Set of equations for transient enhanced diffusion in shallow ion-implanted layers

TL;DR

This paper develops a set of equations to model transient enhanced diffusion in shallow ion-implanted layers, accounting for defect distributions and electric fields, and validates the model with experimental data.

Contribution

It introduces a comprehensive mathematical model for impurity diffusion that includes charge states, electric fields, and defect nonuniformity, improving understanding of surface diffusion phenomena.

Findings

The model explains uphill impurity diffusion near surfaces.

Numerical calculations match experimental boron profiles.

Considering defect nonuniformity enhances diffusion understanding.

Abstract

To simulate the transient enhanced diffusion near the surface or interface, a set of equations describing the impurity diffusion and quasichemical reactions of dopant atoms and point defects in ion-implanted layers is proposed and analyzed. The diffusion equations obtained take into account different charge states of mobile or immobile species and drift the mobile species in the built-in electric field and field of elastic stresses. The absorption of self-interstitials on the surface and drift of the defects due to elastic stresses result in the nonuniform distributions of point defects. It was shown analytically and by means of numerical calculations that consideration of the nonuniform defect distributions enables one to explain the phenomenon of "uphill" impurity diffusion near the surface during annealing of ion-implanted layers. The performed calculations of the boron concentration profile after annealing of a shallow implanted layer agree well with the experimental data confirming the efficiency of the proposed equations.