Capacitance of p-n Junctions: Space-Charge Capacitance

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Abstract
Exact calculations of the total space‐charge density in a p‐n junction reveal it to be unrelated to the charge density assumed in the Schottky theory. The difference can be as large as orders of magnitude. Consequently, the space‐charge capacitance is also found, by detailed analysis, to be unrelated to the Schottky result. A simplified closed‐form solution is then obtained for the space‐charge capacitance using the Shockley injection relation. In symmetrical junctions, there is some agreement between the exact space‐charge capacitance and the Schottky result. In asymmetrical junctions, the space‐charge capacitance is nearly constant for negative biases. These results indicate the need for further detailed analysis of the capacitance of p‐n junctions.