Refined Conformal Mapping Model for MOSFET Parasitic Capacitances Based on Elliptic Integrals

In this paper, the main MOSFET parasitic capacitances of planar devices (i.e., bulk, Fully depleted silicon-on-insulator (FDSOI), and planar double gate) are computed using two successive conformal mapping transforms. First, the structure is mapped to the real axis of the complex plane, and then the second transform, deduced directly from the Schwarz-Christoffel theorem, reduces the capacitance to the trivial parallel electrodes case. This second step involves elliptic integrals, which provide a generic expression for all parasitic capacitances. This method is later compared against other models based on conformal mapping. Finally, the results are validated with finite-element method simulations of the inner and outer fringe capacitances in different architectures, including metallic contacts and raised and faceted junctions.