摘要
SrTiO_3是一种钙钛矿金属氧化物绝缘体,它被广泛用于晶界电容器、氧敏传感器、光开关、生长高温超导薄膜的衬底,作为高电容率材料在超晶格和下一代超大规模集成器件中具有潜在的应用价值。目前,对SrTiO_3电子结构、半导化掺杂、导电模型、缺陷态、表面/界面态等方面已有了不少的理论和实验研究。其中对于n型掺杂前人研究较多,对于p型掺杂和各种空位缺陷研究较少。本文采用基于密度泛函理论框架下的第一性原理软件VASP,对SrTiO_3材料的电子结构、本征缺陷、掺杂改性进行研究,所用软件为VASP(Vienna Ab-initio Simulation Package)软件包。主要研究内容及结果如下:
一、系统地计算了SrTiO_3几何和电子结构,包括晶体结构、能带结构、态密度。计算结果表明SrTiO_3是一种间隙半导体。比较总态密度和各原子得分波态密度可知,价带顶(R点)电子主要由O 2p态电子提供,导带底(г点)电子主要由Ti 3d提供。
二、系统地计算了不同空位浓度下SrTiO_(3-x),Sr_(1-x)TiO_3和SrTi_(1-x)O_3(X=0.125,0.25,0.33)的几何结构和电子结构,包括晶格常数,能带结构、态密度、分波态密度。结果表明:通过引入O空位,使体系费米能级进入导带中。并且随着空位浓度的增大,进入到导带中的位置越深,属于n型掺杂,在禁带中产生了缺陷能级;引入Sr空位或Ti空位后,体系的费米能级进入到价带中,并且随着空位浓度的增大,进入到价带中的位置越深,属于p型掺杂,在价带项附近引入了缺陷能级。三种空位的引入,都使体系从绝缘性向金属性转变,其中Ti空位对体系导电性改善效果最好。
三、研究了不同掺杂浓度替位掺杂对SrTiO_3几何结构和电子结构的影响。结果显示Y替位Sr掺杂属于n型掺杂,体系Sr_(1-x)Y_xTiO_3(X=0.125,0.25,0.33)的费米能级进入导带中,在导带底出现大量由掺杂原子贡献的自由载流子-电子,明显提高了电导率,改善了SrTiO_3的导电性能。In或Al替位Ti掺杂为p型掺杂,体系SrTi_(1-x)In_xO_3(SrTi_(1-x)Al_xO_3)(X=0.125,0.25,0.33)的费米能级进入价带中,掺杂在价带顶附近引入缺陷能级,费米能级处电子态密度不为零,从而使得体系的导电能力增强。三种情况下的掺杂都使体系转变为金属性,其中Y替位Sr对体系导电性改善效果最好。
As a typical perovskite material, strontium titanate (SrTiO_3) has been widely used in oxygen-gas sensor, optical switch, epitaxial growth substrate fields. It has potential application in superlattice and large-scale integration fields for its high permittivity. At present, much theoretical and experimental investigations of SrTiO_3 have been carried out on electronic structure, doping, conductivity model, defect states, surfaces and interface of SrTiO_3. Among the researches, much focus on n-type doping and there is little study on the p-type doping and vacancy defect. The first principle package (VASP) based on the density functional theory (DFT) is used to study the n-type doping, electronic structures, intrinsic oxygen vacancies, strontium vacancies and titanium vacancies. The main contents are as the following:
1. The detailed investigations have been carried out, including the geometry and electronic structure, crystal structure, band structure, density of states (DOS) and sub-wave density of states of SrTiO_3 in the cubic phase. The results show that SrTiO_3 is indirect band gap semiconductor. The valence band top was at the point of R and the electrons are supplied by 2p state of oxygen atom, while the bottom of conduction band was at the point ofΓand the electrons are supplied by 3d state of titanium atom.
2. The geometry and electronic structure calculations of SrTiO_(3-x), SrTiO_(3-x) and SrTi_(1-x)O_3(X=0.125, 0.25, 0.33) were investigated. Due to the O vacancy electron doping, the Fermi level moves into CBs and the position got deeper while the doping concentration increased. The defect band level appeared in the forbidden band as a result of the O vacancy. Due to the Sr vacancy or Ti vacancy cavity doping, the Fermi level moves into VBs and the position was deeper while the doping concentration increased. The defect band level appeared at the top of valence band as a result of the Sr vacancy (or Ti vacancy). So by introducing one of the three types of vacancy, the system shows metallic behavior.
3. Both n-type and p-type doping for SrTiO_3 were carried out. The results show that strontium atom substituted by yttrium atom was n-type doping. The Fermi level of Sr_(1-X)Y_XTiO_3 (X=0.125, 0.25, 0.33) moves into CBs and there are lots of free electrons provided by the impurity atoms in the bottom of conduction band and the conductivity of SrTiO_3 is well improved. While indium or aluminum substituted titanium was p-type doping. The Fermi level of SrTi_(1-X)In_XO_3(SrTi_(1-x)Al_XO_3)(X=0.125, 0.25, 0.33) moves into VBs and the defect band appeared upon the top of valence band. So the conductivity of the system is enhanced. In conclusion, the system shows metallic behavior by the three types of doping.
引文
[1]Cheng H F,Lin T F,Hu C T,et al.Effect of sintering aids on microstructures and PTCR characteristics of(Sr_(0.2)Ba)TiO_3 ceramics[J].J Am Ceram Soc,1993,76(4):827
[2]Zhu W,Wang C C,Akbar S A,et al.Fast sintering of hydrothermally synthesized BaTiO_3powder and their dielectric properties[J].J Mater Sci,1997,32:4302
[3]Eemst F,Kienzle O,Ruhle M.Structure and Composition of Grain Boundaries in Ceramics[J].J Eur Ceram Soc,1999,19:665
[4]孔令兵,张良莹.溶胶.凝胶制备铁电材料(Sr_(0.5)Ba_(0.5-x)Pbx)TiO_3微粉及其表征[J].功能材料,1997,28(2):146
[5]Kim N K,Yow S G.Electric and structure properties of SrTiO_3 thin films deposited by plasma enhanced metalorganic chemical vapor deposition[J].J Mater Res,1997,12(4):1160
[6]Hong Z,Toft S O,Liu X Q,et al.Influence of water vapor on the response of Mg-doped SrTiO_3 ceramic oxygen sensors[J].J Electroceram,1999,3(3):301
[7]Yamaoka N,Masuyama M,fukkui M,SrTiO_3-based boundary layer capacitor having varistor characteristics[J],Am Ceram Soc Bull,1983,62(6):698-703
[8]Kaino D,Funayama J,Yamaoka N.Electrical properties of a(Sr,Ca)TiO/sub 3/base ceramic varistor[J],Jpn J Appl Phys,1985,24(Supplement 24-3):120-122
[9]Zhao T,Chen Z H,Chen F,Shi W S,Lu H B,Yang G Z.Enhancement of second-harmonic generation in BaTiO3/SrTiO3 superlattices[J].Phys.Rev.B,1999,60(3):1697
[10]Eisenbeiser K,Finder J M,Yu Z,Ramdani J,Hallmark J A,Droopad R,Ooms W J,Salem L,Bradshaw S,Overgaard C D.Field effect transistors with SrTiO_3 gate dielectric on Si[J].Appl.Phys.Lett.,2000,76:1324
[11]Kinase W,Inumiya S,Harada K.Theory of stuctural phase transition in SrTiO_3[J].Ferroelectric,1995,169:27
[12]Akimov L,Sirenko A A,et al.Electric-Field-Induced Soft-Mode Hardening in SrTiO_3 films[J].Phys.Rev.Lett.,2000,84(20):4625
[13]Balasubramanian M R[J].Indian.Chem Soc,1978,64:453
[14]Gerbinger J,Lampe H,Meixner U,Perczel I V.Cross-sensitivity of various doped strontium titanate films to CO,CO_2,H_2,H_2O and CH_4[J].Sensors and Actuators B,1994,18-19:529
[15]Feynman R P[J].Science,1991,274:1300
[16]Avudaithai M,Kutty T R N.Ultrafine powders of SrTiO_3 from the hydrothermal preparation and their catalytic activity in the photolysis of water[J].Mat Res Bull,1987,22:641
[17]闻立时.固体材料界面研究的物理基础[M].北京:科学出版社,1991
[18]曹全喜,邓亮雄,杨鹏,黄云霞,王毓鹏.镁在钙钛矿型氧敏材料中的作用[J].西安电子科技大学学报,2005,3(32):353
[19]陈铜,李文钊,于春英,季亚英,于作龙.掺杂钛酸盐对乙烷氧化脱氢催化性能的研究[J].高等学校化学学报,1996,17(10):1617
[20]哨鸣山,张承琚,王成建,兰建胜[J].功能材料,1996,27(5):441
[21]Takanori I,Noriaki S,Jun-ichi K,Koichi E,Hiromichi A.The conduction mechanism and defect structure of acceptor- and donor-doped SrTiO_3[J].Solid State Ionics,1991,48:283
[22]Park H D,Payne D A.Advances in Ceramics[J].ed.L.M.Levinson(the American Ceramic Society,Columbus),1981,1:242
[23]于德君,棒治轮,李龙土,化学法制备的(Sr,Pb)TiO_3基PTCR陶瓷[J].功能材料,1996,27(6):543
[24]Shen H,Song Y W,Gu H,et al.A high-permittivity SrTiO_3 based grain boundary layer capacitor material single fired under low temperature[J].Materials Letters,2002,56:802
[25]Van Benthem K,Elsassser C,French R H.Bulk electronic structure of SrTiO_3:Experiment and theory[J].J Appl Phys,2001,90:6156
[26]Arques M,Teles L K,et al.Full-relativistic calculations of the SrTiO_3 carrier effective mass and complex dielectric function[J].Appl.Phys Lett,2003,82(18):3074
[27]Tomohito T,Katsuyuki M,Yuichi I,et al.First-principles study on structures and energetics of intrinsic vacancies in SrTiO_3[J].Phys Rev B,2003,68:205213
[28]Guo X G;Chen X S,Sun Y L,et al.Electronic band structure of Nb doped SrTiO_3 from first principles calculation[J].Physics Letters A,2003,317:501
[29]Yun J N,Zhang Z Y,Deng Z H,Zhang F C.First-Principle Calculation of the Electronic Structure of Sb-Doped SrTiO3[J].Chinese Journal Of Semiconductors,2006,27:1537
[30]Luo W D,Duan W H,Steven G L,et al.Structural and electronic properties of n-doped and p-doped SrTiO_3[J].Phys Rev B,2004,70:214109-1
[31]Zhang Z Y,Yun J N,Zhang F C,Electronic structure and optical properties of In-doped SrTiO_3 by density function theory[J].2007 16(9):2791-2797
[32]廖沐真,吴国是,刘洪霖.量子化学从头计算方法[M].北京:清华大学出版社1984.26
[33]Richard M.Martin.Electronic Structure:Basic Theory and Practical Methods[M].Cambridge University Press,2004
[34]Kaxirs E.Atomic and Electronic Structure of Solids[M].Cambridge University Press,2003
[35]Levine I.Quantum Chemistry[M].prentice hall,2004.480
[36]Born M,Oppenheimer J R.Zur Quantentheorie der Molekeln[J].Ann.Phys.,1927,84:457
[37]Born M,Huang K.Dynamical Theory of Crystal Lattices[J].Oxford:Oxford University Press,1954
[38]Hartree D R.The wave mechanics of an atom with a non-Coulomb central field[J].Proc.Camb.Pil.Sot.,1928,24:111
[39](a)Fock V.Noherungsmethode zur Losung des quantenmechanischen mehrkorper problems[J].Z.Phys.1930,61:126;ibid.1930,62:795
(b) Fock V,M.J.Petrashen.On the numerical solution of generalised equations of the self-consistent field[J].Phys.Z.Sowjetunion,1934,6:368
[40]Hohenberg P,Kohn W.Inhomogeneous Electron Gas[J].Phys.Rev.B,1964,136:864
[41]Kohn W,Sham L J.Self-Consistent Equations Including Exchange and Correlation Effects[J].Phys.Rev.A 1965,140:1133
[42]谢希德,陆栋.固体能带理论[M].上海:复旦大学出版社,1998
[43]曾雉.第一原理电子结构计算研究RNi_2B_2C新型超导体[D].中国科学院固体物理研究所博士论文,1997
[44]郑小宏.分子尺度导体输运性质的第一性原理研究[D].中国科学院固体物理研究所博士论文,2005
[45]许英.关联电子体系的基态性质[D].中国科学院固体物理研究所博士论文,2005
[46]袁定旺.金属团簇与小分子相互作用的第一性原理研究[D].中国科学院固体物理研究所博士论文,2005
[47]李顺方.团簇和表面氧化过程的第一性原理研究[D].中国科学院固体物理研究所博士论文,2004
[48]王江龙.新型超导体材料的电子结构研究[D].中国科学院固体物理研究所博士论文.2003
[49]肖慎修,王崇愚,陈天朗.密度泛函理论的离散变分法在化学和材料物理中的应用[M].北京:科学出版社,1998
[50]徐光宪,黎乐民,王德民.量子化学(中册)[M].北京:科学出版社,1985
[51]唐敖庆,杨忠治,李前树.量子化学[M].北京:科学出版社,1982
[52]McWeeny R.Methods of Molecular Quantum Mechanics[M].London:Academic Press,1989
[53]王金兰.金属、半导体团簇结构和性质及金纳米线热力学稳定性的理论研究[D].南京大学博士论文,2001
[54]Moller C,Plesset M S.Note on an Approximation Treatment for Many-Electron Systems[J].Phys.Rev.,1934,46:618
[55]Thomas L H.The calculation of atomic fields[J].Proc.Camb.Phil.Soc.,1927,23:542
[56]Fermi E.Un metodo statistico per la determinazione di alcune priorieta dell'Atome[J]. Accad. Naz. Lincei, 1927, 6: 602
[57] Heer W A. The Physics of Simple Metal Clusters: Experimential Aspects and Simple Model[J]. Rev Mod Phys., 1993,65: 611
[58] Perdew J P, Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy[J]. Phys. Rev. B, 1992,45: 13244
[59] Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals[J]. Phys. Rev. B, 1993,47:558
[60] Kresse G, Furthmuller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[J]. J. Comput. Mater Sci, 1996, 6: 15
[61] Tomio T, Miki H, Tabata H. Control of electrical conductivity in laser deposited SrTiO_3 thin films with Nb doping[J]. J. Appl. Phys., 1994, 76: 5886
[62] Schooley J F, Hosier W R, Cohen M L. Superconductivity in Semiconducting SrTiO_3[J]. Phys. Rev. Lett. 1964, 12: 474
[63] Delacruz R M, Pareja R. Porous silicon investigated by positron-annihilation[J]. Physica Status Solidi(a),1989, 111: 463
[64] Gong W H, Yun H, Ning Y B, greendan J E, Datars W R, Stager C V. Oxygen-deficient SrTiO_(3-x), X = 0.28, 0.17, and 0.08. Crystal growth, crystal structure, magnetic, and transport properties[J]. Solid State Chem, 1991, 90: 320
[65] Ossmu S, Atsushi O. Vacancy in Si: Successful Description within the Local Density Approximation[J]. Phys. Rev. Lett., 1992, 68: 1858
[66] Shanthi N, Sarma D D. Electronic structure of electron doped SrTiO_3: SrTiO_(3_δ) and Sr_(1-x)La_xTiO_3[J]. Phys Rev B, 1998, 57: 2153
[67] Huang H H, Shin S, Ishigame M. Protonic conduction in the single crystals of Y-doped. SrZrO_3[J]. Solid State Ionics, 1991,47: 251
[68] Higuchi T, Tsukamoto T, Sata N, Ishigame M, Tezuka Y , Shin S. Electronic structure of p-type SrTiO_3 by photoemission spectroscopy[J]. Phys. Rev. B, 1998, 57: 6978
[69] Zhang C, Wang C L, Li J C, Yang K, Zhang Y F, Wu Q Z. Substitutional position and Insulator to metal transition in Nb-doped SrTiO_3[J]. Materials Chemistry and Physics. 2008, 107:215-219
