High order model for describing the pattern formation processes on semiconductor surfaces

TL;DR

This paper introduces a sixth-order nonlinear mathematical model to describe nanopattern formation on semiconductor surfaces during ion beam bombardment, highlighting the impact of high-order terms on surface morphology evolution.

Contribution

The paper presents a novel sixth-order nonlinear evolution equation model for surface pattern formation, along with a pseudo-spectral numerical method for its solution.

Findings

High-order terms significantly influence surface morphology evolution.

The pseudo-spectral method effectively solves the new model.

The model enhances understanding of nanopattern formation processes.

Abstract

The self-organization processes of nanopattern formation on semiconductor surfaces under low energy ion beam bombardment is considered. The new mathematical model based on nonlinear evolution equation of the sixth order is presented. The pseudo--spectral method for periodic boundary value problem for this equation is discussed. The influence of high order terms on the evolution of the semiconductor surface morphology is studied.