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vivkr

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Re: Series transistors
Reply #15 - Nov 23^rd, 2006, 12:43am

Croaker wrote on Nov 21^st, 2006, 8:58pm:

For those series transistors, the body effect of course is going to come into play and reduce current drive.

Hi Croaker,

This argument seems thin. There should be no additional problem due to body effect in a series cascade of transistors as in a single MOS
device. After all, each segment of the channel (going from source to drain) has the same voltage distribution in either case, and so the body
effect is the same. It is misleading to treat devices in series as separate transistors as this leads to confusing deductions.

Regards
Vivek

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Croaker

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Re: Series transistors
Reply #16 - Nov 23^rd, 2006, 7:29am

Hmm, two series transistors look just like a 2*L single transistor: i=k*w/(2*l)*(Vgs-Vth)^2. However, the derivation to show this assumes the Vth in each transistor is equal.

So what value of Vth should be used for the equivalent transistor? The top transistor Vth is larger than the bottom one due to body-effect.

Assuming Vth stays constant with L, the long transistor should be driving more current than the series combination. It gets the full Vgs and Vth does not have body-effect. In the series chain, the Vgs for each additional transistor is a little less than the one before it, and each source is higher than the lower sources; less Vgs and higher Vth.

My point was I think there is a difference between one long one and a series chain. I hadn't thought about it too deeply before seeing this discussion.

Personally I'd use the series chain in order to keep the same L throughout the design (better for ratioing and Vth may vary significantly with L)

---

Here's a sim I did with 5 series transistors vs. one long one (m5 is the top of the series chain):

element 0:m1 0:m2 0:m3 0:m4 0:m5 0:meq
model 0:nfet 0:nfet 0:nfet 0:nfet 0:nfet 0:nfet
region Linear Linear Linear Linear Saturati Saturati
id 3.8642u 3.8642u 3.8642u 3.8642u 3.8642u 4.0681u
ibs 0. -241.9926a -516.9747a -843.8618a -1.2720f 0.
ibd -241.9926a -516.9747a -843.8618a -1.2720f -3.0000f -3.0000f
vgs 1.0849 1.0607 1.0332 1.0005 957.6938m 1.0849
vds 24.1993m 27.4982m 32.6887m 42.8133m 172.8005m 300.0000m
vbs 0. -24.1993m -51.6975m -84.3862m -127.1995m 0.
vth 799.7621m 806.9361m 814.9445m 824.2769m 836.2111m 801.5393m
vdsat 246.6516m 220.0844m 189.8273m 153.7734m 106.4267m 245.7596m

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vivkr

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Re: Series transistors
Reply #17 - Nov 23^rd, 2006, 8:21am

Hi Croaker,

Let's put your argument to a simple test. I take one single transistor of L=10um. Now, travelling along the channel with the
device in saturation, I see a varying channel potential with respect to gate as I travel from source (x=0) to drain (x=L).

For the moment, let's ignore all the various effects such as difference between drawn length and
actual length etc. that make a single transistor different from a series of several devices. Let us assume that
this splitting of the transistors is done only for the purpose of analysis.

I can split the channel at any point to create 2 sub-MOSFETs from one single device. I could for example split
the channel at x=5um to get 2 transistors with L=5um each. Now, the source voltage for the top transistor is say Vs1.

Again, I do a different kind of split, splitting the MOS at x=1um to get 1 MOS with L=1um, and another with L=9um.
The top transistor (9um) has source potential Vs2.

Vs2 < Vs1. So, Vth is larger for the top device when I split it into 5um-5um instead of 1um-9um, but it is the same 10um device.
As you can see, there are infinite possibilities for splitting L into 2 or more sub-devices in series, but all of them are the same device,
because a real MOS has a channel which has a finite length. Would there be a different amount of body effect simply because I choose to
analyze the same MOS in different ways?

Real scenarios will be slightly different because the drawn length is not the same as the actual channel length due to various errors
in processing. But, the difference is only because of this, and not because there is any extra body effect.

Perhaps, someone can find a flaw in my reasoning.

Regards
Vivek

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Croaker

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Re: Series transistors
Reply #18 - Nov 23^rd, 2006, 9:06am

That intuitively makes sense to me. I mean, physically, it seems right, since two in series have almost the same structure as a double-length one (except there is an implant in the middle of the series chain).

Well, I just worked out the equivalence and if you include body effect you'll get the result that two MOS in series kind of looks like a single 2*L MOSFET, but with an error term of:

k*W/2*(2*L)*(Vg - Vth)^2 + k*W/2*(2*L)*( -2*dV*(Vg - Vth) + Vx*dV + dV^2 )
^ looks like 2*L device ^ body effect error term

Vth2 = Vth1 + dV, and Vx is the drain voltage of M1. M2 is the top device, M1 is the bottom device.

I think I established through my simulation and my equation above that there is a difference, however slight, between the two structures. I think your statement about it not mattering how you split the L is true for a continuous channel, but perhaps not when there are implants between the top drain and bottom source.

With a long device, there is no body-effect, but if you start putting implants in the channel, each new device will have some body effect.

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imd1

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Re: Series transistors
Reply #19 - Nov 24^th, 2006, 3:59am

Hi all,

regarding the posts about equivalence of n series devices to a single one of n*L length, I'd say there's no difference, if
one ignores geometric effects (undercuts, etc). The implant is of the same type as the channel, so it forms a continuous
conducting path from one end to the other of the composite device. One long device is then equal (minus the geometric effects, etc) to several short ones in series, I agree with Vivek.

The implant will also introduce additional capacitance, and, leakage current, which *may* be the problem of the original post,
since it's biased at a few nano-amps, if I understood correctly. I don't know what is his/her testbench, or on what corner the problem appears (high temperature, high leakage ?).

My point in my earlier post was that , since the composite device and the output device aren't matched, and operate in different
regions (one in quadratic, the other in subthreshold), the simulator/model problems are possibly being magnified, and on some
corners it leads to large errors in the predicted current. It depends also on the testbench, is it a closed-loop transient analysis?
MC, including perhaps geometry variations ?

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Croaker Senior Member Offline Posts: 235	Re: Series transistors Reply #20 - Nov 24^th, 2006, 4:32am Yeah, I think they should be the same, but I'm having trouble reconciling this with my analysis. It doesn't take into account anything besides the fact that the top transistor will have a different Vth due to body-effect.
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RobG

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Re: Series transistors
Reply #21 - Nov 30^th, 2006, 12:59pm

I'm sorry I don't have a reference... but I'm pretty sure the body effect term is cancelled by something else so that two devices in series is the same as one with twice the L (possibly neglecting L's effect on Vt). I had this discussion with Dan Foty of Gilgamesh... he may have something in his book on modeleing devices. In other words, Vivek is correct.

At any rate, mosfets in series are (supposedly) a good way to accurately scale down a current by an integer, but here is the catch: BSIM simulations get it wrong. The reason, according to Foty, is that BSIM uses a source-based model. I don't understand what this means, but the take home point is that you need to be wary of the simulation results... there is something fundamentally wrong with the model when used for series devices.

One other thing, if the devices are not the same size you can get unexpected effects. For example, if the top MOSFET is in subthreshold, and the bottom transsitors are not, the top device will act as a cascode device, with the bottom device being fully saturated. This is called "self cascode" and is a common way to get a cascode without headroom loss if speed isn't an issue.

Personally, I've always had scary results when simulating series mosfets... it seems like they are always doing something funny unless I have long channels and have lots of overdrive (say 150mV or more). I personally try not to put them where it is important.

rg

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Croaker

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Re: Series transistors
Reply #22 - Nov 30^th, 2006, 1:51pm

RobG wrote on Nov 30^th, 2006, 12:59pm:

I'm sorry I don't have a reference... but I'm pretty sure the body effect term is cancelled by something else so that two devices in series is the same as one with twice the L (possibly neglecting L's effect on Vt). I had this discussion with Dan Foty of Gilgamesh... he may have something in his book on modeleing devices. In other words, Vivek is correct.
rg

Dan would be the guy who knows! If you can remember, please post.

Perhaps a source-based model means the device is not treated as truly symmetrical. No clue.

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RobG

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Re: Series transistors
Reply #23 - Nov 30^th, 2006, 2:04pm

Croaker... this is one of those questions that has always nagged me... I actually made a test chip to see how all this played out. It was a mirror with two outputs. The first output was a 1x device. The second output was two series devices in parallel (i.e. four devices). In theory, both should have the same current if the series device gives 1/2 the 1x current. The chip had an array of 256 of these pairs so I could eliminate random effects. I think I also had a 6b dac that used the series devices (like a M-2M dac).

I never found the time to fire up that test chip to measure those things. Now that I'm back in school I may go find that chip and see if I can't get a paper out of it...

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Croaker Senior Member Offline Posts: 235	Re: Series transistors Reply #24 - Nov 30^th, 2006, 8:38pm Hey wait, if the BSIM model is flawed for series devices, that strikes me as very bad. There are series devices all over the place! :o Are there specific cases where one has to be wary?
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RobG

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Re: Series transistors
Reply #25 - Nov 30^th, 2006, 9:34pm

Here is a simulation you can run. All transistors are W=20um amd L=10um (to keep things simple). The currents I1 and I2 should be equal, as should I3 and I4. I've plotted the ratio I2/I1 and I4/I3 versus the bias current (the current source on the far left). As you can see from the plot in the next post, there is a fair amount of error.

If we keep the gate/drain voltage constant, this error seems to be less than 10% (this is I2/I1). However, if the drains of the transistors are fixed while the gate votlage increases there is substantial error... the ratio is 0.6 at low currents when it should be unity. For what it is worth, the Vgs-Vt is 1.9v at 1mA for this process.

Keep in mind that I've never been able to verify that this is indeed a model error, and not something that happens in real life. I got the impression from Foty that in silicon I2 will match I1, and I3 will match I4. His take was that the EKV model handles this type of circuit correctly.

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RobG Community Fellow Offline Posts: 570 Bozeman, MT	Re: Series transistors Reply #26 - Nov 30^th, 2006, 9:45pm Here is the plot of the ratios (which should be unity) versus current for the circuit in the above post.
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vivkr

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Re: Series transistors
Reply #27 - Dec 1^st, 2006, 1:17am

Croaker wrote on Nov 23^rd, 2006, 9:06am:

That intuitively makes sense to me. I mean, physically, it seems right, since two in series have almost the same structure as a double-length one (except there is an implant in the middle of the series chain).

Well, I just worked out the equivalence and if you include body effect you'll get the result that two MOS in series kind of looks like a single 2*L MOSFET, but with an error term of:

k*W/2*(2*L)*(Vg - Vth)^2 + k*W/2*(2*L)*( -2*dV*(Vg - Vth) + Vx*dV + dV^2 )
^ looks like 2*L device ^ body effect error term

Vth2 = Vth1 + dV, and Vx is the drain voltage of M1. M2 is the top device, M1 is the bottom device.

Hi Croaker,

Quite many replies on this topic I see. I just have a quick question. How did you do the above derivation? I think you would need to make certain assumptions about the region of operation of each transistor which may/may not hold. Anyway, regarding the BSIM3 models being source-based, your understanding of this is correct (model source-oriented instead of bulk-oriented in BSIM3). Just to point out, the calculations that you do using a long-channel MOS model are implicitly source-oriented as well and should suffer from some errors that the simulator will also make.

I could try to explain a bit about why the body effect does not come into play with series transistors when looking at MOS operation in a bulk-oriented viewpoint, but I think there are others who can do a much better job.

Tsividis and the EKV model people both provide very good literature on how the MOS transistor should be modelled. Perhaps a look at their books/papers would be useful for you, but as Rob points out, don't hope to be able to simulate series transistors accurately anytime soon. Acually, simulation models always will have errors, and although BSIM3 has quite many, it is unlikely to be replaced soon as all companies and foundries have invested too heavily into these.

For now, the best answer to your original question may be found by delving into:

Yannis Tsividis - Operation & Modelling of the MOS Transistor
EKV model literature can be found online by searching their homepage.

Regards
Vivek

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Croaker

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Re: Series transistors
Reply #28 - Dec 1^st, 2006, 4:44am

Vivkr,

You can prove that two series transistors are equal to one double-length transistor by setting the current eqn for each FET to be equal.

The bottom one is always in triode, and the top one can be triode or sat. Then you just re-arrange until you make one side of the eqn look like the current for a double-length transistor.

E.g.

I1( in triode ) = I2 ( saturation )
or
I1 ( in triode ) = I2 ( triode )

To get an answer such that Lseries = 2 * L, you need to assume that Vth1 = Vth2. If Vth2 != Vth1, you get an extra term.

As for the bulk-effect not mattering, for a series chain, it should physically not be different from a long transistor (as you said). I guess you could say any point in the channel of the long transistor could be considered a source, and this source will have body-effect because it is not at the same potential as the reference source (actual source of long device).

As for the proof discussed above, I think body-effect does matter, but as RobG mentioned, something else (not considered) cancels it out.

Marc

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Croaker

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Re: Series transistors
Reply #29 - Dec 1^st, 2006, 5:01am

OK, I remember reading about symmetrical models. It was the ACM model and there are some good papers on it as well as a detailed write-up in the Low-voltage book by Sanchez-Sinencio. I believe EKV is symmetrical as well. I heard PSP is also a good new model to use.

It strikes me as a pretty odd situation if the most widely used BSIM model can't even handle series MOSFETs properly! Shocked

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