李宝兴
论文题目：硅和锗团簇的稳定结构及硅团簇吸附特性的研究
作者简介：李宝兴，男，1960年05月出生，1997年09月师从于浙江大学曹培林教授，于2001年03月获博士学位。
摘 要
本论文用全势能Muffin-Tin轨道分子动力学（FP-LMTO-MD）方法对重要的半导体材料硅和锗的纳米团簇的几何结构、电子结构以及它们的吸附特性进行了系统的理论研究，得到了许多前人未曾报道过的结果，满意地解释了一些实验现象。全篇博士论文的主要内容及创新点介绍如下：
第一章：介绍了全势能Muffin-Tin轨道分子动力学方法（Full-potential
Linear-muffin-tin-orbital Molecular-dynamics, i.e., FP-LMTO-MD）。该方法是目前国际上计算研究固体（包括固体表面和原子团簇）的几何结构和电子结构的最好方法之一。它有两套程序，一套用于晶体研究，而另一套就是我们所用的适用于纳米团簇的研究。我们已经对该程序进行了全面的改进，收敛速度比原有的提高了几十倍，目前它已适合于离子性团簇的研究和团簇在固体表面上沉积和运动的研究。该方法是在密度泛函近似下自洽求解Kohn-Sham基本方程。
在该方法中，把空间分为以原子为中心的Muffin-Tin球和球间的间隙区，这些球区域互不重叠。波函数按Muffin-Tin 线性轨道展开，它们在球内是缀加的Hankel函数，基函数包括s,
p 和d波函数。在实际的动力学计算过程中，是在网格上作数值计算。在我们的研究中，对硅和锗的Muffin-Tin球半径分别取2.0和2.2个原子单位。给定一个初始结构，经多次迭代动力学计算，到力的最大值小于0.001原子单位时，这时系统已达到自洽，总的结合能保持不变，获得了局域最小的稳定结构。该方法计算精度高，数据可靠，与实验结果符合较好。
第二章：我们对小硅团簇Sin（n £10）的结构进行了系统研究。小硅团簇Si2-10在硅团簇的研究中占据十分重要的地位，这是由于它们是研究较大硅团簇的基础。另外，小硅团簇的结构和性质与块状晶体硅不同。用FP-LMTO-MD方法，我们得到了一系列结构。我们不仅获得了以前报道过的所有结构，而且还获得了未曾报道过的更为稳定的结构，如Si9的基态结构，Si8基态结构的一个简并结构和多个与Si10基态结构结合能相近的重要结构。目前，7个原子以下（包括7个原子）硅团簇的基态结构（除5以外）已得到实验证实，我们的结果与实验完全一致。这些结构的获得对我们全面探讨半导体硅团簇的物性有了理论基础。
第三章：在第二章的基础上，我们对另一种重要的半导体材料的小锗团簇Gen（n £10）的结构进行了研究，所得结果与小硅团簇进行全面的比较。相对于硅而言，对锗团簇的研究报道要少一些，但已有的理论数据和实验结果都表明它们与相应的硅团簇非常相似。我们的研究有如下创新：（1）虽然锗团簇和硅团簇其几何结构有一一对应关系，但它们的能量排序是不同的，特别发现了Ge8和Ge10的基态结构与相应硅的不同；（2）光电子谱研究表明Si10-有大的能隙而Ge10-没有，我们的研究可以解释这一实验结果。这是由于Si10-和Ge10-的基态结构虽然都是四帽三棱锥，有C3v对称性，其能隙（该能隙指对应于它们中性团簇最高占据态HOMO和最低未占据态LUMO之间的能差）都比较大，但我们发现存在另一个Cs对称性的四帽三棱锥，这个结构有较小的能隙。在求电子态密度（DOS）时，由于能隙小，其最高占据态HOMO和最低未占据态LUMO会略过这个能隙小窗口，因此我们可以期望这个新结构的DOS态密度中观察不到在阈值附近的小峰结构。对Ge来说，这个新结构与基态结构只有0.04
eV能差，而对于Si它们之间的能差为0.45 eV。所以，对于Ge10-，我们观察到的光电子谱应该是它的基态结构和这个新结构共同产生的谱，而对于Si10-，观察到的光电子谱只是它的基态结构产生的。
第四章：我们研究了一氧化碳在小硅团簇上的吸附。吸附研究以利于揭示它们的物理和化学性质。Jarrold等简短地在nature上报道过CO分子在室温下既不会与块状硅也不会与部分硅团簇离子（如Si25+）发生反应。我们的研究表明对CO分子而言，在小的Si2-7团簇表面上都存在吸附能较大的活性位置，CO分子能被吸附在这些位置上，然而在研究范围内吸附能随硅团簇原子数的增加而迅速减小；而且CO分子的取向是以C原子朝向活性位置为最佳方向，这与我们所期望的相一致。我们预计，对于较大的硅团簇，CO分子可能不会有象小硅团簇那样大吸附能。
第五章：我们研究了另一个重要的小分子H2O在稍大一些的硅团簇Si8-10上的吸附。已有的实验结果表明硅团簇对水的反应活性要比晶体硅小得多。我们的理论计算与这些实验事实吻合。水分子被吸附后，硅团簇和水分子的几何构型都没有大的变化，其吸附能的最大值也只有0.49
eV。深入研究成键情况发现，水分子被吸附后，只有很少的电荷被转移到硅团簇上，因此其吸附能不会太大。
第六章：20个原子的硅团簇由于存在特殊的物理和化学性质而引起人们的重视，如饱和研究显示氨分子在这个团簇上的平均吸附数在很低压力的氨气中为3个，压力增加3个量级后，其平均吸附数增加到8个。Si20+的质谱分析表明它以10个原子为分裂单位。我们结合这些实验事实，对Si20团簇的堆积结构和球型结构进行了系统研究，结果发现它的最稳定结构是以Si10团簇的基态结构（四帽三棱锥，C3v对称性）为单元的一个堆积结构。这个结构容易分裂成2个Si10团簇，这与碎片实验相一致。从下一章的吸附研究表明它的活性位置可以多达12个，由于小分子之间的排斥作用，在较小的压力下，最佳吸附位为3个，这可解释氨分子的吸附实验结果。类似地，我们首次对Ge20团簇的稳定结构进行了同样的研究，发现它的基态结构与Si20团簇的不同，但它同样以Ge10团簇的基态结构（四帽八面体，Td对称性）为单元的一个堆积结构，这与碎片实验结果吻合。另一个重要的结果是，锗团簇的结构畸变没有相应的硅团簇严重。从理论角度分析，是由于锗元素更具有金属性一面引起的。
第七章：目前对较大硅团簇（如Si20）的理论吸附研究由于计算上的困难而研究较少，针对Si20团簇的特殊性，我们选择了它对水分子的吸附作为研究对象，理论结果与实验观察到的相一致。找到的活性位置为解释氨分子在Si20团簇的吸附实验结果奠定了基础。
第八章和第九章：我们对碳傅氏笼子结构相对应的硅傅氏笼子结构（Si20，Si24，Si26，Si28，Si30，Si32
和Si60）进行了全面的研究。我们的结论有如下四点：（1）除Si20之外，其它所有的硅傅氏笼子结构都要发生较大的结构畸变，但完美傅氏笼子结构Si20的结合能与Si20的基态结构相比要小7.74
eV；（2）结构畸变后，其表面出现一些四面体构型，而内部还有较大的空间，若按小硅团簇原子间的距离2.2 Ao到2.7 Ao计算，还可容纳1-3个原子；（3）畸变后的结构其对称性要降低；（4）对Si28和Si26团簇的深入研究表明，其内部有硅原子要比空的笼子稳定，对晶体硅取出部分原子进行结构优化发现，优化后的结构没有畸变的中空笼子稳定。另一方面，我们还对Ge60进行了类比研究，发现Ge60虽有类似于Si60的畸变，但畸变没有Si60严重，这正是如第二章所说的是由于锗更具有金属特性引起的。
作者取得博士学位之后的一年时间内，对攻博期间因时间关系而未做完的工作进行了完善，同时还对氧原子和氧分子与Si2-7团簇的反应情况和短而细长的硅纳米线的几何和电子结构作了较详细的研究，得到了一些重要的结果，其研究成果分别发表在J.
Phys.: Conden. Matter，14 (2002) 1723 和Phys. Rev. B65 (2002) 125305 上.
Study
on the stable structures of Si and Ge clusters and the adsorption properties about
Si clusters
Abstract
In this paper, the geometrical and electronic structures of important semiconductor Si and Ge clusters and their adsorption properties are investigated systematically using Full-potential Linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method. Some results never reported before have been obtained. The results can be used to explain some experimental phenomena satisfactorily. The elemental contents and innovations in the paper are introduced as follows:
Chapter 1: Full-potential Linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method is presented briefly. This method is one of the best methods for calculating and investigating the geometrical and electronic structures for solid (including solid surface and atomic clusters). It consists of two programs. One is for investigation on crystal. The other, which is used by us, is suited for calculating on clusters. We have improved the program completely. Its speed of convergence is fast several dozen times in comparison with original speed. Now it can be used for investigating ionic clusters and the deposit and movement of clusters on the solid surface. This method is a self-consistent implementation of the Kohn-Sham equations in the local-density approximation. In this method, space is divided into two parts: non-overlapping muffin-tin (MT) spheres centered at the nuclei and the remaining interstitial region. The electron wave functions are expanded in terms of muffin-tin orbitals. The LMTO's are augmented Hankel functions only inside the spheres. The basis sets include s, p and d wave functions. In the process of dynamics calculation, direct numerical integration on a mesh can be used. When we investigate the Si and Ge clusters, MT sphere radii for Si and Ge are taken as 2.0 and 2.2 au, respectively. For a selected initial geometrical configuration, when the maximum of the forces is less than 0.001 au after a lot of iterations, the system remains close to self-consistency because the total energy remains nicely constant. Thus a stable structure with local minimum is obtained. This method gives high precision to the calculated reliable results, which are in agreement with experimental results.
Chapter 2: The structures for small Sin (n£10) clusters are investigated systematically. The small Si2-10 clusters play an important role in the process of investigating Si clusters because they are the basis of studying the larger silicon clusters. In addition, their structures and properties are different from those of bulk silicon. A series of structures are obtained by using FP-LMTO-MD method. We have obtained not only all the structures reported before, but also some more stable structures never reported previously, such as the ground state structure of Si9, a isoenergetic structure as its lowest energy structure and many almost stable structures as the ground state structure for Si10. At present, the ground state structures with less than 8 (except for 5) have been confirmed experimentally, our results are in good agreement in the experimental results. The structures provide us with theoretical basis of investigating the properties of semiconductor clusters.
Chapter 3: On the basis of chapter 2, the geometrical structures of other important semiconductor Ge small clusters Gen (n£10) have been investigated and a comparison with those of Si small clusters is made overall. At present, the reports about Ge clusters are much fewer relative to Si clusters. However, both theoretical calculations and experimental results have shown that Ge clusters are very similar to the corresponding Si clusters. There are the following innovations in our research: (1) their orders in energy are different although there is a corresponding relation one by one between Ge and Si clusters in structure. In special, it is found that the ground state structures of Ge8 and Ge10 are different from those of Si8 and Si10; (2) Photoelectron spectrum indicates Si10- has a large electronic gap. But, Ge10- does not. The experimental result can be explained by our results. The ground state structures of Si10- and Ge10- are both tetracapped trigonal prisms (C3v symmetry), which have large gaps (the energy gap here refers to the eigenvalue difference between the states corresponding to the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) of the neutral cluster). Our investigations show that another tetracapped trigonal prism with Cs has a small gap. When the density of states (DOS) is calculated, the HOMO and LUMO states would sweep over the energy windows due to small gap. Therefore, it is expected to observe no peak structure near the threshold in the density of states (DOS) of the new structure. For Ge, the new structure is only 0.04 eV less stable than its ground state structure, whereas the energy difference between them is 0.45 eV for Si. Therefore, for Ge10-, the photoelectron spectrum observed should result from the ground state structure and the new structure, whereas for Si10-, the spectrum results from only its ground state structure.
Chapter 4: Adsorption of CO on the small Si clusters is studied. Adsorption investigation helps us disclose their physical and chemical properties. Jarrold et al reported briefly that CO molecule dose not react with crystal silicon and some silicon cluster ions (such as Si25+). Our results show that there are some active positions with large adsorption energies on the small Si2-7 clusters for CO molecule. CO molecule can be adsorbed on the positions. However, their adsorption energies decrease as the atomic number of the Si clusters increases within the scope of our calculation. The orientation of CO molecule normal to the surface toward which the carbon end faces is the most favorable one, as we expected. We think that the adsorption energies of CO molecule on larger Si clusters maybe not so large as that on the small Si clusters.
Chapter 5: Adsorption of another important small molecule H2O on Si8-10 clusters is investigated. Experimental results reveal that silicon clusters appear to be much less reactive than bulk silicon surfaces. Our theoretical results are in good agreement with the experimental facts. After H2O molecule is adsorbed, the geometrical configurations of the silicon clusters and H2O molecule do not change significantly. The maximum of their adsorption energies is only 0.49 eV. It is found from further investigation on their bonding that only small part of charge is transferred into the silicon clusters. Therefore, it is expected that their adsorption energies are not very large.
Chapter 6: Silicon cluster with 20 atoms cause people's attention due to its exceptional physical and chemical properties. For example, saturation studies suggest that the average number of ammonia molecules adsorbed onto the cluster appears to saturate at a small number 3 with very low exposure and then increases up to 8 when the exposure is increased by three orders of magnitudes. The mass spectrum of Si positive cluster ions suggests that the Si20+ cluster ion often appear to photofragment by the fission channel as Si20. Considering the experimental facts, we have investigated the stacked structures and spherical structures of Si20 systematically. It is found that the most stable structure of Si20 is a stacked structure from the ground state structure of Si10 (tetracapped trigonal prism with C3v symmetry). This structure is easy to break into two Si10, which is in agreement with fragment experiment. It is found from adsorption investigation in the next chapter that its active positions would be up to 12. The most favorable positions are 3 at low exposure due to the interaction between them. Similarly, we have investigated the stable structure of Ge20 and found that its ground state structure is different from that of Si20. But the most stable structure is also a stacked structure from the ground state structure of Ge10 (tetracapped octahedron with Td symmetry), which is in agreement with the fragment experiment. Our another important result is that the structural distortion of Ge cluster is not severe as that of corresponding Si clusters. This is resulted from the more metallic properties of Ge element theoretically.
Chapter 7: Few adsorption investigations on larger silicon clusters have been reported due to difficulties in the process of calculations. We selected adsorption of H2O on Si20 as investigation object due to specialty of Si20. Our theoretical results are in agreement with experimental results. The active positions found by us lay the foundation for explaining the experimental result of adsorption of ammonia molecule.
Chapter 8 and Chapter 9: silicon fullerene cage structures (Si20, Si24, Si26, Si28, Si30, Si32 and Si60) of corresponding to carbon fullerene cage structures are investigated overall. Our conclusions are as follows. (1) Except for Si20, all the silicon fullerene cages would undergo obvious structural distortion, but the binding energy of the perfect fullerene cage Si20 is 7.74 eV less than that of its ground state structure. (2) After structural distortion, some tetrahedral configurations appear on their surfaces, but there are larger spaces inside. For the small silicon clusters with 2-10 atoms, the bond lengths are approximately 2.2 Ao to 2.8 Ao. If we were to fill interior silicon atoms into its inside up to this distance, we could still add 1-3 silicon atoms. (3) The symmetry of the distorted structures decreases. (4) Further investigations on Si28 and Si26 clusters show that the compact structures with interior atoms are more stable than the cages with no interior atoms inside. After structural optimization of a piece of Si crystal network, it is not so stable as the cages. In addition, we have also performed investigation on Ge60 and made a comparison with Si60. It is found that the distortion of Ge60 is less than that of Si60 although there is similar structural distortion between them. The difference results from the more metallic properties of Ge element.
After obtaining doctor’s degree, author continues to consummate the undone work due to limited time during three years for doctor’s degree. In addition, the reaction of oxygen atoms and oxygen molecules with the small Si2-7 clusters and the geometrical and electronic structures of short and thin silicon nanowires have been investigated in detail, some important results are obtained. The results have been published in Phys. Rev. B65 (2002) 125305 and J. Phys.: Conden. Matter, 14 (2002) 1723.
