| Over the past two decades, as important one dimension materials, nanowires have attracted intense interest. Especially, the number of papers published on nanowires has increased exponentially in the last ten years. Semiconductor nanowires exhibit unique electronic, optical and mechanical properties. Thus, it has great research value in fundamental science and nanotechnology. Silicon nanowire (SiNW) is one of the most important one dimension semiconductor materials because of their interface compatibility with existing silicon based technology. SiNWs are commonly grown by the vapor-liquid-solid technique, where an Au nanoparticle is used to catalyze SiH4 decomposition. Briefly, the Au nanoparticle is deposited onto a Si surface and reacts with the Si atoms of the substrate, forming Au-Si alloy droplets. These droplets adsorb Si from the vapor phase, resulting in a supersaturated state where the Si atoms precipitate and the SiNW starts nucleating. Since bulk quantities of uniform single-crystal SiNWs were prepared by a method combining laser ablation, various techniques were developed to fabricate SiNWs, such as chemical vapour deposition, oxide-assisted growth, solution-phase synthesis, chemical etching, lithography technique and molecular beam epitaxial growth. In addition, different patterns of SiNWs, such as cone, kinking and coiled shape, can be synthesized by controlling different growth conditions. The reduction of device size results in the approach to the physical limit of material scaling. Fortunately, SiNWs can lead to an obvious benefit concerning the miniaturization, which could improve the density and performances of electronic devices. It is demonstrated the wide applications of SiNWs, ranging from electron devices, logic gates, nonvolatile memories, photovoltaics, photonics to biological sensors, and also solar cell, lithium battery anodes, thermoelectric materials and catalyst.In nanodevices, the size of SiNWs becomes smaller with the miniaturization. The performances of many nanoscale devices are sensitive to the variation of local atomic configurations and so elemental identification and electronic state analysis at the scale of individual atoms is becoming increasingly important. Especially, when the diameter of SiNWs below 5 nm, it is challenged for studying in experiments. Thanks to the development of computer techniques, the computing power becomes stronger. The first principle calculations have advantage on the detailed control of properties of SiNWs at the atomic level, which could be used to investigate the atomic and electronic structures. The external fields, such as electric field and strain field, are ubiquitous in nanodevices. Especially, the coexistence of the external fields has significant effect on the performance of lower stable integrated circuits. It is induced by the interaction between the external fields and the size of materials. In the area of using solar energy, the choice of photocatalyst is a key factor in the process of water splitting. It is promising for SiNWs in the application as photocatalyst because of its excellent optical properties and stability. In this thesis, utilizing the first principle calculations based on density functional theory, the effect of the external field on the properties of SiNWs was investigated and SiNWs were predicted as photocatalysts for water splitting. The main results obtained are divided into four parts as following:Firstly, the electronic band structures and atomic structures of<111> SiNWs with different diameters were studied under the axial electric field. The results show that the band gap of SiNWs decreases with increasing diameter due to the quantum confinement effect. Under the electric field, the band gap of SiNWs decreases with increasing the strength of electric field. The effect of electric field is size-dependent, where it is enhanced with increasing diameter. The rapid drop of conduction band minimum brings out the decreasing of band gap. When the strength of electric field further increasing, the band gap approaches 0, which results in the semiconductor to metal transition. The electrons segregate to one side of the Si-Si bond and the distributed range of bond length and bond angle broadened under the electric field. Both variables of diameter and electric field could modify the band gap of SiNWs in wider rang, which supplies a new research avenue.Secondly, effects of external fields on electronic band structures of H-terminated <100>,<110>,<111> and<112> SiNWs are studied. Both axial strain field and radial electric field can drop the band gap of SiNWs while it changes fascinatingly under multi-fields due to the interaction between strain field and electric field. The electric field could weaken or enhance the effect of the strain field on variations of the band gap where the interaction is orientation-dependent. By presenting energy variations of the conduction band minimum and valence band maximum under multi-fields, it gives understanding on how the interaction influences the band gap. From the analysis of the density of states, the strain field changes splitting of states induced by the electric field, which brings out the interaction between strain field and electric field. The combination of strain field and electric field may provide additional flexibility in accommodating greater capabilities to satisfy the need of the properties for SiNWs in the applications.Thirdly,<112> SiNWs have certain configuration and stable structures. However, the indirect band gap prevents its optical applications. The calculated results demonstrate that not only the magnitude of the band gap and the characteristics of the electronic band structure can be significantly altered, where the indirect to direct band gap transition occurs when the electric bias is applied on (110) surfaces of SiNWs. The band gap decreases with increasing the electric bias due to simultaneous energy of conduction band minimum decreasing and that of valence band maximum increasing. With further increasing the electric bias, the semiconductor to metal transition occurs and the critical bias is several voltages, which is realized easily in the application. This realizes the application of undoped SiNWs on the field effect transistors. The electron redistribution in (110) facet layers under the electric bias dominates these changes. These results suggest the electric bias enhances the optical properties of SiNWs and it is promising for application of SiNWs in optical and electronic nanodevices.Lastly, as well known, it is an ultimate goal to produce hydrogen from water using solar energy for the supply of clean and recyclable energy. By calculating the band structures of SiNWs, the feasibility of SiNWs as photocatalyst for water splitting was predicted. It is demonstrated that SiNWs terminated with common surface coverage of H and Cl atoms should be a promising photocatalyst for the water splitting by using solar energy. Coexistence of H and Cl atoms on the surfaces effectuates SiNWs to present mezzo reducing and oxidizing powers simultaneously. It is found that the interaction between Cl-3p and surface Si-3p states brings out the drop of the energy of valence band maximum, which results that SiNWs satisfy the needs of photocatalyst. Simultaneously, Cl atoms in the surfaces separate the distributions of the highest occupied molecular orbital and the lowest unoccupied molecular orbital for SiNWs, which prevents the electron-hole recombination. The realization of SiNWs as photocatalyst for water splitting is hopeful.Although SiNWs used in many promising applications are larger than those studied by first principle calculations, it is clear that SiNWs will play an important role in the next generation of electronic devices. Many of the properties of these thin SiNWs pose severe technological challenges, but at the same, time represent extraordinary opportunities. Once the growth orientation and diameter can be controlled with great precision, the use of such thin SiNWs will be practical.
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