单层含硫空位MoS2光伏效应的第一性原理研究

罗文铭, 邵志刚, 杨谋

罗文铭, 邵志刚, 杨谋. 单层含硫空位MoS2光伏效应的第一性原理研究[J]. 华南师范大学学报(自然科学版), 2019, 51(4): 7-13. DOI: 10.6054/j.jscnun.2019057
引用本文: 罗文铭, 邵志刚, 杨谋. 单层含硫空位MoS2光伏效应的第一性原理研究[J]. 华南师范大学学报(自然科学版), 2019, 51(4): 7-13. DOI: 10.6054/j.jscnun.2019057
LUO Wenming, SHAO Zhigang, YANG Mou. A First Principle Study of the Photogalvanic Effect of Monolayer MoS2 with Sulfur Vacancies[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(4): 7-13. DOI: 10.6054/j.jscnun.2019057
Citation: LUO Wenming, SHAO Zhigang, YANG Mou. A First Principle Study of the Photogalvanic Effect of Monolayer MoS2 with Sulfur Vacancies[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(4): 7-13. DOI: 10.6054/j.jscnun.2019057

单层含硫空位MoS2光伏效应的第一性原理研究

基金项目: 

国家自然科学基金项目 11774100

广东省科技计划项目 2018A030313322

详细信息
    通讯作者:

    邵志刚,教授,Email:zgshao@scnu.edu.cn

  • 中图分类号: O469

A First Principle Study of the Photogalvanic Effect of Monolayer MoS2 with Sulfur Vacancies

  • 摘要: 基于非平衡态格林函数——密度泛函理论,采用第一性原理研究方法,对单层含硫空位MoS2的光伏效应进行了研究.利用能带图和联合态密度分析单层含硫空位MoS2的光响应函数.结果表明:对于单层含硫空位的MoS2,线偏光电流效应不明显,而圆偏光电流效应比较明显.计算模拟了随偏振角(相位角)变化的光响应函数,计算结果符合唯象理论.单层含硫空位的MoS2可被应用于新型电子和光电子器件中,为进一步认识单层硫空位MoS2的光电流效应提供了新的理论基础.
    Abstract: The photogalvanic effect of monolayer molybdenum disulfide (MoS2) with sulfur vacancies is investigated with first-principle calculations based on the density functional theory within the nonequilibrium Green's function formalism. A detailed analysis of the behavior of photoresponse is given based on the band structure and joint density of states. The results reveal that the linear photovoltaic effect (LPGE) is unconspicuous and the circular photogalvanic effect (CPGE) is obvious. The variation of photoresponse function with polarization angle (phase angle) is simulated and the calculation results are consistent with the phenomenological theory. The monolayer MoS2 with sulfur vacancies can be applied to novel electronic and optoelectronic devices, which provides a new theoretical basis for further understanding the photogalvanic effect of the monolayer MoS2 with sulfur vacancies.
  • 近年来,与石墨烯结构类似的单层MoS2,在实验上可以被剥离出来[1].块体MoS2是间接带隙半导体,而单层MoS2拥有类似三明治的结构,是直接带隙半导体[2]. MoS2的能隙随层数的改变而变化,单层MoS2能隙更大.由于其突出的光学性质和电学性质引起了人们的关注[3].单层MoS2具有较大的光吸收率[4-7],其载流子的迁移率高,可以作为晶体管的优良材料[8],也可被用于光探测器[9].

    最近,光伏效应[10-17](Photogalvanic Effect, PGE)又掀起了一波热潮.不仅在二维电子气[18]上实现线偏光电流效应(LPGE)和自旋光电流效应(SPGE)[19],而且,对于拓扑绝缘体[20-22](例如HgTe量子阱,Sb2Te3等)也可以观察到量子圆偏光电流效应(CPGE)[23].此外,对于外尔半金属[24],例如TaAs,通过理论计算,会出现CPGE. GUO研究组采用第一性原理[25-27]计算研究了掺杂硼、氮原子对的石墨烯以及掺杂硫原子的黑磷等材料的非平衡态光电流.

    到目前为止,对于含硫空位的单层MoS2,从实验研究[28-32]到理论研究[33-39]已成为热点,其电学性质及光学性质已受到广泛关注.但是,单层含硫空位MoS2的光伏效应研究鲜有报道,所以本文采用第一性原理的方法,来研究其在零偏压下的光电流.

    基于密度泛函理论的第一性原理计算,在Material Studio中用CASTEP软件包[40-41]对含硫空位的单层MoS2原胞进行结构优化,考虑了电子分布的不均匀性,采用广义梯度近似(Generalized Gradient Approximation, GGA)、交换关联泛函(Perdew-Burke-Ernzehof, PBE).在倒格矢空间中,平面波的截断能为500 eV,k点的取值为6×12×1,每个原子能量的收敛精度为10-6 eV,以保证结构的合理性.

    计算光电流的器件模型如图 1所示,它由中心散射区和2个电极组成,其中2个电极是半无限长的. 图 1A是计算光电流的器件图,图 1B图 1A经过结构驰豫后的侧视图.在零偏压下,光子垂直照射在器件的中心散射区.对于线偏光来说,偏振角θ是与输运方向相关的.对于椭偏光来说,相位角φ与椭圆离心率有关.

    图  1  单层含硫空位MoS2的两端口器件结构
    Figure  1.  The two-probe device structures of monolayer MoS2 with sulfur vacancies

    基于第一性原理的量子输运软件Nanodcal对原胞进行自洽计算[42-43],然后绘制能带图和联合态密度图.在自洽计算中,使用了交换关联泛函GGA_PBE96,k空间格点数为1×12×1,能量的收敛精度为10-6 eV,原子的基矢设置为(Double-Zeta Polarization, DZP).然后,利用Device Studio软件构建器件,温度设置为100 K、光照区域为中心散射区.最后,利用非平衡态格林函数-密度泛函理论的方法计算无偏压下的光电流.其中,光子偏振的类型由偏振矢量决定,

    e=[cosθcosφisinθsinφ]e1+[sinθcosφ+icosθsinφ]e2,

    其中,θ为偏振角,φ为相位角,表示椭圆离心率. eα (α=1, 2)表示单位矢量.当入射光为线偏光时,φ=0°.当入射光为椭圆偏振光时,θ=0°.特别地,当φ=±45°时,表示右旋/左旋圆偏振光.在计算的材料中,由于打破了空间反演对称性,所以可以产生光伏效应.值得注意的是,光电流〈I(ph)的正方向是从电极流向中心区域,量子输运软件Nanodcal中运用的方法是非平衡态格林函数-密度泛函理论.计算的光电流都是归一化光电流R,也可以称为光响应函数,其表达式[25-27]

    RII(ph)eIω,

    其中,Iω是单位时间通过单位面积的光子数,即光子通量.在Nanodcal中,左电极的光电流IL(ph)可以写成:

    I(ph)L=iehTr{ΓLG<(ph)+ΓLfL(E)(G<(ph)G<(ph))}dE,

    其中,G < (ph)G>(ph)分别是小于格林函数和大于格林函数; ΓL表示中心散射区与左电极之间的耦合作用.对于线偏光电流效应,光电流可以写成:

    I(ph)L=ieh{cos2θTr{[G<(ph)1+fL(G>(ph)1G<(ph)1)]}+sin2θTr{ΓL[G<(ph)2+fL(G>(ph)2G<(ph)2)]}+2sin(2θ)Tr{ΓL[G<(ph)3+fL(G>(ph)3G<(ph)3)]}}dE.

    对于圆偏光电流效应,左电极的光电流可以写成:

    I(ph)L=ieh{cos2φTr{[G<(ph)1+fL(G>(ph)1G<(ph)1)]}+sin2φTr{ΓL[G<(ph)2+fL(G>(ph)2G<(ph)2)]}+sin(2φ)2Tr{ΓL[G<(ph)3+fL(G>(ph)3G<(ph)3)]}}dE.

    对于LPGE和CPGE,G1>/ < (ph)G2>/ < (ph)具有相同的表达式:

    G>/<(ph)1=Σα,β=x,y,zC0NGr0e1αp+αG>/<0e1βpβGa0.G>/<(ph)2=Σα,β=x,y,zC0NGr0e2αp+αG>/<0e2βpβGa0.

    其中,G0aG0r分别是超前格林函数和推迟格林函数,pα/β表示电子动量在笛卡尔坐标系上的分量,e1/2β表示在笛卡尔坐标系上的单位矢量.

    C0=Iω(e/m0)2ħμrεr/2Nωεc,

    其中,N是光子数,ωc分别是光子的频率和光速,εεr分别是介电常数和相对介电常数. μr是相对磁化率,m0为净电子质量.特别地,对于线偏振光来说,

    G>/<(ph)3=Σα,β=x,y,zC0N(Gr0e1αpαG>/<0e2βpβGa0+Gr0e2αpαG>/<0e1βpβGa0).

    对于圆偏振光来说,

    G>/<(ph)3=±iΣα,β=x,y,zC0N(Gr0e1αpαG>/<0e2βpβGa0Gr0e2αpαG>/<0e1βpβGa0.

    联合态密度(Joint Density of States, JDOS)是研究光伏效应的工具,其定义:在光学跃迁的过程中,设1个光子的能量为ħω,计算从价带到导带之间电子跃迁的数目[44].联合态密度的一般表达式如下:

    Jcv(ħω)=BZ2dk(2π)3δ[Ec(k)Ev(k)ħω].

    其中,Ec(k)和Ev(k)分别是在特定k值下,导带和价带的能量,Ec(k)-Ev(k)表示为带间能量差.特别地,对于准二维材料来说,当材料打破空间反演对称性,能带产生劈裂的时候,联合态密度可以写成:

    Jcv(ħω)=BZ2dk(2π)2δ[Ec(k)Ev(k)ħω].

    在计算与能量有关的光电流之前,先研究单层含硫空位MoS2的电学性质. 图 2A为单层MoS2能带图,图 2B是单层含硫空位MoS2的能带图.对比能带图不难发现,单层含硫空位的MoS2在费米能附近多了3条能带,而且能带发生了劈裂.一般来说,分析能带间的能量是了解电子跃情况的关键一步.在图 2B的高对称点Y处,费米能两边最近邻两条缺陷能带的能量差为0.80 eV,次近邻两条缺陷能带的能量差为1.10 eV.而价带顶到导带底的能量差为1.90 eV.此外,在高对称点Γ处,费米能附近最近邻两条缺陷能带的能量差为0.75 eV,次近邻两条缺陷能带的能量差为1.10 eV.并且,价带顶到导带底的能量差为2.10 eV.

    图  2  单层MoS2、单层含硫空位MoS2的能带图
    Figure  2.  The band structure of monolayer MoS2 and monolayer MoS2 with sulfur vacancies

    基于非平衡态格林函数-密度泛函理论的方法研究单层含硫空位MoS2的光学性质. 图 3模拟出用线偏光和圆偏光垂直照射单层含硫空位MoS2的光响应函数.对于LPGE,θ=π/4, φ=0°;对于CPGE,φ=π/4, θ=0°.光子的能量范围在0~2.20 eV,能量间隔为0.10 eV.从整体上来看,由于图 1的器件结构打破了空间反演对称,所以在垂直光照下,LPGE和CPGE都会产生光电流.但是,CPGE所产生的光响应强度比LPGE的大1个数量级.一方面,因为在圆偏光照射下,会使能带进一步劈裂,发生Rashba自旋轨道耦合,而线偏光并不会发生上述过程,所以CPGE产生更大的光电流;另一方面,单层含硫空位的MoS2以杂质电导为主.与纯的单层MoS2相比,由于其发生了杂质散射,使得电阻率增大、电导率减小,所以LPGE产生的光电流很小.从局部来看,对于LPGE,当线偏光能量为1.20 eV时,光电流开始产生.因为在图 2B中高对称点X处,费米面附近最近邻两条缺陷能带间的能量差为1.20 eV.当线偏光能量为1.70 eV时,光电流也会出现1个弱峰.因为在高对称点S处,电子从价带跃迁到缺陷带的最小能量为1.70 eV.对于CPGE,在光子能量不小于0.80 eV时,才会产生光电流,因为在图 2B中高对称点Y处,电子从费米能附近最近邻两条缺陷能带间跃迁的能量为0.80 eV.在能量为1.90 eV和2.10 eV时,光响应函数会出现2个峰.这分别是在高对称点Y、Γ处,从价带顶到导带底的最小能量.

    图  3  单层含硫空位MoS2的光响应函数随能量的变化
    Figure  3.  The photoresponse function with the energy of monolayer MoS2 with sulfur vacancies

    为了进一步理解单层含硫空位MoS2的光响应行为,利用联合态密度来分析(图 4).当光子能量在0~0.75 eV时,JDOS均为零.这是电子发生光学跃迁所需要的最小能量(0.75 eV),对应于图 2B中Γ处缺陷能带之间的能量.同时也对应于图 3B中只有光子能量大于0.70 eV才会有光电流的现象.此外,电子质量在1.10、1.30、1.38时代表电子在缺陷能带之间跃迁的能量值,但前两者的JDOS明显大于后者.这是因为前两者的电子是在高对称点Y、Γ、S处被激发,所以被激发的数量比较多,JDOS出现峰值;而后者不是在高对称点处被激发,所以JDOS出现波谷.而当光子能量为1.44 eV时,JDOS出现峰值,此时电子可以从价带跃迁到缺陷带.随后能量在2.10 eV之前,JDOS振荡上升,这里对应于电子从缺陷带跃迁到导带的过程.在2.10~2.15 eV之间,JDOS急速上升,意味着受光激发电子的数量急速增长,这里对应于高对称点Γ处以及Γ~X处价带顶到导带底的能量.这也是CPGE在能量为2.10 eV时出现一个较大峰的原因.所以能带图结合联合态密度在一定程度上能够分析光响应行为.

    图  4  单层含硫空位MoS2的联合态密度图
    Figure  4.  The JDOS of monolayer MoS2 with sulfur vacancies

    为了进一步了解光响应函数的行为,研究单层含硫空位的MoS2在垂直光照下随θ变化的光响应函数(图 5).由于LPGE在1.10 eV之后才出现光电流(图 3),所以本文研究线偏光的能量范围为1.10~2.20 eV,能量间隔为0.10 eV.结果表明:LPGE的光响应函数绝大多数正比于sin(2θ),基本上与唯象理论相符[13, 18, 45-46].在唯象理论中,具有Cs对称性的材料,在光子的垂直照射下,光电流为

    图  5  用线偏光垂直照射单层含硫空位的MoS2θ变化的光响应函数
    Figure  5.  The variation of photoresponse function with θ when monolayer MoS2 with sulfur vacancies is vertically irradiated by the linearly polarized light
    RxE20χxxysin(2θ)

    其中,E02是入射光的电场强度;χxxy是一个张量.但是,在1.60 eV能量下的光响应强度正比于cos(2θ).而1.60 eV对应的是从价带到缺陷带的能量.这说明非均匀材料的光响应函数不能完全符合均匀材料的唯象理论.总之,当光子能量在1.20、1.70、2.00 eV时,LPGE光响应函数的振幅比较大;对于其他能量,LPGE光响应函数的振幅都不大.对于单层含硫空位的MoS2,LPGE产生的光电流振幅小且不明显.

    对比研究单层含硫空位的MoS2在垂直光照下随φ变化的光响应函数,光子的能量范围为0.70~2.20 eV,能量间隔为0.10 eV.结果表明,光响应函数正比于sin2φ,完全符合唯象理论.在图 6A中,光子能量范围为0.70~1.00 eV,只有在0.80 eV能量下才会出现光电流,这对应于电子在缺陷带间跃迁的能量. 0.80 eV对应于红外光的能量.在图 6B描述的是电子从价带跃迁到缺陷带的光响应函数,其光响应函数的趋势类似.在图 6C中,光子的能量范围是1.50~1.80 eV,对应于红光能量.此时,光响应的振幅随光子的能量并非线性增加.例如,当光子能量为1.80 eV时,光响应的振幅很小,而且与1.50 eV能量下的光响应函数趋势相反.在图 6D中能量值对应于电子从价带及缺陷带跃迁到导带.此时,描述的是随红光(1.90 eV)、黄光(2.10 eV)到绿光(2.20 eV)变化的光电流.结果表明,在能量为1.90 eV的圆偏光照射下,单层含硫空位MoS2的光响应强度达到最大值,其次是能量为2.10 eV的光.总体上CPGE光响应函数的振幅比LPGE大1个数量级.所以,用圆偏光照射单层含硫空位的MoS2能获得更大的光电流,由于光子的能量在可见光范围,所以单层含硫空位的MoS2适用于光电子器件.

    图  6  用椭偏光垂直照射单层含硫缺陷的MoS2φ变化的光响应函数
    Figure  6.  The variation of photoresponse function with φ when monolayer MoS2 with sulfur vacancies is vertically irradiated by the elliptically polarized light

    基于非平衡态格林函数-密度泛函理论的第一性原理方法,研究了单层含硫空位MoS2的光伏效应.利用能带图与联合态密度有效分析了光响应行为.硫空位打破了材料的空间反演对称性,使得能带发生劈裂,为光电流的产生提供前提条件.联合态密度能够表征电子受激跃迁的情况,结合能带图可以分析光响应行为.结果表明:圆偏光电流效应产生的光电流比线偏光电流效应产生的光电流大1个数量级,并且线偏光(圆偏光)随偏振角(相位角)变化的光响应函数与唯象理论相符合.通过计算可知,用1.90 eV能量的圆偏光垂直照射单层含硫空位的MoS2能获得最大光电流.本文通过对单层含硫空位MoS2的研究,为二维材料光伏器件的设计提供了理论基础.优良的光电性能使单层含硫空位的MoS2成为光电子和微电子器件应用的潜在材料.

  • 图  1   单层含硫空位MoS2的两端口器件结构

    Figure  1.   The two-probe device structures of monolayer MoS2 with sulfur vacancies

    图  2   单层MoS2、单层含硫空位MoS2的能带图

    Figure  2.   The band structure of monolayer MoS2 and monolayer MoS2 with sulfur vacancies

    图  3   单层含硫空位MoS2的光响应函数随能量的变化

    Figure  3.   The photoresponse function with the energy of monolayer MoS2 with sulfur vacancies

    图  4   单层含硫空位MoS2的联合态密度图

    Figure  4.   The JDOS of monolayer MoS2 with sulfur vacancies

    图  5   用线偏光垂直照射单层含硫空位的MoS2θ变化的光响应函数

    Figure  5.   The variation of photoresponse function with θ when monolayer MoS2 with sulfur vacancies is vertically irradiated by the linearly polarized light

    图  6   用椭偏光垂直照射单层含硫缺陷的MoS2φ变化的光响应函数

    Figure  6.   The variation of photoresponse function with φ when monolayer MoS2 with sulfur vacancies is vertically irradiated by the elliptically polarized light

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  • 收稿日期:  2019-03-24
  • 网络出版日期:  2021-03-21
  • 刊出日期:  2019-08-24

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