Static thermal coupling factors in multi-finger bipolar transistors: Part I—model development

In this part, we propose a step-by-step strategy to model the static thermal coupling factors between the fingers in a silicon based multifinger bipolar transistor structure. First we provide a physics-based formulation to find out the coupling factors in a multifinger structure having no-trench isolation (cij,nt). As a second step, using the value of cij,nt, we propose a formulation to estimate the coupling factor in a multifinger structure having only shallow trench isolations (cij,st). Finally, the coupling factor model for a deep and shallow trench isolated multifinger device (cij,dt) is presented. The proposed modeling technique takes as inputs the dimensions of emitter fingers, shallow and deep trench isolations, their relative locations and the temperature dependent material thermal conductivity. Coupling coefficients obtained from the model are validated against 3D TCAD simulations of multifinger bipolar transistors with and without trench isolations. Geometry scalability of the model is also demonstrated.