Fast, quasi-3D modeling of base resistance for circuit simulation

Modifications are made to a finite-difference device simulator (PISCES) to model distributed base resistance. The simulator is modified to run in a quasi-3-D mode in which two numerically simulated dimensions model the lateral flow of the base current, and the third dimension is modeled with the modified Gummel-Poon (MGP) equations. The modulation of the intrinsic base sheet resistivity and the base current injection at each node are determined by the MGP model. Basewidth modulation, high injection, emitter debiasing, bias dependence of current paths, and interactions among these effects are studied for a variety of drawn geometries, sheet resistances, and temperatures. It is found that the standard models used in circuit simulation (SPICE) do not adequately model some of these effects. A model that adds an extra term into the function of base resistance is introduced to model these effects. Performing curve fits to the simulation results allows the base resistance parameters to be expressed as a polynomial sum in terms of geometry, the intrinsic and extrinsic sheet resistivities, and temperature