硅基光电子材料和稀磁材料的计算设计
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摘要
众所周知,硅是当今微电子技术的首选材料,而且硅微电子工艺也已经发展的很成熟。然而,由于体材料硅是一种间接带隙半导体,其跃迁过程必须要借助于声子的参与,因此不能成为有效的光发射体。近来的研究表明采用硅基纳米结构有可能得到具有直接带隙的硅基材料,可是当前的固体电子理论对一个给定的晶体结构,只有在计算它的电子结构后才能断定其是否具有直接带隙。如何通过已有的物理学原理和可行的微加工技术设计具有直接带隙特性的硅基新材料并使其成为有效的光发射体就成为一项极具挑战性的工作。
长期以来,人们都知道固体的能带结构与其对称性是密切相关的。通过对大量半导体的能带结构与对称性关系的分析,我们发现Oh点群对称的材料几乎全是间接带隙材料;化合物半导体主要有两种对称性,Td和C6v,具有Td对称性的闪锌结构材料大部分为直接带隙,小部分为间接带隙;而对称性更低的C6v六角对称材料则几乎全是直接带隙材料。因此,我们相信通过降低晶体的对称性可以作为设计具有直接带隙硅基材料的一个经验性原则。要降低硅晶体的对称性通常有两种较简便的方法:一种是通过原子的替位,也即在硅晶中用其他的原子替代硅原子;另一种称为插入层生长,将插入的原子周期性的整层生长在硅晶上。在本文中,考虑了插入原子的电负性差效应和芯态效应,我们分别用上述两种方法设计了两类硅基超晶格材料,得到了几种具有直接带隙结构的硅基材料。
另一方面,人们一直对发展将电、磁集为一体的稀磁半导体抱有浓厚的兴趣。最近有实验报道,在锗上获得了居里温度达到285K的铁磁性稀磁材料MnxGe1-x。而后的理论计算表明在硅上也可能获得接近室温下的Mn掺杂硅基稀磁半导体材料MnxSi1-x。研究人员试图用长程铁磁性与短程反铁磁性的竞争,平均场理论,RKKY理论等对它们的铁磁性进行解释,可是,对于它们为什么表现出铁磁性的机理还有待进一步的探索。我们尝试通过改变掺入的过渡金属原子的种类和掺入时的位置两种途径来分析硅、锗稀磁材料中磁性的变化特点,并利用RKKY理论对相应稀磁半导体的居里温度作了预测。
本论文可分为两部分。第一部分介绍了研究工作所涉及的基本理论和第一原理方法。首先介绍了密度泛函理论,包括密度泛函理论的基本思想、Hobenberg-Kohn定理、Kohn-Sham方程、交换关联近似和GW修正等。接着介绍了本研究工作中所采用的具体电子结构计算方法,即平面波展开的第一性原理赝势法。并对基于平面波赝势法的VASP程序包的特点作了介绍。第二部分共有三章,分别介绍我们的研究工作和结果。
在第三章中,我们采用插入层生长的方法,分别在Si(001)面周期性的插入单层VI族、V族和III-V族原子。同时考虑到Si(001)表面不同的重构方式,即(2×1)和(2×2)两种结构,分别进行了第一性原理计算。经过计算,我们得到了两种在Г点具有直接带隙的超晶格Se/Si5/VI/Si5/Se和Se/Si6/VI/Si6/Se(VI=O,S,Se),而且研究表明(2×2)结构的Se/Si5/VI/Si5/Se超晶格比(2×1)结构的超晶格Se/Si6/VI/Si6/Se具有更好的能带特性。而在第四章中,我们用原子替位的方法在Si(001)面上设计了一种新的超晶格Si1-yXy/Si(X=C,Ge,Sn,Ti,Zr; y=0.125,0.25,0.5),计算表明超晶格Si1-ySny/S(iy=0.125)和Si1-yGey/Si(y=0.125,0.25)具有直接带隙结构。对上面两类超晶格能带结构的分析,使我们认识到降低晶体的对称性能有效改变晶体的能带结构,而选择芯态较大且与硅的电负性差小的插层原子能有助于硅基超晶格的能带结构向直接带隙转变。
在第五章中,尝试在硅和锗中分别掺入V、Cr、Mn、Fe、Co、Ni,讨论了它们对硅,锗稀磁半导体的影响。认为掺入Cr、Mn、Fe原子容易获得较大的磁矩,而且掺Mn的铁磁性最明显。而后讨论了在硅,锗不同的格点上掺入Cr、Mn、Fe的稀磁性质。研究表明,Cr掺杂的稀磁材料大多表现为反铁磁性;Mn掺杂的硅基材料铁磁性满足长程铁磁性与短程反铁磁性竞争理论,而锗基Mn掺杂稀磁材料的铁磁性更适合用RKKY模型解释;Fe掺杂的稀磁材料的铁磁性与Fe的浓度密切相关,随着Fe浓度的增加,铁磁性也增强,而且增大Fe掺杂稀磁半导体的晶格常数,也会有助于其向铁磁性的转变。
As well known, silicon is the dominant material for microelectronics and the fabrication technology is quite mature. However, due to its indirect band-gap, the light emission can occur only when accompanied with an emission of phonons and it has been considered unsuitable as bulk material for optoelectronic applications. Using Si-based nanostructures, this problem can be solved partly as has been recently reported. In conventional electronic structure theory of solids, about the band-gap type, direct gap or indirect-gap under a given crystal structure, the answer is always provided after the electronic structure calculations. As a result, a great challenge to experimenters and theorists is that how to make or design an efficient Si-based light emission material using an advanced technology and physics principles.
As one known, the band structure of solid depends on the crystal symmetry, this is a fact known for a long time. Based on a statistical analysis for the band gap type and crystal symmetry, we find that all of the semiconductors with Oh point group symmetry have an indirect gap property, whereas those of C6v symmetry have a direct gap, and the semiconductors with Td symmetry are laid between them. The results indicate clearly that the symmetry reduction (i.e., decreasing a group order) will be advantageous to develop a direct band-gap semiconductor. In order to reduce symmetry, there are two conventional methods can be provided to selection: one is the atomic substitute method, i.e., substitute other atoms for silicons in Si lattice. Another method is so-called the intercalation growth, in which the intercalation atoms are located on a same crystal plane in silicon lattice. With the consideration of the size of core states and the electro-negativity difference between the component atoms in solids, we design several kinds of Si-based superlattices (SLs). The results show that some of them are direct band-gap semiconductors.
On the other hand, diluted magnetic semiconductors (DMSs) have stimulated a great deal interest because of their potential application in the spintronics, in which the electron spin becomes another degree of freedom in addition to the usual charge degree of freedom. Ferromagnetism (FM) in the MnxGe1-x compound has been reported and the Curie temperature is up to 285K. Moreover, a recent calculation where both MnxGe1-x and MnxSi1-x were studied declared that it were possible to make room-temperature FM MnxSi1-x. However, the origin of the FM in IV semiconductors is still a matter of debate, and several different mechanisms, such as the competition between a long-range FM interaction and a short-range AFM interaction, mean field theory, Ruderman-Kittel-Kasuya-Yoshida (RKKY), have been proposed. In the dissertation, a similar study is extended to the different transition metals (TM). Comparison between these DMSs allows us to investigate variations of magnetic properties with a change of dopants and their site locations. The Curie temperature is also predicted by RKKY theory.
This dissertation consists of two parts. The first part presents the calculation methods and its theoretical basis. We firstly introduce the density functional theory (DFT), including Hobenberg-Kohn theorem, Kohn-Sham equations, the approximations for exchange and correlations and GW approximation. And then, we describe the details of computational methods used in our work, i.e., the ab initio pseudopotential methods with the plane wave basis expansion of the wavefunction. We also present the major characters of the Vienna ab initio Simulation Packages (VASP). The second part which divided into three chapters presents the main results of the present dissertation.
In the third chapter, ab initio pseudoptential method has been employed to investigate the electronic properties of Si-based SLs designed by the intercalation growth method, which consisted of one monolayer inserted atoms, such as group-VI, group-V or group III and V atoms, along the Si(001) direction periodically. The different surface reconstruction models, (i.e., (2x1) and (2x2)), were also discussed. The results show that the SLs Se/Si5/VI/Si5/Se and Se/Si6/VI/Si6/Se (VI=O,S,Se) have a direct band-gap atГpoint. Furthermore, the band structure of Se/Si5/VI/Si5/Se with a (2x2) surface structure is better than that of Se/Si6/VI/Si6/Se with a (2x1) structure. In the fourth chapter, we presented computational design of SLs Si1-yXy/Si (X=C,Ge,Sn,Ti,Zr; y=0.125,0.25,0.5) using the atomic substitute method. Our calculations reveal that the SLs Si1-ySny/Si (y=0.125) and Si1-yGey/Si (y=0.125,0.25) are theГ-point direct band-gap semiconductors. Based on the analysis of those SLs mentioned above, we draw some conclusions that the symmetry reduction, accompanied with a bigger core states of inserted atoms and less electronegativity difference between the component atoms, will be advantageous to develop a direct band-gap semiconductor.
In the fifth chapter, the magnetic properties of TM-doped Si or Ge (TM=V,Cr,Mn,Fe,Co, Ni) has been studied. It is believed that the magnetic properties on Cr-, Mn- and Fe-doped DMSs is better, especially for Mn. Furthermore, we investigated the variations of magnetic properties on Cr-, Mn- and Fe-doped DMSs respectively, with a change of their site locations. The main results can be described as below. For the Cr-doped DMSs, the AFM order is energetically more favored than the FM order. For the Mn-doped Si DMSs can be explained by the competition between a long-range FM interaction and a short-range AFM interaction, and for the Mn-doped Ge DMSs are more like a RKKY FM semiconductors. For the Fe-doped DMSs, we found the higher Fe concentrations and larger lattice constants will enhance the ferromagnetism.
长期以来,人们都知道固体的能带结构与其对称性是密切相关的。通过对大量半导体的能带结构与对称性关系的分析,我们发现Oh点群对称的材料几乎全是间接带隙材料;化合物半导体主要有两种对称性,Td和C6v,具有Td对称性的闪锌结构材料大部分为直接带隙,小部分为间接带隙;而对称性更低的C6v六角对称材料则几乎全是直接带隙材料。因此,我们相信通过降低晶体的对称性可以作为设计具有直接带隙硅基材料的一个经验性原则。要降低硅晶体的对称性通常有两种较简便的方法:一种是通过原子的替位,也即在硅晶中用其他的原子替代硅原子;另一种称为插入层生长,将插入的原子周期性的整层生长在硅晶上。在本文中,考虑了插入原子的电负性差效应和芯态效应,我们分别用上述两种方法设计了两类硅基超晶格材料,得到了几种具有直接带隙结构的硅基材料。
另一方面,人们一直对发展将电、磁集为一体的稀磁半导体抱有浓厚的兴趣。最近有实验报道,在锗上获得了居里温度达到285K的铁磁性稀磁材料MnxGe1-x。而后的理论计算表明在硅上也可能获得接近室温下的Mn掺杂硅基稀磁半导体材料MnxSi1-x。研究人员试图用长程铁磁性与短程反铁磁性的竞争,平均场理论,RKKY理论等对它们的铁磁性进行解释,可是,对于它们为什么表现出铁磁性的机理还有待进一步的探索。我们尝试通过改变掺入的过渡金属原子的种类和掺入时的位置两种途径来分析硅、锗稀磁材料中磁性的变化特点,并利用RKKY理论对相应稀磁半导体的居里温度作了预测。
本论文可分为两部分。第一部分介绍了研究工作所涉及的基本理论和第一原理方法。首先介绍了密度泛函理论,包括密度泛函理论的基本思想、Hobenberg-Kohn定理、Kohn-Sham方程、交换关联近似和GW修正等。接着介绍了本研究工作中所采用的具体电子结构计算方法,即平面波展开的第一性原理赝势法。并对基于平面波赝势法的VASP程序包的特点作了介绍。第二部分共有三章,分别介绍我们的研究工作和结果。
在第三章中,我们采用插入层生长的方法,分别在Si(001)面周期性的插入单层VI族、V族和III-V族原子。同时考虑到Si(001)表面不同的重构方式,即(2×1)和(2×2)两种结构,分别进行了第一性原理计算。经过计算,我们得到了两种在Г点具有直接带隙的超晶格Se/Si5/VI/Si5/Se和Se/Si6/VI/Si6/Se(VI=O,S,Se),而且研究表明(2×2)结构的Se/Si5/VI/Si5/Se超晶格比(2×1)结构的超晶格Se/Si6/VI/Si6/Se具有更好的能带特性。而在第四章中,我们用原子替位的方法在Si(001)面上设计了一种新的超晶格Si1-yXy/Si(X=C,Ge,Sn,Ti,Zr; y=0.125,0.25,0.5),计算表明超晶格Si1-ySny/S(iy=0.125)和Si1-yGey/Si(y=0.125,0.25)具有直接带隙结构。对上面两类超晶格能带结构的分析,使我们认识到降低晶体的对称性能有效改变晶体的能带结构,而选择芯态较大且与硅的电负性差小的插层原子能有助于硅基超晶格的能带结构向直接带隙转变。
在第五章中,尝试在硅和锗中分别掺入V、Cr、Mn、Fe、Co、Ni,讨论了它们对硅,锗稀磁半导体的影响。认为掺入Cr、Mn、Fe原子容易获得较大的磁矩,而且掺Mn的铁磁性最明显。而后讨论了在硅,锗不同的格点上掺入Cr、Mn、Fe的稀磁性质。研究表明,Cr掺杂的稀磁材料大多表现为反铁磁性;Mn掺杂的硅基材料铁磁性满足长程铁磁性与短程反铁磁性竞争理论,而锗基Mn掺杂稀磁材料的铁磁性更适合用RKKY模型解释;Fe掺杂的稀磁材料的铁磁性与Fe的浓度密切相关,随着Fe浓度的增加,铁磁性也增强,而且增大Fe掺杂稀磁半导体的晶格常数,也会有助于其向铁磁性的转变。
As well known, silicon is the dominant material for microelectronics and the fabrication technology is quite mature. However, due to its indirect band-gap, the light emission can occur only when accompanied with an emission of phonons and it has been considered unsuitable as bulk material for optoelectronic applications. Using Si-based nanostructures, this problem can be solved partly as has been recently reported. In conventional electronic structure theory of solids, about the band-gap type, direct gap or indirect-gap under a given crystal structure, the answer is always provided after the electronic structure calculations. As a result, a great challenge to experimenters and theorists is that how to make or design an efficient Si-based light emission material using an advanced technology and physics principles.
As one known, the band structure of solid depends on the crystal symmetry, this is a fact known for a long time. Based on a statistical analysis for the band gap type and crystal symmetry, we find that all of the semiconductors with Oh point group symmetry have an indirect gap property, whereas those of C6v symmetry have a direct gap, and the semiconductors with Td symmetry are laid between them. The results indicate clearly that the symmetry reduction (i.e., decreasing a group order) will be advantageous to develop a direct band-gap semiconductor. In order to reduce symmetry, there are two conventional methods can be provided to selection: one is the atomic substitute method, i.e., substitute other atoms for silicons in Si lattice. Another method is so-called the intercalation growth, in which the intercalation atoms are located on a same crystal plane in silicon lattice. With the consideration of the size of core states and the electro-negativity difference between the component atoms in solids, we design several kinds of Si-based superlattices (SLs). The results show that some of them are direct band-gap semiconductors.
On the other hand, diluted magnetic semiconductors (DMSs) have stimulated a great deal interest because of their potential application in the spintronics, in which the electron spin becomes another degree of freedom in addition to the usual charge degree of freedom. Ferromagnetism (FM) in the MnxGe1-x compound has been reported and the Curie temperature is up to 285K. Moreover, a recent calculation where both MnxGe1-x and MnxSi1-x were studied declared that it were possible to make room-temperature FM MnxSi1-x. However, the origin of the FM in IV semiconductors is still a matter of debate, and several different mechanisms, such as the competition between a long-range FM interaction and a short-range AFM interaction, mean field theory, Ruderman-Kittel-Kasuya-Yoshida (RKKY), have been proposed. In the dissertation, a similar study is extended to the different transition metals (TM). Comparison between these DMSs allows us to investigate variations of magnetic properties with a change of dopants and their site locations. The Curie temperature is also predicted by RKKY theory.
This dissertation consists of two parts. The first part presents the calculation methods and its theoretical basis. We firstly introduce the density functional theory (DFT), including Hobenberg-Kohn theorem, Kohn-Sham equations, the approximations for exchange and correlations and GW approximation. And then, we describe the details of computational methods used in our work, i.e., the ab initio pseudopotential methods with the plane wave basis expansion of the wavefunction. We also present the major characters of the Vienna ab initio Simulation Packages (VASP). The second part which divided into three chapters presents the main results of the present dissertation.
In the third chapter, ab initio pseudoptential method has been employed to investigate the electronic properties of Si-based SLs designed by the intercalation growth method, which consisted of one monolayer inserted atoms, such as group-VI, group-V or group III and V atoms, along the Si(001) direction periodically. The different surface reconstruction models, (i.e., (2x1) and (2x2)), were also discussed. The results show that the SLs Se/Si5/VI/Si5/Se and Se/Si6/VI/Si6/Se (VI=O,S,Se) have a direct band-gap atГpoint. Furthermore, the band structure of Se/Si5/VI/Si5/Se with a (2x2) surface structure is better than that of Se/Si6/VI/Si6/Se with a (2x1) structure. In the fourth chapter, we presented computational design of SLs Si1-yXy/Si (X=C,Ge,Sn,Ti,Zr; y=0.125,0.25,0.5) using the atomic substitute method. Our calculations reveal that the SLs Si1-ySny/Si (y=0.125) and Si1-yGey/Si (y=0.125,0.25) are theГ-point direct band-gap semiconductors. Based on the analysis of those SLs mentioned above, we draw some conclusions that the symmetry reduction, accompanied with a bigger core states of inserted atoms and less electronegativity difference between the component atoms, will be advantageous to develop a direct band-gap semiconductor.
In the fifth chapter, the magnetic properties of TM-doped Si or Ge (TM=V,Cr,Mn,Fe,Co, Ni) has been studied. It is believed that the magnetic properties on Cr-, Mn- and Fe-doped DMSs is better, especially for Mn. Furthermore, we investigated the variations of magnetic properties on Cr-, Mn- and Fe-doped DMSs respectively, with a change of their site locations. The main results can be described as below. For the Cr-doped DMSs, the AFM order is energetically more favored than the FM order. For the Mn-doped Si DMSs can be explained by the competition between a long-range FM interaction and a short-range AFM interaction, and for the Mn-doped Ge DMSs are more like a RKKY FM semiconductors. For the Fe-doped DMSs, we found the higher Fe concentrations and larger lattice constants will enhance the ferromagnetism.
引文
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