Clustering of phosphorus atoms in silicon

TL;DR

This paper models negatively charged phosphorus clusters in silicon to explain electron density saturation at high doping levels, showing good agreement with experimental data and aiding high-concentration phosphorus diffusion simulations.

Contribution

It introduces a model of negatively charged phosphorus clusters that accurately predicts electron density saturation and matches experimental data across different temperatures.

Findings

Clusters with 3-4 phosphorus atoms fit experimental data well.

Doubly negatively charged clusters are most likely formation.

Model can be used for high concentration phosphorus diffusion simulation.

Abstract

To explain the effect of electron density saturation at high phosphorus concentrations the model of negatively charged phosphorus clusters was compared with the experimental data. A number of negatively charged clusters incorporating a point defect and phosphorus atoms were investigated at temperatures of 920 and 1000 Celsius degrees. It was established that for clusters incorporating more than one phosphorus atom calculated electron density reached a maximum value and then monotonically and slowly decreased with increasing the total dopant concentration. If the cluster incorporates 3-4 phosphorus atoms the calculated dependencies of carrier concentration agree well with the experimental data for both temperatures regardless of the negative charge state of the cluster (- or 2-). Moreover, for all investigated doubly negatively charged clusters the fitting parameter is independent on the temperature. It means that formation of doubly negatively charged clusters is most likely but it is difficult to choose between clusters incorporating two, three or four phosphorus atoms. From a good agreement of the calculated curves with the experiments it follows that the model based on the formation of negatively charged clusters can be used in simulation of high concentration phosphorus diffusion.