Characterization of the Static Thermal Coupling Between Emitter Fingers of Bipolar Transistors

Abstract

A strategy for compact modeling the static thermal coupling between the emitter fingers of SiGe heterojunction bipolar transistors (SiGe-HBTs) is described. An extraction methodology that includes the nonlinear temperature dependence of the thermal conductivity is introduced and applied to suitable test structures. The experimental results are used for calibrating a 3-D numerical solution of the equation for heat conduction based on a Green's function approach. The latter can then be employed for generating thermal coupling networks for arbitrary transistor configurations.

Efficient modeling of static self-heating and thermal-coupling in multi-finger SiGe HBTs

“…It is observed that the high-V BE curves (0.9 V and 0.95 V) exhibit significant effects of electro-thermal heating. Also the predictions of the state-of-the-art thermal model of [6] [5] are identical with the results of our model. This proves that our model implementation indeed preserves the physical basis of [5].…”

“…2 does not use any VCVS in its implementation. Although the reduction in complexity for n = 2 is not visible, it is quite significant for n = 5 which requires only 10 extra nodes in our model in contrast to 25 extra nodes in conventional approach [5] [6]. In case of discarding the thermal coupling and considering only the selfheating effect in a multi-finger transistor simulation (which is very much unlikely), our approach still uses 2n extra nodes whereas the conventional approach uses only n extra nodes since the nodes across the VCVS (with 0 V) will collapse.…”

“…In case of n = 2, the problem is solved by using the four-node subcircuits as shown in Fig. 1, which is obtained following the state-of-the-art model described in [5] [6]. It is clear that the number of the circuit nodes increases as n 2 in such a model with n as the number of emitter-fingers in a transistor system.…”

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

“…The reduction of c ij with increasing P diss is due to the positional temperature-dependent thermal conductivity of silicon within the device. The same trend has been reported in other works such as [17,18,20]. For the multifinger device housed within DT, we employed the thermal spread model as detailed in Section 2.4 considering adiabatic boundary conditions at DT [13] to estimate ∆T jj,dt .…”

“…Figure 2b shows that in case of shallow trench isolated (STI) multifinger structures, the model of [19] yields further erroneous results for c ij with maximum error of around 57% when compared with 3D TCAD simulation. Note that following the standard practice, c ij is represented in percentage which is obtained by multiplying Equation (2) by 100 [17,18,20]. The poor modeling results in Figure 2a,b indicate the importance of using a temperature dependent thermal conductivity in the modeling framework and further to include the specific effects originating from the trench-isolations.…”