Compact Modeling of Base Current High Injection Effect in SiGe HBTs
Authors: Li Yiao , Niu Guofu , Scholten Andries , Willemsen Marnix 
Published: December 2024

In bipolar transistor compact modeling, the forward mode base current typically consists of three components: space-charge recombination, back injection into the emitter, and neutral-base-recombination (NBR). At medium and high base-emitter voltages (VBE), the emitter back injection and NBR components dominate, and both increase exponentially with VBE. Deviation from the ideal behavior occurs at high VBE due to parasitic base and emitter resistance or self-heating.
However, in many SiGe HBTs, standard compact models fail to capture experimentally observed IB-VBE characteristics, where the base current (IB) exhibits a high injection behavior that is more evident at lower collector-base voltages (VCB), as shown in Fig. 1. The simulation is done with Mextram 505.2 with resistance and self-heating parameters already calibrated. At a relatively low VBE of 0.72 V, the measured IB starts to bend downward compared to its typical behavior shown by the model, causing the increase of beta with VBE from 0.72 to 0.82 V. Parameter optimization cannot possibly fit silicon data and a new base current model is called for.
Similar behavior has been observed by other groups and attributed to carbon-induced NBR [1]-[3]. Interestingly, the onset of this IB high injection occurs at a lower VBE than the onset of collector current (IC) high injection, which is typically due to Kirk's effect or quasi-saturation effect. Such IB high injection behavior also exhibits a complex VCB dependence. The change of IB-VBE slope is less visible at higher VCB due to self-heating, which increases IB.
We present a recently developed compact model of base current that models this high-injection effect. The foundation of the high-injection effect model is an analytical expression of the neutral base recombination rate applicable to all injection levels derived from SiGe HBT NBR physics. Based on experimental data measured on devices with different geometries, we model both the area component and peripheral component with separate temperature coefficients. The area component is subject to neutral base width modulation modeled by the same parameters used for the Early effect. A quasi-saturation-induced component is included to model the NBR after the electrical neutral base pushes out at high current densities. The quasi-saturation component has its dedicated parameters to account for the NBR at the SiGe-base/Si-substrate epitaxial growth interface discussed in [4] and [5]. This component comes into play at higher VBE.
Fig. 2 demonstrates the new model's capability in capturing the measured IB high injection behavior and its complex VCB dependence, as well as the much-improved fitting of the beta vs. VBE characteristics. The inclusion of the NBR high-injection effect in the base current model enables more accurate modeling of SiGe HBTs. The model has been implemented in Mextram 505.3 and later versions [6].
References:
[1] B. Barbalat, et al., Semicond. Sci. Technol., vol. 22, no. 1, pp. s99-102, 2007.
[2] A. Ildefonso et al., IEEE Transactions on Nuclear Science, vol. 70, no. 8, pp. 1797-1804, Aug. 2023.
[3] H. P. Lee et al., IEEE BCICTS, pp. 253-256, 2023.
[4] G. Niu et al., IEEE TED, vol. 45, no. 12, pp. 2499-2504, 1998.
[5] T. Takagi et al., IEEE BCTM, pp. 114-117, 2000.
[6] G. Niu, Mextram 505.3, released 2022.

Figure 1