The theoretical DFT study of electronic structure of thin SiSiO2 quantum nanodots and nanow

㊀第53卷第1期郑州大学学报(理学版)Vol.53No.1㊀2021年3月J.Zhengzhou Univ.(Nat.Sci.Ed.)Mar.2021收稿日期:2020-05-20基金项目:河南省重点研发与推广专项科技攻关项目(182102210516);河南省高等学校青年骨干教师培养计划项目(2017GGJS116)㊂作者简介:陈永生(1976 ),男,副教授,主要从事钙钛矿材料和太阳电池研究,E-mail:chysh2003@㊂CsSnI 3稳定性的第一性原理研究陈永生1,㊀李文标1,㊀刘㊀萍2,㊀杨仕娥1(1.郑州大学物理学院㊀河南郑州450001;2.中原工学院电子信息学院㊀河南郑州450007)摘要:采用基于密度泛函的第一性原理方法,比较了CsSnI 3四种不同结构(α㊁β㊁γ和Y 相)的本征稳定性,并进一步研究了H 2O 分子的插入对两个室温相(γ和Y 相)的影响㊂计算结果表明,在0K 下γ和Y 相具有相对较低的总能量;将一个H 2O 分子插入到γ和Y 相超胞中的插入能分别为-0.52和1.10eV,表明γ相钙钛矿是亲水相,而非钙钛矿结构的Y 相是疏水相㊂差分电荷密度分析结果表明,由于H 2O 分子中的O 原子与Cs +之间的强耦合以及H 原子与I -之间的氢键作用使得γ相结构发生明显变形㊂关键词:钙钛矿;稳定性;第一性原理中图分类号:O469㊀㊀㊀㊀㊀文献标志码:A㊀㊀㊀㊀㊀文章编号:1671-6841(2021)01-0102-05DOI :10.13705/j.issn.1671-6841.20201470㊀引言近年来,有机-无机杂化的钙钛矿材料如CH 3NH 3PbI 3等,成为低成本㊁高效率太阳电池制备中的明星材料[1],目前该类太阳电池的光电转换效率达到25.2%[2]㊂然而,由于材料组分中的Pb 具有毒性[3],且有机物质具有高吸湿性和高挥发性[4],一些研究者开始将目光转向无Pb 的无机钙钛矿材料[5]㊂其中用离子半径较大的Cs +替代有机离子,同时用Sn 替代同一主族的Pb 以得到CsSnI 3钙钛矿材料,成为该领域材料设计和制备中的理想选择㊂实验上,以CsSnI 3钙钛矿为光吸收层的薄膜太阳电池已获得了超过10%的光电转换效率[6]㊂研究发现,CsSnI 3材料有四种不同的晶体结构[7],其中三种呈黑色,分别为立方相(α相)㊁四方相(β相)和正交相(γ相)钙钛矿结构,三者之间的相变温度依次为426K 和351K㊂黑色的钙钛矿相具有良好的光电性能,如高的光吸收系数[8]和高的载流子迁移率[9],可用作太阳电池的光吸收层㊂另一种结构的CsSnI 3材料呈黄色,故称为黄相(Y 相)㊂在室温下,当黑色的CsSnI 3薄膜暴露在潮湿的空气中,会很快变为黄色[10],表明CsSnI 3薄膜发生了相变,相变后薄膜的光吸收性能显著下降,这将导致太阳电池器件的性能下降,寿命减少㊂在理论研究方面,Yu 等[11]研究了CsSnI 3三种黑色相的相变温度,预言α相在任何温度都是不稳定的,仅作为一种中间相存在;Silva 等[12]利用准简谐近似研究了四种不同相CsSnI 3的晶格动力学,发现四方和立方结构的钙钛矿相中均出现了软声子膜;Huang 等[13]也报道了CsSnI 3中软声子膜与相变的关系㊂上述工作主要是基于晶体动力学研究了不同温度下各种CsSnI 3结构的稳定性,而有关环境气氛如H 2O 分子或O 2分子对CsSnI 3相变影响的研究则很少[14]㊂因此,本文采用基于密度泛函的第一性原理方法,分别对0K 下α㊁β㊁γ和Y-CsSnI 3结构进行了优化,并计算了包含20个原子的超胞的总能量,以比较不同相的本征稳定性㊂为了进一步研究H 2O 分子对CsSnI 3结构稳定性的影响,分别计算了H 2O 分子在γ和Y 相中的插入能,以及H 2O 分子插入前后晶体结构的变化,并通过计算差分电荷密度分析了H 2O 分子与γ相之间的相互作用,从而可以部分地解释CsSnI 3钙钛矿相在潮湿环境下的不稳定性㊂1㊀模型与参数计算中采用的四种不同相CsSnI 3的晶体结构如图1所示,其中α㊁β和γ相中SnI 6八面体通过共顶点连㊀第1期陈永生,等:CsSnI 3稳定性的第一性原理研究(a)α相;(b)β相;(c)γ相;(d)Y 相㊂图1㊀CsSnI 3的四种晶体结构示意图Figure 1㊀Four crystal structure diagrams of CsSnI 3接形成三维钙钛矿结构,而Y 相中SnI 6八面体通过共边连接形成一维双链非钙钛矿结构㊂图1中四种不同相CsSnI 3的结构参数来自于文献[7,10]的X 射线衍射(XRD)数据㊂文中所有计算均是在基于密度泛函理论(DFT)的维也纳从头计算模拟软件包(Vienna ab-inito simulation package,VASP)[15]中进行的㊂电子间的交换关联能采用广义梯度近似(general gradient approximate,GGA )的PBE (Perdew-Burke-Ernzerhof)泛函[16-17],离子实与价电子间的相互作用采用投影缀加平面波(projector augmented wave,PAW)赝势[18]㊂价电子组态包括Cs 6s 1㊁Sn 5s 25p 2和I 5s 25p 5㊂布里渊区中k 点采用Monkhorst-Pack 网格[19],其中α相为8ˑ8ˑ8,β相为8ˑ8ˑ9,γ相为6ˑ5ˑ6,Y 相为4ˑ6ˑ3,平面波截断能为520eV㊂结构优化时系统能量收敛标准为1ˑ10-5eV,原子间相互作用力最大为0.1eV /nm㊂另外,在结构优化时还考虑了系统间范德华力的相互作用[20],采用以上参数获得了较好的收敛结果㊂2㊀结果与讨论2.1㊀CsSnI 3不同相的稳定性为了比较CsSnI 3不同相的本征稳定性,采用图1中的晶体结构分别构建计算单元,然后对体系进行结构优化,获得0K 下不同相的总能量㊂为了便于比较,需要对α和β相进行扩胞,使得每个计算单元均包含20个原子(即4个CsSnI 3分子)㊂理论上讲,一般体系总能量越低,相应的结构就越稳定㊂CsSnI 3不同相的总能量计算结果为:对称性最高的立方相(α相),在0K 下总能量(-56.18eV)也最高,表明其稳定性最差;其次是四方相(β相),总能量为-56.29eV;γ和Y 相的总能量几乎相同,分别为-56.36eV 和-56.35eV,且明显低于α和β相㊂上述结果与Silva 等[12]关于CsSnI 3不同相形成焓的计算结果是一致的㊂此外,XRD 实验[7]也发现,γ和Y-CsSnI 3可以在室温下共存,而α和β-CsSnI 3只能在更高的温度下存在,四个相的总能量数据能够很好地解释这一实验结果㊂CsSnI 3钙钛矿中高对称的α和β相的不稳定性可能是由于组分离子的尺寸不匹配造成的,ABX 3型三维钙钛矿的结构稳定性可以用容忍因子(τ)[21]来表征,τ=r A +r X 2(r B +r X ),(1)式中:r A ㊁r B 和r X 分别为钙钛矿组分中A㊁B 和X 的离子半径㊂大量研究和经验表明[22-23],结构稳定的ABX 3型钙钛矿的τ值一般为0.78~1.05㊂当τ值接近1.0时,易形成具有等轴晶系的Pm3m 结构;当τ值偏离1.0较多时,通常会形成其他低对称结构㊂CsSnI 3钙钛矿的τ值约为0.9,这表明尽管无机Cs +是尺寸较大的金属离子,但相对于Sn I 八面体间隙而言还是偏小㊂为了稳定Cs +,Sn I 八面体通常会发生旋转或倾斜,甚至Sn +也会偏离立方位置,导致立方钙钛矿结构的变形,进而形成低对称的钙钛矿或非钙钛矿结构㊂2.2㊀H 2O 分子对CsSnI 3稳定性的影响环境湿度是影响大多数钙钛矿材料及其太阳电池稳定性的重要因素之一[10,24]㊂在室温大气环境中,黑色的CsSnI 3薄膜会很快变成黄色,即发生了γ相到Y 相的转变[10]㊂为了进一步探讨H 2O 分子与γ和Y 相CsSnI 3之间的作用,将H 2O 分子分别插入到γ和Y-CsSnI 3晶体结构中,经过结构优化后,计算H 2O 分子插入前后体系的能量,进而计算H 2O 分子的插入能E int ,E int =E tot -E bulk -E water ,(2)式中:E int 是插入能;E water 是一个H 2O 分子的能量;E bulk 是H 2O 分子插入前体系的能量;E tot 是H 2O 分子插301郑州大学学报(理学版)第53卷入后体系的总能量㊂考虑到CsSnI 3材料中H 2O 分子的浓度不宜过大,插入能计算中γ相采用1ˑ1ˑ2超胞,Y 相采用1ˑ2ˑ1超胞㊂上述CsSnI 3超胞中均包含40个原子(即8个CsSnI 3分子),当将一个H 2O 分子插入到上述超胞时,体系中H 2O 与CsSnI 3的分子数之比为0.125㊂H 2O 分子插入前后体系的能量及插入能数据见表1㊂值得注意的是,H 2O 分子在γ相超胞中的插入能为-0.52eV,表明H 2O 分子进入γ相是一个放热过程,而在Y 相中的插入能为1.10eV,则为一个吸热过程㊂插入能的计算结果表明,γ-CsSnI 3是亲水相,而Y-CsSnI 3则是疏水相,这可能正是黑色的γ相CsSnI 3钙钛矿容易受环境湿度影响的重要原因㊂表1㊀H 2O 分子在γ和Y 相CsSnI 3中的插入能Table 1㊀Insertion energies of a water molecule in γand Y-CsSnI 3单位:eV 物相E tot E bulk E water E int γ-127.49-112.72-14.25-0.52Y -125.85-112.70-14.25 1.10㊀㊀图2给出了H 2O 分子插入前后γ和Y-CsSnI 3超胞的优化结构㊂对比图2(b)和(d)可以看出,插入到γ和Y 相中的H 2O 分子的位置和取向均不相同㊂在γ相中,H 2O 分子位于Cs +附近的八面体间隙中,且O 原子靠近Cs +,两个O H 键分别指向附近的两个I -;在Y 相中,H 2O 分子位于双链间隙中,O 原子靠近其中一个I -㊂对比图2(a)和(b)可以看出,H 2O 分子进入γ相后,H 2O 分子周围γ-CsSnI 3超胞的结构明显变形㊂水平方向上两个Sn I Sn 键角分别由158.6ʎ减小至156.6ʎ和151.7ʎ,竖直方向上两个Sn I Sn 键角分别由173.5ʎ减小至162.6ʎ和160.1ʎ㊂同时,这些Sn I 键都不同程度地被拉长,使得H 2O 分子所在的八面体间隙增大㊂而H 2O 分子进入Y 相前后,Y-CsSnI 3超胞中键角和键长的变化则相对较小,如图2(c)和(d)所示㊂(a)插入前γ相;(b)插入后γ相;(c)插入前Y 相;(d)插入后Y 相㊂图2㊀H 2O 分子插入前后CsSnI 3的优化结构Figure 2㊀The optimal structure of CsSnI 3before and after a water molecule insertion 为了分析H 2O 分子与γ-CsSnI 3之间的相互作用,计算了H 2O 分子插入前后γ-CsSnI 3超胞中的差分电荷密度,结果如图3所示㊂从图3可以看出,H 2O 分子附近的Cs +周围的电荷分布发生了明显变化,其中靠近O 原子的一侧失去电子,远离O 原子的一侧得到电子,从而发生极化㊂这是由于H 2O 分子中的O 原子从该Cs +中获得了部分电子,O 与Cs 之间较高的差分电荷密度证实了二者之间存在强的耦合作用㊂另外,在H 2O 分子中的两个H 原子与附近的两个I -之间的区域,电荷分布也有显著变化,表明极性的H 2O 分子与其附近八面体结构中的I -之间存在氢键作用㊂以上计算结果表明,当环境气氛中的H 2O 分子进入到γ-CsSnI 3钙钛矿晶格中后,由于H 2O 分子中的O 原子与Cs +之间的强耦合作用以及H 原子与I -之间的氢键作用,导致γ-CsSnI 3的晶格结构发生明显畸变,使得Cs +周围的八面体间隙增大㊂这种畸变的产生可能会使更多的H 2O 分子进入晶格中,并进一步加剧晶格401㊀第1期陈永生,等:CsSnI 3稳定性的第一性原理研究图3㊀H 2O 分子插入前后γ-CsSnI 3超胞中的差分电荷密度Figure 3㊀Differential charge density of γ-CsSnI 3supercell before and after a water molecule insertion 畸变,甚至导致部分Sn I 键的断裂,从而使CsSnI 3由三维的钙钛矿结构降解为低维的非钙钛矿结构㊂3㊀结论采用基于密度泛函的第一性原理方法,研究了不同结构CsSnI 3的本征稳定性以及H 2O 分子对其稳定性的影响㊂计算结果表明,在0K 下γ和Y 相CsSnI 3具有较低的总能量;将一个H 2O 分子插入到γ和Y 相超胞中的插入能分别为-0.52和1.10eV,说明γ相CsSnI 3钙钛矿具有亲水性;当H 2O 分子插入到γ-CsSnI 3钙钛矿晶格后,O 原子与Cs +之间的强耦合作用以及H 原子与I -之间的氢键作用,使得γ-CsSnI 3的晶格结构发生了明显的畸变,这可能是γ-CsSnI 3钙钛矿在潮湿环境中发生相变的重要原因㊂参考文献:[1]㊀ONO L K,QI Y B.Research progress on organic-inorganic halide perovskite materials and solar cells[J].Journal of physics D:applied physics,2018,51(9):093001.[2]㊀GREEN M A,DUNLOP E D,HOHL-EBINGER J,et al.Solar cell efficiency tables:version 55[J].Progress in photovoltaics:research and applications,2020,28(1):3-15.[3]㊀BABAYIGIT 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perovskite oxides andhalides[J].Science advances,2019,5(2):1-9.[22]RANDALL C A,BHALLA A S,SHROUT T R,et al.Classification and consequences of complex lead perovskite ferroelectricswith regard to B-site cation order[J].Journal of materials research,1990,5(4):829-834.[23]SASAKI S,PREWITT C T,BASS J D,et al.Orthorhombic perovskite CaTiO3and CdTiO3:structure and space group[J].Acta crystallographica section C,1987,43(9):1668-1674.[24]HUANG J B,TAN S Q,LUND P D,et al.Impact of H2O on organic-inorganic hybrid perovskite solar cells[J].Energy andenvironmental science,2017,10(11):2284-2311.First-principles Study of Stability in CsSnI3CHEN Yongsheng1,LI Wenbiao1,LIU Ping2,YANG Shiᶄe1(1.School of Physics,Zhengzhou University,Zhengzhou450001,China;2.School of Electronic andInformation Engineering,Zhongyuan University of Technology,Zhengzhou450007,China) Abstract:The first-principle calculation based on density functional method was used to compare the in-trinsic stability of four different structures of CsSnI3(α,β,γand Y phase),and the effect of water mole-cule insertion on two room-temperature phases(γand Y phase)was further investigated.It was founded that the total energies of theγand the Y phase were relatively low at0K.The insertion energies of a wa-ter molecule in theγand Y phase supercells were-0.52and1.10eV respectively,indicating that theγphase perovskite was hydrophilic,while the Y phase of the non-perovskite structure was hydrophobic. Differential charge density analysis showed that obvious deformation of theγphase structure was caused by the strong coupling between O atom and Cs+and the hydrogen bond between H atom and I-.Key words:perovskite;stability;first-principle(责任编辑:孔㊀薇㊀王浩毅)。

苏忠民教授简历学院：化学学院姓名：苏忠民性别：男出生年月：1960年4月一、主要学习工作经历1978年9月—1983年7月，东北师大化学系本科学生1986年9月—1989年6月，东北师大化学系硕士研究生1994年9月—1997年6月，东北师大化学系博士研究生1998年4月—2000年4月，吉林大学理论化学研究所博士后1985年5月—1988年10月，东北师大化学系助教1988年10月—1992年12月，东北师大化学系讲师1992年12月—1994年9月，东北师大化学系物理化学专业副教授1994年9月—现在，东北师大化学系物理化学专业教授1998年10月—现在，东北师大化学系博士生指导教师2000年6月—现在，东北师大化学学院教授委员会教授1998年4月—现在，东北师大化学学院，功能材料化学研究所所长1999年1月—1999年10月，东北师大校长助理1999年10月—2003年12月，东北师大校长助理兼科技处处长2003年11月—现在，东北师大研究生院院长（副校级）2004年2月—现在，东北师范大学学位评定委员会副主席2006年3月—现在，东北师范大学自然科学学术委员会委员2007年3月—现在，东北师范大学自然科学学术委员会副主任2007年1月—现在，东北师范大学化学学院教育部长江学者特聘教授(无机化学专业)2008年1月—2010年12月，东北师范大学化学学院2007度教育部“长江学者和创新团队发展计划”创新团队负责人1995年11月—1997年11月，香港大学化学系访问学者2006年6月—现在，吉林省第六届化学会副理事长2006年11月—现在，中国化学会第二十七届理事会理事2006年11月—现在，第三届吉林省学位委员会委员2005年7月—现在，吉林省高校科研与学位管理学会，吉林省研究生教育与学位管理专业委员会理事长2005年7月—现在，香港大学内地校友联谊社第五届理事会理事2005年12月—2006年10月，长春市南关区第十五届人民代表大会代表2006年10月—现在，长春市南关区第十六届人民代表大会代表2008年1月—2012年12月，《科学通报》编辑委员会委员2009年1月—2014年12月，国务院学位委员会第六届学科评议组化学组成员2009年1月—2011年12月，长春市科学技术协会常委二、主要研究方向或领域(一) 功能材料化学的理论和实验研究1．有机分子/聚合物的导电性质研究(1) 合成表征聚并苯半导体导电材料并进行改性研究，其可作为电极材料用于制作二次电池和双电层电容器，性能指标达到国际先进水平，并曾小批量投放市场。

Fourteen Easy Lessons in Density Functional TheoryJOHN P.PERDEW,ADRIENN RUZSINSZKYDepartment of Physics and Quantum Theory Group,Tulane University,New Orleans,LA70118Received1April2010;accepted5May2010Published online in Wiley InterScience().DOI10.1002/qua.22829ABSTRACT:Density functional theory(DFT)is now the most commonly usedmethod of electronic structure calculation in both condensed matter physics andquantum chemistry,thanks in part to the focus it has received over the first50years ofthe Sanibel Symposium.We present a short history,and review fourteen short and easybut important lessons about nonrelativistic DFT,with some partiality but with aminimum of technical complication.V C2010Wiley Periodicals,Inc.Int J Quantum Chem000:000–000,2010Key words:density functional theory;exchange–correlation energy;electronicstructure theory;Kohn–Sham theoryIntroduction and Short History of Density Functional TheoryT his article summarizes a talk given at the 50th anniversary Sanibel Symposium on Quantum Chemistry.Its original title,‘‘Some Things We have Learned About Exchange and Correlation in the Last Fifty Years,’’was some-what too restrictive in both subject matter and time frame.It presents14easy lessons in nonrela-tivistic density functional theory(DFT)at a quali-tative level.The selection of lessons is partial in both senses of the word:it is incomplete,and it reflects our own biases about what is most impor-tant and interesting(or at least most familiar). The same can be said of the short history we present.Our subject is appropriate to the occa-sion,since the Sanibel Symposium has played a major role in the development of modern elec-tronic structure theory,including but not limited to DFT.Possible companion pieces to this article are our short discussion[1]of‘‘perplexing’’issues in DFT and a detailed review[2]of the exact theory and its approximations.Often we need to predict the ground-state properties of an atom,molecule,solid,nanostruc-ture,or other system.We might need the equilib-rium geometry or structure,vibrational frequen-cies,electron density,total energy,and various total energy differences such as atomization and surface energies,as well as the linear and nonlin-ear responses to external static probes.One way to find the needed properties is to solve theCorrespondence to:J.P.Perdew;e-mail:*****************Contract grant sponsor:National Science Foundation.Contract grant number:DMR-0854769.International Journal of Quantum Chemistry,Vol.000,000–000(2010) V C2010Wiley Periodicals,Inc.N -electron Schroedinger equation for the N -elec-tron ground-state wavefunction.This approach is potentially accurate and complete (providing all the information that can be known),but it is com-putationally inefficient and impractical for large N .A second way is to solve for more limited in-formation,as provided by a Green’s function,density matrix,or electron density.This approach may be less accurate and complete,but it can achieve a useful computational efficiency even for large N .Kohn–Sham DFT [2,3]uses spin orbitals to predict the ground-state electron density,total energy,and related important properties.It pro-vides an often useful and improvable compromise between accuracy and computational efficiency.Thus,it is now the most widely used method of electronic structure calculation in both condensed matter physics and quantum chemistry,two sub-jects that have long been intertwined at the Sani-bel Symposia.However,other methods [4],including full wavefunction methods,continue to improve in accuracy and efficiency,providing for selected systems a benchmark of accuracy.Orbital-free DFT began in the 1920s with the Thomas–Fermi theory [5,6],which expresses the total energy E approximately in terms of the elec-tron density n ð~r Þ,where n ð~r Þd 3r is the average number of electrons in volume element d 3r at position ~r ,using the simplest density functional that makes sense.The density is then varied atfixed electron number N ¼R d 3rn ð~r Þto minimize the energy functional.This approach gives simple and useful estimates for the density and total energy of an atom (defined as minus the mini-mum work to strip all the electrons from the nu-cleus)but it is far too crude for chemistry.In fact,Teller [7]proved that in Thomas–Fermi theory,atoms do not bind together to form molecules and solids.Without the exchange–correlation energy,‘‘nature’s glue’’[8],chemical bonds are ei-ther absent or far too long and weak.However,orbital-free methods continue to improve;see recent work by Trickey and others [9–11].Spin orbitals or fictitious one-electron wave-functions w i ð~r ;r Þwere introduced in the 1930s by Hartree,Fock,and Slater [12].The energy (includ-ing sometimes exchange but not Coulomb correla-tion)was expressed in terms of these orbitals and their occupation numbers f i (1or 0,since electrons are fermions),and minimized with respect to them.This approach binds atoms into molecules and solids,although usually too weakly [8],andgenerally improves the total energy E and elec-tron density n ð~r Þ¼P i r f i r w i r ð~r Þj j 2over orbital-free methods.The Hartree and Hartree-Fock methods were not easy to implement on early computers and omitted important correlation effects.In the 1950s,Slater combined the orbital and density functional approaches by creating a local density approxima-tion (LDA)for the exchange–correlation energy and potential (which he called the X a approxima-tion [12]).He found that it could be easily imple-mented self-consistently on the computer and that it included a rough but useful estimate of correla-tion.After retiring from MIT in 1966,Slater joined the Quantum Theory Project at the University of Florida,Gainesville,which held the first Sanibel Symposium in 1961.In 1964–1965,the Hohenberg–Kohn [13]and Kohn–Sham [3]theorems,the twin pillars of mod-ern DFT,were published.These theorems showed that,given the right density functionals,one can find the exact ground-state density and energy of an N -electron system in an external scalar poten-tial using either the total density or the orbitals as variational objects.Kohn and Sham also proposed an LDA for the exchange–correlation energy,which,unlike Slater’s,is exact for an electron gas of uniform or slowly varying density.Kohn–Sham theory was not widely known until around 1970,when condensed matter physi-cists started to find that this theory in the LDA gives a remarkably realistic description of bulk solids and their surfaces.Since then,DFT has dominated electronic structure calculations for solids.For the surface energy [14,15]of a solid,density functionals proved to be more accurate than early correlated wavefunction calculations.The densities of many solids,especially simple metals,are sufficiently like those of uniform elec-tron gases for the LDA to work well.However,it did not work so well for atoms and molecules.In particular,the atomization energies of molecules were strongly overestimated (although they were still better than those of Hartree-Fock theory).In the period 1970–1986,DFT in chemistry had only a few prophets,including notably Parr [16],Jones and Gunnarsson [17],and Levy [18].This was however a time when theoretical work by Langreth and Per-dew [19,20],and by Gunnarsson and Lundqvist [21],explained why the local approximation worked as well as it did and suggested approaches to improve it.The new approaches included generalized gradient approximations and hybridPERDEW AND RUZSINSZKY2INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/qua VOL.000,NO.000functionals,which greatly increased the accuracy of atomization energies and thus the relevance of the theory to chemistry.Since about1992,DFT has swept chemistry,as it earlier swept condensed matter physics.This development was led notably by Becke[22],who proposed many creative approaches to functional construction,and by John Pople and Nick Handy.Since the1920s,many important lessons have been learned about DFT.We summarize14of these lessons below.Lesson1:Density vs.Correlated WavefunctionThe electron density nð~rÞhas a lower dimen-sionality than the N-electron wavefunction Wð~r1;r1;…;~r N;r NÞ.Using n instead of W as thebasic variational object makes electronic structure calculations much faster but typically much less accurate.This lesson comes from Thomas[5]and Fermi [6].In his lecture for the1998Nobel Prize in Chemistry[23],Walter Kohn explained this fact in a clear if oversimplified way,which we para-phrase here:suppose we use a mesh of points in real space,with10points along each of the x,y, and z axes.Then we can compute and store the density on the mesh as103numbers.A one-elec-tron wavefunction can also be represented by 103numbers,but a10-electron correlated wave-function must be represented by(103)10¼1030 numbers.There are of course cleverer ways[4] to compute a10-electron wavefunction,but the fact remains that the effort to compute an N-electron wavefunction scales up very rapidly with N.Lesson2:Orbitals vs.Correlated WavefunctionWhile too much accuracy can be lost by using the density nð~rÞas the basic variational object, considerable accuracy can be restored by using also the occupied orbitals or fictitious one-electron wavefunctions w1ð~r;rÞ…w Nð~r;rÞ.This lesson comes from Hartree and Fock in the1920s and from Slater in the1950s[12].In our example from Lesson1,an orbital description of the10-electron system requires computing and storing only10Â103¼104numbers.Lesson3:Something Proved to Exist That Cannot be FoundIn principle,we can find the exact ground-state energy and density of N electrons in an external potential vð~rÞa.by solving an Euler equation for the densitynð~rÞas proved by Hohenberg and Kohn[13],orb.by solving self-consistent one-electronSchroedinger equations for the orbitals asproved by Kohn and Sham[3].In approach(b),the functional derivative d E xc=d nð~rÞserves as the exchange–correlation contribu-tion v xcð~rÞto the effective one-electron orKohn–Sham potential v KSð~rÞ.In practice,the exact density functional E v[n] for the total energy needed for approach(a),and the exact density functional E xc[n]for the exchange–correlation energy needed for approach (b),are not accessible in any practical way and must be approximated.Although the Hohenberg–Kohn–Sham theo-rems are only existence theorems,the knowledge that exact density functionals exist has strongly driven the quest for better and more accurate approximations.Lesson4:From Uniform ElectronGas to Atoms,Molecules,and SolidsThe local density approximation(LDA)E LDAxc½n ¼Zd3rnð~rÞe unifxcðnð~rÞÞ;(1)or better the local spin density approximation (LSDA)E LSDAxc½n";n# ¼Zd3rnð~rÞe unifxcðn"ð rÞ;n#ð~rÞÞ;(2)which start from e unifxc,the exchange–correlation energy per particle of a uniform electron gas,areFOURTEEN EASY LESSONS IN DENSITY FUNCTIONAL THEORY VOL.000,NO.000DOI10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY3accurate enough for useful calculations on solids and solid surfaces but not accurate enough for atoms and molecules.LDA comes from Kohn and Sham[3]and LSDA from von Barth and Hedin[24].The accu-racy of these local approximations for solids and surfaces was established by Lang and Kohn[25] and by Moruzzi et al.[26].Jones and Gunnarsson [17]found good structures but overestimated atomization energies for molecules.For open-shell or magnetic systems,in the ab-sence of an external magnetic field,one can use either the total density or the separate spin den-sities in principle,but in practice LSDA is more accurate than LDA because it inputs more infor-mation about the system[27].This was the first indication of a possible ladder of density func-tional approximations for the exchange–correla-tion energy to be discussed in Lessons9and10 below.All rungs of the ladder are actually imple-mented on the spin densities,but we will use the total density below to simplify the notation. Lesson5:The Electron Digs a HoleThe exact exchange–correlation energy is[19–21]the electrostatic interaction between the elec-tron density nð~rÞand the density n xcð~r;r0Þat r0of the exchange–correlation hole around an electronat~r:E xc¼ð1=2ÞZd3rnð~rÞZd3r0n xcð~r;~r0Þ=~r0À~rj j:(3)The exchange–correlation hole n xc¼n xþn c is the sum of the separate exchange and correlation holes.The exchange hole is the same as in Har-tree–Fock theory,with the Hartree–Fock orbitals replaced by Kohn–Sham orbitals,and the correla-tion hole is an average of an expectation value over the coupling constant for the electron–elec-tron interaction at fixed electron density.The exact holes satisfy the constraintsn x<0;Zd3r0n xð~r;~r0Þ¼À1;Zd3r0n cð~r;~r0Þ¼0:(4)These constraints are also satisfied by the LDA hole(that of a uniform gas)and this fact explains why LDA works as well as it does.The con-straints can also be imposed to develop other approximations that can improve over LDA by satisfying additional exact constraints.This lesson comes from Langreth and Perdew [19,20]and from Gunnarsson and Lundqvist [21].Lesson6:Searching Over Wavefunctions for theDensity FunctionalThe original proof of the Hohenberg–Kohn the-orem[13]was by reductio ad absurdum and thus not a constructive proof.Alternatively,the vari-ous density functionals,including E xc[n],can be defined by searches over N-electron wavefunc-tions constrained to yield a given electron density [18].Thus,the functionals can be intuitively understood and their exact properties can be derived.This lesson comes from Levy[18].It is an im-portant one because the derived exact properties (e.g.,Refs.[28,29])can be used to constrain the needed approximations.Lesson7:After the Local Density Comes its GradientSecond-order gradient expansionsE GEAxc½n ¼E LDAxc½n þZd3rC xcðnÞr nj j2=n4=3(5)improve on LDA for very slowly varying den-sities but are typically less accurate than LDA for realistic densities[30,31],because[31]the sec-ond-order gradient expansion of the hole violates the exact hole constraints of Lesson5.However, generalized gradient approximations or GGAs [30–35]E GGAxc½n ¼Zd3rn e GGAxcðn;r nÞ(6)can be derived with or without nonempirical parameters,and are more accurate than LDA for the separate exchange and correlation energies of atoms and for the atomization energies of mole-cules and solids.Nonempirical constructions often impose exact constraints on(1)the hole[33],or(2)the energyPERDEW AND RUZSINSZKY4INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI10.1002/qua VOL.000,NO.000functional[35],or(3)the coupling constant de-pendence[36].This lesson comes from Ma and Brueckner[30], Langreth and Perdew[31],Langreth and Mehl [32],Perdew and Wang[33],Becke[34,22],Per-dew et al.[35],and Seidl et al.[36].It was the main development that made DFT of interest to chemists.Lesson8:What is a Fractionof an Electron?The exact density functional E v[n]for the energy can be defined for an open system with noninteger average electron number N[37]by extending the constrained search of Lesson6from wavefunctions to ensembles.The energy E varies linearly between adjacent integer electron num-bers,with derivative discontinuities at the inte-gers.This explains why neutral molecules dissoci-ate to integer-charged atoms,and why the fundamental band gap[38,39]in the exact Kohn–Sham band structure is unphysical.This lesson comes from Perdew et al.[37], Perdew and Levy[38],and Sham and Schlueter [39].Lesson9:The More Information Input,the More Accuratethe OutputWe can make more accurate functionals by adding ingredients to the exchange–correlation energy density beyond n and!n:a.Meta-GGAs add the orbital kinetic energydensitysð~rÞ¼ð1=2ÞXi rf i r r w i rð~rÞj j2;(7)as proposed by Becke[40]with other non-empirical constructions by Perdew et al.[41–43].b.Hyper-GGAs or hybrid functionals addexact exchange information,such as the exact exchange energy or the exact exchange hole,as proposed by Becke[44]and refined by Savin[45],Vydrov and Scuseria[46],etc.Most hyper-GGAs do not properly scale to exact exchange under uniform density scal-ing to the high-density limit but some do[47].c.Random phase approximation(RPA)-likefunctionals add the unoccupied orbitals asdeveloped by Furche[48,49],Harl andKresse[50],etc.Lesson10:We are ClimbingJacob’s LadderThere is a five-rung Jacob’s ladder of common density functional approximations(LSDA,GGA, meta-GGA,hyper-GGA,and RPA-like functionals), as proposed by Perdew and Schmidt[51]and explained in Lesson9.All rungs except the hyper-GGA rung now have nonempirical constructions. Accuracy tends to increase up the puta-tional cost increases modestly from LSDA to GGA to meta-GGA(the three semilocal rungs)but can increase considerably on ascent to higher rungs.The Perdew-Burke-Ernzerhof(PBE)GGA[35] provides a moderately accurate description of atoms,molecules,and solids but is too simple to achieve high accuracy for all three kinds of sys-tems.The optimum GGA for solids has a weaker gradient dependence than the optimum GGA for atoms and molecules,as argued by Perdew and coworkers[52–54].However,a single nonempirical meta-GGA(revTPSS)can work well for the equi-librium properties of atoms,molecules,and solids, as shown by Perdew et al.[43].A meta-GGA can provide different GGA descriptions for solids(especially metals),which have important regions of strong orbital overlap where sð~rÞ)s Wð~rÞ r nj j2=ð8nÞ,and for atoms and mol-ecules,which have important regions where a sin-gle orbital shape dominates the density(as in an electron-pair bond),making sð~rÞ%s Wð~rÞ.Lesson11:Where Semilocal Functionals Fall DownSemilocal functionals(LSDA,GGA,and meta-GGA)necessarily fail(and thus full nonlocality is needed)when the exact exchange–correlation hole has a long-range tail,because semilocal function-als know nothing about the electron density far from an electron.This failure occurs when long-FOURTEEN EASY LESSONS IN DENSITY FUNCTIONAL THEORY VOL.000,NO.000DOI10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY5range van der Waals interactions between sepa-rating systems are important;the needed correc-tion is present in RPA-like functionals[48–50]but neither in semilocal functionals nor in hyper-GGAs.The failure also occurs when electrons are shared across stretched bonds between distant centers(as in certain transition states and dissoci-ation limits).Semilocal functionals cannot describe such stretched bonds,but hyper-GGAs and RPA-like functionals can do so by displaying more or less the right derivative discontinuities of Lesson8.Dramatic stretched-bond effects have been dis-cussed by Ruzsinszky et al.[55,56],Vydrov et al.[57],Tsuchimochi and Scuseria[58],and Yang and coworkers[59].Lesson12:Elaborate Functionals Need Corrections TooThe RPA,which uses the unoccupied orbitals in the simplest way that makes sense for all sys-tems,is not quite good enough for chemistry.It underestimates atomization energies of molecules by about the same amount that the PBE GGA overestimates them as discovered by Furche[48]. For this property,RPA is far less accurate than meta-and hyper-GGAs.RPA uses exact exchange but makes the correlation energy too negative by roughly0.02hartree/electron.Thus,a correction to RPA is needed.The needed correction to RPA is semilocal(de-scribable by LSDA or GGA)in atoms and at solid surfaces[60]but it is fully nonlocal in molecules [61].An accurate nonempirical nonlocal correction remains to be found.Lesson13:The Kohn–ShamPotential Shapes UpStarting from an orbital functional,the exact Kohn–Sham potential v KSð~rÞof Lesson3can be constructed by the optimized effective potential method of Talman and Shadwick[62,63].Starting from the correlated N-electron wave-function,we can directly construct the energy and electron density.However,it is also computation-ally practical to construct therefrom the exact Kohn–Sham potential and so to study its features. This can be done in two different ways:(1)The Zhao et al.[64]approach first constructs the den-sity and then numerically varies the Kohn–Shampotential to reproduce this density in a system of N noninteracting electrons.(2)Another approach due to Sahni[65]and others constructs the Kohn–Sham potential from expectation values computed from the correlated N-electron wavefunction.Lesson14:After Statics Comes DynamicsDFT can be extended(exactly in principle and approximately in practice)to time-dependent and excited states.The essential idea is to solve time-dependent one-electron Schroedinger equations in which the time-dependent exchange–correlation potential v xcð~r;tÞis a functional of the electron density nð~r0;t0Þ.Poles of the frequency-dependent linear density response function then yield the ex-citation energies.This lesson comes from Runge and Gross[66] and from others[67].ACKNOWLEDGMENTSThe authors thank Sam Trickey for the invita-tion to speak at the50th Sanibel Symposium,and Kieron Burke and Jianwei Sun for suggestions on the manuscript.References1.Perdew,J.P.;Ruzsinszky,A.;Constantin,L.A.;Sun,J.;Csonka,G.I.J Chem Theory Comput2009,5,902.2.Perdew,J.P.;Kurth,S.In A Primer in Density FunctionalTheory;Fiolhais,C.,Nogueira,F.,Marques,M.,Eds.;Lecture Notes in Physics;Springer:Berlin,2003;Vol.620,p1.3.Kohn,W.;Sham,L.J.Phys Rev1965,140,A1133.4.Shavitt,I.;Bartlett,R.J.Many Body Methods in Chemistryand Physics:MBPT and Coupled-Cluster Theory;Cambridge University Press:Cambridge,2009.5.Thomas,L.H.Proc Cambridge Philos Soc1926,23,542.6.Fermi,E.Zeit fuer Physik1928,48,73.7.Teller,E.Rev Mod Phys1962,34,627.8.Kurth,S.;Perdew,J.P.Int J Quantum Chem2000,77,819.9.Perdew,J.P.;Constantin,L.A.Phys Rev B2007,75,155109.10.Karasiev,V.V.;Jones,R.S.;Trickey,S.B.;Harris,F.E.Phys Rev B2009,80,245120.11.Huang,C.;Carter,E.A.Phys Rev B2010,81,045206.12.Slater,J. 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关于电路理论的英语作文In the vast and intricate world of electronics, circuit theory stands as the fundamental pillar, governing the behavior and interaction of electrical components. At its core, circuit theory is the study of electric currents and voltages within closed loops, known as circuits. These circuits can be as simple as a single battery connected to a light bulb or as complex as the intricate wiring within a modern smartphone.The foundation of circuit theory can be traced back to the early works of pioneering scientists such as Michael Faraday and James Clerk Maxwell. Their groundbreaking research on electromagnetism laid the groundwork for the understanding of how electrical charges and magnetic fields interact. From these principles, circuit theory evolved, providing a framework for analyzing and designingelectrical systems.One of the fundamental principles of circuit theory is Ohm's Law, which states that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. This lawforms the basis for understanding how components such as resistors, capacitors, and inductors affect the flow of electric current in a circuit.Another crucial concept in circuit theory is the concept of impedance, which extends the idea of resistance to alternating currents. Impedance takes into account both the resistive and reactive components of a circuit, allowing for a more comprehensive analysis of circuits involving capacitors, inductors, and other reactive elements.Circuit theory also deals with the concept of power, energy, and efficiency. It explains how electrical energyis transformed and dissipated within a circuit, providing insights into the design of energy-efficient electrical systems.Moreover, circuit theory is not limited to the analysis of linear circuits. It also delves into the complex world of nonlinear circuits, where components exhibit non-ohmic behavior. This area of study is crucial in understanding the behavior of modern electronic devices such as transistors and diodes.In the modern era, circuit theory finds applications in a wide range of fields, from consumer electronics to aerospace engineering. The design of complex systems suchas computers, smartphones, and communication networksrelies heavily on circuit theory. By understanding the principles of circuit theory, engineers are able to create innovative and reliable electronic systems that power our modern world.Circuit theory is not just a collection of formulas and equations; it is a fundamental understanding of howelectrical systems work. It is the language of electronics, allowing engineers to communicate, design, and innovate in this dynamic field. As we continue to push the boundariesof electronics, circuit theory will remain at the forefront, guiding us in the design and development of the next generation of electronic systems.**电路理论：现代电子学的基础**在电子学这个庞大而复杂的世界里，电路理论扮演着基础支柱的角色，它支配着电子元器件的行为和相互作用。

第53卷第4期2024年4月人㊀工㊀晶㊀体㊀学㊀报JOURNAL OF SYNTHETIC CRYSTALSVol.53㊀No.4April,2024单层SnS的光电效应及应变工程的第一性原理研究徐中辉1,2,许晟源1,刘川川1,刘国港3(1.江西理工大学信息工程学院,赣州㊀341000;2.上海市特种人工微结构材料与技术重点实验室,上海㊀200092;3.同济大学物理科学与工程学院,微结构材料教育部重点实验室,上海㊀200092)摘要:光电探测器在工业制造和军事国防等各领域用途广泛㊂近年来,研究者在寻找一种兼具极化灵敏度高与光响应强的特点的光电探测器㊂在可见光范围内,SnS是一种制作具有各向异性光电探测器的半导体材料㊂本文基于第一性原理,采用非平衡态格林函数(NEGF)与密度泛函理论(DFT)结合的方法对单层SnS两个器件方向(Armchair和Zigzag)的光电性质进行理论计算㊂研究发现,在零偏压下,两个方向的光电流数值均较小,通过加偏压的方法可以获得稳定的光电流㊂计算了小偏压0.1~1.0V(间隔0.1V)㊁线性偏振光照射下最大光响应随光子能量的变化,发现单层SnS在光子能量为2.4与3.2V时最大光响应数值较大且十分稳定,并结合能带图和态密度图分析了光响应产生的微观机制㊂本文通过计算消光比,发现单层SnS具有极强的偏振灵敏度㊂最后,通过施加双轴应变的方法,器件的不对称性显著增加,极大增强器件在零偏压下的光电流,其中压缩应力数值为-6%时对光电流的提升十分明显㊂希望以上结果能为单层SnS设计用于光电探测器提供理论参考㊂关键词:单层SnS;光电探测器;第一性原理;最大光响应;偏振灵敏度;应变工程中图分类号:O472;O469㊀㊀文献标志码:A㊀㊀文章编号:1000-985X(2024)04-0676-08 First-Principles Study on Photogalvanic Effect and StrainEngineering of Monolayer SnSXU Zhonghui1,2,XU Shengyuan1,LIU Chuanchuan1,LIU Guogang3(1.School of Information Engineering,Jiangxi University of Science and Technology,Ganzhou341000,China;2.Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology,Shanghai200092,China;3.MOE Key Laboratory of Microstructured Materials,School of Physics Science and Engineering,Tongji University,Shanghai200092,China)Abstract:Photodetectors are widely used in various fields,such as industrial manufacturing and military defense.Researchers have recently sought a photodetector that combines high polarization sensitivity and a robust optical response.As an anisotropic semiconductor material,SnS holds potential for photodetection across the visible light spectrum.This study employs first-principles density functional theory(DFT)along with the non-equilibrium Green's function(NEGF)method to theoretically investigate the optoelectronic properties of the SnS monolayer in two device orientations:Armchair and Zigzag.It is found that the maximum photocurrent values between the two orientations are small at zero bias voltage,and stable photocurrent can be obtained by adding bias voltage.We examine the maximum photocurrent variation under linearly polarized light irradiation within a small bias voltage range(0.1to1.0V),found for the maximum photoresponse of monolayer SnS to be large and stable at photon energy of2.4and3.2eV,and analyze the underlying mechanism of photoresponse,employing energy band and density of state diagrams.Additionally,we have calculated the extinction ratio of the SnS monolayer,confirming its strong polarization sensitivity.Finally,by subjecting the device to biaxial strain,we significantly speculate to enhance its asymmetry,leading to a substantial increase in photocurrent at zero bias.A compressive strain of-6%notably increases the photocurrent.These findings offer valuable theoretical insights for the design of SnS monolayers as photodetectors.Key words:monolayer SnS;photodetector;first-principle;maximum photoresponse;polarization sensitivity;strain engineering㊀㊀收稿日期:2023-12-04㊀㊀基金项目:国家自然科学基金(12364024,11864014);江西省自然科学基金(20224BAB201023);上海市特种人工微结构材料与技术重点实验室开放项目(ammt2021A-3);江西省研究生创新专项基金(203200800337)㊀㊀作者简介:徐中辉(1982 ),男,江西省人,博士,教授㊂E-mail:longxister@㊀第4期徐中辉等:单层SnS 的光电效应及应变工程的第一性原理研究677㊀0㊀引㊀㊀言自石墨烯[1]被发现以来,二维(2D)材料受到广泛关注㊂之后,如二硫化钼(MoS 2)[2]㊁P 类石墨烯磷烯[3]㊁六方氮化硼(h-BN)[4]和MXenes [5]等其他二维材料也陆续被发现㊂近年来,黑鳞[6]因类似于石墨烯的层状结构吸引了众多学者,但与石墨烯相比,黑鳞晶体不仅在实验上易于剥离成二维材料,其还具有一定带隙且能通过改变层数来调节带隙[7]㊂目前,VI 族金属硫属化合物(group-IV metal chalcogenides,GIVMCs)[8-9]成为研究热点,他们都是与黑鳞相似的层状结构,其中亚硫化锡(SnS)因成本低㊁储量丰富㊁环境友好㊁稳定度高和对人体无毒成为众多学者关注的对象[10-12],不仅具有带隙可调节的特性且禁带比黑鳞更宽㊂有学者预测单层SnS 相比其他二维材料压电系数高数十倍,具有巨压电效应[13],后经实验证实[14],其特性可应用于制作压电纳米发动机;当一般材料变薄到临界值以下时,铁电性将会消失,而SnS 材料变薄到单层时依然具有铁电相变[15];SnS 拥有卓越的电子和声子传输,是一种很有前途的新型热电材料[16];单层SnS 对NO 2分子具有较强敏感性,可作为对NO 2分子的气体传感器[17];二维SnS 纳米片电流开关比高达104,具有很强的各向异性[18];SnS 在制造太阳能电池和发光二极管等光电子器件领域也具有很大潜力[19-20],并具有高效的光电转换效率[21]㊂尽管二维本征SnS 已被应用于诸多方面,但仍可通过材料改进实现物尽其用㊂研究人员常通过各种方法来改进材料性质,如替位掺杂[22]㊁空位缺陷[23]等㊂其中应变工程[24]是调节材料电学和光学性质的有效方法,能实现高性能的二维材料器件,并且在理论和实验上均已被证实[25-26]㊂磁各向异性能量(magnetic anisotropy energy,MAE)定义了相对于晶格在特定方向上的磁化稳定性,并且是纳米级应用的重要参数,在施加压缩应变时,会发生反铁磁状态的相变[27];双轴应变能提高半导体的电子和空穴的电子迁移率,用于制作纳米级机械传感器[28];拉伸应变能降低材料的晶格导热率,诱导单层ZrSe 2电子能带简并来提高热电性能[29];在零偏压下,线性偏振光照射下的二维材料产生的光电流通常较小㊂最近的研究显示,应力能使光电流显著增强[30-31];在非中心对称材料中才容易表现出光伏效应,但应变使中心对称的SrTiO 3㊁TiO 2和Si 单晶中产生巨大的光伏电流[32];应变能改变晶体的晶格常数从而降低其对称性,提高光电转换效率[33-34]㊂上述的研究结果表明SnS 是一种有潜力且应用价值高的材料,关于单层SnS 的电子结构㊁磁学性质等方面已经有所研究,截至目前,光电性质以及应力对其影响的理论研究还鲜有报道㊂本文基于第一性原理对单层SnS 在可见光范围内的光电性质进行研究,并对单层SnS 的原胞及其器件施加应力,研究对其带隙和光电性质的影响㊂希望本文研究能对单层SnS 制备光电探测器提供参考㊂1㊀模型与计算方法本文选用空间群结构为Pnma (#62)的正交晶系SnS 作为器件搭建输运体系的原胞㊂图1为SnS 单层光电探测器模型图㊂利用软件Device Studio 进行建模,如图2所示,单层SnS 器件模型分为中心散射区㊁左电极和右电极三个部分,其中左右电极是沿各自的输运方向伸展至无穷㊂图2(a)㊁(b)表示在X ㊁Y ㊁Z 方向进行1ˑ7ˑ1扩胞,输运方向为Y ,图2(c)㊁(d)表示在X ㊁Y ㊁Z 方向进行1ˑ1ˑ7扩胞,输运方向为Z ,其中θ图1㊀线偏振光辐照下单层SnS 光电探测器的器件模型Fig.1㊀Device models of monolayer SnS photodetector irradiated by linearly polarized light代表线性偏振光与输运方向的夹角,曲线为照射在中心散射区的线性偏振光㊂曲线箭头表示线性偏振光的照射㊂本文基于第一性原理[35-36]采用密度泛函理论结合非平衡格林函数的方法,并利用量子输运软件Nanodcal [37-38]进行光电流计算工作㊂利用Vienna Ab-initio Simulation Package (VASP)[39-41]软件进行结构优化与电子结构计算㊂交换关联泛函采用GGA-PBE96[42],Zigzag 和Armchair 器件方向分别设置K 点678㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷数为1ˑ3ˑ15㊁1ˑ15ˑ3,原子基矢设置为DZP,原子能量收敛精度为10-4eV,为避免原子间相互影响,Z方向设置了20Å真空层㊂中心区在线性偏振光的照射下,产生的光电流可近似成[43-44]:J(ph)L=i e hʏ{cos2θT r{ΓL[G<(ph)1+f L(G>(ph)1-G<(ph)1)]}+sin2θT r{ΓL[G<(ph)2+f L(G>(ph)2-G<(ph)2)]}+sin(2θ)/2T r{ΓL[G<(ph)3+f L(G>(ph)3-G<(ph)3)]}}d E(1)G>/<(ph)1=ðα,β=x,y,z C0NG r0e1αp†αG>/<0e1βpβG a0G>/<(ph)2=ðα,β=x,y,z C0NG r0e2αp†αG>/<0e2βpβG a0G>/<(ph)3=ðα,β=x,y,z C0NG r0p†αG>/<0pβG a0(e1αe2β+e2αe1β)(2)式中:i为虚数单位,e为电子电荷,h为普朗克常数,T r为矩阵,ΓL为左电极线宽函数,G>/<(ph)1,2,3为光子与电子反应的大于/小于格林函数,f L为左电极费米-狄拉克分布函数,N为光子数,G r0/G a0为推迟格林函数/超前格林函数,e1α㊁e1β㊁e2α㊁e2β为单位矢量,p†α㊁pβ为电子动量在笛卡尔坐标系上的分量㊂C0=(e/m)2hμrεr2Nωεc Iω(3)式中:e=cosθe1+cosθe2,θ为偏振角,m为净电子质量,μr为相对磁化率,εr为相对介电常数,ω为光子频率,ε为介电常数,c为光速,I w为单位时间单位面积的光子流动数㊂将电流进行归一化,最后得到光响应R为:R =J (ph) LeIω(4)图2㊀Zigzag方向的俯视图(a)和侧视图(b),以及Armchair方向的俯视图(c)和侧视图(d)Fig.2㊀Top view(a)and side view(b)of the Zigzag direction,the top view(c)and side view(d)of the Armchair direction 2㊀结果与讨论2.1㊀光电性质图3(a)为稳定的SnS原胞,晶格常数为b=4.050Å且c=4.242Å㊂如图3(b)所示,单层SnS为间接带隙半导体,能带为1.47eV,与前人数据基本相符[45-47]㊂首先计算了单层SnS在Armchair与Zigzag方向在零偏压与不同光子能量下,光响应与偏振角的变化关系,如图4所示㊂以光子能量3.1㊁3.3㊁4.0eV为例,在Armchair方向,线性偏振光致使光电流随偏振角呈cos2θ形式变化,光子能量为3.1eV时产生的最大光响㊀第4期徐中辉等:单层SnS的光电效应及应变工程的第一性原理研究679㊀应约为0.3088a20/phonon;而在Zigzag方向,线性偏振光导致光响应呈sin2θ形式变化,光子能量为3.1eV 时产生的最大光响应约为0.0004a20/phonon,两个方向均产生了较小的光电流㊂为了获得稳定的光电流,本文对单层SnS构建了Armchair和Zigzag两个器件输运方向,施加0.1~1.0V(间隔0.1V)的偏压㊂图5所示为0.1V偏压下单层SnS光电探测器产生的光响应随偏振角θ的变化情况,设置光子能量范围为1.4~3.6V,能量间隔为0.2V,包含整个可见光光子能量范围㊂结果表明:线性偏振光致使的光响应呈cos2θ形式变化,在偏振角为90ʎ时取得最大光响应,与唯象理论相符[48-49]㊂图3㊀单层SnS电子结构图Fig.3㊀Electronic structure of monolayer SnS图4㊀零偏压下,不同光子能量对Armchair和Zigzag两个方向产生的光响应Fig.4㊀Photocurrent of Armchair and Zigzag with different photon energy under zero bias voltage图5㊀偏压0.1V下,不同光子能量对Armchair和Zigzag两个方向的光响应Fig.5㊀Photocurrent of Armchair and Zigzag directions with different photon energy under a bias voltage of0.1V 为进一步探究偏压下光子能量和最大光响应之间的变化关系,本文提取了不同偏置电压㊁不同光子能量下偏振角在90ʎ时取得的最大光响应的数值,如图6所示㊂将Armchair与Zigzag方向的图结合来看,最大光680㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷响应随光子能量先增大后减小,光子能量为2.4㊁3.2eV 时最大光响应出现小高峰,不同偏压下的数值分别在35㊁29a 20/phonon 左右,在偏压为0.1V 时,就几乎达到饱和光电流,随着偏压的增大对最大光响应影响不大㊂而光子能量在2.6㊁2.8与3.0eV 等处,均出现了较大光响应且随着偏压的增大而增大,器件可以通过施加偏压的大小来调节最大光响应㊂特别指出,在Armchair 方向,当偏压升至1.0eV,光子能量为2.6eV 时,最大光响应可以达到59.7a 20/phonon;在Zigzag 方向,当偏压升至0.4eV 且光子能量为2.6eV,最大光响应数值为38.4a 20/phonon 且达到饱和光电流㊂图6㊀不同偏压下,不同光子能量对Armchair 和Zigzag 两个方向的最大光响应Fig.6㊀Maximum photocurrent of Armchair and Zigzag directions with different photon energy under different bias voltages 为了分析光响应的内在起源,本文计算了单层SnS 的能带结构和态密度,如图3(b)和图7所示㊂在图6中我们得知,无论是在Armchair 还是Zigzag 方向,在光子能量为2.4㊁3.2eV 时均产生较大光电流且偏压变化对其影响不大㊂为进一步证实结论,首先分析图3(b),在第一布里渊区X 点,两个圆圈标示符之间表示价带底和导带顶之间带隙的差值,约为2.4eV,圆圈与三角形标示符(箭头标注)之间带隙差值约为3.2eV,这说明在线性偏振光的照射下,电子吸收相应的光子能量,从价带直接跃迁到导带与次导带上,导致最大光电流出现㊂在图7中,c 点㊁d 点和f 点均出现了较大的态密度峰,c 点与d 点㊁c 点与f 点的差值分别为2.4和3.2eV,正好对应价带底与导带㊁次导带的能量差值㊂依据费米黄金定律,半导体电子跃迁概率和态密度大小成正比㊂这说明当外界施加电压时,价带与导带态密度峰值之间的电子跃迁概率会变大㊂结合图3(b)与图7分析可知,带隙与峰值间的高迁跃概率导致了光子能量在2.4和3.2eV 时产生了较大光电流且迅速达到饱和光电流㊂图7㊀单层SnS 的态密度Fig.7㊀Density of states (DOS)of monolayer SnS 2.2㊀偏振灵敏度偏振灵敏度是衡量单层SnS 器件能否作为光电探测器重要指标,而消光比是偏振灵敏度的主要判断依据,所以本文引入消光比㊂消光比表示光电流大小的比值:R ||/R ʅ或R ʅ/R ||,R ||㊁R ʅ分别是偏振角为0ʎ㊁90ʎ的光响应㊂由于R ʅ的光响应均大于R ||的,本文只计算R ʅ/R ||㊂如图8所示,在Armchair 器件方向,当光子能量为2.0㊁2.6㊁3.4㊁3.6eV 时随偏压增大能获得一个极其稳定的消光比,数值分别约为12㊁28㊁11㊁3,其中小偏压范围内光子能量为2.6eV 时获得的消光比既能保持稳定性也能保持很高的数值,光子能量为2.8eV 在零偏压下就能取得70的消光比㊂在Zigzag 器件方向,整体光子能量在小偏压范围内同样能产生很大的消光比,但相对来说不如Armchair 方向的消光比数值平稳㊂从整体上看,两个方向上同一光子能量下偏压为0.1V 时产生的消光比相对较大㊂消光比越大偏振灵敏度越强,证明器件性能越好㊂单层SnS 在小偏压范围内能产生较大消光比且具有一定稳定性,在二维材料中表现较为优秀㊂作为对比,在零偏压下光响应表现优秀的ZrNBr-ZrNCl 异质结光电探测器的最大消光比仅为5.0[50]㊂㊀第4期徐中辉等:单层SnS的光电效应及应变工程的第一性原理研究681㊀图8㊀不同光子能量下,Armchair和Zigzag方向消光比随偏压的变化Fig.8㊀Variation of extinction ratio with bias voltage in Armchair and Zigzag directions under different photon energies 2.3㊀应变工程应变工程是调节单层二维材料电子结构和改变PBE光电流的有效方法㊂对单层SnS的y和z轴方向同时进行压缩或拉伸的双轴应变,观察其对单层SnS电子结构和零偏压下垂直照射器件所产生光电流大小的影响㊂引入公式β=(w-w0)/w0ˑ100%,w表示比例应变后的晶格常数,w0表示原晶格常数,β为应变数值,正值为拉伸应变,负值为压缩应变㊂如图9(a)所示,为说明应变工程对单层SnS电子结构的影响,本文分析其带隙㊁价带和导带的变化㊂在双轴应变下,随着应变数值的增大,带隙单调增加,但拉伸应变下增加的幅度相对平缓,在压缩数值为-6%时,其带隙为0.659eV,在拉伸数值为+6%时,其带隙为1.695eV㊂在-6%到+6%的数值变化范围内,应变对价带的影响很小,所以导带与带隙的变化幅度相近㊂如图9(b)所示,对单层SnS构建了Armchair器件输运方向,偏压设置为0,设置光子能量范围为1.6~3.6V,能量间隔为0.2V,施加应力时固定住两侧电极,仅对中心区施加应力㊂双轴应变下的光电流随余弦形式变化,在θ=90ʎ时取得最大值,所以只统计在垂直线性偏振光的照射条件下,光电流的变化情况㊂结果表明:双轴应变对器件的光电流有明显的增强作用㊂压缩应力数值为-6%对光电流的提升十分明显,其中光子能量为2.2㊁3.2eV时光电流数值分别达到20.97与12.97a20/phonon;当调节拉伸应力数值为+4%时,垂直线性偏振光照射下的光子能量3.4eV处光电流增强数值达到最大,约为37.90a20/phonon㊂根据PGE的现象学理论,应变工程能改变晶体结构的对称性,因此适当的应力改变可调节光电流大小㊂希望以上数据能为单层SnS应用到高速数字通信或光电探测器等领域提供理论参考㊂图9㊀在双轴应变下,单层SnS能带结构与最大光电流的变化㊂(a)单层SnS的带隙㊁价带和导带变化;(b)在零偏压且垂直线性偏振光照射下,单层SnS最大光电流的变化Fig.9㊀Change of band structure and maximum photocurrent under biaxial strain in monolayer SnS.(a)Changes in band gap, valence band and conduction band in monolayer SnS;(b)maximum photocurrent of monolayer SnS changes under zerobias and vertically linearly polarized light irradiation3㊀结㊀㊀论本文搭建了单层SnS两个方向的器件模型(Armchair和Zigzag),分析了其在线性偏振光照射下产生的682㊀研究论文人工晶体学报㊀㊀㊀㊀㊀㊀第53卷光电效应,利用计算数据绘制了能带结构㊁态密度㊁光响应和消光比等图形㊂小偏压范围内的光子能量为2.4㊁3.2eV时,两个方向的器件在线性偏振光照射下均能产生较大且稳定的光响应㊂光响应主要源于电子在第一布里渊区X点的迁跃,从价带跃迁到导带与次导带㊂通过绘制消光比图发现单层SnS器件具有较高的偏振灵敏度,在小幅度偏压范围内能保持一定的稳定性㊂最后,通过应变工程改变单层SnS的能带结构和光电流,在应力数值为-6%~6%时,单层SnS带隙单调递增,零偏置电压下的光电流整体提升幅度很大,其中,应力数值为-6%和+4%时,光电流提升较为明显㊂综上所述,SnS在光电探测器领域是一种有广阔发展前景的材料㊂参考文献[1]㊀NOVOSELOV K S,GEIM A K,MOROZOV S V,et al.Electric field effect in atomically thin carbon films[J].Science,2004,306(5696):666-669.[2]㊀LOPEZ-SANCHEZ O,LEMBKE D,KAYCI M,et al.Ultrasensitive photodetectors based on monolayer MoS2[J].Nature Nanotechnology,2013,8:497-501.[3]㊀LIU H,NEAL A T,ZHU Z,et al.Phosphorene:an unexplored2D semiconductor with a high hole mobility[J].ACS Nano,2014,8(4):4033-4041.[4]㊀WENG Q H,WANG X B,WANG X,et al.Functionalized hexagonal boron nitride nanomaterials:emerging 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研究电子产品的作文英文回答：Electronic products have become an integral part of our daily lives. From smartphones to laptops, we rely heavily on these devices for communication, entertainment, and productivity. In this essay, I will discuss the impact of electronic products on our lives and the reasons why they are so popular.Firstly, electronic products have revolutionized the way we communicate. With the advent of smartphones, we can easily connect with people from all over the world through calls, messages, and social media platforms. This has made the world a smaller place and has brought people closer together. Additionally, electronic products have made it possible for us to access information instantly. With just a few taps on a screen, we can search for any information we need, whether it's news, weather updates, or even recipes. This convenience has greatly enhanced our dailylives.Furthermore, electronic products have transformed the way we entertain ourselves. We no longer need to go to a movie theater to watch a film or buy CDs to listen to music. With streaming services like Netflix and Spotify, we can enjoy a wide variety of movies and music right at our fingertips. This has made entertainment more accessible and affordable for everyone. Moreover, electronic products have also provided us with new forms of entertainment, such as video games and virtual reality experiences. Theseimmersive experiences have taken entertainment to a whole new level.In terms of productivity, electronic products have greatly improved our efficiency and effectiveness. With the help of laptops and tablets, we can work from anywhere and collaborate with colleagues in real-time. This flexibility has allowed us to achieve a better work-life balance andhas increased productivity in many industries. Additionally, electronic products have also made tasks like shopping and banking much easier. We can now make purchases and manageour finances online, saving us time and effort.Overall, electronic products have had a profound impact on our lives. They have revolutionized communication, transformed entertainment, and enhanced productivity. It is no wonder that they have become so popular and indispensable in today's society.中文回答：电子产品已经成为我们日常生活中不可或缺的一部分。

氮化镓的最高密度1. 引言氮化镓（GaN）是一种重要的半导体材料，具有广泛的应用前景。

其最高密度是氮化镓作为固体的质量除以固体体积的比值，是一个重要的物理参数。

本文将探讨氮化镓的最高密度及其相关性质。

2. 氮化镓的基本介绍氮化镓是由镓原子和氮原子组成的化合物，化学式为GaN。

它具有良好的热稳定性、高电子迁移率和宽的能带隙，使其成为一种重要的半导体材料。

氮化镓的最高密度是指在固态下，氮化镓的质量除以其体积所得到的数值。

3. 氮化镓的晶体结构氮化镓晶体结构属于六方晶系，空间群为P63mc。

每个氮化镓晶胞中包含2个氮原子和2个镓原子。

氮化镓晶体具有六边形的晶格结构，其中氮原子和镓原子交替排列。

4. 氮化镓的密度计算氮化镓的密度可以通过实验测量或理论计算得到。

理论计算常用的方法包括密度泛函理论（DFT）等。

通过计算得到的氮化镓密度可以与实验测量值进行比较，以验证计算方法的准确性。

5. 氮化镓的最高密度值根据实验测量和理论计算，氮化镓的最高密度约为6.15克/立方厘米。

这个数值是在标准温度和标准压力下得到的。

氮化镓的最高密度与其晶体结构和原子间的相互作用有关。

6. 氮化镓最高密度的影响因素氮化镓的最高密度受多种因素的影响，包括晶体结构、温度和杂质等。

晶体结构的改变会导致氮化镓的密度变化。

温度的升高会使晶体膨胀，从而降低氮化镓的密度。

杂质的存在也会对氮化镓的密度产生影响。

7. 氮化镓最高密度的应用氮化镓的最高密度是其重要的物理性质之一，对于材料的应用具有重要意义。

氮化镓广泛应用于光电子器件、功率器件、射频器件和光学器件等领域。

其高密度使得氮化镓能够在小尺寸器件中发挥重要作用。

8. 氮化镓最高密度的发展趋势随着科学技术的不断进步，人们对氮化镓最高密度的研究也在不断发展。

研究人员通过改变氮化镓的晶体结构、控制杂质含量等手段，努力提高氮化镓的最高密度。

同时，新的计算方法和实验技术的应用也为研究提供了更多的可能性。

大学英语推荐信范文模板第1篇i have meet miss hao xiaoni’s for four years, being his teacher in “database structure” and her tutor in the experiment of “digital electronics”.in the class, her thinking was very active and she completely understood what i said in the lecture. she showed her strong interest in computer science and often did further discussion with me after the class. in particular, her experimental methods were so innovative and creative that the experiment done by her was often more intensive than required. i was much impressed by her because of her quick thinking, serious logic and independence. besides, she was able to sort out various problems in the experiment, having the ability in debugging of both software and hardware.大学英语推荐信范文模板第2篇Dear Michael,I’m writing to tell you about a fantastic movie I have just watched, as we always share the same taste of movies.The movie is Avatar, which tells a story of a soldier who, on an alien planet filled with exotic life forms, finds himself torn between two worlds in a fight for the survival of the alien people. Besides the touching and thrilling story, the movie also features brilliant visual effects, thanks to the talented director and advanced computer technology.So I recommend it to you as one of the b est movies I have ever watched. I’m sure you will love it as much as I do. I’m looking forward to discussing more with you after you watch it. Yours sincerely,Li Ming大学英语推荐信范文模板第3篇Dear xxx:Thank you again for your email. From the sounds of your scores and grades, you should have no problem entering Princeton. I am quite familiar with the program that you are in and have had several close friends that have been there at Beijing University. In fact, xxx was in graduate school with me and she was in the accelerated program. She has done extremely well in the . and after graduation went on to do some first rate science at a university in California. Since 20xx is your target date, I can begin to arrange funding for a research assistantship for you. These are nicer than teaching assistantships because they allow you to focus only on your research. Naturally, you will not be obligated to accept should you find other options. However, I believe that you will be most welcomed here in my group.You had asked about some of my publications, if you send me your address I can send preprints. They may take some time to get to China. You can find some of our work listed on our web site under my cv. This is an incomplete list but the PRL of last year is there and the latest hasnt yet been released from the publishers.We have been doing some interesting things lately with topological defects on tube manifolds that you might like. We have recently imaged nanotubes which exhibit a change in chirality along the tube! Tunneling spectra show that this produces subtle changes in the LDOS as predicted in some of X. Blase’s work. We have also begun optical studies on individual nanotubes using near-field scanning optical microscopy and spectroscopy. We are particualry interested in how the surface plasmon resonances (governed by tube topology) effects the third order nonlinear susceptability in these objects.Thank you again for your interest in our group. May I suggest that we keep in contact over the year. Let me know your progress and I will try to help with the application procedures should you decide to join us.Sincerely,Alison大学英语推荐信范文模板第4篇to whom it may concern,ms. has been my student since . she is one of my most favorite students and on hearing that she is planning to pursue further study in your university i feel quite pleased to share with you my perspectives of ms. .i taught her english which is a very important course for senior high school student. since i am always interested in student-oriented teaching method, i prefer the predomination of student’s presentation and discussions during the classes. we always hold drama performance related to our text book, which offered me excellent opportunity to observe my students’ understanding of english literature works an d their unique perspectives concerning it. that’s how i gradually noticed ms. and paid special attention to her. she was a very active student and eager to express her own opinion in the discussion. and in each drama performance, she was active to help organize the performance and was happy to be one of the roles.also it’s worthy to mention that ms. has a superb command of the english language. her clear and fluent expression, whether in oral or written english, is excellent. she is among the top 3 students of english course in the class. and as the president of the english club, she organized the english corner, which provided an outdoor space for students to communicate with each other in english. in this role, she frequently contacted foreign teachers in our school to invite them to the club’s events, and in doing so, often made good friends with them. during her years of senior high school life, she actively took part in the national english competition and ‘star of outlook’ english talent competition. though she didn’t get the award, she really did good performance in these competitions. through these kinds of activities, her oral english was improved a lot and her view was broadening greatly.she once discussed with me that there are many problems in english teaching in china. many senior students can get a high score in exam but can’t speak and communicate with others in english fluently. she said that she want to learn much more professional knowledge of education in usa and then comes back to develop china’s education. i was moved a lot by her spirit.it is for these reasons that i offer high recommendations for ms. without reservation. her drive and abilities will truly be an asset to your establishment. if you have any questions regarding this recommendation, please do not hesitate to contact me. it would be greatly appreciated if you consider her application carefully.yours sincerely,大学英语推荐信范文模板第5篇To Whom It May Concern：It is my great pleasure to recommend Miss xxx to you, as she was one of my finest students in our department.Miss xxx began attending my English classes in the Department of International Trade University in 19xx and graduated in spring of 19xx. Though it has been over eight years since I last saw her, the deep impression she made on me has not faded in the least. She is very intelligent, honest, creative, articulate, adaptive person. Her high academic achievement speaks for itself: she consistently scored in the top 5% in class.I am certain that Miss xxx would make great contributions to your company, and I strongly recommend her for the position. Please do not hesitate to inquire further if I can be of help to you.Sincerely,xxx大学英语推荐信范文模板第6篇Dear xx:Thank you for the email and your interest in our research program.I am very intersted in your application and would like to hear more. Are you interested in Fall 20xx or fall 20xx? Certianly for 20xx there should be no problem getting research support, provided that your test scores, grades, etc. are acceptable to the university. For 20xx, it would be a little tougher because of the short notice, but might be arranged under special circumstances. You asked about the nature of research here. In the laboratory, students generally couple calculations with experiment. We specialize in spectroscopic determinations of transport and electronic structure using scanning probes (STM and NSOM). To gain a detailed understanding of this, ab initio calculations must be compared with data. We have worked closely with J-C Charlier in Belgium, A. Rubio in Spain, and X. Blase in France using a variety of theoretical techniques including tight binding for structural information and LDA of DFT for electronics calcs.Our tunneling microscope is a low temperature Besoke design copied from the Julich group. We are capable of running at LHe temperatures for good energy resolution. We are in theprocess of constructing a near-field scanning optical microscope and a photon scanning tunneling microscope. These two new instruments should be on line around Dec.Our group focus is to understand the quantum dynamics and optical response of individual nano-systems like carbon nanotubes, B-doped nanotubes and filled nanotubes. Look for our latest publications coming out in the next months in PRL, JMR, and Advanced Materials. The entire group will also be at the MRS meeting in Boston.We would be pleased to consider your application for this year or next.Professor of PhysicsPrinceton University大学英语推荐信范文模板第7篇Dear Sir/Madam,It has always been a great pleasure to write to you since I can never fail to get help, inspiration or enlightenment from you. Now I am writing to recommend to you Miss Liu Ming who wants to pursue her graduate study for the Master’s Degree under your supervision.Miss Liu Ming was one of my classmates in Tianjin University. She was one of the most excellent students in our university as can be seen from her straight A grades on all subjects. After graduation she worked in Tianyi Biological Company for three years, which considerably added to her practical experience.It is my belief that with her intelligence, diligence and rich experience, Miss Liu Ming has great potential for further development in the field of pharmacology both theoretically and practically. Therefore, I recommend her to you with no reservations.your sincerely，XXXX大学英语推荐信范文模板第8篇Dear Sir or Madam,I’m Li hua in Class 8, grade 3. From the notice put up on the wall in our school, I have learned that our school radio station needs an English broadcaster. Here I was writing to you to recommend myself.I take interest in broadcasting and am willing to work as a volunteer program host. Moreover, the training course I took makes it easy for me to work as an English broadcaster. / I have attended the course about the skills in broadcasting and taken some professional training in the past five years. Now I would like to put what I have learned into practice. / I am eager tohave the opportunity to work as a broadcaster so that I can apply what I learned to practice. I am particularly good at spoken English.So I hold the belief that I am quite suitable for the post. I would appreciate it if you give me the chance to work for our radio station.Look forward to your reply soon.大学英语推荐信范文模板第9篇Respect leadership:First, extends the deep respect to your industrious work, in spite of being very busy very thanks you to glance through my material. Also hoped that it can open the opportunity and the success gate of for me.My name am Ni XX, is the foreign language foreign trade Training college international trade specialized 06 sessions of graduates. The graduation in namely, is facing the future and enterprise's choice, I the position which provides to your firm is interested very much.“in the work the academic society work, the academic society studies in the study”. Three year university life, I record “one point to do farm work sincerely frequently, one point harvest” the maxim and loves the hillock professional spirit, and merges it to the study and the work. Three year study, I mainly studied foreign trade Shan Zheng to study, curricula and so on economic, accounting, market marketing, international trade and practice, foreign trade letters and telegrams, international commerce English, Through the international trade practice's study and the practice, caused my to further be familiar with the foreign trade service detailed flow, while learned the specialized knowledge, I have also studied computer's related knowledge, could utilize Office series office softwares well and so on Word, had the good team spirit and the very strong sense of responsibility, could bear hardships and stand hard work, honestly, is self-confident, is professional.As a graduating university graduate, I also lack the rich work experience, but I will work even more diligently, will enrich themselves and consummates unceasingly. Simultaneously also believed that through own diligently the help which can provide with your firm, I can be competent this work and with your firm together diligently, promotes company's enterprise unceasing development forward. Even if your firm thought that my present condition has not met your requirement, I will pay attention to your firm's development as always, and expresses I sincerest wish!“the sea depends on the fish dive extravagantly, day Gao Renniao flies.”I hoped earnestly your firm can give me an opportunity, I take the work filled with warm, the rigorous practical work will serve as the companySets sail, depends strength of your east wind. Will be anticipating your soon answer!your sincerely，XXXX大学英语推荐信范文模板第10篇Dear Professor xxx:Thank you very much for your kind reply. I am sorry that during the summer vacation I cannot read and reply your email in time.As stated in my first letter, my desired entrance date is in Fall of 20xx. And I would like to provide my test scores. My TOEFL test score is 647 (Oct. 1997) with a TWE score of . My GRE test score is 2340 (Oct. 1996, V770 M800 A770). My GRE Subject score is 920 (Oct. 1998, Physics). And I will take the TSE test in the coming August. And my undergraduate and graduate GPA are both about in , about top 10%-20% in my class.I wish to make a note that during my undergraduate study I was quite young, and during my graduate study I take many efforts to study the basic courses in Physics by myself, which may be the reason my GPAs are not in the top 5%. But now I believe that I have been quite familiar in the knowledges of Physics, both the courses and the researches. So I hope that my test scores and grades are acceptable to Priceton with financial supports.As to the research, I am very glad to learn the research background you provided in your letter. I am quite familiar with the works of X. Blase published in PRL and APL. I also know that J-C Charlier is a famous specialist in this field. So perhaps I could do theoretical research works in your group. Also, I am very glad to know that you have the needed main instruments for carbon nanotubes in your group, so that both theoretical and experimental works can be done.I am puzzled at the _MRS meeting in Boston_ you mentioned in your letter. What is the full-name of MRS? Is it a meeting specialized in nano-systems? I do research works on carbon nanotubes almost totally by myself, and perhaps are not familiar with such fixed terms. Would you please explain the contents of this meeting? Thanks. And you mentioned that your latest publications will come out in next months in PRL. Would you please send me the page number of this paper in PRL, and if possible, the full text of this paper? The journal PRL reaches to China very late, usually several months to half a year after published, and I don't have the account to find the full-texts of PRL on-line.I am looking forward to receiving your warmhearted reply.Thanks.Yours sincerelyxxx大学英语推荐信范文模板第11篇Dear Mr. Smith,I take great pleasure to introduce one of my students, Kate Lawrence to you. She is going to pursue her further education as a postgraduate in September this year.Now, I recommend her to do an internship in your company. In the last four years, she studied hard and got excellent grads in exams.Besides, as the main membership of student union, she develops strongly comprehensive ability to deal with various situations calmly.In addition, she has a very pleasant and favorable personality that helps her building good relationships with other.I strongly recommend this promising young lady without any reservation.Will you please consider my recommendation and offer her a position in your company? Your favorable consideration and assistance to her would be appreciated.Sincerely yours,David Brow大学英语推荐信范文模板第12篇To Whom it may Concern：In my capacity as a professor of am pleased to have this opportunity to write a letter of recommendation to support his application for your scholarship.Since his enrollment into our department, Chen has embodied the fine character of strong inquisition and industriousness in learning, which has gained him significant academic success during his college years. I am aware of his distinctive academic performance as reflected in his transcripts. He maintains a very high GPA through the past 3 years,ranking first in the grade and winning scholarships of the department almost every year .In the senior Independent Research course, Chen impressed me with his reasoning ability and unwavering perseverance. He looked for a large amount of literatures from libraries and networks for a more in-depth research and the beginning of the project, Chen demonstrated his understanding of the new theories and his exactitude of procedures. This could be only done due to his strong logical ability, which facilitate to define his research objective and make the plan. From this project, Chen showed his ability to do independent research and to solve problems.With his excellent logical reasoning and hardworking personality, I am sure that can meet the challenge of his master program. Therefore, I strongly recommend him, a student with a great potentialand I firmly believe that he can be a great asset to your company.Sincerely yours,Professor of Optoelectronic InformationUniversity of Electronic Science and Technology of ChinaChengdu, 64, China。

Theoretical study of quantum effectsin materials量子力学，是20世纪物理学中最重要的新理论之一。

它不仅揭示了物质在微观尺度下的本质，而且为我们提供了控制这种微观世界的方法。

在大自然中，我们看到的物质通常在经典物理学的框架中被描述，但是在最近的研究中，人们越来越关注在量子规律的控制下制造材料的可能性。

本文将讨论量子效应对材料性质的影响以及如何在理论上研究这些效应。

量子力学的一个重要规律是不确定性原理，它表明在粒子的位置和动量之间存在的基本限制。

在微观世界中，对量子态进行精确描述是十分困难的，由此产生了许多奇特的现象，例如量子诱导隧穿效应和量子纠缠。

这些现象因微观粒子的波动特性而发生，这样一来，我们可以控制这些粒子的波动而不是直接控制它们的位置和速度。

近年来，科学家们越来越向材料方向研究量子效应。

例如，在透明电子器件中，量子隧穿是一个重要的效应，它允许电子穿过一个电势垒而不必满足经典物理学中所需的条件。

这种隧穿效应已经成功地应用于场发射显示器（FED），电视和照明设备中。

量子效应还可以导致一些在经典物理学中不可能存在的现象。

例如，许多材料在低温下表现出超导性质，这是因为在量子力学的作用下，电子可以在晶格之间传输而不受能量损失。

这种超导性质可以最大化电子设备的效率。

现在让我们来看看如何在理论上研究这些量子效应。

一种成功的方法是通过密度泛函理论（DFT）来模拟材料的量子行为。

DFT是一种基于电子密度的计算方法，用于研究原子和分子的量子行为。

在DFT中，原子和分子的电子密度被视为连续变化的函数，而不是单个点的电子。

在DFT中，我们需要使用能量泛函，这是一个描述电子间相互作用的数学表达式。

这个公式可以使用各种近似方法来求解，例如，局部密度近似（LDA）和广义梯度近似（GGA）。

一旦我们确定了能量泛函，我们就可以预测材料在不同条件下的物理性质，例如能带结构，磁性，电导率和光学性质。