过渡金属双原子掺杂硅团簇的理论研究
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摘要
团簇作为连接微观原子分子和宏观凝聚态物质间的桥梁,具有许多奇特的性质,其物理、化学性质随尺寸发生显著变化。人们希望通过对团簇的研究,实现以团簇作为基元组装出各种纳米功能材料和器件的目标。硅基半导体材料在微电子工业上的重要地位,使得硅团簇倍受重视。然而由于硅原子具有sp3杂化性质,不适合作为稳定的组装单元,为了稳定硅团簇,人们提出通过掺杂一些其它原子的方法来饱和硅团簇表面的悬键,而过渡金属原子以其独特的电磁特性,成为被研究最多的掺杂原子。由于计算量与结构复杂程度等因素的制约,以往的研究以掺杂单个过渡金属原子为主,对于多个金属原子共同掺杂的情况研究较少。本文通过基于密度泛函的第一性原理方法,对3d过渡金属双原子掺杂双棱柱硅笼MM'Si18 (M,M'=Ti,V,Cr,Mn,Fe,Co,Ni, Cu,Zn)以及过渡金属钨原子掺杂硅团簇WmSin(m=1,2;n=1-18)的几何结构、电磁性质、稳定性与电子数规则等进行了系统的研究。
采用第一性原理计算方法,我们对同种3d金属双原子掺杂双棱柱硅团簇M2Si18(M =Ti,V,Cr,Mn,Fe,Co,Ni,Cu,Zn)进行了系统地几何优化、电荷分析和能量计算。从几何结构来看,只有当掺杂金属原子的3d电子数在半满以下时.掺杂后团簇能够形成类双六棱柱的结构。自旋多重度和对称性与两过渡金属原子间的距离之间相互影响。除MMn外的3d过渡金属掺杂的M2Si18其金属原子间的距离都大于金属二聚物键长。结构相似的异构体中,自旋多重度较高的构型其过渡金属原子间距离较大。对称(?)较高的,特别是类双六棱柱的结构,其过渡金属原子间距离小于对称性较低的异构体。除Zn原子外,电荷总是从硅原子向过渡金属原子转移。除Co2Si18和Cr2Si18为自旋三重态外,其余M2Si18的磁矩均湮灭了,这与掺杂后体系的几何对称性下降有关。过渡金属原子闭壳层18电子数规则不能准确判定MM'Si18的稳定性,而基于电子气闭壳层模型的电子数幻数规则结合自旋守恒约束条件则成功预言了Fe2Si18的特殊稳定性。
为了丰富磁性与电子数样本,我们又进一步对异种3d金属双原子混合掺杂MM'Si18进行了系统研究。按照几何结构特点,MM'Si18团簇可以分为七类。除了某些Ti和V原子与Cr、Mn、Fe、Co等磁性原子混合掺杂外,其余情况下团簇中过渡金属间的距离均大于相应金属二聚物中的键长值。一些磁性较高的二聚物如VMn和CrMn:惨杂硅团簇MM'Si18后,体系的磁矩都下降到6μB以内,说明硅笼的存在导致磁性下降。在CrZuSi18以及所有不包含Zn原子的团簇中,电荷总是从硅原子向过渡金属原子转移。磁性方面,过渡金属原子的组合方式与团簇的磁性间存在明显的周期规律性,异种原子混合掺杂的团簇中只有3种磁性完全湮灭,其余团簇都具有一定的磁性,同时硅原子对整体磁性的贡献有所增加,特别是出现了硅原子对磁矩贡献大于金属原子的情况,这可能主要是由于体系对称性下降造成的。含有Ti原子的MM'Si18团簇往往比较稳定,而含有Zn的团簇则稳定性较差。过渡金属闭壳层的18电子数规则不能正确判定MM'Si18的稳定性,而基于电子气闭壳层的电子数规则结合自旋守恒条件约束,虽然在同种掺杂时成功预言了满足幻数34价电子要求的Fe2Si18的特殊稳定性,但是进一步研究发现在异种金属混合情况下幻数价电子的团簇稳定性明显低于Fe2Si18,因此这一电子数规则的确定性也令人质疑。除电子数规则外,团簇的对称性、掺杂原子的种类、过渡金属间距离、平均配位数、电子转移、磁矩分布都与MM'Si18团簇稳定性具有密切关系。
随后我们对单个钨原子掺杂的’WSin(n=1-12)进行了系统研究。随着硅原子数从1增加到12,团簇中钨原子的平衡位置从团簇的顶点、表而逐渐向团簇内部转移,到硅原子数目n=9时钨原子完全落入由硅原子构成的笼形结构中心位置,构成了包裂钨原子的硅笼结构。在这一转变临界尺度前后,WSin团簇的几何结构参数、电荷密度分布、稳定性等都发生了明显的变化。电荷总是从硅原子向钨原子转移,随着钨原了内嵌,钨原子上的电子数目明显增加。磁性方而,除子WSi和WSi2之外,其余基态结构均为自旋单重态无磁矩。掺杂钨原子后的硅团簇稳定性高于相应尺寸的纯硅团簇,最稳定的是六棱柱结构的WSi12,这与实验和之前的计算结果符合。
最后我们还对两个钨原子掺杂的W2Sin(n=1-18)进行了系统的计算。随着硅原子数目从7增加到18,两个钨原子依次嵌入硅笼,当n=10时一个钨原子完全嵌入硅笼中而另一个仍位于笼外,当n=14时,另一个的钨原子也开始嵌入硅笼,到n>16后两个钨原子完全嵌入硅笼。在钨原子依次嵌入的两个临界点前后,体系的几何结构、电荷分布和稳定性等许多物理量都出现了明显变化。随着尺寸的增加,团簇中两个钨原子的距离总体上呈现增加的趋势,体系表现出以钨原子为中心的笼形局域化分布趋势。虽然双钨原子掺杂后体系对称性较低,但存在着一些棱柱或层状结构随硅原子增加而连续演化的路径。电荷总是从硅原子向钨原子转移。内嵌的钨原子上的电荷数目大于笼外的钨原子,这一差异随着笼外钨原子的逐步内嵌而减小。在n=7-18的尺度范围之内,W2Sin的基态结构均为自旋单重态,净磁矩为零。结构最稳定的是W2Si18。在两个内嵌点前后,体系的平均结合能与嵌入能出现明显增加,说明内嵌有利于团簇稳定性的提高。同时片段能在内嵌点出现了明显的峰值,能量出现了明显地突变,这可以作为判定团簇尺度结构相变的重要依据。
The cluster is the bridge between microscopic atoms or molecules and macroscopic condensed materials. Clusters exhibit various size-dependent properties, which are differ-ent from those of bulk materials. It is expected that clusters could act as building blocks of various nanoscale function materials and devices. Silicon-based semiconductor occu-pies an important position in microelectronics industry,which makes silicon cluster the focus of extensive research. However,silicon clusters are unsuitable for building blocks due to their sp3 nature. Some people suggested that the dangling bonds on the surface of silicon cluster could be terminated by doping other atoms. Among all the doping atoms, transition metal (TM) atoms were paid more attentions for their unique electromagnetic properties. Restricted by calculating conditions, previous studies were mainly on single TM atoms doped into silicon clusters,and (?),ed silicon were seldom mentioned. In this work,the geometries,stabilities, electronic and magnetic properties of double 3d TM atoms doped biprism cagelike silicon clusters MM'Si18 (M,M'= Ti, V, Cr. Mn, Fe. Co. Ni, Cu, Zn) and W doped silicon clusters WmSin(m=1,2;n=1-18) have been investigated systematically.
Homogeneous double 3d TM atoms doped silicon clusters M2Si18(M=Ti,V,Cr. Mn,Fe, Co, Ni, Cu, Zn)have been systematically studied using density functional theory (DFT), and the optimized geometries,charge population and energies have been analyzed. It has been found that the biprism structure could keep only when the electron number of doping atoms is less than half-filled, The spin multiplicity and symmetry are related to the distance between two TM atoms. All the distance between TM atoms in the clusters are greater than that in the corresponding metal dimers, except Mn. Among isomers with similar structure, the distance between TM atom in the cluster is greater in clusters that has higher spin multiplicity. Charge always transfers from Si to TM atoms except Zn. Co2Si18 and Cr2Si18 have ground states of spin triplet, and in other clusters the magnetic moments annihilate,which may be concerned by the symmetry declines. 18 electron counting rule based on TM atoms closed shell fails to predict, stabilities of M2Si18,but the counting rule based on electron gas closed shell combined with spin conservation condition successfully predicts the special stability of Fe2Si18.
Additional calculation has been performed on heterogeneous double 3d TM atoms doped MM'Si18 clusters systemically in order to enrich the samples of magnetic moments and electron numbers.MM'Si18 could be divided into 7 classes by structural feature. Most of the distances in MM'Si18 is greater than that of corresponding TM dimer, except some clusters doped by Ti, V combined with magnetic atom such as Cr,Mn, Fe and Co. Some dimers with magnetic moments up to 10μB quench under 6μB after doped into silicon cages,indicating that silicon atoms reduce the magnetic moments of TM atoms. Charge always transfers from silicon atoms to TM atoms in CrZnSi18 and all the clusters with Zn atom. There are some interesting periodic laws between total magnetic moments and the compound mode of TM atoms. Among all the clusters doped by two different TM atoms, only 3 of them are nonmagnetic.The contribution of silicon atoms to the magnetic moments of clusters increased in the heterogeneous cases,and in some clusters the magnetic moments mainlv come from silicon atoms. Clusters with Ti atom doped are often more stable than others, while those containing Zn atom show poor stabilities. 18-electron counting rule based on the TM atoms closed shell also fails to predict stabilities of MM'Si18.The counting rule from electron gas closed shell combined with spin conservation condition is also doubtable, as stabilities of heterogeneous TM atoms doped cluster which meet the requirements of magic number of electron gas are much lower than Fe2Si18 Besides electron counting rule,other factors such as symmetries,heterogeneous doping, averaged coordination numbers and magnetic moments are concerned with stabilities of MM'Si18 clusters.
The structures,charge populations and stabilities of WSin(n=1-12) clusters have been studied systematically using density functional theory (DFT).For each cluster size, extensive search of lowest-energy structure has been conducted by considering a number of structural isomers. The equilibrium site of the W atom in the ground state structures of WSin clusters moves from the surface to the interior sites gradually, with the number of silicon atoms increasing from 1 to 12. Starting from WSi9,W atom is fully encapsulated by the silicon cage. At the critical point of embedding, the geometries, charge populations and stabilities change obviously. Charge always transfers from silicon to W atom, and the charge on W atom increases notable after embedding of tungsten. The magnetic moment of W atom completely quenched after n=3. The stability of doped cluster is higher than that of pure silicon at the corresponding size. The most stable cluster is WSi12 with a prim configuration,which is agree with the previous results.
Finally we calculated W2Sin(n=1-18),silicon clusters doped by double W atoms, based on the DFT method. With the increase of silicon from 7 to 18. the two doped W atoms embedded into silicon cluster one by one. When n-10, one tungsten atom is encapsulated by the silicon cage while another tungsten atom still stands outside the cage. Starting from n = 14, W atom outside begins to move into the cage,and completely embeds into cage after n = 16. At the critical points of embedding ,the geometries,charge populations and stabilities change obviously. With the increase of silicon atoms,the distance between two W atoms shows a tendency to increase, and the geometry of cluster tends to have a distribution that it forms two silicon cages centered by W atom. There is an obvious evolution path in which prim structure grows into biprim one. Charge always transfers from silicon to W atoms. The charge population of embedded tungsten atom is greater than that outside the cage,and the difference between them decreases gradually with the embedding of the W atom outside. At the size of n =7-18 all the magnetic moments of W2Sin quench. The most stable cluster is W2Si18.At the two critical points of embedding, the averaged binding energies and embedding energies of clusters increase obviously,indicating that embedment is in favor of improving stability. Meanwhile the fragment energies have two peak at critical points.showing the energy mutations.which may be regarded as a structural phase transition criterion of embedding.
采用第一性原理计算方法,我们对同种3d金属双原子掺杂双棱柱硅团簇M2Si18(M =Ti,V,Cr,Mn,Fe,Co,Ni,Cu,Zn)进行了系统地几何优化、电荷分析和能量计算。从几何结构来看,只有当掺杂金属原子的3d电子数在半满以下时.掺杂后团簇能够形成类双六棱柱的结构。自旋多重度和对称性与两过渡金属原子间的距离之间相互影响。除MMn外的3d过渡金属掺杂的M2Si18其金属原子间的距离都大于金属二聚物键长。结构相似的异构体中,自旋多重度较高的构型其过渡金属原子间距离较大。对称(?)较高的,特别是类双六棱柱的结构,其过渡金属原子间距离小于对称性较低的异构体。除Zn原子外,电荷总是从硅原子向过渡金属原子转移。除Co2Si18和Cr2Si18为自旋三重态外,其余M2Si18的磁矩均湮灭了,这与掺杂后体系的几何对称性下降有关。过渡金属原子闭壳层18电子数规则不能准确判定MM'Si18的稳定性,而基于电子气闭壳层模型的电子数幻数规则结合自旋守恒约束条件则成功预言了Fe2Si18的特殊稳定性。
为了丰富磁性与电子数样本,我们又进一步对异种3d金属双原子混合掺杂MM'Si18进行了系统研究。按照几何结构特点,MM'Si18团簇可以分为七类。除了某些Ti和V原子与Cr、Mn、Fe、Co等磁性原子混合掺杂外,其余情况下团簇中过渡金属间的距离均大于相应金属二聚物中的键长值。一些磁性较高的二聚物如VMn和CrMn:惨杂硅团簇MM'Si18后,体系的磁矩都下降到6μB以内,说明硅笼的存在导致磁性下降。在CrZuSi18以及所有不包含Zn原子的团簇中,电荷总是从硅原子向过渡金属原子转移。磁性方面,过渡金属原子的组合方式与团簇的磁性间存在明显的周期规律性,异种原子混合掺杂的团簇中只有3种磁性完全湮灭,其余团簇都具有一定的磁性,同时硅原子对整体磁性的贡献有所增加,特别是出现了硅原子对磁矩贡献大于金属原子的情况,这可能主要是由于体系对称性下降造成的。含有Ti原子的MM'Si18团簇往往比较稳定,而含有Zn的团簇则稳定性较差。过渡金属闭壳层的18电子数规则不能正确判定MM'Si18的稳定性,而基于电子气闭壳层的电子数规则结合自旋守恒条件约束,虽然在同种掺杂时成功预言了满足幻数34价电子要求的Fe2Si18的特殊稳定性,但是进一步研究发现在异种金属混合情况下幻数价电子的团簇稳定性明显低于Fe2Si18,因此这一电子数规则的确定性也令人质疑。除电子数规则外,团簇的对称性、掺杂原子的种类、过渡金属间距离、平均配位数、电子转移、磁矩分布都与MM'Si18团簇稳定性具有密切关系。
随后我们对单个钨原子掺杂的’WSin(n=1-12)进行了系统研究。随着硅原子数从1增加到12,团簇中钨原子的平衡位置从团簇的顶点、表而逐渐向团簇内部转移,到硅原子数目n=9时钨原子完全落入由硅原子构成的笼形结构中心位置,构成了包裂钨原子的硅笼结构。在这一转变临界尺度前后,WSin团簇的几何结构参数、电荷密度分布、稳定性等都发生了明显的变化。电荷总是从硅原子向钨原子转移,随着钨原了内嵌,钨原子上的电子数目明显增加。磁性方而,除子WSi和WSi2之外,其余基态结构均为自旋单重态无磁矩。掺杂钨原子后的硅团簇稳定性高于相应尺寸的纯硅团簇,最稳定的是六棱柱结构的WSi12,这与实验和之前的计算结果符合。
最后我们还对两个钨原子掺杂的W2Sin(n=1-18)进行了系统的计算。随着硅原子数目从7增加到18,两个钨原子依次嵌入硅笼,当n=10时一个钨原子完全嵌入硅笼中而另一个仍位于笼外,当n=14时,另一个的钨原子也开始嵌入硅笼,到n>16后两个钨原子完全嵌入硅笼。在钨原子依次嵌入的两个临界点前后,体系的几何结构、电荷分布和稳定性等许多物理量都出现了明显变化。随着尺寸的增加,团簇中两个钨原子的距离总体上呈现增加的趋势,体系表现出以钨原子为中心的笼形局域化分布趋势。虽然双钨原子掺杂后体系对称性较低,但存在着一些棱柱或层状结构随硅原子增加而连续演化的路径。电荷总是从硅原子向钨原子转移。内嵌的钨原子上的电荷数目大于笼外的钨原子,这一差异随着笼外钨原子的逐步内嵌而减小。在n=7-18的尺度范围之内,W2Sin的基态结构均为自旋单重态,净磁矩为零。结构最稳定的是W2Si18。在两个内嵌点前后,体系的平均结合能与嵌入能出现明显增加,说明内嵌有利于团簇稳定性的提高。同时片段能在内嵌点出现了明显的峰值,能量出现了明显地突变,这可以作为判定团簇尺度结构相变的重要依据。
The cluster is the bridge between microscopic atoms or molecules and macroscopic condensed materials. Clusters exhibit various size-dependent properties, which are differ-ent from those of bulk materials. It is expected that clusters could act as building blocks of various nanoscale function materials and devices. Silicon-based semiconductor occu-pies an important position in microelectronics industry,which makes silicon cluster the focus of extensive research. However,silicon clusters are unsuitable for building blocks due to their sp3 nature. Some people suggested that the dangling bonds on the surface of silicon cluster could be terminated by doping other atoms. Among all the doping atoms, transition metal (TM) atoms were paid more attentions for their unique electromagnetic properties. Restricted by calculating conditions, previous studies were mainly on single TM atoms doped into silicon clusters,and (?),ed silicon were seldom mentioned. In this work,the geometries,stabilities, electronic and magnetic properties of double 3d TM atoms doped biprism cagelike silicon clusters MM'Si18 (M,M'= Ti, V, Cr. Mn, Fe. Co. Ni, Cu, Zn) and W doped silicon clusters WmSin(m=1,2;n=1-18) have been investigated systematically.
Homogeneous double 3d TM atoms doped silicon clusters M2Si18(M=Ti,V,Cr. Mn,Fe, Co, Ni, Cu, Zn)have been systematically studied using density functional theory (DFT), and the optimized geometries,charge population and energies have been analyzed. It has been found that the biprism structure could keep only when the electron number of doping atoms is less than half-filled, The spin multiplicity and symmetry are related to the distance between two TM atoms. All the distance between TM atoms in the clusters are greater than that in the corresponding metal dimers, except Mn. Among isomers with similar structure, the distance between TM atom in the cluster is greater in clusters that has higher spin multiplicity. Charge always transfers from Si to TM atoms except Zn. Co2Si18 and Cr2Si18 have ground states of spin triplet, and in other clusters the magnetic moments annihilate,which may be concerned by the symmetry declines. 18 electron counting rule based on TM atoms closed shell fails to predict, stabilities of M2Si18,but the counting rule based on electron gas closed shell combined with spin conservation condition successfully predicts the special stability of Fe2Si18.
Additional calculation has been performed on heterogeneous double 3d TM atoms doped MM'Si18 clusters systemically in order to enrich the samples of magnetic moments and electron numbers.MM'Si18 could be divided into 7 classes by structural feature. Most of the distances in MM'Si18 is greater than that of corresponding TM dimer, except some clusters doped by Ti, V combined with magnetic atom such as Cr,Mn, Fe and Co. Some dimers with magnetic moments up to 10μB quench under 6μB after doped into silicon cages,indicating that silicon atoms reduce the magnetic moments of TM atoms. Charge always transfers from silicon atoms to TM atoms in CrZnSi18 and all the clusters with Zn atom. There are some interesting periodic laws between total magnetic moments and the compound mode of TM atoms. Among all the clusters doped by two different TM atoms, only 3 of them are nonmagnetic.The contribution of silicon atoms to the magnetic moments of clusters increased in the heterogeneous cases,and in some clusters the magnetic moments mainlv come from silicon atoms. Clusters with Ti atom doped are often more stable than others, while those containing Zn atom show poor stabilities. 18-electron counting rule based on the TM atoms closed shell also fails to predict stabilities of MM'Si18.The counting rule from electron gas closed shell combined with spin conservation condition is also doubtable, as stabilities of heterogeneous TM atoms doped cluster which meet the requirements of magic number of electron gas are much lower than Fe2Si18 Besides electron counting rule,other factors such as symmetries,heterogeneous doping, averaged coordination numbers and magnetic moments are concerned with stabilities of MM'Si18 clusters.
The structures,charge populations and stabilities of WSin(n=1-12) clusters have been studied systematically using density functional theory (DFT).For each cluster size, extensive search of lowest-energy structure has been conducted by considering a number of structural isomers. The equilibrium site of the W atom in the ground state structures of WSin clusters moves from the surface to the interior sites gradually, with the number of silicon atoms increasing from 1 to 12. Starting from WSi9,W atom is fully encapsulated by the silicon cage. At the critical point of embedding, the geometries, charge populations and stabilities change obviously. Charge always transfers from silicon to W atom, and the charge on W atom increases notable after embedding of tungsten. The magnetic moment of W atom completely quenched after n=3. The stability of doped cluster is higher than that of pure silicon at the corresponding size. The most stable cluster is WSi12 with a prim configuration,which is agree with the previous results.
Finally we calculated W2Sin(n=1-18),silicon clusters doped by double W atoms, based on the DFT method. With the increase of silicon from 7 to 18. the two doped W atoms embedded into silicon cluster one by one. When n-10, one tungsten atom is encapsulated by the silicon cage while another tungsten atom still stands outside the cage. Starting from n = 14, W atom outside begins to move into the cage,and completely embeds into cage after n = 16. At the critical points of embedding ,the geometries,charge populations and stabilities change obviously. With the increase of silicon atoms,the distance between two W atoms shows a tendency to increase, and the geometry of cluster tends to have a distribution that it forms two silicon cages centered by W atom. There is an obvious evolution path in which prim structure grows into biprim one. Charge always transfers from silicon to W atoms. The charge population of embedded tungsten atom is greater than that outside the cage,and the difference between them decreases gradually with the embedding of the W atom outside. At the size of n =7-18 all the magnetic moments of W2Sin quench. The most stable cluster is W2Si18.At the two critical points of embedding, the averaged binding energies and embedding energies of clusters increase obviously,indicating that embedment is in favor of improving stability. Meanwhile the fragment energies have two peak at critical points.showing the energy mutations.which may be regarded as a structural phase transition criterion of embedding.
引文
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