Analytical estimation of breakdown voltage in insulated-gate bipolar transistors

In this paper, we derive closed-form equations for the breakdown voltage of punch-through and non-punch-through insulated-gate bipolar transistors (IGBTs). The derivation is based on computing the electric field in the drift region by invoking the depletion approximation and expressing the ionization coefficient as a function of the electric field using a power law. These approximations allow us to find closed-form solutions for the ionization integral and, then, compute the breakdown voltage of the IGBTs analytically as a function of the length of the drift region and doping concentrations in the buffer layer, drift region, and emitter junction. The analytical predictions are then compared to more reliable finite element simulations, and despite the approximations made in the analytical derivation, a very good agreement is observed for a large range of doping variations. In addition to designing purposes, the analytical model derived in this paper can be useful in developing new or improving existing compact modes for punch-through and non-punch-through IGBTs.