Theoretical Assessment of Impacts of Energy Band Valley Occupation on Diffusion Coefficient of Nano-Scale Ge Wires

Abstract

The purpose of this paper is to theoretically predict the significant impacts of valley occupation on the overall diffusion coefficient of Ge nanowires physically confined by various surfaces. This paper derives an approximate analytical expression of the diffusion coefficient that exists around room temperature. In Ge wires physically confined by {100} surfaces, the overall diffusion coefficient is, around room temperature, almost constant for wire widths larger than 10 nm. However, a step-like decrease is found for wire widths smaller than 7 nm. This behavior of the overall diffusion coefficient stems from the fall in the L-valley component of diffusion coefficient and the rise of X-valley component of diffusion coefficient for wire widths smaller than 10 nm. The behavior of diffusion coefficient of wires physically confined by {111} surfaces is also investigated around room temperature. The overall diffusion coefficient is almost the same as the diffusion coefficient component of X valley because electrons primarily occupy X valleys. It is clearly revealed that the behavior of the diffusion coefficient is primarily ruled by the valley occupation fraction of electrons in Ge wires. These dominant features of the diffusion coefficient of Ge wires are quite different from those of Si wires. Simulation results are assessed in comparisons with past experimental results and past calculation results. Finally, additional consideration is given from the viewpoint of device applications.