Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part I—Model Development

Abstract

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.

Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part II-Experimental Validation

“…A planar heat source is assumed to be placed at the heating finger (z = 0) (see Figure 1 of [11]). If b is the fraction of the total dissipated power (P diss ) flowing towards the FEOL substrate (as sown in the zoomed portion of Figure 1) and (1 − b) is the fraction that flows upwards through BEOL, the substrate temperature profile T(z) under the heating finger along the z-direction can be written as…”

“…Analytical expression of T(z) presented in part-I [11] can be used to include the BEOL effect just by replacing P diss with bP diss . Eventually the resulting expression for T(z) reads…”

“…In a recent work [10], an empirical model considering both FEOL and BEOL effects was reported. In part-I of this work [11], considering the heat flow only through the FEOL substrate, we have reported physics-based geometry-scalable models of the static thermal coupling coefficients for multifinger SiGe HBTs with and without trench isolation. In this part, we extend the model of [11] to include the effects of heat flow through the BEOL metal layers in order to be able to verify our model with experimental data.…”

“…In part-I of this work [11], considering the heat flow only through the FEOL substrate, we have reported physics-based geometry-scalable models of the static thermal coupling coefficients for multifinger SiGe HBTs with and without trench isolation. In this part, we extend the model of [11] to include the effects of heat flow through the BEOL metal layers in order to be able to verify our model with experimental data. Modifications to the proposed model in part-I [11] in the presence of BEOL heat flow are presented in Section 2.…”

“…In this part, we extend the model of [11] to include the effects of heat flow through the BEOL metal layers in order to be able to verify our model with experimental data. Modifications to the proposed model in part-I [11] in the presence of BEOL heat flow are presented in Section 2. This is followed by a model testing with extensive 3D TCAD simulations in Section 3.…”