Multi-finger silicon germanium heterojunction bipolar transistors (SiGe HBTs) are primarily used in power amplifier circuits. High current operations of power amplifiers cause electro-thermal heating inside the device leading to a high junction temperature. Under an actual operating condition, all the fingers dissipate heat simultaneously, and the total junction temperature of a given finger results from self-heating as well as thermal coupling. The peak finger temperature due to these electrothermal effects severely degrades the electrical performance of the transistors. One needs an accurate prediction of the total temperature to precisely estimate the degraded electrical characteristics of the device and eventually a safe operating area. Also, in a conventional layout, a multi-finger transistor consists of uniformly spaced emitter fingers, which leads to an uneven temperature distribution across the fingers. Significantly higher temperatures at the inner fingers can worsen the reliability of the device and can lead to electro-thermal instability behaviours such as snapback. One can overcome these issues with a carefully optimized non-uniform finger spacing in order to obtain nearly uniform temperature at all the fingers. To date, such optimization is achieved through numerical simulations or complex analytical formulations, which are not suitable with a compact modelling framework. A simple, fast and accurate analytical model to solve this optimization problem is missing in the literature.

To cater to such needs, we have devised a new framework for extraction and modelling strategy of the total finger (or junction) temperatures in multi-finger transistors for the real operating condition. In this seminar, first, we present a new method to accurately extract the total finger temperatures from self-heating and thermal coupling measurements. Our approach requires no additional measurements than the current state-of-the-art heat-sense-based technique. The method has been validated with 3D-TCAD simulations and implemented for a fabricated on-wafer HBT. Following this, we put forward a new physics-based model formulation to accurately predict total finger temperature. The model has been validated against TCAD simulations and extracted measurement values of the total finger temperature. Finally, we show how this model can be deployed as an algorithm for achieving optimized values of finger spacing in multi-finger transistors. Such finger spacing results in an almost uniform total temperature value at all the fingers.