Analytical current-voltage relations for compact SiGe HBT models. I. The “idealized” HBT

Based on the generalized integral charge control relation (GICCR), analytical current-voltage relations for “true” SiGe heterojunction bipolar transistors (HBTs) are derived, which are well suited for compact physically based transistor models. For this, the weighted minority charge in the collector, which proved to be of dominating influence at high current densities, is calculated from simple physical expressions. They contain the operating point as well as physical and technological parameters. The model equations, which serve as a basis for a new physically based compact SiGe HBT model called SIGEM, are verified up to high current densities by numerical device simulations. It is shown that not only the static behavior but also the small-signal parameters y₂₁ and y₂₂, which are more sensitive to potential model errors, are well described even far within the high-current region. In this first part of the paper, the work is restricted to HBTs with idealized and simplified doping profile. In the second part [2] it is shown how these equations can also he applied to HBTs with modified, more practical doping profiles and how the model parameters can be extracted