Unidimensional model of the ad-atom diffusion on a substrate submitted to a standing acoustic wave II. Solutions of the ad-atom motion equation

TL;DR

This paper analyzes and solves a Langevin-type equation describing ad-atom diffusion on a substrate under a standing acoustic wave, revealing how the wave creates an effective potential influencing ad-atom behavior.

Contribution

It introduces a detailed analytical and numerical solution to the ad-atom motion equation, highlighting the acoustic wave's role in shaping the effective potential landscape.

Findings

Acoustic waves induce an effective potential for ad-atom diffusion.

Minima of the effective potential indicate preferred ad-atom sites.

The effective potential's strength is compared to thermal and substrate potentials.

Abstract

The ad-atom dynamic equation, a Langevin type equation is analyzed and solved using some non-linear analytical and numerical tools. We noticeably show that the effect of the surface acoustic wave is to induce an effective potential that governs the diffusion of the ad-atom: the minima of this effective potential correspond to the preferential sites in which the ad-atom spends more time. The strength of this effective potential is compared to the destructuring role of the thermal diffusion and to the crystalline potential induced by the substrate.