Heat transport and current crowding in IMPATT diodes

The current crowding due to the temperature dependence of avalanche breakdown is analyzed for the steady-state operation of an IMPATT diode mounted on a semi-infinite heat sink. The solution depends on a single new nondimensional number, the "Lambda" number, which we define here. This number can be determined from experimental data, and the current density and temperature distribution can then be determined from the results given in this paper. Experimental measurements of the I-V plot for a laboratory diode are shown to agree with the theoretical predictions. The theoretical model, which is based upon the assumption that the heat is entirely produced at the interface between the diode and the heat sink, is shown to agree with numerical results from a finite-difference program in which heat is introduced into a GaAs diode in a plane 0.5 µm above the interface. It is shown that electrical measurements of thermal resistance are related to an "effective" temperature which is about 15 percent below the temperature on the diode axis.