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subthreshold slope parameter n (Read 2927 times)
PalmRunner
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subthreshold slope parameter n
Oct 24th, 2008, 2:00am
 
Hello all,

Before asking my question, could someone give me a reference or expression about Id for transistor operating in subthreshold. In the books I have it is assumed that Vbs = 0. Unfortunately it is not so in my case, so I am looking for more complete equation to better understand the influence from the bulk.

Now to the question: it is about the subthreshold slope parameter ‘n’ which appears in the equation for Id. I have a circuit, which shows big device to device spread on a silicon especially at low temperatures. I tried to reproduce this behavior on a simulation with no success until now - MC simulation shows much less spread of the output. The point is that the output is directly proportional to ‘n’ and I suspect that namely ‘n’ is the main source of spread. From a simulation I extract n=1.27 and run Spectre Process&Mismatch MC analysis on it. The result tells me that the parameter ‘n’ has almost no process, temperature and device to device variations, which is quite doubtful in my eyes. My question is: Could it be that this factor ‘n’ is really so stable over different devices (and I have to look for the problem on another place) or it is simply not properly modeled in Monte Carlo?

Thanks in advance!
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raja.cedt
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Re: subthreshold slope parameter n
Reply #1 - Oct 24th, 2008, 3:09am
 
hi,
   u can get the expression in vlsi devices by taur and ning text book.or simply introduce body effect in VTH,and substitute VTH id expression.But this expression wont for most simulation becaz  lot of  short channel effects.
   Coming to u r question N is depends on Cox and Cdep.so there  is lot process dependence(tox),voltage dependence(Cdep),Cdep also depends on doping of the substrate,temp(mobility in Cdep expression). But i dont know how u r getting results are nonindependent on PVT variations.
Thnak you
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Berti
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Re: subthreshold slope parameter n
Reply #2 - Oct 24th, 2008, 3:33am
 
"Tradeoffs and Optimization in Analog CMOS Design" by David M . Binkley is an other good book on device modeling using the EKV MOS model.
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PalmRunner
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Re: subthreshold slope parameter n
Reply #3 - Oct 24th, 2008, 6:10am
 
Thanks for the references. I’ll try to find these books.

I also think ‘n’ should be more process/temperature dependent parameter. If its spread is poorly modeled then I would get too good results from the simulator.
The actual (+-3 sigma) variations I get for ‘n’ are about +/-2.8% over all process corners and full temperature range (-40-120)
Currently I have only nominal silicon in hand, which means that only device to device variations are measured. Running “mismatch only” MC at nominal process and temperature I get only +/- 0.1% variations for ‘n’. Could it be that ‘n’ is really so constant parameter over one complete wafer? Or simply there is no statistical model for this parameter?

Thanks!
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