Speaker
Description
Semiconductor technology plays an essential role in modern life today. Devices in \linebreak nanoscale including sensors using semiconductor technology have crucial real-world applications ranging from bio-sensing medical applications to energy conversion in solar cells as well as the generation of security keys in cyber-security. Modeling charge transport in semiconductor devices has been of great importance especially when random effect of dopant atoms are taken into account. Furthermore, reconstructing the unknown doping profile introduces a challenging infinite-dimensional inverse problem in semiconductor devices. Here, first, an overview of the mathematical modeling of charge transport in semiconductor devices using PDE models incorporating uncertainty sources is given. Then, a PDE-based Bayesian inverse problem for semiconductors is formulated, in which the goal is to reconstruct the uncertain doping function. To solve this inverse problem, an infinite-dimensional Bayesian approach is presented to sample the posterior using a Markov chain Monte Carlo method with a preconditioned Crank-Nicolson proposal. Furthermore, the presented approach is enhanced by a physics-informed prior to tackle the challenges including the high-dimensionality, ill-posedness, and limited electrode measurement data. Some numerical results of the reconstruction from the voltage-current measurements are presented.
