二氧化铀光学性质的实验和理论研究
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摘要
本文通过直流磁控溅射技术在单晶Si(111)基底上沉积UO2薄膜,在相同工艺条件不同沉积时间下分别制备了三组薄膜。通过扫描电子显微镜,原子力显微镜,X射线衍射仪以及X射线光电子能谱仪对所制备薄膜的表面形貌,粗糙度,相结构以及元素化学状态进行了分析。通过反射光谱仪和椭偏光谱仪对薄膜的光学性质进行了测量和分析。研究了不同厚度下薄膜的表面形貌,粗糙度,相结构以及元素状态和光学性质。利用几种不同的厚度测量方法分别对所制备的薄膜厚度进行了测量,并进行了分析比较。研究表明随着沉积时间的延长,薄膜的厚度增加,粗糙度增加,晶粒尺寸增大。光学性质测量结果表明薄膜的折射率随厚度的增加而减小,消光系数随厚度的增加而增加,最厚的薄膜的折射率出现了强吸收现象。几种厚度测量方法所测得的厚度结果在薄膜厚度较小的情况下符合得比较好,在厚度较大的情况下出现了一定的差别。
在理论计算方面主要基于密度泛函理论,首先利用广义梯度近似(GGA)对UO2进行结构优化,再利用局域密度近似(LDA)方法对UO2的电子结构,能带以及光学性质进行了计算,引入了Hubbard U校正项来处理5f电子的强关联效应。计算所得的UO2晶体的晶胞参数为5.39(?),体模量为240 GPa,带隙为1.87 eV与实验结果吻合较好,态密度计算结果表明UO2价带主要由U 6p,U 6d和O 2p轨道组成,导带主要由U6d和U 5f轨道组成。在此基础上计算了UO2的介电函数,反射率,折射率,消光系数,能量损失谱和吸收系数,并与现有文献报道的实验值和自己的实验值进行了分析比较,本文的光学性质计算结果与文献报道值以及实验结果吻合较好,尤其在峰值位置和变化趋势上。
Uranium dioxide films were deposited on Si(111) substrates by dc magnetron sputtering method, and the films were grown at same conditions with different sputtering time. The morphology, roughness, structure, and chemical state of the films were studied by field emission scanning electron microscopy, atomic force microscopy, X-ray diffraction and X-ray photoelectron spectroscopy, respectively. The optical properties of the films were obtained by reflectometry and ellipsometry. The influences of film thickness and roughness on the morphology, micro structure, chemical state and optical properties were investigated. Different thickness measurement methods were used to obtain the thickness of the films. The results show that thickness, roughness and crystalline grain size increase with sputtering time. The optical properties measurements show that the refractive indices decrease with the film thickness, while the extinction coefficients have the opposite trend. The thickest film turns out to have strong absorption tendency. The results of different thickness measurement methods agree well with each other at low film thickness, while the discrepancy appears when the film thickness becomes larger.
Theoretical calculations were based on density functional theory (DFT).Generalized gradient approximation (GGA) was used to optimize the structure of the unit cell, and then the local density approximation (LDA) was used to calculate the electronic structure, band gap and optical properties.Hubbard U is employed to evaluate exchange-correlation energy of 5f electrons.The calculated cell parameter was 5.39 A, bulk modulus was 240 GPa, band gap was 1.87 eV, which all agree well with the experimental results. Calculated density of states show that the valence band of UO2 consists mainly of U 6p, U 6d and O 2p orbitals, while the conduction band is mainly derived from U 6d and 5f orbitals. Furthermore, the dielectric function and the optical properties, such as reflectivity, refractive index, extinction coefficient, energy-loss spectrum and absorption coefficient were derived and analyzed.The calculated results were compared with experimental data from both published literature and our own results. Our calculated optical properties agree well with experimental data, especially in peak positions and trend.
在理论计算方面主要基于密度泛函理论,首先利用广义梯度近似(GGA)对UO2进行结构优化,再利用局域密度近似(LDA)方法对UO2的电子结构,能带以及光学性质进行了计算,引入了Hubbard U校正项来处理5f电子的强关联效应。计算所得的UO2晶体的晶胞参数为5.39(?),体模量为240 GPa,带隙为1.87 eV与实验结果吻合较好,态密度计算结果表明UO2价带主要由U 6p,U 6d和O 2p轨道组成,导带主要由U6d和U 5f轨道组成。在此基础上计算了UO2的介电函数,反射率,折射率,消光系数,能量损失谱和吸收系数,并与现有文献报道的实验值和自己的实验值进行了分析比较,本文的光学性质计算结果与文献报道值以及实验结果吻合较好,尤其在峰值位置和变化趋势上。
Uranium dioxide films were deposited on Si(111) substrates by dc magnetron sputtering method, and the films were grown at same conditions with different sputtering time. The morphology, roughness, structure, and chemical state of the films were studied by field emission scanning electron microscopy, atomic force microscopy, X-ray diffraction and X-ray photoelectron spectroscopy, respectively. The optical properties of the films were obtained by reflectometry and ellipsometry. The influences of film thickness and roughness on the morphology, micro structure, chemical state and optical properties were investigated. Different thickness measurement methods were used to obtain the thickness of the films. The results show that thickness, roughness and crystalline grain size increase with sputtering time. The optical properties measurements show that the refractive indices decrease with the film thickness, while the extinction coefficients have the opposite trend. The thickest film turns out to have strong absorption tendency. The results of different thickness measurement methods agree well with each other at low film thickness, while the discrepancy appears when the film thickness becomes larger.
Theoretical calculations were based on density functional theory (DFT).Generalized gradient approximation (GGA) was used to optimize the structure of the unit cell, and then the local density approximation (LDA) was used to calculate the electronic structure, band gap and optical properties.Hubbard U is employed to evaluate exchange-correlation energy of 5f electrons.The calculated cell parameter was 5.39 A, bulk modulus was 240 GPa, band gap was 1.87 eV, which all agree well with the experimental results. Calculated density of states show that the valence band of UO2 consists mainly of U 6p, U 6d and O 2p orbitals, while the conduction band is mainly derived from U 6d and 5f orbitals. Furthermore, the dielectric function and the optical properties, such as reflectivity, refractive index, extinction coefficient, energy-loss spectrum and absorption coefficient were derived and analyzed.The calculated results were compared with experimental data from both published literature and our own results. Our calculated optical properties agree well with experimental data, especially in peak positions and trend.
引文
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[4]Artioukov I A, Chefonov O V, Gilev O N, et.al. Experimental research of stability of thin films on the basis of depleted uranium as reflecting coating for wavelength of 4.5 nm. Nucl. Inst. Methods Phys. Res. A, 2007;575:248～250
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[6]Siekhaus W, Nelson A J.The optical properties of a polished uranium surface and its epitaxial oxide, and the rate of oxide growth determined by spectrophotometry. Materials Research Society Fall 2005, Boston
[7]Ritehie A G, Greenwood R C. The kinetics of the uranium-oxygen-water vapour reaction between 40 and 100℃[J].J.Nucl.Mater,1986; 139:121-136
[8]Lin S, Lai X, Lv X, et al. Study of the initial oxidation characteristics of uranium with pure oxygen below 100℃ by spectroscopic ellipsometry. Surf. Interface. Anal,2008;40:645～648
[9]Meek T T, B.von Roedern. Semiconductor devices fabricated from actinide oxides. Vacuum,2009; 83: 226-228
[10]Meek T T, B.von Roedern, Chem P G, et.al. Some optical properties of intrinsic and doped UO2 thin films.Jr.,Mater. Lett,2005;59:1085～1088
[11]Pirie J D, Smith T. Lattice distortion in uranium dioxide near 30(?).Phys. stat. sol.1970;41:221-224
[12]Nerikar P, Watanabe T, James S, et al. Energetics of intrinsic point defects in uranium dioxide from electronic-structure calculations. J. Nucl.Mater,2009; 384:61-69
[13]Gupta F, Brillant G, Pasturel A. Correlation effects and energetics of point defects in uranium dioxide: a first principle investigation. Philos. Mag,2007;87:2561
[14]Konstantin N K, Gustavo E.S, Richard L M.Hybrid density-functional theory and the insulating gap of UO2.Phys.Rev. L,2002;89:266402
[15]Crocombette J P, Jollet F, Nga T,et al. Plane-wave pseudopotential study of point defects in uranium dioxide [J].Phys.Rev. B,2001;64:104～107
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[19]Kohn V G. On the theory of reflectivity by an x-ray multilayer mirror [J].Phys.Sta.Sol.1995;185: 61-70
[20]李芳,张诚,林永昌.膜系优化设计中的模糊输入及评价函数的改进.北京理工大学学报,2000(20)
[21]Forouhi A R. Optical dispersion relations for amorphous semiconductors and amorphous dielectrics [J]. Phys. Rev. B,1986; 34(10):7018-7026
[22]Lin C C, Chen S Y, Cheng S Y, et al.Properties of nitrogen-implanted p-type ZnO films grown on SisN4/Si by radio-frequency magnetron sputtering [J].Appl Phys Lett,2004; 84:5040-5042
[23]铀与氧气反应的初始氧化动力学的椭偏技术研究[D].硕士论文.北京：中国工程物理研究院,2007
[24]Lhotka J, Kuzel R, Cappueeio G, et al.Thickness determination of thin polyerystalline film by grazing incidence X-ray diffraction [J].Surf. Coat. Tech,2001;148:95-100
[25]J.M. Myoung, W.H.Yoon, D.H.Lee, et al. Effects of Thickness Variation on Properties of ZnO Thin Films Grown by Pulsed Laser Deposition. Jpn. J.Appl.Phys.2002;41:28-31.
[26]Moore K T, Gerrit van der Laan. Nature of 5f states in actinide metals. Reviews of Modern Physics, 2009; 81:235
[27]何开华.典型半导体材料第一性原理研究[D].硕士论文.成都：四川师范大学,2005
[28]Hohenberg P, Kohn W. Inhomogeneous Electron Gas [J].Phys. Rev,1964,136:B864-B871
[29]Kohn W, Sham J.Self-Consistent Equations Including Exchange and Correlation Effects [J].Phys Rev. B,1965;140:A1133-A1138
[30]Caperley D M, Alder B J.Ground State of the Electron Gas by a Stochastic Method [J].Phys.Rev. Lett,1980;45:566-569
[31]Perdew J P, Zunger A. Self-interaction correction to density-functional approximations for many-electron systems [J].Phys.Rev.B,1981;23:5048
[32]Perdew J P,Wang Y.Accurate and simple analytic representation of the electron-gas correlation energy[J]. Phys. Rev. B,1992;45:13244-13249
[33]Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple [J].Phys.Rev. Lett,1996;77:3865-3868
[34]Bagno P, Jepsen O, Gunnarsson O.Ground-state properties of third-row elements with nonlocal density functions [J].Phys. Rev. B,1989;40:1997
[35]Dufek P, Blaha P, Sliwko V, Schwarz K. Generalize gradient approximation description of band splittings in transition-metal oxides and fluorides [J].Phys.Rev. B,1994; 49:10170
[36]谭世勇.铀和二氧化铀光学性质第一性原理计算[D].硕士论文.北京：中国工程物理研究院,2009
[37]Puddu G. C Comparison between different computational schemes for variational calculations in nuclear structure [J].Eur. Phys. J.A,2009;39:335-340
[38]Jeong T S,Han M S,Kim J H,et al.Crystallinity-damage recovery and optical property of As-implanted ZnO crystals by post-implantation annealing[J].J Cryst Growth,2005,275:541-547.
[39]沈学础.半导体光谱和光学性质[M].北京,科学出版社,1992:76
[40]Larson D T,Lottand LA, Cash D L. Surface film thickness determination by refleetivity Measurements[R].RFP-1911.
[41]Dufek P, Blaha P, Sliwko V, Schwarz K. Generalize gradient approximation description of band splittings in transition-metal oxides and fluorides [J].Phys.Rev. B,1994;49:10170
[42]Villars P, CalvertL.D, Person's Handbook of Crystallographic Data for Intermetallic Phases [M], Editor, ASM, Metals Park, Ohio(1985)
[43]Dudarev S L, Botton G A, Humphreys, et al.Electron-energy-loss spectra and the structural stability of nickel oxide:an LSDA+U study. Phys.Rev. B,1997;57:1505～1509
[44]邢海英、范广涵、章勇等.p,n型掺杂剂与Mn共掺杂GaN的电磁性质.物理学报,2009(58):3324～3330
[45]彭丽萍、徐凌、尹建武.N掺杂锐钛矿TiO2光学性能的第一性原理研究.物理学报2007(56)：1585～1589
[46]王渊旭、王春雷、钟维烈.光折变晶体Kta0.5Nb0.5O3光学特性的第一性原理研究.物理学报,2004(53)：3141～3145
[2]Sandberg R L, Allred D D, Johnson J E, at al. A comparison of uranium oxide and nickel as single-layer reflectors from 2.7 to 11.6 nm. Proc. SPIE,2003;5193:191～203
[3]Artioukov I A, Fechtchenko R M, Udovskii A L, et al. Soft X-ray multilayer mirrors based on depleted uranium. Nucl.Inst. Methods Phys. Res. A,2004;517:372～377
[4]Artioukov I A, Chefonov O V, Gilev O N, et.al. Experimental research of stability of thin films on the basis of depleted uranium as reflecting coating for wavelength of 4.5 nm. Nucl. Inst. Methods Phys. Res. A, 2007;575:248～250
[5]Schoenes J.Optical properties and electronic structure of UO2.J.Appl. Phys,1978;49:1463
[6]Siekhaus W, Nelson A J.The optical properties of a polished uranium surface and its epitaxial oxide, and the rate of oxide growth determined by spectrophotometry. Materials Research Society Fall 2005, Boston
[7]Ritehie A G, Greenwood R C. The kinetics of the uranium-oxygen-water vapour reaction between 40 and 100℃[J].J.Nucl.Mater,1986; 139:121-136
[8]Lin S, Lai X, Lv X, et al. Study of the initial oxidation characteristics of uranium with pure oxygen below 100℃ by spectroscopic ellipsometry. Surf. Interface. Anal,2008;40:645～648
[9]Meek T T, B.von Roedern. Semiconductor devices fabricated from actinide oxides. Vacuum,2009; 83: 226-228
[10]Meek T T, B.von Roedern, Chem P G, et.al. Some optical properties of intrinsic and doped UO2 thin films.Jr.,Mater. Lett,2005;59:1085～1088
[11]Pirie J D, Smith T. Lattice distortion in uranium dioxide near 30(?).Phys. stat. sol.1970;41:221-224
[12]Nerikar P, Watanabe T, James S, et al. Energetics of intrinsic point defects in uranium dioxide from electronic-structure calculations. J. Nucl.Mater,2009; 384:61-69
[13]Gupta F, Brillant G, Pasturel A. Correlation effects and energetics of point defects in uranium dioxide: a first principle investigation. Philos. Mag,2007;87:2561
[14]Konstantin N K, Gustavo E.S, Richard L M.Hybrid density-functional theory and the insulating gap of UO2.Phys.Rev. L,2002;89:266402
[15]Crocombette J P, Jollet F, Nga T,et al. Plane-wave pseudopotential study of point defects in uranium dioxide [J].Phys.Rev. B,2001;64:104～107
[16]Skomurski F N, Shuller L C, Ewing R C, Becker U. Corrosion of UO2 and ThO2 A quantum-mechanical investigation [J].J.Nucl.Mater,2008;375:290～310
[17]Petit T, Lemaignan C, Jollet F,et al.Point defects in uranium dioxide. Phil.Mag. B,1998;77:779
[18]Kohn. V G. On the theory of reflectivity by an x-ray multilayer mirror. Phys.Stat.Sol. 1995,185(6):61-70.
[19]Kohn V G. On the theory of reflectivity by an x-ray multilayer mirror [J].Phys.Sta.Sol.1995;185: 61-70
[20]李芳,张诚,林永昌.膜系优化设计中的模糊输入及评价函数的改进.北京理工大学学报,2000(20)
[21]Forouhi A R. Optical dispersion relations for amorphous semiconductors and amorphous dielectrics [J]. Phys. Rev. B,1986; 34(10):7018-7026
[22]Lin C C, Chen S Y, Cheng S Y, et al.Properties of nitrogen-implanted p-type ZnO films grown on SisN4/Si by radio-frequency magnetron sputtering [J].Appl Phys Lett,2004; 84:5040-5042
[23]铀与氧气反应的初始氧化动力学的椭偏技术研究[D].硕士论文.北京：中国工程物理研究院,2007
[24]Lhotka J, Kuzel R, Cappueeio G, et al.Thickness determination of thin polyerystalline film by grazing incidence X-ray diffraction [J].Surf. Coat. Tech,2001;148:95-100
[25]J.M. Myoung, W.H.Yoon, D.H.Lee, et al. Effects of Thickness Variation on Properties of ZnO Thin Films Grown by Pulsed Laser Deposition. Jpn. J.Appl.Phys.2002;41:28-31.
[26]Moore K T, Gerrit van der Laan. Nature of 5f states in actinide metals. Reviews of Modern Physics, 2009; 81:235
[27]何开华.典型半导体材料第一性原理研究[D].硕士论文.成都：四川师范大学,2005
[28]Hohenberg P, Kohn W. Inhomogeneous Electron Gas [J].Phys. Rev,1964,136:B864-B871
[29]Kohn W, Sham J.Self-Consistent Equations Including Exchange and Correlation Effects [J].Phys Rev. B,1965;140:A1133-A1138
[30]Caperley D M, Alder B J.Ground State of the Electron Gas by a Stochastic Method [J].Phys.Rev. Lett,1980;45:566-569
[31]Perdew J P, Zunger A. Self-interaction correction to density-functional approximations for many-electron systems [J].Phys.Rev.B,1981;23:5048
[32]Perdew J P,Wang Y.Accurate and simple analytic representation of the electron-gas correlation energy[J]. Phys. Rev. B,1992;45:13244-13249
[33]Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple [J].Phys.Rev. Lett,1996;77:3865-3868
[34]Bagno P, Jepsen O, Gunnarsson O.Ground-state properties of third-row elements with nonlocal density functions [J].Phys. Rev. B,1989;40:1997
[35]Dufek P, Blaha P, Sliwko V, Schwarz K. Generalize gradient approximation description of band splittings in transition-metal oxides and fluorides [J].Phys.Rev. B,1994; 49:10170
[36]谭世勇.铀和二氧化铀光学性质第一性原理计算[D].硕士论文.北京：中国工程物理研究院,2009
[37]Puddu G. C Comparison between different computational schemes for variational calculations in nuclear structure [J].Eur. Phys. J.A,2009;39:335-340
[38]Jeong T S,Han M S,Kim J H,et al.Crystallinity-damage recovery and optical property of As-implanted ZnO crystals by post-implantation annealing[J].J Cryst Growth,2005,275:541-547.
[39]沈学础.半导体光谱和光学性质[M].北京,科学出版社,1992:76
[40]Larson D T,Lottand LA, Cash D L. Surface film thickness determination by refleetivity Measurements[R].RFP-1911.
[41]Dufek P, Blaha P, Sliwko V, Schwarz K. Generalize gradient approximation description of band splittings in transition-metal oxides and fluorides [J].Phys.Rev. B,1994;49:10170
[42]Villars P, CalvertL.D, Person's Handbook of Crystallographic Data for Intermetallic Phases [M], Editor, ASM, Metals Park, Ohio(1985)
[43]Dudarev S L, Botton G A, Humphreys, et al.Electron-energy-loss spectra and the structural stability of nickel oxide:an LSDA+U study. Phys.Rev. B,1997;57:1505～1509
[44]邢海英、范广涵、章勇等.p,n型掺杂剂与Mn共掺杂GaN的电磁性质.物理学报,2009(58):3324～3330
[45]彭丽萍、徐凌、尹建武.N掺杂锐钛矿TiO2光学性能的第一性原理研究.物理学报2007(56)：1585～1589
[46]王渊旭、王春雷、钟维烈.光折变晶体Kta0.5Nb0.5O3光学特性的第一性原理研究.物理学报,2004(53)：3141～3145
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