(Invited) Physics and Compact Modeling of Sige HBT Linearity
Authors: Niu G. , Zhang Huaiyuan , Li Yiao , Ding Xuewei , Willemsen Marnix , Scholten Andries 
Published: February 2020

SiGe HBTs, like other semiconductor devices, are in general nonlinear circuit elements. The exponential IC-VBE nonlinearity common to all bipolar transistors represents the strongest possible nonlinearity for all devices in which currents are produced by drift and diffusion of electrons and holes. Nonlinearity is desired for frequency translation and oscillation, but undesired for signal reception, amplification and transmission. In this talk we will review the fundamentals of various physical nonlinearities in SiGe HBTs, their complex interactions, experimental biasing current and voltage dependence of 2nd and 3rd order intercept points, IP2 and IP3, as well as recent developments in compact modeling of linearity using Mextram, an industry standard transistor model we are developing, for both common-base and common-emitter configurations.
From a circuit point of view, the consequence of nonlinear IC-VBE is to make effective transconductance gm,eff a function of small signal base-emitter junction voltage vbe , as opposed to a constant in a linear circuit. The nonlinear contributions in general increase with vbe, which in general decreases with increasing biasing current before high injection, making gm,eff closer to a constant. The linearity of a SiGe HBT amplifier can therefore generally be improved by increasing biasing current.
At radio frequencies, however, at relatively higher current, the 3rd order current produced by the nonlinear base-collector junction capacitance becomes important, and can interact with the 3rd order currents produced by the nonlinear IC, leading to a peak of IP3. Likewise, at higher VCB, as found in the common-base stage of a cascode amplifier, avalanche multiplication current Iavl produces an important 3rd order current that interacts with 3rd order currents from IC (without avalanche) and CBC, which can lead to a peak of IP3 in VCB dependence. Such peaks of IP3 are important for transistor biasing and sizing in circuit design, but also pose more stringent requirements on compact modeling than DC I-V and linear s-parameters. While both CBC and Iavl are straightforward to characterize and model at low currents, difficulties in both characterization and modeling increase at higher currents of interest.
Latest Mextram 505.00 provides several options for modeling VCB and IC dependence of CCB, which give similar y-parameters but different IP3, particularly for common-emitter configuration, as illustrated in Figure 1. New CCB model options for junction voltage and capacitance smoothing, swvjunc=1, swvchc=0, lead to much better modeling of peak OIP3 than swvjunc=2, swvchc=1, which reduces to 504.12. Recommendations of best options and parameters for accurate modeling of IP3 will be made. While CCB model also affects IC nonlinearity through Early effect, we will show that its impact on IP3 is primarily through capacitive current. We will also show that the IC dependence of CCB is import to include for IP3.
Common-base transistors often operate at higher VCB and hence with significant amount of Iavl. Mextram 505.00 has a new Iavl model that allows better current dependence and temperature dependence. Figure 2 shows this new avalanche model (swavl=1) has improved current dependence modeling of OIP3 over 504.12 (swavl=2 reduces model to 504.12) for a common-base SiGe HBT.

Figure 1