Analysis of the Impurity Atom Distribution Near the Diffusion Mask for a Planar p-n Junction

Presented here are the results from a mathematical investigation of the impurity atom distribution within a planar p-n junction. Two fundamentally different diffusion processes are considered: In the first, a constant impurity atom concentration is maintained at the semiconductor surface; in the second, a fixed quantity of impurity atoms is involved in the entire diffusion process. The results of this investigation show than a one-dimensional approximation inadequately characterizes the impurity atom distribution within a planar junction, and that in theory, the planar junction is not at a constant distance from its impurity atom source. Instead, the junction is closer to its source at the semiconductor surface than deep within the bulk material. Further, it is shown that when diffusion takes place from a source of constant concentration density, the junction impurity atom gradient is maximum at the semiconductor surface. In contrast, this junction impurity atom gradient is shown to exhibit a minimum at the semiconductor surface when the total number of impurity atoms is time invariant throughout the entire semiconductor material.