铜基多元半导体的电子结构和光学性质
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摘要
类金刚石结构的铜基三元半导体Cu-III-VI_2（III=Ga、In; VI=S、Se、Te）和四元半导体Cu_2-II-IV-VI_4（II=Zn、Cd; IV=Ge、Sn; VI=S、Se）及其固熔体（例如CuIn_xGa_(1-x)S_(2y)Se_(2(1-y))和Cu_2ZnSnS_(4x)Se_(4(1-x))）因其优良的光学性质而被广泛地用作光伏电池的吸收层材料，无论在基础理论还是在应用研究领域中都受到重视。该类材料由多种元素构成，这为材料设计和性能优化提供了更多的自由度，但增加了晶体结构和电子结构性质的复杂性。
基于局域密度近似（Local density approximation，LDA）和广义梯度近似（Generalized gradient approximation，GGA）的各种第一性原理计算方法在研究凝聚态电子结构性质方面取得了巨大成功，目前已有大量采用该方法的铜基多元半导体的相关研究。禁带宽度参数是光伏电池吸收层材料最重要的参数之一，而对铜基三元材料，即使采用基于多体微扰理论的GW方法得到的禁带宽度也严重偏离可靠的实验结果。所以，理论上迫切需要探索造成这种困难的原因，提出解决方案，进而理论上预测具有潜在应用价值但更加复杂的铜基四元材料。另外，由于上述电子结构性质研究上的困难和光学性质计算方法本身的复杂性，目前已有的光学性质的理论研究往往忽略了激子效应对光学性质的影响。所以，从理论上获得准确的电子结构性质和光学性质信息，这将为相关实验研究提供重要的参考信息。
本文对比类金刚石结构的二元材料ZnS，采用密度泛函理论并结合基于格林函数的多体微扰方法GW和Bethe-Salpeter Equation（BSE）方法研究铜基三元半导体Cu-III-VI_2和四元半导体Cu_2-II-IV-VI_4的晶体结构性质、电子结构性质和光学性质。本文的研究发现：（1）造成理论研究困难的原因来自于Cu d电子的特殊性质。Cu d电子在价带顶附近有大量态密度分布，并且它具有双重性质：一方面Cu d电子与VI p电子强烈杂化，在很大的能量区间形成共价键；另一方面Cu作为过渡金属，Cu d电子本质上是局域的。（2）理论方法上，Heyd-Scuseria-Ernzerhof（HSE）势函数由于包含了部分真实的Fock-exchange势函数，比LDA和GGA更好地给出了阴离子位置偏移参数μ，进而得到更加合理的晶体结构参数；而且，在LDA+U（U=4eV）近似基础上的多体微扰修正G_0W_0方法（即LDA+U+G_0W_0），很好地描述了Cu d的双重性质。本文计算得到的铜基三元材料的禁带宽度与可靠的实验结果相比误差在±0.2eV范围以内，而态密度也很好的符合了实验X射线光电子谱测量结果。（3）研究铜基四元材料的晶体结构和能带结构性质，给出了八种材料黄锡矿和锌黄锡矿结构的可靠的禁带宽度信息。并发现由于Cu_2ZnSnS_4、Cu_2CdSnS_4、Cu_2ZnGeSe_4和Cu_2CdGeSe_4具有合适的禁带宽度值从而可以被用作光伏电池吸收层材料。（4）对以CuGaS_2和CuInS_2为例的铜基材料光学性质的研究表明，光吸收过程中材料的激子效应通常被有效抑制，所以独立粒子近似给出的介电函数谱很好地符合了实验结果；导致不同铜基材料光学性质存在差异的关键影响因素是带边附近导带的电子结构性质，Cu_2GeS_3、Cu_2GeSe_3和Cu_2SnS_3具有较好的太阳照射光谱响应性质，是具有潜在应用价值的光伏电池吸收层材料。
铜基半导体材料比其它薄膜太阳电池材料（如GaAs和CdTe）具有更高的吸收系数，有利于提高光伏电池的光电流进而光伏电池的光电转换效率。在铜基材料本征禁带宽度中间引入新的被电子部分占据的能带，则可以进一步吸收能量小于本征禁带宽度的光子，成为提高这类材料的光吸收能力的一种有效方法。对于体块材料通常采用杂质掺杂的方法获得中间能级，相关研究无论是在实验上还是理论上都处于初步探索阶段。根据中间能带光伏电池（Intermediateband solar cell，IBSC）材料的功能特点，从理论上进行材料设计与性质研究有助于促进相关的实验研究。
根据对铜基材料电子结构和光学性质研究得到的信息和建立的理论研究方法，本文设计了两种基于铜基半导体的中间能带材料，并研究了它们的电子结构性质和光学性质及作为光伏电池材料的可行性。在CuGaS_2基体材料中掺杂Sn或者Fe元素，从而在CuGaS_2本征禁带宽度中间引入了与杂质电子态相关的中间能级。结果表明：Cu_8Ga_7SnS_(16)满足了IBSC材料设计的基本要求，是一种非常具有潜力的光伏电池材料；Cu_8Ga_7FeS_(16)材料中从价带到中间能带的光吸收能力非常强，但是从中间能带到导带的光吸收效率较低从而限制了其应用。
综上所述，本文首先理论研究类金刚石结构的铜基光伏电池材料的基本性质，指出Cu d电子具有成键和局域性双重性质，并影响了晶体结构性质、电子结构性质和光学性质。理论方法上，建立了计算精确晶体结构、电子结构和光学性质的流程，即首先采用HSE势函数优化晶体结构，然后采用LDA+U+G_0W_0（U=4eV）方法计算能带结构性质，采用独立粒子近似计算光学性质。给出了铜基四元材料的晶体结构和能带结构性质的系统信息，相关信息为实验研究提供了重要参考依据。基于上述研究结果，本文设计了Cu_8Ga_7SnS_(16)和Cu_8Ga_7FeS_(16)两种中间能带材料，Cu_8Ga_7SnS_(16)满足了IBSC材料设计的基本要求，是一种具有潜在应用价值的光伏电池材料；而Cu_8Ga_7FeS_(16)材料中从中间能带到导带的光吸收效率较低从而限制了其应用。
Adamantine Cu-based ternary semiconductors Cu-III-VI_2(with III=Al, Ga,and In; VI=S, Se, and Te), quaternary semiconductors Cu_2-II-IV-VI_4(with II=Znand Cd; IV=Ge and Sn; VI=S and Se), as well as their solid solutions (e.g.,CuIn_xGa_(1-x)S_(2y)Se_(2(1-y))and Cu_2ZnSnS_(4x)Se_(4(1-x))) have been intensively studied owing totheir desired optical properties for photovoltaic application. These materials arecomposed of multinary elements. As a result, although it is widely recognized that thechemical flexibility of these systems provide a vast space for materials design andoptimization, this flexibility inevitably comes at the cost of complexity.
The first principles calculation methods that based on the local densityapproximation (LDA) and generalized gradient approximation (GGA) functionalsare widely used for electronic properties of solids. There are also lots of reports thatstudying the electronic and optical properties Cu-based semiconductors. However,these methods usually seriously underestimate the band gap of a semiconductor,which is one of the most important parameters for photovoltaic applications. Eventhe advanced many-body method of GW fails to produce reliable band gaps ofCu-based ternary semiconductors. So, it is of great importance to investigate theseunresolved theoretical issues and to investigate the electronic properties of Cu-basedquaternary semiconductors in order to find new candidates for photovoltaicapplications. Besides the electronic properties, the investigation of optical propertiesare further complicated because of the computation methods, especially when theexcitonic effect is involved. So, reliable information of their electronic and opticalproperties from theoretical investigation is strongly needed for experiments.
This thesis deals with structural, electronic, and optical properties of Cu-basedmultinary semiconductors using the GW and Bethe-Salpeter Equation (BSE).Because of the similarity, we also compare with binary analogy of ZnS. We find that:(1) the difficulties for theoretical research come from the dual nature of Cu d states.Cu d states are only slightly shallower than VI p and contribute to the strong pdhybridization, leading to the interplay of strong pd hybridization and intrinsicallylocalization of Cu d states;(2) The established procedure that firstly relax the crystalstructures in the Heyd-Scuseria-Ernzerhof (HSE) functional and then calculate theband structures in the methods of LDA+U (U=4eV) and GW (i.e., LDA+U+G_0W_0)can give reasonable anion displacement μ and electronic band structures,respectively. The error bar for band gaps of ternary semiconductors are within±0.2eV compared with measured values and the calculated density of states agree wellwith X-ray photoelectron spectroscopy;(3) The structural and band structures of quaternary semiconductors are also investigated. The band gaps of both the stanniteand kesterite structures are calculated, which show that Cu_2ZnSnS_4、Cu_2CdSnS_4,Cu_2ZnGeSe_4, and Cu_2CdGeSe_4have suitable band gaps for photovoltaic applications;(4) Taking CuGaS_2and CuInS_2as examples, we study the optical properties ofCu-based semiconcutors. Results show that the excitonic effect is effectivelysupressed in real experiments. As a consequence, the dielectric function is welldescriped in independent partical approximation. The differences of opticalproperties of Cu-based semiconductors are induced by the near-edge conductionstates. Cu_2GeS_3, Cu_2GeSe_3, and Cu_2SnS_3are potential candidates for photovoltaicapplications because of their excellent properties for the sun irradiation.
The optical absorption coefficient of Cu-based semiconductors are much higherthan other thin film materials (e.g., GaAs and CdTe), which is of great advantage toimprove the photocurrent and thus the efficiency of solar cell. By impurity doping,intermediate bands which are partially occupied by electrons can be introduced intothe intrinsic band gap of the host material. As a result, the photons with energiessmaller than the intrinsic band gap can also be absorbed via two-step transition. Theresearch of intermediate band solar cell (IBSC) materials is in its infancy stagewhich calls for theoretical studies to guide the experiments.
Based on the above obtained information about electronic and opticalproperties and the established calculating methods, we design two IBSC materials.Intermediate bands are observed by doping Sn or Fe element into host CuGaS_2material. Our results manifest that Cu_8Ga_7SnS_(16)is a suitable candidate as an IBSCmaterial. The absorption from the valence band to the intermediate band is quitestrong in Cu_8Ga_7FeS_(16). However, it is rather weak for absorption from theintermediate band to the conduction band which limits the potential usage.
In summary, we theoretically study several properties of Cu-based multinarysemiconductors, which are found to be sensitively influenceed by dual nature of Cud states, i.e., hybridization and localization. This thesis also establises a procedurethat using the HSE functional, LDA+U+G_0W_0(U=4eV) method, and independentpartical approximation for the reliable structural, electronic, and optical properties.The structural and electronic band structructure of Cu-based quaternarysemiconductors are investigated, which provided useful and informative guidancefor future material design and selection. Based on above findings, we design twoIBSC materials, i.e., Cu_8Ga_7SnS_(16)and Cu_8Ga_7FeS_(16), which show that Cu_8Ga_7SnS_(16)is a suitable candidate as an IBSC material and that the weak absorption from theintermediate band to the conduction band limits the potential usage of Cu_8Ga_7FeS_(16).
基于局域密度近似（Local density approximation，LDA）和广义梯度近似（Generalized gradient approximation，GGA）的各种第一性原理计算方法在研究凝聚态电子结构性质方面取得了巨大成功，目前已有大量采用该方法的铜基多元半导体的相关研究。禁带宽度参数是光伏电池吸收层材料最重要的参数之一，而对铜基三元材料，即使采用基于多体微扰理论的GW方法得到的禁带宽度也严重偏离可靠的实验结果。所以，理论上迫切需要探索造成这种困难的原因，提出解决方案，进而理论上预测具有潜在应用价值但更加复杂的铜基四元材料。另外，由于上述电子结构性质研究上的困难和光学性质计算方法本身的复杂性，目前已有的光学性质的理论研究往往忽略了激子效应对光学性质的影响。所以，从理论上获得准确的电子结构性质和光学性质信息，这将为相关实验研究提供重要的参考信息。
本文对比类金刚石结构的二元材料ZnS，采用密度泛函理论并结合基于格林函数的多体微扰方法GW和Bethe-Salpeter Equation（BSE）方法研究铜基三元半导体Cu-III-VI_2和四元半导体Cu_2-II-IV-VI_4的晶体结构性质、电子结构性质和光学性质。本文的研究发现：（1）造成理论研究困难的原因来自于Cu d电子的特殊性质。Cu d电子在价带顶附近有大量态密度分布，并且它具有双重性质：一方面Cu d电子与VI p电子强烈杂化，在很大的能量区间形成共价键；另一方面Cu作为过渡金属，Cu d电子本质上是局域的。（2）理论方法上，Heyd-Scuseria-Ernzerhof（HSE）势函数由于包含了部分真实的Fock-exchange势函数，比LDA和GGA更好地给出了阴离子位置偏移参数μ，进而得到更加合理的晶体结构参数；而且，在LDA+U（U=4eV）近似基础上的多体微扰修正G_0W_0方法（即LDA+U+G_0W_0），很好地描述了Cu d的双重性质。本文计算得到的铜基三元材料的禁带宽度与可靠的实验结果相比误差在±0.2eV范围以内，而态密度也很好的符合了实验X射线光电子谱测量结果。（3）研究铜基四元材料的晶体结构和能带结构性质，给出了八种材料黄锡矿和锌黄锡矿结构的可靠的禁带宽度信息。并发现由于Cu_2ZnSnS_4、Cu_2CdSnS_4、Cu_2ZnGeSe_4和Cu_2CdGeSe_4具有合适的禁带宽度值从而可以被用作光伏电池吸收层材料。（4）对以CuGaS_2和CuInS_2为例的铜基材料光学性质的研究表明，光吸收过程中材料的激子效应通常被有效抑制，所以独立粒子近似给出的介电函数谱很好地符合了实验结果；导致不同铜基材料光学性质存在差异的关键影响因素是带边附近导带的电子结构性质，Cu_2GeS_3、Cu_2GeSe_3和Cu_2SnS_3具有较好的太阳照射光谱响应性质，是具有潜在应用价值的光伏电池吸收层材料。
铜基半导体材料比其它薄膜太阳电池材料（如GaAs和CdTe）具有更高的吸收系数，有利于提高光伏电池的光电流进而光伏电池的光电转换效率。在铜基材料本征禁带宽度中间引入新的被电子部分占据的能带，则可以进一步吸收能量小于本征禁带宽度的光子，成为提高这类材料的光吸收能力的一种有效方法。对于体块材料通常采用杂质掺杂的方法获得中间能级，相关研究无论是在实验上还是理论上都处于初步探索阶段。根据中间能带光伏电池（Intermediateband solar cell，IBSC）材料的功能特点，从理论上进行材料设计与性质研究有助于促进相关的实验研究。
根据对铜基材料电子结构和光学性质研究得到的信息和建立的理论研究方法，本文设计了两种基于铜基半导体的中间能带材料，并研究了它们的电子结构性质和光学性质及作为光伏电池材料的可行性。在CuGaS_2基体材料中掺杂Sn或者Fe元素，从而在CuGaS_2本征禁带宽度中间引入了与杂质电子态相关的中间能级。结果表明：Cu_8Ga_7SnS_(16)满足了IBSC材料设计的基本要求，是一种非常具有潜力的光伏电池材料；Cu_8Ga_7FeS_(16)材料中从价带到中间能带的光吸收能力非常强，但是从中间能带到导带的光吸收效率较低从而限制了其应用。
综上所述，本文首先理论研究类金刚石结构的铜基光伏电池材料的基本性质，指出Cu d电子具有成键和局域性双重性质，并影响了晶体结构性质、电子结构性质和光学性质。理论方法上，建立了计算精确晶体结构、电子结构和光学性质的流程，即首先采用HSE势函数优化晶体结构，然后采用LDA+U+G_0W_0（U=4eV）方法计算能带结构性质，采用独立粒子近似计算光学性质。给出了铜基四元材料的晶体结构和能带结构性质的系统信息，相关信息为实验研究提供了重要参考依据。基于上述研究结果，本文设计了Cu_8Ga_7SnS_(16)和Cu_8Ga_7FeS_(16)两种中间能带材料，Cu_8Ga_7SnS_(16)满足了IBSC材料设计的基本要求，是一种具有潜在应用价值的光伏电池材料；而Cu_8Ga_7FeS_(16)材料中从中间能带到导带的光吸收效率较低从而限制了其应用。
Adamantine Cu-based ternary semiconductors Cu-III-VI_2(with III=Al, Ga,and In; VI=S, Se, and Te), quaternary semiconductors Cu_2-II-IV-VI_4(with II=Znand Cd; IV=Ge and Sn; VI=S and Se), as well as their solid solutions (e.g.,CuIn_xGa_(1-x)S_(2y)Se_(2(1-y))and Cu_2ZnSnS_(4x)Se_(4(1-x))) have been intensively studied owing totheir desired optical properties for photovoltaic application. These materials arecomposed of multinary elements. As a result, although it is widely recognized that thechemical flexibility of these systems provide a vast space for materials design andoptimization, this flexibility inevitably comes at the cost of complexity.
The first principles calculation methods that based on the local densityapproximation (LDA) and generalized gradient approximation (GGA) functionalsare widely used for electronic properties of solids. There are also lots of reports thatstudying the electronic and optical properties Cu-based semiconductors. However,these methods usually seriously underestimate the band gap of a semiconductor,which is one of the most important parameters for photovoltaic applications. Eventhe advanced many-body method of GW fails to produce reliable band gaps ofCu-based ternary semiconductors. So, it is of great importance to investigate theseunresolved theoretical issues and to investigate the electronic properties of Cu-basedquaternary semiconductors in order to find new candidates for photovoltaicapplications. Besides the electronic properties, the investigation of optical propertiesare further complicated because of the computation methods, especially when theexcitonic effect is involved. So, reliable information of their electronic and opticalproperties from theoretical investigation is strongly needed for experiments.
This thesis deals with structural, electronic, and optical properties of Cu-basedmultinary semiconductors using the GW and Bethe-Salpeter Equation (BSE).Because of the similarity, we also compare with binary analogy of ZnS. We find that:(1) the difficulties for theoretical research come from the dual nature of Cu d states.Cu d states are only slightly shallower than VI p and contribute to the strong pdhybridization, leading to the interplay of strong pd hybridization and intrinsicallylocalization of Cu d states;(2) The established procedure that firstly relax the crystalstructures in the Heyd-Scuseria-Ernzerhof (HSE) functional and then calculate theband structures in the methods of LDA+U (U=4eV) and GW (i.e., LDA+U+G_0W_0)can give reasonable anion displacement μ and electronic band structures,respectively. The error bar for band gaps of ternary semiconductors are within±0.2eV compared with measured values and the calculated density of states agree wellwith X-ray photoelectron spectroscopy;(3) The structural and band structures of quaternary semiconductors are also investigated. The band gaps of both the stanniteand kesterite structures are calculated, which show that Cu_2ZnSnS_4、Cu_2CdSnS_4,Cu_2ZnGeSe_4, and Cu_2CdGeSe_4have suitable band gaps for photovoltaic applications;(4) Taking CuGaS_2and CuInS_2as examples, we study the optical properties ofCu-based semiconcutors. Results show that the excitonic effect is effectivelysupressed in real experiments. As a consequence, the dielectric function is welldescriped in independent partical approximation. The differences of opticalproperties of Cu-based semiconductors are induced by the near-edge conductionstates. Cu_2GeS_3, Cu_2GeSe_3, and Cu_2SnS_3are potential candidates for photovoltaicapplications because of their excellent properties for the sun irradiation.
The optical absorption coefficient of Cu-based semiconductors are much higherthan other thin film materials (e.g., GaAs and CdTe), which is of great advantage toimprove the photocurrent and thus the efficiency of solar cell. By impurity doping,intermediate bands which are partially occupied by electrons can be introduced intothe intrinsic band gap of the host material. As a result, the photons with energiessmaller than the intrinsic band gap can also be absorbed via two-step transition. Theresearch of intermediate band solar cell (IBSC) materials is in its infancy stagewhich calls for theoretical studies to guide the experiments.
Based on the above obtained information about electronic and opticalproperties and the established calculating methods, we design two IBSC materials.Intermediate bands are observed by doping Sn or Fe element into host CuGaS_2material. Our results manifest that Cu_8Ga_7SnS_(16)is a suitable candidate as an IBSCmaterial. The absorption from the valence band to the intermediate band is quitestrong in Cu_8Ga_7FeS_(16). However, it is rather weak for absorption from theintermediate band to the conduction band which limits the potential usage.
In summary, we theoretically study several properties of Cu-based multinarysemiconductors, which are found to be sensitively influenceed by dual nature of Cud states, i.e., hybridization and localization. This thesis also establises a procedurethat using the HSE functional, LDA+U+G_0W_0(U=4eV) method, and independentpartical approximation for the reliable structural, electronic, and optical properties.The structural and electronic band structructure of Cu-based quaternarysemiconductors are investigated, which provided useful and informative guidancefor future material design and selection. Based on above findings, we design twoIBSC materials, i.e., Cu_8Ga_7SnS_(16)and Cu_8Ga_7FeS_(16), which show that Cu_8Ga_7SnS_(16)is a suitable candidate as an IBSC material and that the weak absorption from theintermediate band to the conduction band limits the potential usage of Cu_8Ga_7FeS_(16).
引文
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