Generalized Model for the Clustering of As Dopants in Si

Abstract

A model for As clustering in single crystal silicon is presented that allows for the participation of arbitrary numbers of As ions, electrons, and arbitrarily charged vacancies. From this model the saturation behavior of the concentration of unclustered, electrically active As impurities is derived. It is shown that saturation (or electrical solubility) demands the participation of at least one negative charge in the formation of positively charged clusters, be it electron or negative vacancy. By analysis of our own experimental results and those by other authors, this general cluster model indicates that the participation of exactly one negative charge is the most likely case. In the course of this discussion the equilibrium saturation concentration of electrically active As is deduced from experiment as a function of temperature.

Phosphorus vacancy cluster model for phosphorus diffusion gettering of metals in Si

“…Deactivation of arsenic in silicon is known to be dominated by the vacancy cluster mechanism based on both theoretical and experimental evidence. [9][10][11][12][13][14] The deactivation mechanism of phosphorus is still under debate due to the lack of conclusive experimental observations. While some propose the formation of SiP precipitates as the major deactivation mechanism, 15 others suggest a vacancy cluster model similar to arsenic deactivation based on the similarities of phosphorus and arsenic in silicon.…”

Mechanisms of arsenic clustering in silicon

“…Here m is assumed to have the values between 2 and 4 to take into account the fact that the As cluster was formed around a vacancy with the subsequent injection of the self-interstitial. It is important to note that reaction (6) was first theoretically studied by Guerrero et al in paper, 23 which will be considered below.…”

“…were used in the basic model for the clustering of As in silicon proposed by Guerrero et al 23 Here m and k are the numbers of arsenic atoms and electrons participating in the clustering process; r is the electric charge of a cluster. The function C = C(C T ) was investigated by means of the mass action law combined with the charge conservation law for the cluster formation reaction on the assumption of local charge neutrality…”

Electro-Reaction-Diffusion Systems Including Cluster Reactions of Higher Order

“…In this paper we focus our attention to the treatment of electro -reaction -diffusion problems where a broad class of higher order reactions is involved. Again motivated from semiconductor technology among other volume and boundary reactions we consider reactions which describe the formation and disintegration of clusters (see [2,13,14,15])…”