Adjoint Method for Increasing the Breakdown Voltage and Reducing the On-State Resistance in Wide Band Gap Power Transistors
Authors: Zhu Chen , Andrei Petru 
Published: February 2020

A central problem in the power semiconductor industry is the design of wide band gap (WBG) devices with high breakdown voltage (BV) and low on-state resistance (RON). This problem is particularly difficult to solve because high BV requires large devices, in which the separation between the source and drain electrodes in the case of FETs or anode and cathode in the case of p-n junctions is relatively large, while low RON requires relatively small devices with high doping concentrations. For any given semiconductor material there is a trade-off between BV and RON, trade-off that is generally given by the overall dimensions and geometry of the device.
In this work we focus on the optimization of standard WBG MOSFET configurations [1], in which we optimize the doping profiles in order to increase the BV while keeping the on-state resistance constant. Our approach is based on applying an adjoint space technique that our group has recently developed for the design of nanoscale semiconductor devices, and which can be used to perform a multidimensional optimization of the doping concentration at each location inside the device using a doping sensitivity approach [2-4]. Note that traditional optimization techniques based on heuristic methods such as genetic algorithms or evolutionary methods are impractical in this case because of the large number of independent variables. For instance, for a finite element mesh with 104 nodes there are 104 independent variables (given by the doping concentration at each finite element), which makes the problem difficult to solve even on parallel or distributed computer clusters.
The method that we introduce in this presentation is based on the computation of the doping sensitivity functions of the BV and RON, which show how sensitive the BV and RON are when we add one additional acceptor or donor impurity inside the semiconductor. The doping sensitivity functions are instrumental in the optimization of WBG power devices. As we will describe in the full paper, the doping sensitivity functions can be computed efficiently by using the adjoint method. They can be coupled with gradient-based optimization methods to compute the optimum doping profiles for acceptors, Na(r), and donors, Nd(r). At the conference we will describe the numerical implementation of the adjoint method for the optimization of WBG power devices and present sample simulation results for a few standard structures. Our initial results show that by properly designing the doping profiles in standard power transistors we can increase the BV by 15-20% without affecting the on-state resistance.

References:

[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] 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.
[4] S. Aghaei, et al., "Challenges and Opportunities in Atomistic Dopant Profiling Using Capacitance-Voltage Measurements," in Advanced Semiconductor Manufacturing Conference (ASMC), 25th Annual SEMI, 2014, Saratoga Springs, NY, pp. 130-135, 2014.