Avalanche Modeling in Mextram 505 and Implications on Circuit Simulations
Authors: Niu Guofu , Li Yiao , Zhang Huaiyuan , Scholten Andries , Willemsen Marnix 
Published: November 2022

This paper presents several recent advances in compact modeling of avalanche multiplication in Mextram 505, an industry standard transistor model, including both new model features and improved model implementations. Implications of these improvements on circuit simulation are illustrated using RF SiGe HBTs.
Feature wise, Mextram 505 adds a new physics-based model of the avalanche multiplication factor that accounts for the complex evolution of the epi-layer electric field at high current density, which can be activated with swavl=3. At a given collector-base bias VCB, the avalanche factor Gem is constant at low collector current density JC, starts to decrease when mobile electron density becomes comparable to epi-layer doping density due to charge compensation, and ultimately increases again when the base pushes out, and the electrical CB junction shifts to the epi-layer/buried layer interface. A parameter exavl can be used to turn on/off the rise of Gem at very high JC. An example of fitting IB versus IE for a common-base RF SiGe HBT at a fixed VCB=3V is given in Fig. 1. The measured base current is calculated from the difference of measured IE and IC, and hence shows some measurement noise. At low IE, Gem is constant, IB is linearly proportional to IE, with exavl=0, only the decrease of Gem with increasing JC is modeled, the IB bends upward at 0.05 A. With exavl=1, the rise of Gem at high JC is modeled, allowing the fitting of the downward bending of IB above 0.1 A. We will also discuss implications of such complex Gem behavior for RF linearity, particularly on the modeling of linearity sweet spots, i.e. biasing currents and voltages at which linearity peaks.
Implementation wise, Mextram 505 uses the main current In as the initiating current in calculating the avalanche current Iavl, i.e. Iavl = In*Gem, as opposed to using the epi-layer current Ic1c2, i.e. Iavl = Ic1c2*Gem in Mextram 504. While for DC I-V, one can always use slightly different Gem model parameters to achieve the same degree of fitting, we found that the Mextram 504 approach can lead to unphysically high avalanche noise in voltage-controlled oscillator (VCO) circuits in some cases. Users should inspect the waveforms of Iavl as well as In to determine if this problem exists. The root problem is that the epi-layer current Ic1c2 also includes the CB junction capacitive charge current, which should not experience avalanche as the corresponding electron motion occurs outside the space charge region. While the Iavl error introduced has a small absolute value, the noise it introduces is often significant, and significantly increases oscillator phase noise.
At the device level, this unphysical avalanche of capacitive charge current comes into play during modeling of the CB depletion capacitance, CCB, which is often extracted from off state y-parameter. Fig. 2 compares the CCB vs VCB simulated using In (505) and Ic1c2 (504) as avalanche initiating current, together with the CCB from measurement. The Gem value is shown on the right y-axis. When Gem approaches 1, the simulated CCB using Iavl = Ic1c2*Gem increases sharply, and becomes negative when Gem>1, a unphysical result users of Mextram 504 need to be aware of for high Gem biases. Using Iavl = In*Gem, as is in Mextram 505, the simulated CCB remains physical when Gem is high. An analytical model of such discrepancy has been developed using small signal frequency domain analysis and will be presented.
In Mextram 504 and earlier versions of Mextram 505, Gem is limited to be less than 1 and then further limited through elegant considerations that ensure the collector current increases monotonically with the external VBE. Such limiting, however, cannot possibly work for the dynamic charge current which is the issue in the off-state CCB example as well as the VCO example above, due to how model equations are implemented in circuit simulators. One side effect of this Gem limiting is that avalanche induced runaway cannot be modeled for investigating safe operating area (SOA). A switch swgemlim is introduced in Mextram 505.3 to allow the users to turn off Gem limiting for such modeling, as shown in Fig. 3. The new avalanche model in Mextram 505 also enhances its ability to accurately predict the SOA boundary due to electrothermal runaway from the combined effects of avalanche and self-heating.

Figure 1