Improved Modeling of High Injection Substrate Current in High Voltage Bipolar Transistors
Authors: Li Yiao , Niu G. , Chen Wei 
Published: February 2020

A vertical NPN transistor is typically built on a p-type substrate, which gives rise to parasitic PNP transistor action when the NPN base-collector junction, which is also the PNP emitter-base junction, is forward biased. In Mextram and Hicum, the PNP base terminal is attached to the NPN collector node that corresponds to the epi layer / buried layer interface, with VB1C1 as the PNP control emitter-base voltage, as illustrated in Fig. 1. A long physics based derivation to justify this choice was given in [1]. In Vbic, an option is provided to use both VB1C1 and VBC2 as PNP control voltage, with VBC2 as default. Using B or B1 is insignificant typically, while the difference between C1 and C2 is. While such approach generally works well for high speed transistors, for high voltage transistors, we experience great difficulty in fitting the substrate current at high VBE when the electrical base pushes out towards the collector, causing the internal NPN base-collector junction to be forward biased despite a reverse bias on the NPN external base-collector junction. Holes injected from the base diffuse downward towards the buried layer, and are retarded by a high electric field near the epi/buried layer interface, making the actual physics of hole transport much more complex than in a standalone PNP transistor. Fig. 2 (a) shows the best results one can possibly get with the standard Mextram model for a typical VBE sweep at VBC=0, -2 and -5V, VBS=2V. It is important to note that the VB1C1 = VBC + ICRCC –IBRBC in Mextram terms, with RCC and RBC being extrinsic collector and base resistances, respectively. Fig. 2 (b) shows the simulated VB1C1. For VBC=-2 and -5V, VB1C1 is still largely negative, while in measurement substrate current starts to rise quickly around VBE of 0.8V, indicating a rapid turn on of PNP action. This clearly suggests that the theory of [1] does not apply to these transistors, and improved modeling of PNP is needed.
An alternative is to use the intrinsic base-collector junction voltage VB2C2, i.e. VB2C2* in Mextram, as the PNP substrate current control voltage, which was suggested in [2]. This leads to a higher Isub as shown in Fig. 3 (a) and (b). However, the onset of Isub, and the high VBE values of IB are all overestimated. IC is underestimated due to overestimation of IBRBC. This, however, does suggest that the PNP action is in fact related to some kind of internal base-collector junction bias which relates to the epi layer state.
Here we propose a new model for the effective PNP emitter-base junction voltage, based on Mextram’s epi layer model. To minimize coupling of PNP and NPN modeling, we create a separate VB2C2, denoted as VB2C2**
, and calculate it exactly the same way VB2C2* is calculated from epi layer current IC1C2 and VB2C1, but with a set of dedicated epi layer model parameters, i.e. rcv, scrcv, ihc, axi and vdc. In parameter extraction, the regular epi layer model parameter set is used for fitting Gummel, output and fT curves, while this new set of Isub dedicated epi layer model parameters is used for fitting substrate current. Fig. 4 (a) and (b) show modeling results of our new model. IB and Isub are much better fitted, including accurate modeling of the onset of Isub.
[1] W. D. Mack and M. Horowitz, “Measurement of series collector resistance in bipolar transistor,” IEEE J. Solid-State Circuits, vol. SC-17, pp. 767-773, Aug. 1982.
[2] J. -S. Park, A. Neugroschel, V. de la Torre and P. J. Zdebel, “Measurement of collector and Emitter Resistances in Bipolar Transistors,” IEEE Transactions on Electron Devices, vol. 38, pp. 365-372, Feb. 1991.

Figure 1