Tight-binding Investigations On The Electronic Structures Of Nano Structures Made By ?-? Group Semiconductor

?-? semiconductor nano-materials have attracted considerable attention due to their novel physical properties and great potential applications in nano devices.The electronic properties of nanostructures have been studied with many theoretical methods,such as the first principles method,k·p,and tight-binding methods.In particular,the first principles calculation methods have been extensively applied in material computed science owing to their accurate predictions in physical properties of tiny nanostructure.However,it is great difficult to consider near-experimental size of nanostructure with the first principles calculation methods for enourmous amount of computation expensively.Recently,k·p method has been successfully predicated the properties of large size nanostructure.A lot of obstacles have still been presented in the calculation for low symmetry system around the ? point of Brillouin zone though it's potential in computations of large size nanostructures.Consequently,k·p methods hardly investigate physical properties of large indirect-band gap semiconductor due to little consideration in crystal symmetry.In this thesis,we have adopted reasonable tight-binding methods to systematically study the electronic properties of III-V semiconductors all around the whole Brillouin zone points.Some interesting and meaningful results have been obtained.Firstly,we report a theoretical study of the electronic structures of the[111]-oriented,free-standing,zinc-blende InAs and InP nanowires with hexagonal cross sections by means of an atomistic sp~3s~*,spin-orbit interactions included,nearest-neighbors tight-binding method,respecviely.We have constructed a start vector by using the characteristics of the double group theory of crystal structures,and obtained energy spectrum structures combining with Lanczos method.A further investigations were conducted to analysis the electronic states corresponding to bands around the band edge.The results have shown that all bands of these nanowires are doubly degenerated at the ?-point and some of these bands will split into non-degenerate bands when the wave vector k moves away from the ?-point as a manifestation of spin-splitting due to spin-orbit interaction.It is also shown that the lower conduction bands of these nanowires all show simple parabolic dispersion relations,while the top valence bands show complex dispersion relations and band crossings.The band structures and the band state wave functions of these nanowires are calculated and the symmetry properties of the bands and band states are analyzed based on the C3v double point group.The band state wave functions are presented by the spatial probability distributions and it is found that all the band states show 2/3?-rotation symmetric probability distributions.The effects of the quantum confinement on the band structures of the[111]-oriented InAs and InP nanowires are also examined and an empirical formula for the description of quantization energies of the lowest conduction band and the highest valence band is presented.The formula can simply be used to estimate the enhancement of the band gaps of the nanowires at different sizes as a result of quantum confinement.In addition,we also studied the electronic of InSb and GaSb nanowires along the[001]-oriented direction with square and rectangular cross section,and hexagonal cross-sectional shape in the[111]-oriented direction,respectively.It is found that the band structures of InSb and GaSb nanowires within[001]direction seem to be similar,which is contrast to the trend observed in that of[111]-direction.In detail,the band structures of[001]-oriented InSb and GaSb nanowires with square cross section preserve anti-crossing features,and appear camelback shape around the top valence band associated with indirect band gap.The formation of camelback shape band structures can be restrained by adjusting the aspect ratios.It was observed that valence band maximum appear at?-point,inducing indirect to direct band gap transition.Meanwhile,we find the quantum confine effect changes with the section size of nanowire according to fitted formula of band gap of varying diameters of nanowires.Additionally,we analyses the relationship between hole effective masses and electron effective masses with aspect ratio,and given the fitted formula.Secondly,we performed a theoretical study of the electronic structures of freestanding nanowires made from gallium phosphide(GaP)-a III-V group semiconductor with an indirect bulk bandgap using tight-binding methods.We consider[001]-oriented GaP nano wires with square and rectangular cross sections,and[111]-oriented GaP nanowires with hexagonal cross sections.Based on tight binding models,both the band structures and wave functions of the nanowires are calculated.For the[001]-oriented GaP nanowires,the bands show anti-crossing structures,while the bands of the[111]-oriented nanowires display crossing structures.Two minima are observed in the conduction bands,while the maximum of the valence bands is always at the ?-point.It is contrast to the results in calculation on InAs,InP,InSb,and GaSb direct-band gap semiconductors.Using double group theory,we analyze the symmetric properties of the lowest conduction band states and highest valence band states of GaP nanowires with different sizes and directions.The band state wave functions of the lowest conduction bands and the highest valence bands of the nanowires are evaluated by spatial probability distributions.For practical use,we fit the confinement energies of the electrons and holes in the nanowires to obtain an empirical formula.As a result,the quantum confine energy and band gap can be obtained easily according to above empirical formula.Thirdly,we investigated the electronic properties of[111]-oriented InAs/GaSb,GaSb/InAs core-shell nanowires with hexagonal cross-section using nearest-neighbor tight-binding methods,respectively,in which spin-orbit interaction was considered.GaSb/InAs heterostructures can be grown without great difficult owning to the small lattice mismatch.The calculated results shown that a hybridization was occured in conduction bands and valence bands at the certain aspect ratio in InAs/GaSb and GaSb/InAs core-shell nanowires.The band gaps of InAs/GaSb and GaSb/InAs core-shell nanowires can be open with various degrees varying core/shell ratio.In addition,we calculated the absolute band gaps with increasing the size at a fixed aspect ratio.It can be observed that the absolute band gap fluctuates abnormally when the thickness increases continuously.The absolute band gap of GaSb/InAs core-shell nanowire can be reached a bang gap as high as 7.744 meV comparing with that 2.818 meV in InAs/GaSb core-shell nanowries.Our results may be valuable in experimental grown of InAs/GaSb and GaSb/InAs core-shell nanowries.Finally,we systematically studied the electronic of[001]and[111]direction InAs/GaSb nanowires superlattices with various aspect ratios and diameters,respectively.The corresponding mini-bands formations in conduction and valence bands were discussed in detail.The formation of the mini-bands in the conduction band presents a simple dispersion relation,and that in the valence band exhibits a complex structural characteristic.Additionally,we studied the physical properties of InAs/GaSb heterostructure films,and changed the formation of mini-bands of conduction and valence bands by inducing voltage field and changing the sizes.