, 2006, 287(1): 58-65.
[53] Zhang S B, Wei S H, Alex Zunger. Intrinsic n-type versus p-type doping asymmetry and the defect physics of ZnO. Phys. Rev. B, 2001, 63(7): 075205-075211.
[2] Robert F., Will UV Lasers Beat the Blues, Science, 1997, 276: 895.
[3] Heo Y. W., Varadarjan V., Kaufman M.,Ren F., et al. Site-specific growth of Zno nanorods using catalysis-driven molecular-beam epitaxy, Appl. Phys. Lett., 2002, 81: 3046-3048.
[4] Tang Z. K., Wang G. K., Yu P., et al. Room-temperature ultraviolet laser emission from self-assembled ZnO microcrystallite thin films, Appl. Phys. Lett., 1998, 72: 3270-3272.
[5] Hideki Tanaka, Kazuhiko Ihara, Toshihiro Miyata, et al, Low resistivity polycrystalline ZnO:Al thin films prepared by pulsed laser deposition, J. Vac. Sci. Technol, 2004, A22: 1757-1762.
[6] Ohta H., Kawamura K., Orita M., et al. Current injection emission from a transparent p–n junction composed of p-SrCu2O2/n-ZnO, Appl. Phys. Lett., 2000, 77: 475-477.
[7] Zayer N. K.,et al., In situ monitoring of sputtered zinc oxide films for piezoelectric transducers, Thin Solid Films, 1999, 352: 179-184.
[8] Kim H. J., Lee H. N., Park J. C., et. al.,The Mechanism of Improvement of Contact Resistivity in TFT-LCDs between IZO Layers and Al-based Metal Lines by Diffusion of Mo Atoms, Curr. Appl. Phys., 2002, 2(6): 451-454.
[9] Wacogne B., Roe M. P., Pattinson T. J., et al., Effective Piezoelectric Activity of Zinc Oxide Films Grown by Radio-frequency Planar Magnetron Sputtering, Appl. Phys. Lett., 1995, 67(12): 1674-1676.
[10] Coutts T. J., Mason T. O., Perkins J. D.,et. al., Uniformity in Large Area ZnO: Al Films Prepared by Reactive Mid Frequency Magnetron Sputtering, Proc. Electrochem Soc., 1999, 11(2): 274-278.
[11] Dayan J. N., Sainkar S. R., Formulation and Characterization of ZnO: Sb Thick-films Gas Sensors, Thin Solid Films, 1998, 325(1-2):254-258.
[12] Makino T, Chia C H, Tuan N T, Segawa Y, Kawasaki M, Ohtomo A , Tamura K. Radiative and nonradiative recombination processes in lattice-matched (Cd,Zn)O/(Mg,Zn)O multiquantum wells, Appl. Phys. Lett. 2000, 77: 1632-1634.
[13] Ma D W, Ye Z Z, Chen L L, Dependence of structural and optical properties of Zn1-xCdxO films on the Cd composition, Phys. Status Solidi. A 2004, 201: 2929-2932.
[14] Sakurai K, Takagi T, Tanabe T, Takasu H, Fujita S Studies of the Growth Mechanism of Polycrystalline Cuinse2 Thin Films Prepared by a Sequential Process, Cryst. Growth 2002,514:237-239.
[15]蔡少华,黄坤耀,张玉容.元素无机化学,广州:中山大学出版社,1995.
[16]徐采栋,林蓉,汪大成.锌冶金物理化学,上海:上海科学技术出版社,1979.
[17]曹惠民,包文滁,安家驹.无机化合物合成手册,北京:化学工业出版社,1983.
[18]叶志镇,陈汉鸿,刘榕等.直流磁控溅射氧化锌薄膜的结构和室温PL谱,半导体学报, 2001, 22 (8): 1015-1018.
[19]梅光贵,王德润,周敬元等.湿法炼锌学,长沙:中南大学出版社,2001.
[20] Xu D H, Deng Z B, Xu Y, et al. An anode with aluminum doped on zinc oxide thin films for organic light emitting devices, Physics Letters A, 2005, 346 (1-3): 148-152.
[21]王丽玉,谢家纯,林碧霞,等. n-ZnO/p-Si异质结UV增强型光电探测器的研究,电子元件与材料, 2004, 23 (1) :42- 44.
[22] Tajahashi Y., Kanamori M, Kondoh A, et al. Photoconductivity of ultra-thin zinc oxide films. Jpn., Appl Phys, 1994, 33:6611-6615.
[23] Zhang D. H., Brodie D. E., Photoresponse of polycrystalline ZnO films deposited by r. f. bias sputtering, Thin Solid Films, 1995, 261:334-339.
[24] Zhang D. H., Fast photoresponse and the related change of crystallite barriers for ZnO films deposited by RF sputtering, Phys D, 1995, 28:1273-1277.
[25] Fabricius H., Skettrup T., Bisgaard P., Ultraviolet detectors in thin sputtered ZnO films, Appl Optics, 1986, 25:2764-2767.
[26] Liu Y., Gorla C. R., Liang S., et al. Ultraviolet detectors based on epitaxial ZnO films grown by MOCVD, Elec Mater, 2000, 29:69-74.
[27] Liang S., Sheng H., Liu Y, et al. ZnO Schottky ultraviolet photodetectors, Cryst Growth,2001, 225:110-113.
[28] Puyane R. Applications and product development in varistor tech-nology. J Mater Proc Tech, 1995, 55(3-4):268-277.
[29] Horio N, Hiramatsu M, Nawata M, et al. Preparation of zinc oxide/metal oxide multilayered thin films for low-voltage varistors. Vacuum, 1998, 51(4):719-722.
[30] Born M, Huang K. Dynamical Theory of Crystal Lattices. London:Oxford University Press, 1954. 166-212.
[31]谢希德,陆栋.固体能带理论.上海:复旦大学出版社,1998.66-139.
[32] Hohenberg P, Kohn W. Inhomogeneous electron gas. Phys. Rev., 1964, 136(3B):864-871.
[33] Kohn W, Sham L J. Self-consistent Equations including exchange and correlation effects. Phys. Rev., 1965, 140(4A): 1133-1138.
[34]黄美纯.密度泛函理论的若干进展.物理学进展,2000,20(3), 199-219.
[35]肖慎修,王崇愚,陈天朗.密度泛函理论的离散变分方法在化学和材料物理学中的应用.北京:科学出版, 1998.10-11.
[36] Troullier , Martins J L. Pseudopotential plane-wave calculations for ZnS. Phys. Rev. B, 1991, 43(3):2213-2217.
[37] Troullier N, Martins J L. Straightforward method for generating soft transferable pseudopotentials. Solid State Communications, 1990, 74(7):613-616.
[38] Hartwigsen C, Goedecker S, Hutter J. Relativistic separable dual-space Gaussian pseudopotentials from H to Rn. Phys. Rev. B., 1998, 58(7):3641-3662.
[39] Goedecker S, Teter M, Hutter J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B., 1996, 54(3): 1703-1996.
[40] Fuchs M, Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory. Comput. Phys. Commun, 1999, 119(1):67-98.
[41] Perdew J P, Zunger A. Self-interaction correction to density functional approximations for many-electron systems. Phys. Rev. B, 1981, 23(10): 5048-5079.
[42] Perdew J P, Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B, 1992, 45(23):13244-13249.
[43] Perdew J P, Burke K, Ernzerhof M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett, 1996, 77(18):3865-3868.
[44] Line D R, Handbook of Chemistry and Physics, CRC Press, 2003-2004.
[45]基泰尔,固体物理导论(原著第八版),化学工业出版社,2005.
[46] Chelikowsky J R. An oxygen pseudopotential:Application to the electronic structure of ZnO. Solid.State.Comm, 1977, 22(6): 351-354.
[47] Ivanov I, Pollmann J. Electronic structure of ideal and relaxed surfaces of ZnO: A prototype ionic wurtzite semiconductor and its surface properties. Phys. Rev. B, 1981, 24(12): 7275-7296.
[48] Schroer P, Kruger P, Pollmann J. First-principles calculation of the electronic structure of the wurtzite semiconductors ZnO and ZnS. Phys. Rev. B, 1993, 47(12): 6971-6980.
[49] Yang C K, Dy K S. Band structure of ZnO using the LMTO method. Solid State Comm, 1993,88(6): 491-494.
[50] Massidda S, Resta R, Posternak M et al. Polarization and dynamical charge of ZnO within different one-particle schemes. Phys. Rev. B, 1995, 52(24): R16977-R16980.
[51] Oshikiri M, Aryasetiawan F. Band gaps and quasiparticle energy calculations on ZnO, ZnS, and ZnSe in the zinc-blende structure by the GW approximation. Phys. Rev. B, 1999, 60(15): 10754-10757.
[52] Anderson Janotti, Chris G, Van de Walle. New insights into the role of native point defects in ZnO. Journal of Crystal Growth, 2006, 287(1): 58-65.
[53] Zhang S B, Wei S H, Alex Zunger. Intrinsic n-type versus p-type doping asymmetry and the defect physics of ZnO. Phys. Rev. B, 2001, 63(7): 075205-075211.