A model of high-and low-temperature phosphorus diffusion in silicon by a dual pair mechanism

Abstract

A model of phosphorus diffusion in silicon was developed on the basis of a dual pair mechanism; according to this model, the contribution of the impurity-vacancy (PV) and impurity-self-interstitial (PI) pairs to diffusion is accounted for directly in terms of the phosphorus diffusion coefficient. A violation of thermodynamic equilibrium in relation to native point defects occurs as a result of diffusion of the PI neutral pairs. At the high-temperature diffusion stage, the phosphorus diffusion is described by a single diffusion equation with the diffusion coefficient dependent on both the local and surface phosphorus concentrations; whereas at the next (occurring at lower temperatures) stage, the phosphorus diffusion is described by two diffusion equations for the total concentrations of the components containing phosphorus and self-interstitials. An anomalously high rate of the low-temperature diffusion is ensured by excess self-interstitials accumulated in the doped layer during the preceding high-temperature diffusion. The model makes it possible to quantitatively account for the special features of the phosphorus diffusion in a wide range of the surface concentrations at both the high (900–1100°C) and lower (500–700°C) temperatures.