Spice-compatible modeling of high injection and propagation of minority carriers in the substrate of Smart Power ICs

• Spice compatible substrate model extension for high injection levels of carriers.
• Modelling substrate conductivity modulation due to injection of minority carriers.
• Simulation time improved of a factor 1000 with respect to TCAD.
• A compact model for the influence of contacts on minority carriers is introduced.
• Parasitic BJT base resistance simulated without additional fitting parameters.

Classical substrate noise analysis considers the silicon resistivity of an integrated circuit only as doping dependent besides neglecting diffusion currents as well. In power circuits minority carriers are injected into the substrate and propagate by drift–diffusion. In this case the conductivity of the substrate is spatially modulated and this effect is particularly important in high injection regime. In this work a description of the coupling between majority and minority drift–diffusion currents is presented. A distributed model of the substrate is then proposed to take into account the conductivity modulation and its feedback on diffusion processes. The model is expressed in terms of equivalent circuits in order to be fully compatible with circuit simulators. The simulation results are then discussed for diodes and bipolar transistors and compared to the ones obtained from physical device simulations and measurements.