An Analytical Model of Avalanche Multiplication Factor for Wide Temperature Range Compact Modeling of Silicon-Germanium Heterojunction Bipolar Transistors
Authors: Zhang Huaiyuan , Niu G. 
Published: February 2020

SiGe BiCMOS technology is currently being used to develop electronics for space applications due to the excellent performance of SiGe HBTs over an extremely wide range of temperatures, e.g. from 93K to 393K as found on lunar surface [1]. We have previously developed a Mextram based compact model with extensions to enable wider temperature modeling [2]. In that work, avalanche multiplication factor (M-1) was modeled using standard Mextram M-1 model [3], together with empirical temperature dependences of the two Mextram avalanche parameters, WAVL and VAVL.
This work presents a new analytical model of M-1 with improved performance in modeling both temperature dependence and current dependence, and fewer model parameters. The model equations are summarized in (1)-(3). VCB is collector-base voltage, IC is the collector current without avalanche effect. Voff is an offset voltage which can be made the same as the 300K collector-base junction built-in potential VdC in Mextram for the devices used. Interestingly, Voff is found to be temperature independent, which simplifies modeling. An and BnT are impact ionization coefficients. Like in standard Mextram, An is temperature independent, while BnT is temperature dependent. BnT extracted from our data can be approximately described by a linear temperature dependence between 393K and 93K. This differs from the parabolic temperature dependence in standard Mextram, which was based on fitting of measurements between 240K and 400K [4]. Voff, c, d are parameters needed for low current M-1, and current dependence is modeled through the IT0 parameter, in a similar manner as how current dependence is modeled in the room temperature M-1 model reported in [5]. For practical currents of interest, a single temperature independent IT0 is found to be sufficient. It is possible to lump BnT and d as a single parameter that varies with temperature linearly, one would also then need to make An model parameter as well. That will introduce two more model parameters, which we find unnecessary, at least for the device used.
Fig.1 shows (M-1) – VCB modeling results at low current from 93K-393K obtained using the proposed model and standard Mextram model. The device used is a typical first generation SiGe HBT technology with 50GHz peak fT. A clear improvement in the temperature dependence modeling can be observed. The VCB dependence at each temperature is also improved.
We have implemented this new avalanche model in the wide temperature range Mextram model of [2]. The same measurements and parameter extraction methods used in [2] are used here. Fig. 2 (a) - (e) show IC–VCE and VBE–VCE characteristics under forced IB base drive which are sensitive to the modeling of M-1 from 93-393K. The dash line in the IC–VCE plots indicates peak fT current. To illustrate the importance of current dependence modeling, all simulations are repeated by turning off the current dependence term in M-1. Observe that the decrease of M-1 with increasing IC is significant well below the peak fT current, as can be clearly seen from 300K and 223K IC-VCE plots.
REFERENCES
[1] J. D. Cressler, “On the potential of SiGe HBTs for extreme environment electronics,” Proc. IEEE, vol. 93, no. 9, pp. 1559-1582, Sept. 2005.
[2] L. Luo, Z. Xu, G. Niu, P. Chakraborty, P. Cheng, D. Thomas, K. Moen, J. Cressler, A. Mantooth, “Wide temperature range compact modeling of SiGe HBTs for space applications,” Proc. IEEE Southeastern Symposium on System Theory, pp. 110-113, March 2011.
[3] J. C. J. Paasschens et al., Model derivation of Mextram 504: The Physics behind the Model, Koninklijke Philips Electronics, 2004.
[4] P. Cullen, H. C. de Graaff, and W. J. Kloosterman, A weak avalanche model to be incorporated into the compact transistor model Mextram, Technical Note 353/87, Philips Nat.Lab., 1987.
[5] G. Sasso, M. Costagliola, N. Rinaldi, “Avalanche multiplication and pinch-in models for simulating electrical instability effects in SiGe HBTs,” Microelectronics Reliability, vol. 50, no. 9-11, pp. 1577-1580, 2010.

Figure 1