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.

在本文中，我们推导出了穿通和非穿通绝缘栅双极晶体管 (IGBT) 击穿电压的闭合方程。推导基于通过调用耗尽近似计算漂移区中的电场，并使用幂律将电离系数表示为电场的函数。这些近似值使我们能够找到电离积分的封闭形式解，然后，作为漂移区长度和缓冲层、漂移区和发射结中的掺杂浓度的函数，分析性地计算 IGBT 的击穿电压. 然后将分析预测与更可靠的有限元模拟进行比较，尽管在分析推导中进行了近似，对于大范围的掺杂变化，观察到非常好的一致性。除了设计目的之外，本文导出的分析模型可用于为穿通和非穿通 IGBT 开发新的或改进现有的紧凑模式。