# Calculation of the bidimensional electric potential in a polycrystalline semiconductor Schottky junction

- Authors
- Journal
- Solid-State Electronics 0038-1101
- Publisher
- Elsevier
- Publication Date
- Volume
- 29
- Issue
- 9
- Identifiers
- DOI: 10.1016/0038-1101(86)90007-9

## Abstract

Abstract In a Schottky p-type polycrystalline junction, two kinds of space-charge layers exist, one due to junction and the other due to the grain boundaries (GB). In such a case, the potential V( x, y) is a solution of a two-dimensional Poisson equation, where x is the distance from the junction and y from the GB. A case is considered where the crystallites are columnar, all the grains are identical, and the doping concentration is N A cm −3. We assume that the GB introduces energy states (i.e. traps) which are equivalent with another effective doping N B cm −3. The existence of a junction perpendicular to the GB causes the width of the GB space charge to decrease. The interaction between the two space charges is expressed by a parameter γ = ( W B 0 − W B(0)/ W J, where W B 0 and W B(0) are the widths of the GB space charge without, and with, a Schottky junction, respectively, and W J is the width of the space charge of the junction. The Poisson equation is solved and the potential is V(x,y)= qN A 2ϵ x 2+ N B N A y 2−γ N B N A xy− 2W j−γ N B N A W 0 B x− N B N A [W B(0)+W 0 B]y . The term- γ q N B xy /2 ϵ appears due to the interaction of both space charges. The electric field, the GB energy barrier and the capacitance are calculated from the potential and are x and y dependent. An equivalent circuit for the distribution of space charges is obtained and could be used in the interpretation of experimental results.

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