Transient temperature profiles within the active region of uniformly doped and high—Low doped Schottky IMPATT's

Abstract

Results of an analytical investigation of transient and steady-state temperature and current profiles within the active region of a variety of IMPATT structures are presented. The analyses are based on thermal models which assume power dissipation distributions with an axial dependence proportional to the electric field intensity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E(z)</tex> and a radial dependence proportional to the local current density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j(r)</tex> . Examples are presented in which the local current density is assumed to decrease with the local temperature according to the expression <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j(r) = a [V - V_{0} - b(T(r) - T_{0})]</tex> . The temperature gradients within the active region depend strongly on the doping profile. These analyses show that the maximum temperature at the edge of the active region can be as much as 25 percent higher than at the center of the avalanche region, especially for high-efficiency high-power structures where the ionization is highly localized and the electric-field intensity in the drift region is sufficiently high to prevent unsaturated drift velocities and depletion-layer modulation. Breakdown calculations using temperature-dependent ionization coefficients and axial temperature profiles suggest that actual temperatures within a device can be significantly higher than those measured experimentally by using a predetermined breakdown voltage versus temperature calibration curve. Curves are presented which show normalized current density and axial and radial temperature profiles within the active region of selected devices for various values of time.