To increase the breakdown voltage (BV) and, in the same time, decrease the on-state voltage (OSV) of wide-band gap transistors it is essential to carefully design the doping profile of these transistors in order to decrease the resistivity of the material during the on-state current flow and decrease the impact ionization generation rate in regions with high electric field during off-state. In general, the two problems depend on each other and there is trade-off between the increasing the BV and decreasing the OSV [1]. In this article we will analyze this tradeoff by using the formalism of doping sensitivity functions of the BV and OSV. These functions show how sensitive the BV and OSV are to infinitesimal variations of the acceptor or donor impurities inside the semiconductor. For instance, the doping sensitivity function of the BV, g_BV(r), shows how much the BV increases by adding one donor impurity at location r inside the device. Similarly, the doping sensitivity function of the OSV, g_OSV(r), shows how much the OSV increases by adding one donor impurity at location r inside the device. As we have shown in [2, 3], the doping sensitivity functions are instrumental in the optimization of WBG power devices.

The doping sensitivity functions of the BV and OSV can be computed efficiently by using the adjoint method. Once these functions are computed they can be coupled with gradient-based optimization methods to estimate the optimum doping profiles for acceptors, N_a(r), and donors, N_d(r), in order to increase the BV and decreases the OSV. At the conference we will describe the numerical implementation of the adjoint method for the optimization of WBG power devices and present simulation results for a vertical and horizontal SiC MOSFETs. More importantly, we will show that in general, in wide-band-gap MOSFETs and IGBTs, the doping sensitivity functions of the BV and OSV, g_BV(r) and g_OSV(r), respectively, and are not linearly dependent. Therefore, from a mathematical point of view, the BV and OSV are quantities that can be controlled independently by changing the doing profiles inside the transistor. Different equivalent ways to define and compute the doping sensitivity functions of BV and OSV will also be presented. The different definitions of the doping sensitivity functions will be compared to each other and the computational complexity will be discussed in each case.

[1] J. Baliga, Fundamentals of Power Semiconductor Devices: Springer, 2008.

[2] P. Andrei, "Using Doping Sensitivity Functions to Optimize Power Transistors," IEEE Workshop on Microelectronics and Electron Devices (WMED), Boise, ID, 2015.

[3] C. Zhu and P. Andrei, “Adjoint Method for Increasing the Breakdown Voltage and Reducing the On-State Resistance in Wide Band”, 231 ECS Meeting, New Orleans, 2017.

[4] P. Andrei and L. Oniciuc, "Suppressing Random Dopant-Induced Fluctuations of Threshold Voltages in Semiconductor Devices," Journal of Applied Physics, vol. 104, Art. No. 104508, 2008.