Numerically stable compact strong avalanche model for four-layer device simulation

Abstract

Since strong avalanche is a central phenomenon in four-layer (PNPN) devices such as thyristors and TOVP’s, the usual compact model consisting of two transistors (PNP)-(NPN) must include a numerically stable strong avalanche model. To this end, Miller’s empirical expression for avalanche multiplication M(V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CB</inf> ) in bipolar transistors was modified to eliminate its singularity at the collector-base breakdown voltage (V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CBO</inf> ), by substituting a hyperbolic function for Miller’s equation when the collector-base voltage (V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CB</inf> ) is higher than 0.99999 V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CBO</inf> . The combined function is such that it converges asymptotically to a large but finite value for V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CB</inf> ≫V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CBO</inf> . Furthermore, the function and its first derivative were made continuous at 0.99999 V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CBO</inf> , thus ensuring stability under very strong avalanche. The model, as tested with four layer PSpice (PNP)-(NPN) simulations, did not show any instability or nonphysical results. The resulting limited multiplication factors introduced only a 0.2% voltage overshoot error at breakdown. It was also tested satisfactorily within a circuit based quasi-3D device simulator consisting of several thousand (PNP)-(NPN) transistor pairs.