Anjan Chakravorty

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.

Detailed formulations for DC and AC emitter current crowding are presented in view of developing an extended π-equivalent circuit (EC) model to accurately predict the lateral non-quasi-static effects in silicon germanium heterojunction bipolar transistors. Under negligible DC current crowding, the EC reduces to a simple π-model. The implementation-suitable versions of the models are also developed. Compared to state-of-the-art model formulations, the extended π-model shows better accuracy in predicting device simulated data. If desired, the high level of accuracy obtained by the extended π-model can be traded with the required extra simulation time due to one extra node.

A modified physics-based two-section model is proposed to accurately capture the lateral non-quasi-static effect in SiGe HBTs. A methodology is proposed to include the DC emitter current crowding effect in the existing two-section model framework. The proposed two-section model is implemented in Verilog-A. The large-signal transient and the small-signal AC simulations are carried out and the results are compared with the numerical device simulation data. The proposed model is observed to perform better than the existing two-section model and the state-of-the-art standard model from the perspectives of small-signal frequency-domain characteristics and large-signal transients.

In this paper, we extend the model developed in part-I of this work to include the effects of the back-end-of-line (BEOL) metal layers and test its validity against on-wafer measurement results of SiGe heterojunction bipolar transistors (HBTs). First we modify the position dependent substrate temperature model of part-I by introducing a parameter to account for the upward heat flow through BEOL. Accordingly the coupling coefficient models for bipolar transistors with and without trench isolations are updated. The resulting modeling approach takes as inputs the dimensions of emitter fingers, shallow and deep trench isolation, their relative locations and the temperature dependent material thermal conductivity. Coupling coefficients obtained from the model are first validated against 3D TCAD simulations including the effect of BEOL followed by validation against measured data obtained from state-of-art multifinger SiGe HBTs of different emitter geometries.

A physics-based model is proposed to accurately capture the lateral non-quasi-static (LNQS) effects in SiGe HBTs. The model uses new methodology to implement the internal base impedance of the device using two-RC circuits. Equations of all base impedance related components associated with the two-RC network are derived. The proposed model is implemented in Verilog-A. The small-signal AC and the large-signal transient simulations show that the two-RC model yields significantly more accurate results when compared with those of the state-of-the-art model and the π-model.

The state-of-the-art and π-models for the lateral non-quasi-static (NQS) effect are analyzed. The superiority of the π-model to capture the lateral NQS effect is demonstrated through small-signal simulations of both the models, implemented in Verilog-A. A hybrid model is proposed and a corresponding formulation of the base impedance is obtained. The equation gives the base impedance of the state-of-the-art as well as the π-model under appropriate conditions. The methodology to implement the hybrid model in Verilog-A is discussed. The hybrid model shows significantly higher accuracy than both the state-of-the-art model and the π-model when compared with the device simulation data.

A two-section equivalent circuit model with hybrid topology is proposed to model the base impedance of SiGe HBTs. The formulations suitable for implementation in compact-model are obtained. A simpler yet accurate method is also proposed to implement the hybrid two-section model. The models are implemented in Verilog-A and small-signal simulations are carried out. The proposed models predict the small-signal lateral NQS effect more accurately than the existing models.