Impurity Diffusion in Silicon Based on the Pair Diffusion Model and Decrease in Quasi-Vacancy Formation Energy. Part One: Phosphorus

Abstract

The binding energy, E b, between a vacancy and a P atom or an As atom in Si is large. Therefore the pair diffusion model (PDM) and the decrease in quasi-vacancy formation energy are applicable to P and As diffusions. With the decrease in quasi-vacancy formation energy, E b also decreases. Fermi level obtained from the Boltzmann statistics is used. Anomalous diffusion of P consists of two components, a tail and a plateau. The tail has been attributed to excess vacancies, the generation of which is a characteristic of PDM. The plateau has been explained by PDM and the decrease in quasi-vacancy formation energy. The reason for this is given for the first time. It is emphasized that the large value of the phosphorus effective diffusion coefficient at the plateau is not anomalous but normal.

Non-Gaussian Diffusion of Phosphorus and Arsenic in Silicon with Local Density Diffusivity Model

“…6) are shown, simulating the concentration slope change from phosphorus like diffusion (r=0) to arsenic like diffusion behavior (r=0.4) as shown in Ref. [2] Fig. 10.…”

“…In Ref. [2] a sequence of arsenic diffusion profiles in silicon is published by Yoshida and Arai for arsenic diffusion under inert atmosphere in a temperature range from 850°C to 1000°C. These experimental data are used in this work for LDD model approximation (Equ.…”

“…Experimentally non-Gaussian diffusion profiles of phosphorus and arsenic challenge the mathematical and physical understanding of diffusion since decades. Physical models, like the pair diffusion model [1], result in improved understanding of interstitial and vacancy diffusivity correlation and in complex mathematical models with a number of separate empirical fit parameters for each experiment [1,2]. Based on non-Gaussian mathematical solutions of Fick's Equations a simple rational function diffusion (RFD) model was selected to be applicable for phosphorus diffusion profile approximation in silicon at mid and low concentration range without any empirical fit parameter [3].…”

“…The LDD model includes the rational function diffusion (RFD) model published in [3] and represents an improvement for near surface and tail concentration profile slope approximation by introducing just one single empirical fit parameter "r". This single fit parameter is related to the given combination of impurity species (phosphorus: r=0.18; arsenic: r=0.43) in the applied host lattice system (silicon), but does not vary while approximating different experiments with different impurity surface concentrations and penetration depths [1,2]. Based on the LDD approximation in this work a surface enhanced diffusivity for phosphorus and a tail decelerated diffusion for arsenic is suggested in comparison to RFD model approximation only.…”

Macroscopic description of the diffusion of interstitial impurity atoms considering the influence of elastic stress on the drift of interstitial species

“…Moreover, in [32] the charge states of impurity atoms and point defects were not considered, and the drift of charged particles in the built-in electric field was not taken into account. It was mentioned in [6,22,33,34] that the pair diffusion model is mathematically equivalent to the kick-out mechanism, but only in [22] the equation for impurity diffusion obtained for the kick-out mechanism was compared with the diffusion equation for the pair diffusion mechanism. In all these papers the case of stress-mediated diffusion was not considered.…”