Theoretical study on surface electrical conduction on nanometer scales

项目期内取得的主要成果如下：研究了sp杂化形成的表面态的电导率，阐明了s带和p带宽度、sp杂化强度与电导率之间的关系。该结果可应用于贵金属表面的肖克利表面态。阐明了半导体体带隙中形成的表面态的导电性与带隙值之间的关系。族半导体的电导率。（111）2×1结构我研究了表面结构的影响，特别是屈曲的存在对导电的影响。进一步研究了双尖STM的电导率，明确了双尖STM表面态能带有效质量与电导率的关系。硅纳米线的表面导电性研究了中型纳米线的不均匀导电性。我发现了通过纳米线边缘的边缘状态进行导电的可能性。Si(111)√3×√3-Ag单原子阶跃的电阻和Bloch波的电阻计算了一个阶跃的电阻，并解释了最近一次实验中得到的结果。我发现了一种新的台阶状态，它定位在台阶下层台阶的边缘。进一步给出了波的幅值和相位的新定义，并推导了布洛赫波传输的新公式。我发现布洛赫波的阻力分为两部分，一部分是由于布洛赫波数的不同，另一部分是由于布洛赫波周期部分的对数导数的不连续。

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.