Recovering Space Inhomogeneities by Means of Boltzmann Poison Systems
Thursday, May 2, 2019 - 9:00am - 9:50am
We discuss a numerical approach an inverse problem strategy associated to the Boltzmann-Poisson system of equations for transport of electrons in the reconstruction of space inhomogeneities for the background function associated to total charges. The objective of the (ill-posed) inverse problem is to recover the shape of distributions of ions or hole condensations, sometimes referred as doping profile in a nano scale device. Such inhomogeneous profiles can be viewed as source function in the mathematical model, from its current-voltage characteristics.To reduce the degree of ill-posedness of the inverse problem, we proposed to parameterize the unknown profile function to limit the number of unknowns in the inverse problem. This problem first was solved in the cases for recovering the shape of doping profiles in a Boltzmann Poisson problem for semiconductors in nano scale devices, in collaboration with Yingda Cheng and Kui Ren. This strategy extends to recovering the charge distributions on plasma sheath models by means of the Landau Poisson systems.