Martin Burger, Universität Linz (Koautoren: Heinz W.Engl, Peter Markowich, Paola Pietra)
Over the last decades, semiconductor devices have played a fundamental role in modern electronics. Recently, there has been a growing interest in mathematical methods for designing devices in an optimal way with respect to several criteria and in identifying relevant material properties. The quantity to be identified or optimized is the doping profile, which is the density difference of ionized donors and acceptors. In the most frequently applied doping technique of silicon devices, ion implantation, it is only possible to obtain a rough estimate of the doping profile by process modeling. In order to determine the real doping profile, reconstruction methods from indirect data have to be used.
In this talk we shall discuss two important inverse problems, namely the identification of the doping profile from measurements of the voltage-current map and from capacitance measurements. The voltage-current map links the applied voltage on the contacts to the output current in normal direction on a part of the contacts, close to equilibrium (zero applied voltage) it can be defined as a one-to-one mapping. The capacitance is the variation of the electrical field in normal direction on a part of the contact with respect to the applied voltage. For the sake of simplicity we restrict our attention to the variation around equilibrium. Besides the different types of data we shall also treat some important limiting cases, which arise from the original problem as asymptotics for certain parameters tending to zero, and allow a more detailed analysis.