A compact physical large-signal model for high-speed bipolar transistors at high current densities—Part I: One-dimensional model

A compact physical large-signal transistor model is presented that is suited for simulating high-speed bipolar IC\´s even if the transistors are operated deeply within the high-current region (including quasi-saturation). Like the well-known and currently used Gummel-Poon model, it is based on the integral charge-control relation (ICCR) proposed by Gummel. However, in the high-current region it shows much better accuracy, especially for high-frequency and switching operation. This is mainly a result of the fact that the transit time (and thus the minority-carrier charge) is chosen as a basic model parameter, which is carefully measured and accurately approximated by analytical expressions throughout the total interesting operating range. In Part I of the work, presented here, the model and its parameters are described for the one-dimensional case. Its validity is verified by comparison with exact numerical transistor simulations of both the dc characteristics and the switching behavior. The simulations are based on doping profiles that are typical of transistors in high-speed IC\´s. Methods for determination of the model parameters are presented. In Part II [1], the model is extended to the two-dimensional case, i.e., to real transistors. It is experimentally verified by measuring the dc characteristics and the switching behavior of very fast transistors with high transit frequency (fT≈ 7 GHz) and small emitter stripe width. The complete model, which is called HICUM (from "high-current model"), was already implemented in the circuit analysis program SPICE 2.