Finite difference analysis of radial phosphorus dopant distribution in Czochralski-grown silicon single crystals

The electrical properties of semiconductor devices are directly related to the dopant concentration in single crystals. Therefore, to make semiconduct or devices with controllable electrical properties, it is important to cont rol the dopant concentration accurately, both along the growth axis and in the radial direction. The dopant concentration along the growth direction c an be described by the normal freezing equation and is well understood, but the factors controlling the dopant distribution in the radial direction ar e not well understood. We, therefore, made a detailed, quantitative analysi s of the radial dopant distribution in Czochralski silicon crystals by solv ing the coupled Navier-Stokes, continuity, and energy equations for the sil icon melt flow and temperature fields, and by solving the diffusion and seg regation equations for the phosphorus distribution in the melt and in the c rystal. Good agreement between measured and simulated results of the radial phosphorus concentration in silicon single crystals was obtained. The melt was exposed to a background gas of At into which PH3 was added to countera ct evaporation of the phosphorus from the melt. Simulated radial phosphorus concentration distributions compared well with measured radial distributio ns, and the PH3 added to the background At gas increased the average melt d opant concentration and also improved the radial phosphorus concentration u niformity. (C) 2001 The Electrochemical Society.