Field of Negative Point, Line or Plane Charges in an n-Type Semiconductor

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Abstract
In this paper we study the simplest solutions of the nonlinear differential equation which under certain conditions governs the quasielectrostatic field in a current‐free, n‐type semiconductor with a negative ``point'' charge in one, two, and three dimensions. Approximate solutions, valid for both large and small charges, are derived and compared with exact solutions, obtained by numerical integration. For small charge the approximation provides a useful estimate of the range of validity of the linear Debye‐Hückel theory, while for large charge it yields asymptotic expressions for the potential and the depletion layer radius.

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