First-Principles Study Of Structural And Electronic Properties Of Silicon,Germanium,and Tin Clusters

Clusters are often considered as a bridge for a comprehensive understanding about how matter evolves from atoms to bulk solids.During the past two decades,the structural and electronic properties of semiconductor clusters have become one of the research focuses to elucidate the growth mechanism of semiconductor materials with different length scales and dimensions and to reveal the potential technological applications of the novel semiconductor nanostructures.The knowledge of geometrical structures of clusters is an important prerequisite for the purpose of understanding the physical properties of clusters.It is very dif:ficult to directly measure the geometries of cluster by experimental technology so far.To determine the ground state structure of clusters theoretically requires efficient and accurate global search for their complex potential energy surfaces.which is a great challenge currently for clusters.According to the order of cluster size from small to large,we have investigated semiconductor clusters SnN.Ge N and SiN by global search method.Bulk phase Sn uniquely presents three distinct allotropes.Especially:two-dimensional stanene has attracted enormous interest due to its outstanding properties such as the tunable topological states and sizeable bandgap.Some unique physical properties of Sn clusters and their potential applications in nanotechnology have attracted the intense interests of researchers.A global optimization strategy with genetic algorithm was employed to determine the low-energy structures and their growth process of SnN.SnN-and SnNCl-clusters with N=4-20 on the potential energy surface described by density functional theory.Some low-energy isomers have been described at the first time.It is proposed that there may be degenerate isomers on the potential energy surface of the neutral clusters SnN(N=9,11-13,17-20).the anionic clusters SnN-(N=12.14.16.18-20)and the anionic binary clusters SnNCl-(N=6,7.11,13.19).The electronic properties of clusters.including binding energy.ionization potential,adiabatic detachment energy.and vertical detachment energy.were in agreement with the experimental data.Within the size range concerned,those simulated photoelectron spectra of SnN-and SnNCl-clusters are generally in good agreement with the experimental spectra.After the Cl atom is doped,compared the spectra of SnN-to that of SnNCl-clusters,the first peaks in most of original photoelectron spectra for SnN-一clusters disappear,and other peaks almost remains major original features in spectra of SnN-clusters,because that the doped Cl atom locates outside the configuration of SnN-clusters has almost no effect on the any rearrangement of the framework of SnN-clusters except at N=10,16.19,20.Therefore,this paper provides a valuable reference for the feasible range of the halogen-doping method in experiments.Germanium clusters have attracted much attention due to their potential value in microelectronics as alternatives to silicon-based materials.However.less is known about the structural growth behavior of Ge clusters in the large-sized range beyond 50 atoms.In particular,with increasing cluster size,the number of local minima on the potential energy surface increases exponentially,which makes it difficult to determine the most stable structure.The most stable structures for the large sized Ge clusters with 45-70 atoms are stuffed cages,which are different from the previously proposed "Y-shape" structural motif for medium-sized GeN(N=30-39)clusters but similar to the structural feature of silicon clusters in the same size range,from our unbiased global search by two-step optimization approach.including genetic algorithm combined with non-orthogonal tight-binding method and basin-hopping search coupled with density functional theory.After examining the low-lying isomers of GeN,it shows that the structural transition of GeN clusters occurs around N=70,where their structures transform from near-spherical to spherical-like,in line with the previous experiment.Our theoretical results for binding energy and ionization potential agree well with the available experimental data and their size dependency.HOMO-LUMO gap of GeN clusters decreases with increasing cluster size and is comparable to the bulk value.It is well-known that as the most important elemental semiconductor,silicon is the backbone of modern microelectronics industry.Si clusters have attracted attentions because their potential applications for the Si cluster-based new functional devices.The large-sized Si clusters are in the transition stage from the microscopic phase to the bulk phase.Despite these limited studies without any global search on the potential energy surface,the lowest-energy structures of large-sized silicon clusters(N>80)and their physical properties remain ambiguous and controversial.Our global search by two-step optimization approach shows that the most stable structures for the large Si clusters with 60-170 atoms are stuffed cages,which is a continuation of the structural motif for medium-sized SiN clusters.For the first time.it is found that Si150 and Si170 can be characterized as triple-layered stuffed-cage structures as Si2@Si42＠Si106 and Si2@Si48@Si120.respectively.From the trajectories of basin-hopping search,we also found two bilayer onion-like structures for Si80 and Si100,which may coexist as the degenerate state on the potential energy surface of the lowest-energy stuffed-cage Si20@Si60 and Si28@Si72,respectively.The size-dependent evolution of structural and electronic properties of Si clusters has been discussed in comparison with bulk Si of diamond lattice.Our theoretical results for binding energy,ionization potential,adiabatic detachment energy,and photoelectron spectrum agree well with the available experimental data and their size dependency.The Si clusters with a diameter up to 18 A possess small non-zero gaps,while HOMO-LUMO gap decreases with increasing cluster size partly owing to quantum confinement effect.Due to the surface electronic state,the wave functions of HOMO and LUMO orbitals gradually move to the outer cages of Si clusters as the cluster size increases.The electronic states of the largest Si170 cluster already resemble that of bulk Si.The present investigation of large-sized Si clusters provides a valuable reference for understanding the atomic structures and electronic properties of Si nanostructures.