| Today, the information technology develops rapidly; semiconductor materials play an important role in manufacturing information storage, information exploration, information transmission, laser and optical device with their particular properties. Among these semiconductor materials, silicon and germanium are applied widely in electronic and optoelectronic devices with their unique physical properties. As the scientific research and production of traditional components mature gradually, the size of microelectronic components can reach to a nano-scale. Recently, cluster research has developed rapidly, and the studies about silicon and germanium clusters have became one of the important research topics.The structures of silicon and germanium clusters were studied in detail using GA (Genetic Algorithm) for unbiased search, combined with the DFT (Density Functional Theory) method. In this work, we analyzed the fragmentation behaviors of silicon clusters; and confirmed the most stable geometries of medium-sized germanium clusters; and found series of low-lying energy isomers; their electronic properties, such as binding energies, second differences in energy, HOMO– LUMO gaps, occupations on the HOMO shells, ionization potentials (IPs) and ion mobility, etc. have been discussed in detail. We also found an unambiguous structure of the Si12+ cluster, whose IR spectrum agrees well with the experiment result. In addition, we identified the lowest-energy structures of Ge2-15+ clusters, and compared with the corresponding Si2-15+ clusters.The main results could be summarized as the following four aspects:(1) The binding energies, second differences in energy, HOMO– LUMO gaps and fragmentation behaviors (involving one-step and multi-step fragmentations) of Sin (n =2–33) clusters have been studied at the B3LYP/6-311++G(d) and PW91/6-311++G(d) level. The calculated results indicated that Si4, Si6, Si7 and Si10 are quite stable, and appear frequently in the fragmentation products. For the size range between 11 and 20, the fragmentation energies are obviously small, indicating that Si11?20 can be easily dissociated. We also analyzed the issue about bond broken when cluster dissociate using some examples. In general, in the fragmentation of clusters, the dissociation of a small stable cluster would be favorable. Our calculated results are in good agreement with the experimental observations.(2) The structures of Gen (n = 34 ? 39) clusters were searched by a genetic algorithm (GA) using a tight-binding (TB)interatomic potential. Density functional theory (DFT) calculations have been performed to further identify the lowest-energy structures. The electronic properties such as binding energies, second differences in energy, ionization potentials (IPs), electron affinities (EAs), HOMO– LUMO gaps and occupations on the HOMO shells have been analyzed. The calculated results show that the Gen (n = 34 ? 39) clusters favor prolate or Y-shaped three-arm structures consisted of two or three small stable clusters (Ge6, Ge7, Ge9 or Ge10) linked by a Ge6 or Ge9 bulk unit. The calculated results suggest that the transition point from prolate to Y-shaped three-arm structures appears at Ge35 or Ge36. In addition, we found some low-lying energy isomers of Ge34– Ge39. We found platelike also is a kind of competitive structure except prolate and Y-shaped structures. There is a competition between the prolate and Y-shaped three-arm structures starting at this size range of n = 34– 39; and at the end of this size range the competition appears between the Y-shaped three-arm and platelike motifs. For example, the energy differences between platelike and Y-shaped structures of Ge39 calculated at PBE/DND is only 0.016eV.(3) For the Ge40-44 clusters, platelike structures are dominant, which are consisted of four small magic clusters (Ge9 or Ge10), and a Ge4 core. The Ge4 core along with the parts of the four linked small clusters forms a diamond segment. As the cluster size grows from Ge40 to Ge44, the subunit Ge9 will be replaced by Ge10 one by one. Therefore, while Ge40a is a structure with four Ge9s and a Ge4 core, Ge44a consists of four Ge10s and a Ge4 core. We also calculated the ion mobilities of the most stable structures, and the calculated results are in good agreement with the experimental data. Thus we can see, there are some rules about the growth pattern of Gen (n≤44). The clusters Ge2-10 have spherical-like compact geometries. Among them, Ge6,7,9,10 are very stable, which are the important components of larger clusters. From Ge11 to Ge16, it can be seen that the TTP (tri-capped trigonal prism) motif is prevailing; and they are all prolate structures. Ge17– Ge35 are consisted of two stable Ge6,7,9,10, and linked by the Ge6 or Ge9 bulk fragment. From Ge36 and Ge40, the number of Ge6,7,9,10 up to three and four, respectively; and the linkage is also the bulk fragment of Ge diamond. Therefore, we can see clearly, medium-sized germanium clusters consisted of Ge6,7,9,10; and linked with bulk fragment of Ge diamond. Increasing the components Ge6,7,9,10s is dominant about the growth pattern of germanium clusters. There is great significance about this discover for studying the size range of diamond of Ge clusters.(4) An unambiguous structure of the Si12+ cluster has been determined at the level of B3LYP/6-311G(d), which IR spectrum is quite agreement with the experiment result. The most stable structures of Gen+ (n = 2 ? 15) clusters also have been confirmed using the GA search combined with the DFT method, and compared with the corresponding Sin+. The result shows that most structures between Gen+ and Sin+ clusters are similar except for n = 9, 12, 13 and 14. Furthermore, the motifs of Gen+ (n = 2– 15) clusters differ slightly from the corresponding Sin+ clusters. In Sin+ , the pentagonal bipyramid motif appears in Si7+, Si8+, Si9+ and Si12+; while the TTP (tri-capped trigonal prism) motif exists in the structures with n = 10, 11, 13 and 15. For Gen+, the two types of motifs are contained in the clusters with n = 7– 9 and n = 10– 15, respectively.
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