Cu纳米线结构和性质的第一性原理研究
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摘要
铜(Cu)作为一种广泛使用的商业金属具有许多优良的特性,如较高的强度、极好的延展性和良好的抗腐蚀性,另外,Cu具有较高的电导率、导热率和熔点以及较低的电阻率等优点常被用作电子器件中的互联线。随着纳米科学技术的出现和发展,一维Cu纳米线在大规模集成电路和纳米微机电系统中展现出了良好的应用前景。本文基于密度泛函理论框架下的第一性原理投影缀加波计算方法,对不同结构一维Cu纳米线的稳定性、电子特性、氧化性能以及将Cu纳米线填充纳米管的特性进行了研究,主要得到结如下结论：
(1)系统的研究了不同维数下的Cu结构的结构和电子特性的变化。计算结果表明随着维数的降低,Cu结构中最近邻原子间距和系统结合能逐渐减小,其能带结构越来越密集且逐渐向费米能级靠近,且总态密度的带宽降低、峰值增大且整体态密度也逐渐向费米能级移动。同时,随着维数的降低,Cu原子间的相互作用明显增强。
(2)系统的研究了[100]、[110]和[111]三个低指数晶向Cu纳米线的结构和电子特性,并对其相对稳定性进行了初步探讨。在Cu纳米线的弛豫结构中存在着“倒棱”现象,且随着纳米线尺寸的增加,表面原子的弛豫量也明显增加。起初在同-条直线上的原子弛豫后并不在同一条直线上(尤其是表面原子),因此,被称作“皱褶”的现象也存在于Cu纳米线中。随着线径的增加纳米线的结合能也逐渐增加,且逐渐接近体相结构Cu的结合能；从稳定性方面来讲,[110]晶向Cu纳米线最稳定,这与在实验中最容易形成该晶向Cu纳米线的实验结果一致。在电子特性方面：Cu纳米线表面原子间及表面原子与其最近邻原子间的相互作用明显增强,我们称这种现象为“趋肤效应”,因此相对于体相Cu晶体,Cu纳米线的机械性能得以提高。最后,计算结构表明Cu纳米线的电子传输性能随着线径的增加而增强。
(3)系统的研究了单胞内包含1到14个Cu原子的22种不同截面形状Cu纳米线构型的平衡结构和电子特性。得到了每种构型纳米线在最稳定结构所对应的平衡态晶格常数。Cu纳米线的结合能随着每个单胞中Cu原子数目的增加而增加。对于一个具有固定多边形原子截面构型的纳米线结构,在轴向具有穿过多边形中心的线性原子链且链中原子正好位于两多边形中间位置的交错结构是最稳定的。所有稳定构型的Cu纳米线都具有金属性。最后,电荷密度分析表明相对于体相Cu晶体纳米线中都有所增强。
(4)基于第一性原理计算研究了Cu纳米线与氧原子或氧分子的相互作用,给出了包含杂质的Cu纳米线的稳定性、机械和电子特性。(a)在氧原子和氧分子与Cu原子链的相互作用中,我们发现氧原子和氧分子与一维结构中的Cu原子间形成稳定的强化学键。在轴向应力拉伸过程中,包含氧原子或氧分子的原子链的断裂一般发生在远离氧原子或氧分子的Cu-Cu键处。氧原子或氧分子两侧的最近邻Cu原子上的部分电子转移到了电负性较大的O原子上,表明所形成的Cu-O键具有离子键特性。因此,合适的有氧环境会有助于形成稳定的Cu原子链。(b)在四方形Cu纳米线表面上吸附氧原子研究中,发现氧原子可以自发地吸附在Cu纳米线的表面,计算结果表明在Cu纳米线棱角处的长桥位(LB)是氧原子的最稳定吸附位置,而表面上的洞位(H)为第二稳定吸附位置。从差分电荷密度和投影态密度分析中发现Cu原子与吸附氧原子所形成的化学键在一定程度上表现为混合的离子键/共价键特性。另外,从局部几何结构和电子特性两方面讨论和分析了影响氧原子吸附的Cu纳米线系统中优先吸附位置的主要因素。
(5)系统地研究了将Cu纳米线填充到无机纳米管中成为纳米缆系统时的结构和电子特性。(a)将[001]晶向的不同线径的的四方形Cu纳米线填充到扶手椅型(8,8)GaN纳米管中时,对于Cu5@(8,8)和Cu9@(8,8)复合结构,初始结构在优化后基本保持不变,而对Cu13@(8,8)复合系统,纳米管横截面形状发生变形。相对于Cu13@(8,8)复合结构,Cu5@(8,8)和Cu9@(8,8)复合结构其结合能非常小,表明管-线间的相互作用非常弱。从投影态密度和电荷密度两方面的分析可知,在Cu9@(8,8)复合结构中外部纳米管中Ga原子和N原子的电子对复合系统的电导没有影响,同时内部Cu9纳米线和外围纳米管间没有电荷的交迭,因此传导电子仅仅只是分布在填充在内部的Cu纳米线区域,而外围惰性的GaN纳米管只是起到了一个半导体电缆壳的作用。(b)将螺旋形Cu纳米线填充到一系列不同线径锯齿型(n,0)BeO纳米管中时,所形成Cum@(n,0)复合系统优化后的结构相对最初建立的圆筒结构基本保持不变。管-线间距约为的2.8A的Cu6@(10,0)和Cu8@(11,0)复合结构具有最大的结合能0.06eV,所以这两个复合结构是最稳定的结构,且这两种复合结构在费米能级附近处的能带结构几乎就是其组成成分(Cu纳米线和BeO纳米管)能带结构的叠加,且Cu纳米线填充到纳米管中后其量子电导没有发生变化。同样地,从投影态密度和电荷密度两方面的分析可知,在两种最稳定的复合结构中传导电子仅仅只是分布在填充在内部的Cu纳米线区域,而外围惰性的BeO纳米管只是起到了一个绝缘电缆壳的作用。因此纳米缆复合系统可应用于要求稳定传输电荷的超大规模集成电路和纳米微机电系统中。
Copper is a widely used commercial metal due to its availability and outstanding properties such as good strength, excellent malleability and superior corrosion resistance. There are many qualities that maintain Cu as the material of choice for making interconnects in electron device, for examples, Cu has excellent electrical conductivity, thermal conductivity, lower resistivity and higher melting point. As the advance of the nano science and technology one-dimensional (ID) copper nanowires (CuNWs) are of particular interest, which have been expected to apply in ultra-large-scale integration (ULSI) circuits and nano-electromechanical systems (NEMS) as well as others nanodevices. Therefore, in this paper, by using first-principles projector-augmented wave potential within density-functional theory, we have systematically investigated the stabilities, electronic properties and oxidative activity of CuNWs with different structures as well as the properties of CuNWs encapsulated in nanotubes. The main conclusions can be summarized as follows.
(1) We systematically investigated the changes in the electronic structure of Cu in going from three-dimensional (3D) to two-dimensional (2D) to one-dimensional (1D) structure. The interatomic distance and the binding energy per bond shows significant drop as dimensionality decreases. The band structure and the density of states (DOS) show a gradual sharpening of the DOS bandwidth and an increase in its peak value with the lowering of dimensions. Meanwhile, the peak of the DOS shifts to the Fermi level and the interaction between adjacent Cu atoms becomes stronger as Cu undergo a change of dimensionality from3D to2D to1D.
(2) The relaxed structures and electronic properties have been investigated for CuNWs in [100],[110] and [111] crystallographic directions with different cross sections. For all studied CuNWs, the relaxed structures show a "round corner" phenomenon and the relaxation amount of the surface Cu atoms increases with increasing CuNWs size. The atoms on the same line originally are not on the same line after relaxation, especially the surface atoms; i.e., so-called rumple phenomenon exits. The binding energy per bond shows significant increase as the size of the nanowire increases. The [110] crystallographic wire is more stable than the others and easily synthesize in experiment, in agreement with the experimental result. The enhanced interactions appear between the surface atoms as well as the surface atoms and their first nearest neighbor atoms; we term this phenomenon the "skin effect", which enhances the mechanical properties of the nanowire compared to bulk. Finaly, the electronic transport properties enhances with the increase diameter of CuNWs.
(3) The equilibrium structure and electronic properties of22free-standing CuNWs having different cross sections with1-14Cu atoms per unit cell have been systematically investigated. For each wire the equilibrium lattice constant was obtained. The binding energy increases with increasing atom number per unit cell in different structures. As for the polygonal structures of a fixed cross section, the preferred structures should be the staggered ones which contain a linear chain along the wire axis passes through the center of the polygons, where each chain atom is just located at a point equidistant from the planes of polygons. All the nanowires are metallic. Finally, the density of charge revealed delocalized metallic bonding and an enhanced interaction appears between the atoms for all of the CuNWs compared with that in Cu bulk crystal.
(4) In this study, we have investigated the interaction of atomic or molecular oxygen with the CuNWs via total-energy calculations using first-principles calculations,(a) The energetics, mechanical, and electronic properties of the contaminated CuNWs have been presented. The impurities (O atom or O2molecule) form stable and strong bonds with the monatomic Cu chain. Upon elongation, the nanowires contaminated with atomic impurities usually break from the remote Cu-Cu bond. The electron transferring from neighboring Cu atoms to O atom shows some degree of ionic character of the Cu-O bond. Our findings indicate that the Cu chains can be easily formed in the presence of molecular or atomic oxygen.(b) The structural stability and electronic properties of a single oxygen atom adsorbed on the surface of foursquare Cu nanowires for a wide range of adsorption sites have been systematically investigated. We find that the oxygen atom can adsorb exothermically or spontaneously on the surface of CuNWs. We found that the long bridge site at the edge of the CuNWs is the most stable site for oxygen adsorption, which is always slightly energetically favorable than the hollow site on the surface. The O-Cu chemical bond shows some degree of mixed ionic/covalence character from a detailed investigation of the different charge density and the projected density of states. In addition, the main factors affecting the preferred adsorption site of the oxygen adsorbed CuNW systems are analyzed from the local geometrical configurations and electronic properties.
(5) The structural and electronic properties of nanocables systems formed by CuNWs encapsulated in inorganic nanotubes have been systemically studied.(a) When the four squares CuNWs in [100] crystallographic directions with different cross sections encapsulated into the armchair (8,8) GaNNT, the initial shapes are preserved without any visible changes for the Cu5@(8,8) and Cu9@(8,8) combined systems, but a quadraticlike cross-section shape is formed for the outer nanotube of the Cu13@(8,8) combined system due to the stronger attraction between nanowire and nanotube. The extremely small (larger) formation energies indicating that the interactions between nanowire and nanotube are very weak (stronger) for the Cus@(8,8) and Cu9@(8,8)(Cu13@(8,8)) combined systems (system). The electrons of Ga and N atoms in outer GaN sheath affect the electron conductance of the encapsulated metallic nanowire in the Cu13@(8,8) combined system. But in the Cu5@(8,8) and Cu9@(8,8) combined systems, the conduction electrons are distributed only on the copper atoms, charge transport will occur only in the inner copper nanowire, which are effectively insulated by the outer GaN nanotube.(b) As for the Cum@(n,0) combined systems of helical CuNWs encapsulated in a series of zigzag (n,0) BeONTs, the initial cylindrical shapes are preserved without any visible changes. The most stable combined systems are Cu6@(10,0) and Cug@(11,0) with an optimal tube-wire distance of about2.8A and a simple superposition of the band structures of their components near the Fermi level. A quantum conductance of3G0is obtained for both Cu6and Cu8nanowires in either free-standing state or filled into BeONTs. Both the projected densities of states (PDOS) and charge density analyses also show their conduction electrons are localized on the inner CuNW, therefore, the electronic transport will occur in the inner CuNW and the outer BeONT only function as an insulating sheath. So the combined systems of nanocables is top-priority in the ULSI circuits and MEMS devices that demand steady transport of electrons
(1)系统的研究了不同维数下的Cu结构的结构和电子特性的变化。计算结果表明随着维数的降低,Cu结构中最近邻原子间距和系统结合能逐渐减小,其能带结构越来越密集且逐渐向费米能级靠近,且总态密度的带宽降低、峰值增大且整体态密度也逐渐向费米能级移动。同时,随着维数的降低,Cu原子间的相互作用明显增强。
(2)系统的研究了[100]、[110]和[111]三个低指数晶向Cu纳米线的结构和电子特性,并对其相对稳定性进行了初步探讨。在Cu纳米线的弛豫结构中存在着“倒棱”现象,且随着纳米线尺寸的增加,表面原子的弛豫量也明显增加。起初在同-条直线上的原子弛豫后并不在同一条直线上(尤其是表面原子),因此,被称作“皱褶”的现象也存在于Cu纳米线中。随着线径的增加纳米线的结合能也逐渐增加,且逐渐接近体相结构Cu的结合能；从稳定性方面来讲,[110]晶向Cu纳米线最稳定,这与在实验中最容易形成该晶向Cu纳米线的实验结果一致。在电子特性方面：Cu纳米线表面原子间及表面原子与其最近邻原子间的相互作用明显增强,我们称这种现象为“趋肤效应”,因此相对于体相Cu晶体,Cu纳米线的机械性能得以提高。最后,计算结构表明Cu纳米线的电子传输性能随着线径的增加而增强。
(3)系统的研究了单胞内包含1到14个Cu原子的22种不同截面形状Cu纳米线构型的平衡结构和电子特性。得到了每种构型纳米线在最稳定结构所对应的平衡态晶格常数。Cu纳米线的结合能随着每个单胞中Cu原子数目的增加而增加。对于一个具有固定多边形原子截面构型的纳米线结构,在轴向具有穿过多边形中心的线性原子链且链中原子正好位于两多边形中间位置的交错结构是最稳定的。所有稳定构型的Cu纳米线都具有金属性。最后,电荷密度分析表明相对于体相Cu晶体纳米线中都有所增强。
(4)基于第一性原理计算研究了Cu纳米线与氧原子或氧分子的相互作用,给出了包含杂质的Cu纳米线的稳定性、机械和电子特性。(a)在氧原子和氧分子与Cu原子链的相互作用中,我们发现氧原子和氧分子与一维结构中的Cu原子间形成稳定的强化学键。在轴向应力拉伸过程中,包含氧原子或氧分子的原子链的断裂一般发生在远离氧原子或氧分子的Cu-Cu键处。氧原子或氧分子两侧的最近邻Cu原子上的部分电子转移到了电负性较大的O原子上,表明所形成的Cu-O键具有离子键特性。因此,合适的有氧环境会有助于形成稳定的Cu原子链。(b)在四方形Cu纳米线表面上吸附氧原子研究中,发现氧原子可以自发地吸附在Cu纳米线的表面,计算结果表明在Cu纳米线棱角处的长桥位(LB)是氧原子的最稳定吸附位置,而表面上的洞位(H)为第二稳定吸附位置。从差分电荷密度和投影态密度分析中发现Cu原子与吸附氧原子所形成的化学键在一定程度上表现为混合的离子键/共价键特性。另外,从局部几何结构和电子特性两方面讨论和分析了影响氧原子吸附的Cu纳米线系统中优先吸附位置的主要因素。
(5)系统地研究了将Cu纳米线填充到无机纳米管中成为纳米缆系统时的结构和电子特性。(a)将[001]晶向的不同线径的的四方形Cu纳米线填充到扶手椅型(8,8)GaN纳米管中时,对于Cu5@(8,8)和Cu9@(8,8)复合结构,初始结构在优化后基本保持不变,而对Cu13@(8,8)复合系统,纳米管横截面形状发生变形。相对于Cu13@(8,8)复合结构,Cu5@(8,8)和Cu9@(8,8)复合结构其结合能非常小,表明管-线间的相互作用非常弱。从投影态密度和电荷密度两方面的分析可知,在Cu9@(8,8)复合结构中外部纳米管中Ga原子和N原子的电子对复合系统的电导没有影响,同时内部Cu9纳米线和外围纳米管间没有电荷的交迭,因此传导电子仅仅只是分布在填充在内部的Cu纳米线区域,而外围惰性的GaN纳米管只是起到了一个半导体电缆壳的作用。(b)将螺旋形Cu纳米线填充到一系列不同线径锯齿型(n,0)BeO纳米管中时,所形成Cum@(n,0)复合系统优化后的结构相对最初建立的圆筒结构基本保持不变。管-线间距约为的2.8A的Cu6@(10,0)和Cu8@(11,0)复合结构具有最大的结合能0.06eV,所以这两个复合结构是最稳定的结构,且这两种复合结构在费米能级附近处的能带结构几乎就是其组成成分(Cu纳米线和BeO纳米管)能带结构的叠加,且Cu纳米线填充到纳米管中后其量子电导没有发生变化。同样地,从投影态密度和电荷密度两方面的分析可知,在两种最稳定的复合结构中传导电子仅仅只是分布在填充在内部的Cu纳米线区域,而外围惰性的BeO纳米管只是起到了一个绝缘电缆壳的作用。因此纳米缆复合系统可应用于要求稳定传输电荷的超大规模集成电路和纳米微机电系统中。
Copper is a widely used commercial metal due to its availability and outstanding properties such as good strength, excellent malleability and superior corrosion resistance. There are many qualities that maintain Cu as the material of choice for making interconnects in electron device, for examples, Cu has excellent electrical conductivity, thermal conductivity, lower resistivity and higher melting point. As the advance of the nano science and technology one-dimensional (ID) copper nanowires (CuNWs) are of particular interest, which have been expected to apply in ultra-large-scale integration (ULSI) circuits and nano-electromechanical systems (NEMS) as well as others nanodevices. Therefore, in this paper, by using first-principles projector-augmented wave potential within density-functional theory, we have systematically investigated the stabilities, electronic properties and oxidative activity of CuNWs with different structures as well as the properties of CuNWs encapsulated in nanotubes. The main conclusions can be summarized as follows.
(1) We systematically investigated the changes in the electronic structure of Cu in going from three-dimensional (3D) to two-dimensional (2D) to one-dimensional (1D) structure. The interatomic distance and the binding energy per bond shows significant drop as dimensionality decreases. The band structure and the density of states (DOS) show a gradual sharpening of the DOS bandwidth and an increase in its peak value with the lowering of dimensions. Meanwhile, the peak of the DOS shifts to the Fermi level and the interaction between adjacent Cu atoms becomes stronger as Cu undergo a change of dimensionality from3D to2D to1D.
(2) The relaxed structures and electronic properties have been investigated for CuNWs in [100],[110] and [111] crystallographic directions with different cross sections. For all studied CuNWs, the relaxed structures show a "round corner" phenomenon and the relaxation amount of the surface Cu atoms increases with increasing CuNWs size. The atoms on the same line originally are not on the same line after relaxation, especially the surface atoms; i.e., so-called rumple phenomenon exits. The binding energy per bond shows significant increase as the size of the nanowire increases. The [110] crystallographic wire is more stable than the others and easily synthesize in experiment, in agreement with the experimental result. The enhanced interactions appear between the surface atoms as well as the surface atoms and their first nearest neighbor atoms; we term this phenomenon the "skin effect", which enhances the mechanical properties of the nanowire compared to bulk. Finaly, the electronic transport properties enhances with the increase diameter of CuNWs.
(3) The equilibrium structure and electronic properties of22free-standing CuNWs having different cross sections with1-14Cu atoms per unit cell have been systematically investigated. For each wire the equilibrium lattice constant was obtained. The binding energy increases with increasing atom number per unit cell in different structures. As for the polygonal structures of a fixed cross section, the preferred structures should be the staggered ones which contain a linear chain along the wire axis passes through the center of the polygons, where each chain atom is just located at a point equidistant from the planes of polygons. All the nanowires are metallic. Finally, the density of charge revealed delocalized metallic bonding and an enhanced interaction appears between the atoms for all of the CuNWs compared with that in Cu bulk crystal.
(4) In this study, we have investigated the interaction of atomic or molecular oxygen with the CuNWs via total-energy calculations using first-principles calculations,(a) The energetics, mechanical, and electronic properties of the contaminated CuNWs have been presented. The impurities (O atom or O2molecule) form stable and strong bonds with the monatomic Cu chain. Upon elongation, the nanowires contaminated with atomic impurities usually break from the remote Cu-Cu bond. The electron transferring from neighboring Cu atoms to O atom shows some degree of ionic character of the Cu-O bond. Our findings indicate that the Cu chains can be easily formed in the presence of molecular or atomic oxygen.(b) The structural stability and electronic properties of a single oxygen atom adsorbed on the surface of foursquare Cu nanowires for a wide range of adsorption sites have been systematically investigated. We find that the oxygen atom can adsorb exothermically or spontaneously on the surface of CuNWs. We found that the long bridge site at the edge of the CuNWs is the most stable site for oxygen adsorption, which is always slightly energetically favorable than the hollow site on the surface. The O-Cu chemical bond shows some degree of mixed ionic/covalence character from a detailed investigation of the different charge density and the projected density of states. In addition, the main factors affecting the preferred adsorption site of the oxygen adsorbed CuNW systems are analyzed from the local geometrical configurations and electronic properties.
(5) The structural and electronic properties of nanocables systems formed by CuNWs encapsulated in inorganic nanotubes have been systemically studied.(a) When the four squares CuNWs in [100] crystallographic directions with different cross sections encapsulated into the armchair (8,8) GaNNT, the initial shapes are preserved without any visible changes for the Cu5@(8,8) and Cu9@(8,8) combined systems, but a quadraticlike cross-section shape is formed for the outer nanotube of the Cu13@(8,8) combined system due to the stronger attraction between nanowire and nanotube. The extremely small (larger) formation energies indicating that the interactions between nanowire and nanotube are very weak (stronger) for the Cus@(8,8) and Cu9@(8,8)(Cu13@(8,8)) combined systems (system). The electrons of Ga and N atoms in outer GaN sheath affect the electron conductance of the encapsulated metallic nanowire in the Cu13@(8,8) combined system. But in the Cu5@(8,8) and Cu9@(8,8) combined systems, the conduction electrons are distributed only on the copper atoms, charge transport will occur only in the inner copper nanowire, which are effectively insulated by the outer GaN nanotube.(b) As for the Cum@(n,0) combined systems of helical CuNWs encapsulated in a series of zigzag (n,0) BeONTs, the initial cylindrical shapes are preserved without any visible changes. The most stable combined systems are Cu6@(10,0) and Cug@(11,0) with an optimal tube-wire distance of about2.8A and a simple superposition of the band structures of their components near the Fermi level. A quantum conductance of3G0is obtained for both Cu6and Cu8nanowires in either free-standing state or filled into BeONTs. Both the projected densities of states (PDOS) and charge density analyses also show their conduction electrons are localized on the inner CuNW, therefore, the electronic transport will occur in the inner CuNW and the outer BeONT only function as an insulating sheath. So the combined systems of nanocables is top-priority in the ULSI circuits and MEMS devices that demand steady transport of electrons
引文
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