Physics-based minority charge and transit time modeling for bipolar transistors

It has been well known for many years that the transit time model used in the SPICE Gummel-Poon model (SGPM) is not adequate for reliable design of circuits operating either at high current densities (including quasi-saturation), which is often the case in high-speed integrated circuits, or at low voltages, which is important for low-power applications. In addition, extraction of the SGPM´s transit time model parameters is often very difficult and time consuming. Although various proposals for modeling the transit time were published in the past, most of them are not suited for compact transistor models required in circuit simulation from a numerical, parameter extraction and lateral scaling point of view. In this paper, a set of minority charge and transit time equations is derived which are physics-based and laterally scaleable as well as suitable for incorporation into compact models. Experimental results of the new model are presented in terms of transit time and transit frequency versus bias (I_C, V_CE), geometry, and temperature, showing excellent agreement for different types of silicon homojunction bipolar transistors