Analytical solution of the equations describing interstitial migration of impurity atoms

TL;DR

This paper presents an analytical solution for impurity interstitial diffusion in semiconductors, useful for verifying numerical models and simulating diffusion in ultra-thin layers, demonstrated through nitrogen diffusion in gallium arsenide.

Contribution

The paper provides a new analytical solution for impurity interstitial diffusion with Robin boundary conditions, applicable to modeling diffusion in nanometer-scale layers.

Findings

Analytical solution matches experimental nitrogen diffusion data in GaAs.

Parameter values for impurity diffusion were successfully derived from fitting.

Solution aids in verifying numerical models and simulating interstitial diffusion processes.

Abstract

An analytical solution of the equations describing impurity diffusion due to the migration of nonequilibrium impurity interstitial atoms was obtained for the case of the Robin boundary condition on the surface of a semiconductor. The solution obtained can be useful for verification of approximate numerical solutions, for simulation of a number of processes of interstitial diffusion, and for modeling impurity diffusion in doped layers with the decananometer thickness because in these layers a disequilibrium between immobile substitutionally dissolved impurity atoms, migrating self-interstitials, and migrating interstitial impurity atoms can take place. To illustrate the latter cases, a model of nitrogen diffusion in gallium arsenide was developed and simulation of nitrogen redistribution from a doped epi-layer during thermal annealing of GaAs substrate was done. The calculated impurity concentration profile agrees well with experimental data. The fitting to the experimental profiles allowed us to derive the values of the parameters that describe interstitial impurity diffusion.