Filamentary thermal instabilities in IMPATT diodes

The unstable growth of thermal filaments in a diode with a fixed bias current is calculated on the basis of a model which includes thermal conduction in the plane of the junction, as well as perpendicular to it. The growth time of the instability is shown to be longer than the thermal relaxation time by the ratio of the space-charge resistance to the differential negative resistance. Analytic results are obtained for small temperature disturbances which are initially Guassian functions of the transverse coordinate. If A is the area of the junction, the negative differential resistance must be of the order of the space-charge resistance multiplied by 16W²/π²A (where is the thickness of the active region) or the filament can dissipate itself by diffusing outward and spreading over the entire junction area before the temperature rise becomes very large. The voltage fluctuation relaxes to its equilibrium value in the thermal relaxation time, which is independent of the differential resistance. Pulsing a diode will tend to prevent an instability from becoming destructive, provided the off-time is long enough to cool the heated filaments which develop during the pulse transmission.