Doping process control in silicon epitaxy (I). System identification

The transition behaviour of the phosphorus incorporation in silicon epitaxial layers grown in a CVD reactor has been investigated, considering the reactor as a linear control system with u = lg p⁰_PH3 (t) as the input and y = lg N(t) as the output. The response of system to both upward and downward step inputs has been studied experimentally, using SiH₄ and PH₃ sources. The dopant system of a horizontal silicon epitaxial reactor has been identified and a mathematical model relating to the transient behaviour of the system has been found. The parameters of the model have been estimated from layer growth experiments. The step response functions found can be approximated by an exponential function relating to n time constants T, all equal to each other. It was found for the system investigated that the second order model is of sufficient accuracy for the optimal control calculations described in the next part of this series.