Theoretical study on surface electrical conduction on nanometer scales

本课题取得的主要成果如下：1. Shockley表面态的导电性研究了由sp杂化形成的表面态的导电性，阐明了s、p带宽度、sp杂化强度与电导的关系。这一结果可应用于贵金属表面的Shockley表面态。2.悬键态的导电阐明了半导体体带隙中形成的表面态的导电与带隙值的关系。（111）2×1结构我研究了表面结构，特别是屈曲的存在对导电的影响。进一步研究了双针尖STM的导电性，阐明了表面态带的有效质量与双针尖STM电导的关系。4.硅纳米线的表面导电性研究了中等尺寸纳米线的非均匀导电性。我发现了通过局限于晶体边缘的边缘态导电的可能性。5. Si（111）~（113）× ~（113）-Ag单原子台阶的电阻和Bloch波的电阻我计算了台阶的电阻，并解释了最近的实验结果。我发现了一种新的台阶态，它位于台阶下阶的边缘。在此基础上，给出了包括倏逝波在内的波的振幅和相位的新定义，并导出了布洛赫波的传播公式。我发现布洛赫波的阻力分为两部分：一部分来自布洛赫波数的差异，另一部分来自布洛赫波周期部分的对数导数的不连续性。

Main results obtained within the term of project are as follows.1.Electrical conduction of Shockley surface statesI studied the electrical conduction of the surface states formed by sp hybridization and clarified the relation between the widths of s and p bands, strength of sp hybridization, and the electrical conductance. This result can be applied to the Shockley surface states of the noble metal surfaces.2.Electrical conduction of dangling-bond statesI clarified the relation between the electrical conduction of the surface states formed in bulk band gaps of semiconductors and the band-gap values.3.Electrical conduction of group-IV semiconductor. (111)2×1 structuresI studied the effect of surface structures, particularly, the existence of buckling on electrical conduction. Furthermore I studied the electrical conduction of double-tip STM and clarified the relation between the effective mass of surface-state bands and the electrical conductance of double-tip STM.4.Surface electrical conduction of silicon nanowiresI studied the inhomogeneous electrical conduction in medium-sized nanowires. I found possibility of electrical conduction through edge states localized at the edges of nanowires.5.Electrical resistance of monatomic steps of Si(111) √3×√3-Ag and the resistance of Bloch wavesI calculated the electrical resistance of a step and explained the results obtained in a recent experiment. I found a new type of step state localized at the edge of the lower terrace of a step. Furthermore I provide a new definition for amplitude and phase of waves including evanescent waves and derived a new formula for the transmission of Bloch waves. I found that the resistance of Bloch waves is separated into two parts : One arises from the difference in Bloch wave numbers and the other from the discontinuity of logarithmic derivatives of the periodic part of Bloch waves.