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An asymptotic analysis of the Gunn effect in two-dimensional samples of bulkn-GaAs with circular contacts is presented. A moving pulse far from contacts isapproximated by a moving free boundary separating regions where the electricpotential solves a Laplace equation with subsidiary boundary conditions. Thedynamical condition for the motion of the free boundary is a Hamilton-Jacobiequation. We obtain the exact solution of the free boundary problem (FBP) insimple one-dimensional and axisymmetric geometries. The solution of the FBP isobtained numerically in the general case and compared with the numericalsolution of the full system of equations. The agreement is excellent so thatthe FBP can be adopted as the basis for an asymptotic study of themulti-dimensional Gunn effect.Comment: 19 pages, 9 figures, Revtex. To appear in Phys. Rev.

Free-boundary problems describing two-dimensional pulse recycling and motion in semiconductors