On the Mechanisms of Linearity Peak Modeling in Common-Emitter SiGe HBTs Using Mextram 505
Authors: Ding Xuewei , Niu Guofu , Li Yiao , Zhang Huaiyuan , Scholten Andries , Willemsen Marnix 
Published: December 2020

An important aspect of compact modeling for RF application is to accurately model the biasing current at which transistor linearity is maximized, i.e. where the third order intercept point, IP3, peaks. We have shown recently that for common-emitter SiGe HBTs, Mextram 504.12 has problem modeling the IP3 peak behavior at high injection [1]. We have further developed a couple of new modeling options in Mextram 505 [2] for CB junction depletion capacitance intended to improve IP3 peak modeling [1]. However, the detailed mechanisms of how these improved CB junction depletion capacitance models translate into IP3 peak modeling improvement remains unclear and require further investigation.
For instance, the collector current, which is the output current, consists of the transistor main current In that flows from the collector to the emitter, and the CB junction capacitance discharging current that flows from the collector to the base. With the change of CB junction depletion capacitance model, which distortion current is dominant, In or the CB discharging current, in determining IP3 peak? Through detailed analysis of the harmonic components of the individual branch currents at the collector node of the Mextram large signal equivalent circuit, we find that the In distortion current dominates in determining IP3 peak behavior.
The next logic question is if the In distortion current improvement with the Mextram 505 CB depletion capacitance models is directly due to the normalized base hole charge term, q1I in Mextram terminology, that goes directly into the In expression, or indirectly due to propagation of the CB discharging current induced distortion to IN, through circuit interactions. We will show that it is the later rather than the former with carefully designed custom Verilog-A codes of Mextram, by using separate CB depletion capacitance models in the main current equation formulation and the CB depletion charge equations. Changing the CB depletion capacitance model used in the main current equation leads to no visible changes in IP3, while changing the CB depletion capacitance model used in the CB depletion charge equation leads to obvious changes in third order output current and hence IP3. This proves that the observed third order distortion current improvement in In responsible for the improved IP3 peak modeling in Mextram 505 fundamentally results from the CB depletion charge term, despite the small values of third order distortion in the CB depletion charge current itself.
We will then further examine how reducing the CB junction depletion capacitance might affect IP3 and how the partition between extrinsic and intrinsic CB junction capacitance affects IP3 peak behavior. Interestingly, simply making all CB depletion capacitance extrinsic gets rid of the IP3 peak modeling problem in Mextram 504, implying that the high injection related increase of the intrinsic CB junction depletion charge control voltage Vjunc and its related smooth limiting parameter Vch are the root problems. A reduction of CB depletion capacitance, intrinsic or extrinsic, is found to be beneficial for IP3 peak improvement.
[1] G. Niu, H. Zhang, Y. Li, X. Ding, M. Willemsen, and A. Scholten, “Physics and Compact Modeling of SiGe HBT Linearity Using Mextram,” ECS Transactions, 86 (7), pp. 145-154, 2018.
[2] G. Niu, R. van der Toorn, J. C. J. Paasschens, W. J. Kloosterman, The Mextram Bipolar Transistor Model, 505.10, Model Definition Document, Auburn University, 2019.