Gunn instability in finite samples of GaAs II. Oscillatory states in long samples

Abstract

An asymptotic description is given of the well known phenomenon of charge density waves propagating in long samples of n-type GaAs with Ohmic contacts and voltage bias. Depending on the resistivity of the contacts, two types of waves are identified; charge dipoles appear for high resistivity contacts and charge monopoles for low resistivity contacts. The critical value of the resistivity separating both regimes, as well as the threshold voltages above and below which the waves propagate for a given resistivity are determined for a standard model of the Gunn effect. The processes of birth and growth of a wave near the cathode and of death at the anode are analysed. The period of the waves and the time evolution of the current through the sample can be inferred from the asymptotic analysis.