A method for modeling the distributive effects of RC transmission line is developed which is applicable to cases in which one end or both ends are connected to the input signal. Nonuniform recursive segmentation is used. The segments are categorized into three types, with each modeled by a distinctive and asymmetric lumped circuit in $\pi $ topology. The number of segments is determined by the frequency range required. The new method is applied to model the distributed MOSFET gate and bipolar junction transistor base. Both frequency and transient response characteristics are much better modeled compared with existing methods.

Modeling the Distributive Effects of RC Transmission Line Using Recursive Segmentation and Applications to MOSFETs and BJTs

Two-section models for capturing the lateral ac emitter-current crowding effect, which is also known as the lateral nonquasi-static (NQS) effect, are presented following a consistent approach based on a model formulation for ac operating condition. Following the theoretical results, model formulations suitable for implementation in the large-signal domain are developed. The proposed two-section model performs better than the state-of-the-art model in both the large-signal and small-signal domains and appears to be suitable for accurately capturing the lateral NQS effect.

Modeling of the Lateral Emitter-Current Crowding Effect in SiGe HBTs

Recently, a wide class of market segments (e.g., health, material science, security, and communications) is tackled by circuits fabricated in BiCMOS technology, integrating silicon–germanium (SiGe) heterojunction bipolar transistors (HBTs) and passives. Currently, the reliability of SiGe HBT devices is a major concern, and much attention is given to self-heating (SH), that limits device performance and regulates their degradation during stress. Moreover, its relevance is supposed to increase with device scaling. In this paper, we explore the reliability issues of SiGe HBTs by combining dedicated experiments and TCAD simulations. We develop and calibrate a TCAD model that is then used to investigate SH effects in both operating and stress conditions. Results show the important role played by the back-end-of-line (BEOL) and by the substrate thermal resistance in dissipating the heat generated by impact ionization. The location at which defects are generated during stress and the microscopic properties of the defects are determined experimentally by means of dedicated noise measurements. Including defects in the TCAD model allows reproducing the degradation observed in stress experiments. Simulations of the SH effects on a stressed device in measurement conditions revealed the presence of a hole hot spot that suggests a possible physical mechanism involved in the degradation slowdown at long stress times reported in the literature.

Mixed-Mode Stress in Silicon–Germanium Heterostructure Bipolar Transistors: Insights From Experiments and Simulations

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.

https://hal.archives-ouvertes.fr/hal-02920343/document

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

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.

https://hal.archives-ouvertes.fr/hal-02920341/document

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

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.

http://ieeexplore.ieee.org/iel7/6954699/6981265/06981315.pdf

Small-signal modeling of the lateral NQS effect in SiGe HBTs

An accurate closed-form analytical model is proposed to predict the junction temperature and thermal resistance of silicon germanium heterojunction bipolar transistors, including the effect of back-end-of-line (BEOL) metal layers. A linear approximation is used in a thermal resistivity model of silicon to reduce the model complexity. A simple method is proposed to extract the necessary model parameters along with the BEOL thermal resistance. The model is validated with the TCAD simulation, and the scalability of the model is verified by the comparison with experimental data for different device geometries. The model shows excellent agreement with both TCAD simulation (without BEOL) and experimental data (with BEOL).

Shon Yadav

Papers

Small-signal modeling of the lateral NQS effect in SiGe HBTs

Modeling of the Lateral Emitter-Current Crowding Effect in SiGe HBTs

A Pragmatic Approach to Modeling Self-Heating Effects in SiGe HBTs

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

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