Adjoint Method for Increasing the Breakdown Voltage and Reducing the On-State Resistance in Wide Band Gap Power Transistors

Abstract

In this article we introduce a mathematical algorithm for the optimization of the doping distribution in power semiconductor devices in order to increase the breakdown voltage and decrease the on-state resistance of these devices. The algorithm is based on the computation of the doping sensitivity functions of the breakdown voltage and on-state resistance and uses a gradientbased iterative method to compute the optimum doping profile in metal-oxide-semiconductor field-effect transistors (MOSFET), insulted gate bipolar transistors (IGBT), p-n junctions, etc. Since the optimization is performed using gradient descents it is perfectly suited for the optimization of doping concentration at all the nodes of finite element discretizations simultaneously (in which the number of nodes can be as large as 10 4 -10 6 ). Due to the large simulation time of each individual device, traditional heuristic optimization methods such as genetic algorithms, swarmoptimization, or evolutionary algorithms are practically impossible to use (traditional heuristic optimization algorithms are used when the number of optimization variables is smaller than 10). Numerical results for the doping sensitivity functions of the breakdown voltage and on-state voltage are presented and discussed for a standard IGBT device.

Optimization of Doping Profiles in Insulated-Gate Bipolar-Transistors Using a Large Scale Optimization Technique

“…In the case of finite element models, which often require the IGBTs to be discretized in around 10 4 nodes, the computation time required for the evaluation of the doping sensitivity function becomes unpractical even on large computer clusters since the number of nodes is relatively large. Therefore, in this work we use an algorithm based on the adjoint method, algorithm that we developed previously in ( 6)- (8). Below, we summarize the most important results, but the reader can consult the above references for more information.…”

“…In addition, we denote the magnitude of the electric field in the semiconductor at breakdown by   E, XD . Using these notations, it can be shown that the doping sensitivity function of the breakdown voltage is equal to   E  r can be evaluated by solving the following linear system of equations [8] where g is the unknown variable and X F is the Jacobian of the discretized system of governing equations and, then, calculating [9] where E  are the vector discretized values of   E  r and D F are the derivatives of the governing equations with respect to the doping concentration.…”

Sensitivity of Breakdown Voltage of Power Transistors to Dopant Impurities

“…This method is based on small-signal perturbations and completely circumvents the above drawbacks of the direct method. For more information about how to utilize the adjoint method to compute the sensitivity functions in power devices we recommend (1).…”

“…We have recently presented a method for the optimization of the doping profiles to increase the breakdown voltage (V BR ) and decrease the on-state resistance (R ON ) in power semiconductor devices (1). The method is based on computing the doping sensitivity functions of V BR and R ON and using these sensitivity functions to perform a gradientbased optimization of the doping profile.…”

“…The breakdown voltage and on-state resistance should be regarded as functionals of the doping concentrations. The optimization in [1] and [2] is performed over the entire region of semiconductor material.…”