A Designer's Guide to CMOS RF Models

Clyde Washburn, Senior Scientist, Integre Technologies, LLC

January 11, 2006

Clyde Washburn, Senior Scientist, Integre Technologies, LLC

In recent years we have begun to see references to "RF" CMOS processes and to "RF" models for those processes. This article will explore what the real meanings of such "RF" designations are, and what their importance is for the RF circuit designer.

There tend to be three perspectives on RF CMOS design: that of lower frequency analog designers moving up their designs to higher frequencies; discrete RF/microwave designers making the transition to the integrated medium; and designers moving digital circuits such as SERDES to the highest frequencies that processes will support. Where it is helpful, we will use these viewpoints to frame the explanations of what is different in RF CMOS and in modeling for it.

The Substrate
The use of CMOS for traditional digital applications has evolved toward a low resistivity bulk substrate (Figure 1), with the devices built in a thin, high-resistivity epitaxial (epi) layer; as this tends to optimize both latchup performance and yield.

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Figure 1: The basic digital CMOS model is based on a low resistivity bulk substrate as the base.

The multiple metal interconnect layers tend to be similar in thickness, to preserve flexibility in routing complex digital circuits, making all layers are roughly equally good for routing.

For the low-frequency analog and digital designer, this is a relatively ideal substrate – parasitic capacitances returning through the (grounded) substrate see relatively little resistance compared to the capacitive reactance at the frequencies of interest, so simple extraction of parasitic capacitance is very effective in predicting actual performance. But the RF designer would see four negatives: a) the parasitic capacitances are, in effect, maximized by the low resistance of the substrate, and the transmission lines formed by metal interconnects in the oxide over the substrate, as a result, have a relatively low characteristic impedance; b) coils built over the substrate are, in effect, closely coupled to a shorted turn – the substrate itself – thus decreasing both inductance and Q appreciably; c) currents reaching the substrate, whether as currents in capacitive reactances or by induction from coils, travel freely for long distances in the low resistance of the substrate; and d) attempting to improve coil Q by paralleling metal layers helps little, since if the optimal top layer was used first, additional layers are closer yet to the shorted turn in the substrate, and yield little net improvement.

What is an "RF" CMOS process then, compared to the ubiquitous digital variety just described? In most cases, it is simply making the entire substrate have the high resistivity of the epi layer in a typical "digital" process, Figure 2.

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Figure 2: Changes to the modeling of the substrate make the digital CMOS model more reflective of the RF situation.

Now the RF designer sees something quite different – the significantly insulating substrate, in effect, creates a second (small, due to the thick dielectric) capacitor in series with each parasite, functionally shunted by the (high) substrate resistivity.

Parasitic capacitance acquires an additional, significant series resistive component with several positive effects: large parasites, like the bottom capacitance of a bonding pad, approach a constant resistive impedance at higher frequencies, as the resistance in the substrate return dominates the capacitive parasite above; coils Q’s improve markedly owing to the high resistance of the substrate as a (poor) shorted turn, and substrate currents tend to be inhibited and confined by the significant lateral resistance of the substrate – isolation improves.

Paralleling metal layers for higher coil Q brings better results, and typically a thicker top metal layer, sometimes with higher conductivity copper in lieu of aluminum, is added to give a big boost to coil Q. Note that a device built in this "RF" substrate has essentially the same basic characteristics as in the digital process – the upper few microns where the devices are formed is the same resistivity in both cases.

The BSIM3 Model
Most CMOS designers have encountered the ubiquitous BSIM3 model is its various revisions, such as BSIM3v2 and others. It was enormously important in the success of CMOS for commercial purposes, because it had a sensible mix of physics-based and empirical parameters, and was readily adapted to new processes. The physics analysis anticipated what would happen as dimensions shrunk, while the empirical components allowed useful approximations of the non-uniform elements of fabricated devices. It is important that the RF designer understand what the implications of this important modeling technique are at the higher frequencies, so we will describe how such a model is created by a typical foundry:

The population of the model’s parameters is typically accomplished by fabricating devices of various channel widths and lengths, which are then curve-traced at DC to yield the parameters that describe transconductance and resistance. Low-frequency capacitance measurements are then made to populate the capacitive parameters. Typically, an optimizer such as the Hspice Optimizer will be used, to massage the model parameters such that the best fit is obtained between actual data and modeled. When the resulting fit is not as close as desired over the entire range of possible device dimensions, the modeler may decide to "bin", i.e. cause the model to branch on device dimensions to multiple model parameter sets, each optimized for a smaller device size range. This resulting BSIM3 "compact model", as it is called in the trade, is well suited to rapid execution is simulators, and for use with P-cells (adjustable size parameter physical layout cells) in layout, giving designers great flexibility.

It is important to note what is absent: some device properties are not measured or input to the model--the resistances associated with the gate poly are one important example; nor are any high frequency measurements made. Therefore, the usefulness of the model at high frequencies lies solely in the accuracy as a function of frequency of the equivalent circuit it creates. Fortunately for most purposes, the accuracy is adequate, as the proliferation of commercial CMOS designs bears witness. But let's examine what the RF designer will find lacking:

If you simulate a BSIM3 device driven from a sweep frequency source and look at the phase angle of the AC current into the gate, relative to the voltage, it stays at 90 degrees. The device input fails to look significantly resistive at high frequencies, as it does in reality due to the series resistance of the polysilicon gate, Reference 1.

How does this manifest itself as a design problem? Minimum Noise Figure for RF devices normally occurs when the source impedance is approximately the geometric mean of the total of series noise sources (such as the 1/G_m-related effective resistances, plus the gate effective series resistance) and the parallel-equivalent input impedance, optimizing the signal to noise voltage ratio. But BSIM3 doesn’t represent the gate resistance as a noise source, or place it in series with the input capacitance, to become the parallel input resistance at a given frequency.

As a result, it is not possible to determine optimum RF noise match, nor accurate simulation of RF noise performance, with the BSIM3 model. And the failure to model the parallel resistive component of input impedance has implications for high-speed digital applications like SERDES: the unmodeled, decreasing the parallel resistive input component with frequency causes both the frequency domain and delay behavior to have significant errors in the gigahertz range.

For many years this situation prevailed because the major CMOS foundries’ modeling groups had neither the familiarity nor the equipment to evaluate their processes at higher frequencies. Eventually, the discrepancy in performance between simulation and actual for RF uses could no longer be ignored, and attempts were made to improve results. But since the BSIM3 model was still very effective for the vast majority of CMOS designers, the first attempts at improvement would be additions outside the BSIM model, rather than significant revision.

The BSIM3-plus-Subcircuit Model
The fundamental problem with the BSIM3 model for RF use was not that it was wrong in itself, but rather that it ignored physical factors that influence high frequency operation. This is illustrated by noting that some foundries have used the very same BSIM3 model inside an RF subcircuit as is used in the digital version of the same process; there is nothing about the way the BSIM3 model is extracted that causes it to be populated differently for a epi vs. uniform substrate of the same resistivity at the device level.

But at higher frequencies, the appreciable resistance in the drain- and source-diode substrate returns, and in the back-gate return, may not be insignificant. Typically, the physical layout used for RF devices will differ, often having heavy gate-head connections (and perhaps even double-headed gates) so as to minimize gate resistance, but also altering the overlap and parasitic capacitances in a dimensionally-dependent way.

So it was easy to gain some improvement by enclosing the BSIM3 model in a subcircuit, Reference 2 and Figure 3, which added R and C passives, and sometimes replaced the BSIM3 source- & drain-diode modeling to reflect the substrate change.

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Figure 3: Simple enhancements to the BSIM3 model improve its validity.

The device width per finger is typically fixed to one, or a small number, of values, at which subcircuit values have been extracted at common operating points.

But this was to be a way-station on the route to better RF modeling, for there were significant remaining problems:

• Simulation speeds slowed, as the subcircuits increased component count, a bigger factor in speed than equivalent increases in compact model complexity.
• Subcircuits typically use fixed passives to stand in for what are actually voltage-dependent effects, with the result that distortion and power-efficiency prediction are poorer than desired, and model accuracy degrades at operating points other than the specific operating points at which extraction was done.
• The strongly empirical extraction of the subcircuit component values inhibits the use of P-cells for physical layout and easy device size changes in design, since the dimension-dependent subcircuit component values exist outside the compact model and its heavily physics-based approach to adequately predicting behavior in regions between extracted data points. Sizing is typically restricted to the choosing only the number of fingers at fixed width.

Thus, if we take two-port S-parameter data on a grounded-source CMOS device, then look at the same device in a simulator as a BSIM3 model in the same test circuit, the data won’t match well. If we place the device in a subcircuit, the data can be made to match, but only piece-wise, with many component values changing for different operating points. Still, for several years this was the best available approach, and may successful designs resulted.

BSIM4 – A Solution . . . or Not. . .
Fortunately the mainstream moved on as well. The combined effects of ever-shorter channel devices and increasing frequencies in most designs made the shortcomings of BSIM3 more apparent, which caused the BSIM4 model to emerge, Reference 3. What you need to know as an RF designer is that the BSIM4 model can be better, but it is not necessarily so.

This is because the traditional methods of populating the model parameters do not include high frequency correlation, and many of the parameters that improve high frequency accuracy can be either left out, or turned off, leaving the default high-frequency behavior as no improvement over BSIM3! Conversely, if all the capabilities of BSIM4 are used, it can do a good to very good job of matching S-parameter data over all operating conditions at the highest frequencies. So BSIM4 models are preferable to BSIM3+subcircuits models, if the foundry, or service providing the models, has correlated the models at high frequencies.

Similarly, BSIM4 includes back-gate resistance parameters that improve modeling of back-gate effects if the parameters are correctly populated, but few foundries even have suitable test structures developed to take advantage of this capability at present.

While BSIM4 potentially represents a significant improvement in RF-modeling speed and accuracy, it also is not without shortcomings, and two that are presently known are:

• It does not include polysilicon gate-depletion effects that alter (increase) the series-equivalent input resistance with decreasing frequency in the 0.1-10GHz range, Reference 4. These effects can be added to BSIM3 or BSIM4 models as an external RC subcircuit, but the resistances and capacitances are strongly non-linear, and we are back to spot-fitting the extracted data at one operating point. Investigators have recently shown that failing to include poly-depletion effects can have a significant impact on SERDES modeling for varying data run-lengths, Reference 5, and equivalent extreme wide-bandwidth RF applications such as UWB PHYs.
• The model is not yet fully symmetrical, meaning it doesn’t correctly handle operation in the vicinity of 0 V_ds, where source and drain interchange, and thus simulation of such circuits as passive FET mixers and attenuators is not as accurate as the typical drain-elevated regime, Reference 6.

Symmetry is being addressed in BSIM5, currently under development by the BSIM Committee, and while improvements in poly depletion modeling for BSIM5 have not been announced, the on-going research in that area makes it likely for eventual incorporation.

Conclusion
It is important for the designer to understand more about CMOS models than whether they have the sobriquet "RF" attached. A BSIM4 model which is well-correlated at RF can be highly accurate from DC to microwave frequencies over all operating conditions, while a more elaborate "RF subcircuit" model can be appropriate for only a narrow range of conditions. Find out what type of high frequency correlation is done on the models in your target process, and then consider what the implications of what is not done may be for your design.

About the Author
Clyde Washburn is Senior Scientist at Integre Technologies, LLC, www.integretek.com, where he specializes in CMOS RFIC design and modeling. Previously he was s Distinguished Researcher in the same field at Rochester Institute of Technology, and a Distinguished RF Engineer with LSI Logic Corp. His first CMOS design was begun at Harris Corp. in 1977. He holds 11 issued RF and/or IC-related Patents, and has two patents pending. He can be reached at clydew@integretek.com

References

1. E. Abou-Allam & T. Manku, A Small-Signal MOSFET Model for Radio Frequency IC Applications, IEEE Trans. On CAD of ICAS, May, 1997
2. C. Enz & Y. Cheng, MOS Transistor Modeling for RF IC Design, IEEE JSSC, Feb., 2000.
3. C. Doan et al, Next Generation CMOS Compact Models for RF and Microwave Applications, IEEE RFIC Symp., 2005
4. S. Bandi et al, Effect of gate Poly-silicon Depletion on MOSFET Input Impedance, IEEE MWCL, tbd, 2006
5. S. Bandi et al, Accurate Performance Prediction of Multi-GHz CML with Data Run-Length Variations, IEEE ISCAS, May, 2005
6. C. Doan et al (above)