In the field of micro- and nanoelectronics, feature sizes are steadily shrinking, see e.g. G. E. Moore, “Cramming more components onto integrated circuits”, Electronics, vol. 38, no. 8, 1965. Power densities increase and with them the need for thermal considerations. Since resulting temperature fields may raise system failures, an electrothermal analysis is required. A common example is the failure of bond wires in microelectronic chip packages when exceeding a critical temperature.
Today’s complexity in the design and fabrication of electronic components leads to a great significance of numerical simulations. The simulation of models with large variations in component sizes requires specific numerical techniques to avoid high computational costs. Field-circuit coupling is just one of the possible methods to establish efficient models. Another field of focus is the problem of manufacturing imperfections. Not only the geometry but also the material parameters are subject to uncertainty that needs to be quantified. For the efficient calculation of failure probabilities, reduced order models are essential.