Mathematical Problems in Engineering
Volume 5 (1999), Issue 1, Pages 83-95

A problem related to the hall effect in a semiconductor with an electrode of an arbitrary shape

P. A. Krutitskii, N. Ch. Krutitskaya, and G. Yu. Malysheva

Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia

Received 10 December 1998; Revised 8 February 1999

Copyright © 1999 P. A. Krutitskii et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A problem on electric current in a semiconductor film from an electrode of an arbitrary shape is studied in the presence of a magnetic field. This situation describes the Hall effect, which indicates the deflection of electric, current from electric field in a semiconductor. From mathematical standpoint we consider the skew derivative problem for harmonic functions in the exterior of an open arc in a plane. By means of potential theory the problem is reduced to the Cauchy singular integral equation and next to the Fredholm equation of the 2nd kind which is uniquely solvable. The solution of the integral equation can be computed by standard codes by discretization and inversion of the matrix. The uniqueness and existence theorems are formulated.