Theory of electrothermal behavior of bipolar transistors: Part II - Two-Finger devices

A thorough theoretical and numerical analysis of the electrothermal behavior of two-finger bipolar transistors is presented. It is shown that thermal feedback and coupling effects introduce an additional singularity in the output I-V characteristics, namely a current bifurcation, which manifests itself as multiple solution branches emanating from a branching point. As a result, when the bifurcation condition is reached, the device is triggered in an asymmetrical operation mode in which one device carries most of the current. A unified formulation for the electrothermal behavior of a two-finger device is derived for different bias conditions at the input port: constant voltage, constant base current and constant emitter current. The analysis proofs that the critical condition defining the onset of current bifurcation is the same for all kinds of bias conditions. While operation under a constant base-emitter voltage is limited by the flyback condition, the current bifurcation condition defines the boundary of the normal operation region for the constant base current and constant emitter current cases. Finally, a rigorous method for identifying the conditions of thermal instability for an arbitrary number of emitter fingers is outlined. As an example, the method is used to derive the thermal instability conditions for the general case of temperature dependent thermal conductivity in a two-finger device.