Analytical solution of diffusion equation for point defects

TL;DR

This paper derives an analytical solution for the diffusion of intrinsic point defects in a finite one-dimensional domain, aiding the modeling of defect distributions during semiconductor fabrication.

Contribution

It presents a new analytical solution for point defect diffusion with Robin boundary conditions, applicable to semiconductor device manufacturing processes.

Findings

Distribution of point defects varies with boundary conditions and defect migration lengths.

Surface effects significantly influence defect concentrations during hydrogen ion implantation.

The solution helps predict defect behavior under different fabrication scenarios.

Abstract

The analytical solution of the equation describing diffusion of intrinsic point defects has been obtained for a one-dimensional finite-length domain. This solution is intended for investigating and modeling the changes in defect distributions during fabrication of semiconductor devices with layer-type structures. With this purpose, the Robin-type boundary conditions were imposed on both edges of the domain. Using the solution obtained, the calculations of distributions of point defects for different boundary conditions and different defect migration lengths have been carried out. For the case of generation of nonequilibrium point defects due to implantation of hydrogen ions, the influence of the surface on the concentration and spatial distribution of nonequilibrium point defects was investigated depending upon the implantation energy.