Shape optimization of a power MOS device under uncertainties

In this paper we focus on a shape/topology optimization problem of a power MOS transistor under geometrical and material uncertainties to reduce the current density overshoot. This problem, occurring in the automotive industry, yields a stochastic electro-thermal coupled problem. Its solution enables to investigate the propagation of uncertainties through a 3-D model, which affect yield and performance of a power transistor. In our work, the Stochastic Collocation Method (SCM) has been used for this purpose. In particular, uncertainties, which result from imperfections of an industrial production, are modeled by random variables with known a priori probability density distributions, for example, a Gaussian or uniform type. Then, the Polynomial Chaos Expansion (PCE) with the basis associated to the assumed distribution can be used to construct numerical methods for a stochastic representation of the random-dependent solutions. Furthermore, this optimization is formulated in terms of statistical moments such as the mean and the variance. The gradient directions of a bi-objective cost functional is calculated using the Continuum Design Shape Sensitivity and the PCE in conjunction with the SCM. Finally, the optimization results for a relevant nanoelectronics problem demonstrate that the proposed method is robust and efficient.