An exact derivation of contact resistance to planar devices
Abstract
An imperfect, rectangular contact to a semiconducting sheet is formulated as a mixed boundary-value problem. This problem is solved by conformal mapping to yield the complex potential function as an eigenfunction expansion. The result can be used to calculate exact contact resistance if specific contact resistivity is known. With voltage probing data, it can also be used to confirm estimates of specific contact resistivity. The expression for contact resistance resembles that for a perfect (lossless) contact 1-2 but includes an extra term involving the lowest-order coefficient a0 from the expansion. Contact resistances are calculated and compared with the values obtained from three approximate models; the lossless contact, transmission line, 3-4 and extended transmission line models. 5-6 Up to a common normalization constant, the contact resistances predicted by all models are completely determined by two dimensionless parameters. These define the validity ranges for the approximate models. Compared to the present model, the extended transmission line model appears to be a very satisfactory approximation if the ratio of electrode length to sheet thickness is not less than 0.5.
- Publication:
-
Solid State Electronics
- Pub Date:
- May 1978
- DOI:
- 10.1016/0038-1101(78)90003-5
- Bibcode:
- 1978SSEle..21..715S
- Keywords:
-
- Contact Resistance;
- Metal Surfaces;
- Planar Structures;
- Schottky Diodes;
- Semiconductor Junctions;
- Conformal Mapping;
- Current Distribution;
- Eigenvectors;
- Equipotentials;
- Laplace Equation;
- Mathematical Models;
- Performance Prediction;
- Electronics and Electrical Engineering