A model of clustering of phosphorus atoms in silicon

A model of phosphorus clustering during high concentration diffusion in silicon is proposed and analyzed. The main feature of this model is the assumption that negatively charged phosphorus clusters can be formed. The formation of singly negatively charged clusters incorporating one phosphorus atom and two phosphorus atoms was investigated. To compare the model with the experimental data the total phosphorus concentration, concentration of clustered impurity atoms, and electron density depending on the concentration of substitutionally dissolved phosphorus atoms were calculated for both cluster species. Consideration of clusters with negative charge makes it possible to explain the appearance of “plateau” on the charge carrier profiles obtained at high concentration phosphorus diffusion. The parameters describing phosphorus clustering at a temperature of 920  ° C were extracted from fitting the calculated values of the electron density to the experimental data.