Measuring Fmax for MOS Transistors

The following question has come up in comments: "How do I measure F_max for an MOS transistor?" The measurement methodology -- testbench, analysis, calculator setup, stimulus, etc.-- does not change whether you are measuring bipolar transistors or MOS transistors. On the other hand, the results for MOS transistors often come out looking wrong, or more correctly, non-physical.

Before scratching your head, adjusting your testbench or doing anything else, you need to consider the model that you are using. For review the fmax testbench is shown below. The testbench has two control loops -- a dc control loop that controls the drain current, and an ac loop that for measuring the s-parameters of the transistor. The control loops are isolated using inductors (dc short, ac open) and capacitors (dc open, ac short).  You could use analysis-dependent switches in place of the inductors and capacitors if you prefer.  

Figure 1: Fmax Testbench

Using this testbench, let's explore some different approaches to modeling a MOS transistor and see what happens. We will look at three different device modeling approaches:

1)      Using the standard bsim3v3 model

2)      Using the standard bsim3v3 model with RF extensions. The BSIM3v3 model does not account for the extrinsic elements of the MOS transistor that can affect the RF performance of the transistor, for example, the resistance of the gate, the substrate resistance, etc. 

3)       Use the bsim4 model. The bsim4 model includes the extrinsic components within the model.

We won't discuss the details of device modeling in this blog, if you are interested, you can find more information in the reference[1]. Please note that approach 2 and approach 3 are equivalent methods of implementing the model extensions discussed in the reference.

To compare the models, we will start by simulating the maximum unilateral gain in order to find the F_max, The results are shown in Figure 2 below. Let's look at what the simulation results are telling us about the transistor models. The results for the default bsim3v3 model look non-physical since the maximum unilateral gain has large peaks in the response at frequencies above 10GHz and the response does not roll off until almost 100GHz. However, both the bsim3v3 with RF extensions and the bsim4 model show the results we would expect, the gain is flat at low frequencies and rolls-off at high frequencies.

One additional comment about the simulation results. Due to some PDK limitations, the bsim3v3 models are from a 180nm feature size PDK, while the bsim4 data is from a 45nm feature size PDK. So the simulated F_max  is different due to process scaling and not due to differences in the modeling approach. For devices from the same PDK modeled using the two approaches, the F_max  should be consistent.

Figure 2: Comparing the Maximum Unilateral Gain

In previous blog posts, we have discussed the good things that simulation allows you to do, that is, perform measurements that you cannot perform in the real world. Idealizing testbench behavior or, more correctly, including exactly the phenomena that the designer specifies, is good when creating testbenches. The simulation will ignore all the higher order phenomena that degrade measurement accuracy.

So, for example, we can measure f_t directly in simulation instead of extracting it from s-parameters as we would have to do if we tried to measure it in the lab. On the other hand, simulation also ignores all the higher order device behavior that designers do not specify. As a result, effects that can degrade design performance are ignored.

The solution is to improve model fidelity, which will also increase model complexity and simulation time. So designers need to make a trade-off between how accurately to model a transistor's characteristics and their objectives when simulating. While an RF designer may want to use RF models, not everybody needs them. For example, if you are designing a Band-Gap Reference, then you probably don't need to use an RF model; you are more interested in modeling the effect of process variation on the circuit. 

In summary, simulating the F_max of a MOS transistor is similar to simulating the F_max of a bipolar transistor. As we discussed, you can use the testbench to perform sanity checks on your models to verify that they are appropriate for your application or select the best component from the PDK for your application. You can also use the testbench to optimize the performance for your operating conditions, that is, trade-off gate length and gate width to give the best F_max or Noise Figure for the given bias conditions.

Best Regards,

Art Schaldenbrand

References:

[1]  BSIM4v4.7 MOSFET Model User's Manual, Morshed et al., Chapter 9, High Speed/RF Models, page
       75-84       http://www-device.eecs.berkeley.edu/~bsim3/BSIM4/BSIM470/BSIM470_Manual.pdf