Monday, November 04, 2013

How to Measure FWC

Albert Theuwissen continues his educational series of posts, now talking about full well capacity measurements: part 1 and part 2. The second part explains the difference between the cases when the saturation is caused by clipping the signal in ADC or readout chain and cases when the pixel limits the signal.

27 comments:

  1. There is some interesting device physics in explaining (quantitatively) the drop off in measured noise when the ADC sat exceeds the device sat level. (2nd case). It is messy and so it is rarely explained. I did a mathematical model for the QIS in this region, but haven't seen it done for a conventional CMOS APS yet. Perhaps someone in university land will take an interest in this, for academic sake.

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  2. I would also be interested to know the theoretical relationship between saturation and linear full well capacity.

    Is the saturation FWC equal to the net doping of the well (Nd-Na) and therefore the number of electrons at equilibrium?

    Is the reason for linear FWC being lower due to recombination rate increasing from zero as the well approaches its equilibrium value?

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    1. >Is the saturation FWC equal to the net doping of the well (Nd-Na) and therefore the number of electrons at equilibrium?
      No there is depletion even at equilibrium, and this is a 3D structure, including the "gated-diode" influence of TG.

      >Is the reason for linear FWC being lower due to recombination rate increasing from zero as the well approaches its equilibrium value?
      Sure this has some influence, assuming you mean photo- EHP recombination. The storage area of the PPD is more like the floating base of a phototransistor except the collector is shorted to the emitter. Recombination does not balance diffusion (out of the storage area) until the potential reaches sort of Voc. I think this is well past most of the region of interest for the PPD FWC noise discussion.

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    2. >No there is depletion even at equilibrium, and this is a 3D structure, including the "gated-diode" influence of TG.

      Agreed - sorry I didn't mention this. The number of electrons in the n-region when the TG and FD biases have been applied and the diode is in steady-state should be the saturation FWC.

      >Recombination does not balance diffusion (out of the storage area) until the potential reaches sort of Voc.

      Agreed.

      >I think this is well past most of the region of interest for the PPD FWC noise discussion.

      Agreed. Is this the likely reason why the linear FWC from charge vs. time is higher than the lin FWC from noise?

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  3. Eric, I planned already working on it, and I have in mind to post in on the blog. But I do not know whether I ever come to this point because of time constraints. As you can see, the FWC calculated/measured in the case it is done with the noise variance, is much smaller than in the case it is done with average output signals. Apparently the definition of FWC at the point where the noise reaches a maximum level is too pessimistic. Also this needs further explanation, but falls in the same category of time issues ....

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    1. Great. As you mention, for PPD APS there are at least 4 possible FWC limitation mechanisms. 1) Storage area of PPD overflows under TG or becomes forward biased and injects carriers in path of least resistance, 2) FD capacity is too low and voltage becomes nonlinear as incomplete charge transfer results 3) rest of analog chain clips/distorts the signal from FD or 4) ADC clips signal. I am interested in case (1).

      In this case, carriers that escape the potential barrier (e.g., by thermionic emission or diffusion or photoemission) are not counted as noise, and more escape as the well becomes fuller. The noise is going to be determined by the escape rate which is the fun thing to try to figure out in a real device although I suspect a thermionic emission model with an adjustable rate constant will suffice.

      It would be interesting to see the temperature dependence of the same data you already showed. Could be a student's Masters Thesis all on its own.

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    2. As the pixel size shrinks, the photodiodes are getting vertical (stacked) to maintain the same picture quality (FWC). Here is my question?
      If the pixel size shrinks from 1.1 to 0.9 micron, how deep that it should go to maintain the same full well capacity?

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    3. Eric, for 1) we observed a logarithmic relation between the full well charge and the absolute light level. We explained this by sub-threshold operation of the transfer gate through which the (excess) photocurrent is drained in saturation. More (photo)current results in a larger gate-source voltage of the transfer gate, and the photodiode goes to a lower voltage with a logarithmic relation between voltage (hence full well) and photocurrent. Alternatively, if the TG threshold is too high, the junction will inject the charge in the substrate at saturation, but then some means of anti-blooming is needed.

      I talked about this at the CNES workshop in november 2012, I've put the slides here on dropbox: https://www.dropbox.com/s/xkumud9f32mqacm/meynants%20-%20cnes%20workshop%202012%20slides.pdf

      See slide 9-11 for the equations.

      We've seen other relations between full wel and light level too. It can depend on many parameters of the transfer gate device.

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    4. hi Guy,
      Yes, nice slides, and thanks for sharing. Pretty much what I said. I am not sure you can distinguish between diffusion or thermionic diffusion but they mostly give the same sort of dependence. You can look at MOSFET subthreshold current the same way...is it diffusion or is it thermionic emission....? And yes, path of least resistance, either via TG to FD or down to substrate, depends on the gated-diode electrostatics.

      Too bad you guys didn't show theory v. experiment in your slides!

      So the real problem, once you have a valid model for the current is figuring out the noise part.Shot noise coming in, shot noise or kTC noise going out, and some net suppression of the measured "shot noise" of the signal. Messy, but possible. I just don't think anyone has done that one before.

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    5. HI Eric,

      Thanks, and we did indeed confirm this in measurements, but didn't show it in these slides. The slides were to use this model to explain some dependency of full well on radiation effects, we attributed that to some Vth shifts.

      indeed, the noise part - this reminds me of the noise discussion 10 years ago in 3T pixels with 'soft reset'. I believe B. Pain introduced that term on one of the CCD&AIS workshops (99?) based upon noise observations in 3T. We can probably look at the 4T structure in a similar way. The subthreshold behaviour of the TG gate behaves as a resistor with very high resistance and forms an RC filter with the photodiode capacitance. That gives a 'sub-kTC' noise level on the diode when in saturation.
      interesting stuff, indeed.

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    6. Sure, it is very related to that 3T work. I also gave a subsequent paper that is even more related as you will probably remember:
      "Charge transfer noise and lag in CMOS active pixel sensors" in 2003 at Schloss Elmau. That was a Monte Carlo simulation for the most part. Later someone else (I forget!) verified the model experimentally.

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  4. Suppose the imager is not uniformly illuminated, but only a part of the imager. Does the full-well capacity thus calculated vary with respect a uniformly illuminated imager? (I am now thinking of barrier between photodiodes). How about the FWC of a fully depleted imager ( on high resistivity substrate) using SF topology that is not uniformly illuminated?

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    1. Do you mean that signal is blooming to adjacent pixels, or that there is some sort of electrostatic crosstalk that affects neighboring potentials, or something else? I think either of the first two probably has a negligible effect on FWC. Sometimes with poorly designed power distribution lines the analog signal chain gets affected by column-to-column and that could affect FWC.

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  5. When the PPD is saturated, there are 2 electron mouvements: electron capturing from P-sub and electron releasing to the Psub. If the voltage on the TG is negative enough, there is a preference for electrons to move to FD if it is held to VDD. The net electron current will drop to zero. The integration phenomena disappears in this case, the shot noise vanishes to Johnson noise. And you will observe noise drop in your measurement. This is what happens in a solarcell mode photodiode. The noise decreasing is related to the reduction of the net electron mouvement in PPD.

    -yang ni

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    1. You say the net electron current will drop to zero. You mean the net current into the PPD node is zero (KCL). The current is not zero, it flows from P-sub thru PPD to FD. I guess you are arguing that the instantaneous current into PPD is characterized by shot noise, but somehow it is filtered by the capacitance of the PPD and the transport from PPD to FD is characterized by Johnson noise. I am not sure I completely agree with this model. This same filtering process, you seem to say, results in a net decrease in the noise in measuring the FW signal. I am getting your meaning correctly?

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    2. Eric, if you stand at NPD inside the PPD, you can see electron coming and leaving the NPD. At the beginning the potential is high enough, so few electrons leave the NPD and most electrons come from P-sub. When the PPD is closing saturation, the potential of NPD decreases, more and more electrons leave NPD and finally this dual-direction mouvement reaches an equilibum.

      When you transfer the electrons stored inside PPD, you count these electrons. And you will get a sqrt shot noise depending on the accumulated electron number. But when the dual-direction mouvement reaches equilibrum, the average electron number is constant at each illumination level. The only fluctuation is the instant electron number, this fluctuation can be modeled by Johson noise. When you increase the illumination level, the number of electron will increase and then stablize to a stationary new level. That is why the noise level remains stable, but the signal increases logarithmically with illumination.

      I didn't say that the current is ZERO. I said that the NET current from NPD is zero. I hope that it's better explained :)

      -yang ni

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    3. "That is why the noise level remains stable, but the signal increases logarithmically with illumination."
      Actually the noise level starts to significantly decrease. This is the tricky part to explain esp. with a Johnson noise model. See Fig 2 pf part 2 of Albert's blog*.
      The baseline explanation is that once the full well is full, there is no room for variation in the signal charge; anything larger than FWC bleeds off to FD or elsewhere. This would predict sudden drop off in noise. The gradual drop off is what a quantitative model needs to correctly predict. Not so easy.

      *I assume that when Albert says "temporal noise variance" he means the variance in repeated measurements of the signal, not the variance in the noise. That would be, like, noise in the noise.

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  6. "... the voltage on the TG is negative enough ..." => " ... the voltage on the TG is NOT negative enough ..." Sorry !

    -yang ni

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  7. Hi Yang - yes, but when they go in the P-sub they will be caught by neighbor pixels, resulting in blooming. We generally don't want that unless we implement a vertical anti-blooming mechanism, just like the CCDs.

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    1. Guy, of course I understand this. I'm talking about the modeling of this noise droping. I remember the question asked by Bart after my presentation at IISW. I said "no" to him, since the charge stored in PPD is still increasing in a logarithmic way, but the noise level is unchanged. This is like the wave of the water surface, the wave height depends on wind force but not on the water level...

      -yang

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    2. So if I understand correctly, your measurements indicate that the noise remains unchanged on further illumination, and you did not observe any drooping of the noise?

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  8. I am positively surprised by all the comments and discussion my blog has raised. Thanks to all of you who reacted and who read this and hopefully could something learn from it. That is the reason why we are posting all the technical stuff on the blogs !

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  9. Thank you for this very interesting blog post that generates interesting discussions.

    I was wondering, since, as discussed here, the FWC depends on light level, don't you think it would be interesting to stress out in your course that the photon flux should always be given when a FWC is measured (in order to be able to compare one measurement to another)?

    Another solution could be to provide the FWC achieved in the dark, since this value is indipendent of the photon flux.

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    1. Alice,
      Your question is not fully understood. FWC is a property of the pixel. Why should it depend on the light level? Or you mean something else?

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  10. Hi,
    as shown by G. Meynants in his slides, and in the letter we published last July (http://oatao.univ-toulouse.fr/9226/), under steady illumination conditions the FWC depends logarithmically on the photon flux level (and thus on the photo-current). By illuminating the pixel you can easily double the full well capacity of the pixel with respect to dark conditions (by integrating only the dark current). This experimental fact is often visible in litterature when the output voltage of a PPD CIS is plotted as a function of the photon flux (and fixed integration time).

    This is why in my opinion it is interesting to give the FWC measured at equilibrium, as it represents a fair comparison between different devices.

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    1. This is true. However, there are many other factors that we have to take into account, if we look for "fair" comparison. One of them is linearity. Some sensors keep linear response to about 90% of their full well, while some others lose linearity at 50%. Some (many) sensors have a non-linear crosstalk: the crosstalk is small at small signals, but becomes progressively bigger as signal grows (not blooming, though). There are more effects like these that limit the usable signal range of the pixel. So just the full well number does not tell the whole "fair" story, no matter how it's measured.

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    2. Alice, I know you have been working on an analytical model for the FWC of the PPD. I do think it is rather obvious that the PPD behaves like a solar cell under illumination. Nevertheless, I also agree that one of the most sensible measures of the FWC capacity is the number of carriers stored as close to equilibrium as one can achieve (quasi equilibrium, really) since this is easy to extract from TCAD sim.

      I do think the definition of FWC depends on the question we are asking, as Vlad tries to say, and as Albert said a different way in his blog post. The usual question is "how much useful signal can I store in the PPD?" with the word "useful" being intentionally nebulous. Often it is just the linear response (and then how linear is linear!) and for others perhaps it is some increased DR logarithmic response.

      This reminds me that Donald and I need to wrap up our J-EDS PPD review paper and at the same time ask people to send us copies of papers that are candidates to be referenced. You too Alice!

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