多元半导体及其合金的第一性原理计算研究
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摘要
多元化和合金化是设计新材料的两种重要途径,由于化学成分和结构自由度的增多,多元材料和合金材料将表现出各种丰富、独特的性质,大大拓宽了应用材料的选择范围。最近的发展显示,功能器件选择的半导体朝着多元化、合金化和低维化的方向发展,因而研究这一多元化和合金化过程中性质变化的规律非常重要。然而,自由度增多也意味着性质的更加复杂,相空间维数的增加使得从理论和实验上研究这类材料的难度骤增。值得庆幸的是,基于闪锌矿结构的半导体在这一过程中结构和性质保持着一定的稳定性,同时,第一性原理计算方法对这一体系的描述相对而言最为成熟,这两方面使得我们可以通过第一性原理计算来研究基于闪锌矿结构的半导体在多元化和合金化过程中性质变化的规律,分析元素的演化、替换和结构的转变对性质产生影响的趋势,从微观上系统地去理解大量反映不同侧面的实验结果,为设计具备特定性能参量的半导体提供基础。
本论文共分六章。第一章介绍了最近多元半导体和合金在应用方面的发展、相图及性质的一般规律、有序结构的出现和特点、以及常见半导体的能带偏移。第二章简要介绍了本论文涉及的计算方法,包括基于单电子近似的传统能带计算方法、基于密度泛函理论的第一性原理计算方法、以及用于半导体合金的价力场弹性能方法。本论文主要使用第一性原理计算方法,在第二章,也给出了我们用价力场弹性能方法与第一性原理计算方法对几类半导体合金计算结果的比较。
第三章利用第一性原理计算系统研究了闪锌矿结构硫族半导体通过阳离子的替换从二元向三元、再向四元的演化。发现了三元和四元半导体中几个具有遗传特征的规律:对阳离子处于元素周期表中同行的硫族半导体,其基态结构总是有比较大的α晶格常数、比较小的四角晶系形变参数η=c/2α、负的价带顶晶体场劈裂、和较大的带隙;而对阳离子处于不同行的,这些规律只是部分的正确。基于能带成分和能带偏移计算结果的分析指出:从Ⅱ-Ⅵ向Ⅰ-Ⅲ-Ⅵ_2的演化中带隙的减小主要来自p—d杂化对价带的推高,导带的降低仅有约20%的贡献;而从Ⅰ-Ⅲ-Ⅵ_2到Ⅰ_2-Ⅱ-Ⅳ-Ⅵ_4的演化中,价带顶的移动几乎可以忽略,Ⅳ族原子较低的s轨道能级带来的导带降低决定了带隙的减小。与实验结果比较发现:Cu_2ZnGeSe_4和Cu_2ZnSnS_4类半导体的基态结构应为锌黄锡矿(kesterite)结构,实验上广泛观察到的黄锡矿(stannite)结构可能是由于X射线衍射图谱不能分辨原子序数接近的阳离子或Ⅰ-Ⅱ(001)层的部分无序化引起;Cu_2ZnSnSe_4的带隙应为1.0 eV左右,而非经常被引用的实验测量结果1.5eV,计算结果解释了光致发光谱的异常;根据计算,我们预测Cu_2ZnGeSe_4也有可能成为新的廉价太阳能电池材料。
第四章以三元-三元的混合,二元-三元的混合为思路,研究了两类合金体系的结构、能带结构特征。在CuGa-Ⅵ_2/AgGa-Ⅵ_2合金研究方面,我们系统解释了:Ag_xCu_(1-x)Ga-Ⅵ_2合金带隙随晶格常数增大这一反常能带趋势,并根据能带偏移分析了不同影响因素的贡献;通过SQS模拟黄铜矿结构三元-三元无序合金,研究了合金的微观结构,分析了其大带隙下凹参数的来源。在Ⅱ-Ⅵ/Ⅰ-Ⅲ-Ⅵ_2,Ⅲ-Ⅴ/Ⅱ-Ⅳ-Ⅴ_2有序合金研究方面,我们以设计高量子效率、100%自旋极化的电子源材料为目的,搜索了在x=0.5时不同阳离子组成的两类合金的有序结构,基于晶体场、自旋轨道耦合劈裂和能量稳定性等结果,提出三种合金作为潜在的极化电子源阴极材料。
第五章转向高硬度的BN/C_2合金的结构、弹性和强度等性质的研究。以澄清BC_2N硬度是否可能介于c-BN和金刚石之间为动机,系统研究了不同晶体结构性质上的规律,定量提出了BC_2N合金性质的键数规则,据此进行的无限制的结构搜索显示,BN/C_2(111)超晶格结构在众多相同原胞大小的结构中能量最低,结构最致密,体弹性模量最大。进一步的弹性常数、剪切模量、理想拉伸和剪切强度、以及垂直加压下的剪切强度计算显示,BC_2N和BC_4N(111)超晶格结构的剪切模量、理想强度和垂直加压下的剪切强度都高于其他BC_2N结构,也高于c-BN,这些超晶格结构表现出很强的反抗弹性形变和塑性形变的能力,因而可能具有较c-BN高的硬度。一个重要的发现是,对这类合金系统,计算的剪切模量和垂直加压下的剪切强度都与实验测量的硬度呈准线性关系,表明这两个量是预测这类合金硬度的合适的物理量。该章还讨论了BC_2N不同结构的结构转变、带隙和光学介电函数等性质。
第六章回顾所有章节,并讨论现有研究的不足和未来进一步改进的方法。
As a result of the increased chemical and structural freedom,multiternary and alloy semiconductors exhibit novel and special properties which give rise to potential application as functional materials.The increased freedom also makes the study of these materials so complicated that the dimension of the phase space increases with the number of elements and atomic positions in the primitive cell. The rapidly-developing first-principles calculation methods make it possible to study the changes of properties in the mutation from simple to multiternay and alloy semiconductors theoretically,to show the trend in the element substitution and structural transformation,understand various experimental results and give the theoretical guidelines for knowledge-based design of new semiconductors.
The thesis is composed of six chapters.The first chapter gives an introduction to the recent development in the application of semiconductors,the phase diagram and properties of alloys,the ordered structures,and the band offsets of popular semiconductors.The second chapter devotes to the simulation methods used in the study,including conventional band structure theory,density functional theory and valence force field method.
The third chapter discusses the sequential cation cross-substitution in zincblende chalcogenide semiconductors,from binary to ternary to quaternary compounds. Several universal trends are found for the ternary and quaternary chalcogenides with common-row cations,the lowest-energy structure always has larger lattice constant a,smaller tetragonal distortion parameterη= c/2a,negative crystal field splitting at the top of the valence band,and larger band gap compared to the metastable structures.The band offsets and band character decomposition analysis show,the gap decreases fromⅡ-ⅥtoⅠ-Ⅲ-Ⅵ_2 are mostly due to the p-d repulsion in the valence band,while the decreases fromⅠ-Ⅲ-Ⅵ_2 toⅠ_2-Ⅱ-Ⅳ-Ⅵ_4 are due to the downshift in the conduction band caused by the wavefunction localization on the groupⅣcation site.We propose that common-row-cationⅠ_2-Ⅱ-Ⅳ-Ⅵ_4 compounds are more stable in the kesterite structure, and the band gap of Cu_2ZnSnSe_4 is on the order of 1.0 eV,which are both misunderstood by previous experimental study,and we also propose Cu_2ZnGeSe_4 has a ideal band gap as a single-junction solar cell absorber.
The forth chapter deals with two ternary-ternary,binary-ternary alloys.We first explained the band structure anomaly of Ag_xCu_(1-x)Ga-Ⅵ_2 alloy that the gap increases with the lattice constant,and then using the SQS to describe the disordered alloys,we studied the local structure in the alloy and the reason of large band gap bowing parameter.In the second part,we studiedⅡ-Ⅵ/Ⅰ-Ⅲ-Ⅵ_2,Ⅲ-Ⅴ/Ⅱ-Ⅳ-Ⅴ_2 ordered alloys at x = 0.5,to design high efficiency,100% spin-polarized electron source materials.A series of ordered alloys with different cations are screened based on the crystal field splitting,spin-orbital splitting and energy stability,three of which are proposed as candidates.
The fifth chapter concentrates on the superhard BN/C_2 alloys.To resolve the debate if BC_2N could be harder than c-BN,we systematically studied different crystal structures and gave a quantitative bond counting rule,based on which we performed an unconstrained structure search and identified BN/C_2(111) super-lattices as the lowest-energy,most-compact,most-volume-incompressible struc-tures with the same cell size.The further calculation of elastic constants,shear modulus,ideal strength,and shear strength with normal compression showed that the(111) superlattices possess stronger resistance to elastic and plastic deformation than other BC_2N structures as well as c-BN,thus could be harder than c-BN.The calculated shear modulus and shear strength under normal compression are linearly related with the measured Vickers hardness for BN/C_2 alloys, hence could be used as a predictor of hardness.The structural transformation, band gap and optical dielectric function are also studied for different BC_2N structures.
The sixth chapter summarizes all the research and discusses the potential improvement.
本论文共分六章。第一章介绍了最近多元半导体和合金在应用方面的发展、相图及性质的一般规律、有序结构的出现和特点、以及常见半导体的能带偏移。第二章简要介绍了本论文涉及的计算方法,包括基于单电子近似的传统能带计算方法、基于密度泛函理论的第一性原理计算方法、以及用于半导体合金的价力场弹性能方法。本论文主要使用第一性原理计算方法,在第二章,也给出了我们用价力场弹性能方法与第一性原理计算方法对几类半导体合金计算结果的比较。
第三章利用第一性原理计算系统研究了闪锌矿结构硫族半导体通过阳离子的替换从二元向三元、再向四元的演化。发现了三元和四元半导体中几个具有遗传特征的规律:对阳离子处于元素周期表中同行的硫族半导体,其基态结构总是有比较大的α晶格常数、比较小的四角晶系形变参数η=c/2α、负的价带顶晶体场劈裂、和较大的带隙;而对阳离子处于不同行的,这些规律只是部分的正确。基于能带成分和能带偏移计算结果的分析指出:从Ⅱ-Ⅵ向Ⅰ-Ⅲ-Ⅵ_2的演化中带隙的减小主要来自p—d杂化对价带的推高,导带的降低仅有约20%的贡献;而从Ⅰ-Ⅲ-Ⅵ_2到Ⅰ_2-Ⅱ-Ⅳ-Ⅵ_4的演化中,价带顶的移动几乎可以忽略,Ⅳ族原子较低的s轨道能级带来的导带降低决定了带隙的减小。与实验结果比较发现:Cu_2ZnGeSe_4和Cu_2ZnSnS_4类半导体的基态结构应为锌黄锡矿(kesterite)结构,实验上广泛观察到的黄锡矿(stannite)结构可能是由于X射线衍射图谱不能分辨原子序数接近的阳离子或Ⅰ-Ⅱ(001)层的部分无序化引起;Cu_2ZnSnSe_4的带隙应为1.0 eV左右,而非经常被引用的实验测量结果1.5eV,计算结果解释了光致发光谱的异常;根据计算,我们预测Cu_2ZnGeSe_4也有可能成为新的廉价太阳能电池材料。
第四章以三元-三元的混合,二元-三元的混合为思路,研究了两类合金体系的结构、能带结构特征。在CuGa-Ⅵ_2/AgGa-Ⅵ_2合金研究方面,我们系统解释了:Ag_xCu_(1-x)Ga-Ⅵ_2合金带隙随晶格常数增大这一反常能带趋势,并根据能带偏移分析了不同影响因素的贡献;通过SQS模拟黄铜矿结构三元-三元无序合金,研究了合金的微观结构,分析了其大带隙下凹参数的来源。在Ⅱ-Ⅵ/Ⅰ-Ⅲ-Ⅵ_2,Ⅲ-Ⅴ/Ⅱ-Ⅳ-Ⅴ_2有序合金研究方面,我们以设计高量子效率、100%自旋极化的电子源材料为目的,搜索了在x=0.5时不同阳离子组成的两类合金的有序结构,基于晶体场、自旋轨道耦合劈裂和能量稳定性等结果,提出三种合金作为潜在的极化电子源阴极材料。
第五章转向高硬度的BN/C_2合金的结构、弹性和强度等性质的研究。以澄清BC_2N硬度是否可能介于c-BN和金刚石之间为动机,系统研究了不同晶体结构性质上的规律,定量提出了BC_2N合金性质的键数规则,据此进行的无限制的结构搜索显示,BN/C_2(111)超晶格结构在众多相同原胞大小的结构中能量最低,结构最致密,体弹性模量最大。进一步的弹性常数、剪切模量、理想拉伸和剪切强度、以及垂直加压下的剪切强度计算显示,BC_2N和BC_4N(111)超晶格结构的剪切模量、理想强度和垂直加压下的剪切强度都高于其他BC_2N结构,也高于c-BN,这些超晶格结构表现出很强的反抗弹性形变和塑性形变的能力,因而可能具有较c-BN高的硬度。一个重要的发现是,对这类合金系统,计算的剪切模量和垂直加压下的剪切强度都与实验测量的硬度呈准线性关系,表明这两个量是预测这类合金硬度的合适的物理量。该章还讨论了BC_2N不同结构的结构转变、带隙和光学介电函数等性质。
第六章回顾所有章节,并讨论现有研究的不足和未来进一步改进的方法。
As a result of the increased chemical and structural freedom,multiternary and alloy semiconductors exhibit novel and special properties which give rise to potential application as functional materials.The increased freedom also makes the study of these materials so complicated that the dimension of the phase space increases with the number of elements and atomic positions in the primitive cell. The rapidly-developing first-principles calculation methods make it possible to study the changes of properties in the mutation from simple to multiternay and alloy semiconductors theoretically,to show the trend in the element substitution and structural transformation,understand various experimental results and give the theoretical guidelines for knowledge-based design of new semiconductors.
The thesis is composed of six chapters.The first chapter gives an introduction to the recent development in the application of semiconductors,the phase diagram and properties of alloys,the ordered structures,and the band offsets of popular semiconductors.The second chapter devotes to the simulation methods used in the study,including conventional band structure theory,density functional theory and valence force field method.
The third chapter discusses the sequential cation cross-substitution in zincblende chalcogenide semiconductors,from binary to ternary to quaternary compounds. Several universal trends are found for the ternary and quaternary chalcogenides with common-row cations,the lowest-energy structure always has larger lattice constant a,smaller tetragonal distortion parameterη= c/2a,negative crystal field splitting at the top of the valence band,and larger band gap compared to the metastable structures.The band offsets and band character decomposition analysis show,the gap decreases fromⅡ-ⅥtoⅠ-Ⅲ-Ⅵ_2 are mostly due to the p-d repulsion in the valence band,while the decreases fromⅠ-Ⅲ-Ⅵ_2 toⅠ_2-Ⅱ-Ⅳ-Ⅵ_4 are due to the downshift in the conduction band caused by the wavefunction localization on the groupⅣcation site.We propose that common-row-cationⅠ_2-Ⅱ-Ⅳ-Ⅵ_4 compounds are more stable in the kesterite structure, and the band gap of Cu_2ZnSnSe_4 is on the order of 1.0 eV,which are both misunderstood by previous experimental study,and we also propose Cu_2ZnGeSe_4 has a ideal band gap as a single-junction solar cell absorber.
The forth chapter deals with two ternary-ternary,binary-ternary alloys.We first explained the band structure anomaly of Ag_xCu_(1-x)Ga-Ⅵ_2 alloy that the gap increases with the lattice constant,and then using the SQS to describe the disordered alloys,we studied the local structure in the alloy and the reason of large band gap bowing parameter.In the second part,we studiedⅡ-Ⅵ/Ⅰ-Ⅲ-Ⅵ_2,Ⅲ-Ⅴ/Ⅱ-Ⅳ-Ⅴ_2 ordered alloys at x = 0.5,to design high efficiency,100% spin-polarized electron source materials.A series of ordered alloys with different cations are screened based on the crystal field splitting,spin-orbital splitting and energy stability,three of which are proposed as candidates.
The fifth chapter concentrates on the superhard BN/C_2 alloys.To resolve the debate if BC_2N could be harder than c-BN,we systematically studied different crystal structures and gave a quantitative bond counting rule,based on which we performed an unconstrained structure search and identified BN/C_2(111) super-lattices as the lowest-energy,most-compact,most-volume-incompressible struc-tures with the same cell size.The further calculation of elastic constants,shear modulus,ideal strength,and shear strength with normal compression showed that the(111) superlattices possess stronger resistance to elastic and plastic deformation than other BC_2N structures as well as c-BN,thus could be harder than c-BN.The calculated shear modulus and shear strength under normal compression are linearly related with the measured Vickers hardness for BN/C_2 alloys, hence could be used as a predictor of hardness.The structural transformation, band gap and optical dielectric function are also studied for different BC_2N structures.
The sixth chapter summarizes all the research and discusses the potential improvement.
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