Author Topic: Duane-Hunt limit  (Read 10820 times)

xllovet

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Re: Duane-Hunt limit
« Reply #45 on: April 11, 2024, 12:33:58 AM »
Very interesting results. Too bad you didn't convolve the PENEPMA data with the response of the detector (as you did with the DTSA2 spectrum). If so, the "cliff" predicted by PENEPMA at the end point (arising because the bremsstrahlung DCS is finite at the end-point) would smear out and the agreement with the experimental spectrum would most likely improve.

Nicholas Ritchie

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Re: Duane-Hunt limit
« Reply #46 on: April 11, 2024, 05:58:52 AM »
I'm sure that convolving the PENEPMA data would improve the already quite good agreement.  Maybe John can do this as I don't think that I have the program and this the simulation of Pt that he ran.  (It was a 132 eV @ Mn Ka detector with a silicon nitride window.)  I'd be happy to update the plot.

I am interested in understanding the extent to which the "cliff" contributes to the overestimated Duane-Hunt and the extent to which it is just a detector resolution issue.  Detector resolution is relatively easy to handle.  It will just be a constant offset dependent on the detector resolution.

I'm also curious to understand to what extent there is atomic number variation (and/or beam energy variation.)   Figure 3.13 (Penelope-2011 book) suggests that the "cliff" should be largest between 10 keV and 100 keV (right where we tend to operate) and roughly similar for Al and Au.  If there is little atomic number variation then the overestimate should be similar for both standard and unknown regardless of composition.  This would be better as then we can just compare the two to determine if they were both collected with the same incident beam energy.
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Probeman

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Re: Duane-Hunt limit
« Reply #47 on: April 11, 2024, 06:41:11 AM »
Here is a little data and analysis to inform the conversation.
I measured some deep (12,000 s) spectra from Pt at very low probe current (170 pA) to minimize pulse-pileup.
These spectra were then processed to extract an estimate of the Duane-Hunt limit.  By sub-sampling the deep spectra, I was able to construct 450 more realistic dose spectra.  These too were fit.

The short story...  The D-H was consistently about 70 eV higher than I expected (based on the assumption that my instrument's beam energy is calibrated correctly) and that for 40 nA.s spectra, the one-sigma uncertainty was about 24 eV.



Very nice work.

These plots will be perfect for our Duane-Hunt limit presentation at M&M this summer.
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Probeman

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Re: Duane-Hunt limit
« Reply #48 on: April 11, 2024, 06:44:56 AM »
Very interesting results. Too bad you didn't convolve the PENEPMA data with the response of the detector (as you did with the DTSA2 spectrum). If so, the "cliff" predicted by PENEPMA at the end point (arising because the bremsstrahlung DCS is finite at the end-point) would smear out and the agreement with the experimental spectrum would most likely improve.

I was just going to post the same comment!

I did convolve the PENEPMA photon cliff in this post above:

https://probesoftware.com/smf/index.php?topic=1063.msg12472#msg12472

And it shows that convolution of the the photon cliff by the spectral resolution of detector seems to contribute quite a bit.
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Probeman

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Re: Duane-Hunt limit
« Reply #49 on: April 11, 2024, 06:59:47 AM »
I'm sure that convolving the PENEPMA data would improve the already quite good agreement.  Maybe John can do this as I don't think that I have the program and this the simulation of Pt that he ran.  (It was a 132 eV @ Mn Ka detector with a silicon nitride window.)  I'd be happy to update the plot.

As previously mentioned I did convolve the Pt spectrum above, but it would be nice to plot them together normalized to the 5 keV intensities as you did. 

I am interested in understanding the extent to which the "cliff" contributes to the overestimated Duane-Hunt and the extent to which it is just a detector resolution issue.  Detector resolution is relatively easy to handle.  It will just be a constant offset dependent on the detector resolution.

I'm also curious to understand to what extent there is atomic number variation (and/or beam energy variation.)   Figure 3.13 (Penelope-2011 book) suggests that the "cliff" should be largest between 10 keV and 100 keV (right where we tend to operate) and roughly similar for Al and Au.  If there is little atomic number variation then the overestimate should be similar for both standard and unknown regardless of composition.  This would be better as then we can just compare the two to determine if they were both collected with the same incident beam energy.

It's a good  question. Does Z affect simply the continuum intensities (that is equivalent to electron dose) or is there a contribution to the slope?

I've attached the unconvolved and convolved spectra from PENEPMA for Si, Ge, Ta and Pt below using Convolg.exe.  These spectra are convolved using a Gaussian filter 20 eV wide. Note that the Convolg.exe program that comes with PENEPMA only performs a resolution adjustment (no window absorption effects which at 10 keV probably aren't too important).

Here is the function Convolg uses for EDS convolution:

Code: [Select]
C  ****  Example of FWHM(E) function for a Si(Li) detector.
      FWHM=DSQRT(7849.255D0+2.237253D0*E)
« Last Edit: April 11, 2024, 07:39:40 AM by Probeman »
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Probeman

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Re: Duane-Hunt limit
« Reply #50 on: April 11, 2024, 07:35:37 AM »
OK, attached below are the PENEPMA spectra for Si, Ge, Ta and Pt convolved to 132 eV using Convolg.exe.

Doing this caused there to be many fewer points to plot resulting in slightly "jagged" curves, but I guess that's a feature not a bug...    :)

But the apparent resolution didn't change much:



My suspicion is that higher Z produces a higher photon cliff (as seen in the PENEPMA simulations), and when these are convolved they only further extend the apparent D-H limit.  I think that SEM Geologist mentioned a while back using a low Z material to obtain the best D-H limit estimate?

In any case, give me a bit and I'll also plot up and post the Ti K edge over voltage measurements I did last weekend using 100 eV beam energy steps because I really think that this idea is the best way forward:

https://probesoftware.com/smf/index.php?topic=1063.msg12536#msg12536

It would be neat if Nicholas could perform some overvoltage measurements using his instrument at 5 keV for the Ti K edge and at 11.2 keV for the Ge K edge on the freshly polished metals.

And maybe even at 18 keV (because I don't have an LIF220 Bragg crystal) using the Zr K edge as I don't think Rb or Sr metals would be appropriate since they would oxide pretty fast?
« Last Edit: April 11, 2024, 07:49:20 AM by Probeman »
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Nicholas Ritchie

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Re: Duane-Hunt limit
« Reply #51 on: April 11, 2024, 10:16:42 AM »
Over the years, I've developed a handful of different algorithms for estimating the D-H limit from measured spectra.  Typically, I perform linear regression on the channels just below the cut-off and extrapolate to y=0.   Often, I'll also perform linear regression on the channels above the cut-off to estimate the contribution from pileup.  Then I compute the intersection of the two lines to determine the D-H.   Other times, I've modeled the continuum and fit the modeled continuum to the measured continuum by adjusting the nominal beam energy.  This is much more complex as you need to model the detector and I'm not convinced that it produces better results.

There are a couple of challenges.  First, identifying where the D-H is approximately (since it may be keV off the nominal value with charging) so we know where to fit.  Second, ensuring that there aren't any characteristic lines to complicate the fit.  Finally, I usually fit about 20 to 40 channels about 5 to 10 channels below the cut-off.  On if there are 10 eV channels and the D-H is near 10 keV, I might perform a linear regression on the channels representing 9.75 keV to 9.95 keV and extrapolate to y=0 (or the pileup line).   This ignores the noisy data and the curvature in the continuum near the D-H.  I suspect that it also compensates for the detector resolution issue.  Building a robust algorithm is part insight and part art.

For most uses of the D-H, a stable algorithm (precise, reproducible one) is more valuable than an accurate one.
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Probeman

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Re: Duane-Hunt limit
« Reply #52 on: April 11, 2024, 10:46:35 AM »
Over the years, I've developed a handful of different algorithms for estimating the D-H limit from measured spectra.  Typically, I perform linear regression on the channels just below the cut-off and extrapolate to y=0.   Often, I'll also perform linear regression on the channels above the cut-off to estimate the contribution from pileup.  Then I compute the intersection of the two lines to determine the D-H.   Other times, I've modeled the continuum and fit the modeled continuum to the measured continuum by adjusting the nominal beam energy.  This is much more complex as you need to model the detector and I'm not convinced that it produces better results.

There are a couple of challenges.  First, identifying where the D-H is approximately (since it may be keV off the nominal value with charging) so we know where to fit.  Second, ensuring that there aren't any characteristic lines to complicate the fit.  Finally, I usually fit about 20 to 40 channels about 5 to 10 channels below the cut-off.  On if there are 10 eV channels and the D-H is near 10 keV, I might perform a linear regression on the channels representing 9.75 keV to 9.95 keV and extrapolate to y=0 (or the pileup line).   This ignores the noisy data and the curvature in the continuum near the D-H.  I suspect that it also compensates for the detector resolution issue.  Building a robust algorithm is part insight and part art.

For most uses of the D-H, a stable algorithm (precise, reproducible one) is more valuable than an accurate one.

Yup, there are many issues with the Duane-Hunt limit accuracy and precision as we all have documented. Which is why I think your suggestion to use overvoltage measurements might be a better approach for determining the actual electron beam energy:

https://probesoftware.com/smf/index.php?topic=1063.msg12536#msg12536

I'm going to run more overvoltage measurements this weekend using 50 eV increments at 5 and 11.2 keV on my LiF crystals and let's see how it does. Here are the Ti Ka overvoltage measurements using 100 eV increments. First attempt:



And here is the 2nd effort:



Leaving accuracy aside for the moment, it would appear that the reproducibility is better than ~10 eV or so.  If you get a chance it would be cool to try this using EDS on your instrument...
« Last Edit: April 11, 2024, 01:10:51 PM by Probeman »
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Nicholas Ritchie

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Re: Duane-Hunt limit
« Reply #53 on: April 12, 2024, 06:20:10 AM »
It depends upon what you want out of the measurement.  The Duane-Hunt remains the best way to determine if your sample is charging.
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Probeman

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Re: Duane-Hunt limit
« Reply #54 on: April 12, 2024, 08:01:45 AM »
It depends upon what you want out of the measurement.  The Duane-Hunt remains the best way to determine if your sample is charging.

Absolutely.  If someone needs to know exactly how much their sample is charging then the Duane-Hunt is the way to go, though usually they just need to know if it's charging or not.

But the question we have been discussing in this topic since the very first post in 2018:

https://probesoftware.com/smf/index.php?topic=1063.msg7026#msg7026

is how to determine the accuracy of the electron beam energy in ones SEM or EPMA instrument. If that is the goal, then the Duane-Hunt limit suffers from several problems, including convolution by the detector spectral resolution of the photon "cliff" which completely obscures the actual DH limit, not to mention the problem of continuum coincidence events. On the other hand, the net intensity over voltage curve method using characteristic lines, is direct and relatively fast.

Now I'd like to see over voltage curves from other instruments of net intensities starting just above the K edge energies of various uncoated pure metals and see how precisely/accurately we can determine the electron beam energy of that instrument. 

The over voltage curve approach seems promising, but more data is necessary.   I'm hoping to do some runs this weekend using 40 eV high voltage increments (since SG thinks the minimum high voltage step in a Cameca is ~12 eV), starting at 4.98 keV for the Ti K edge (4.964 KV) and 11.12 keV for the Ge K edge (11.102 KV) and increment upwards by 40 eV for 10 voltage steps and see how reproducibly that extrapolates to a zero intensity.

Does anyone know the minimum high voltage steps attainable for instruments from other manufacturers?
« Last Edit: April 12, 2024, 09:29:27 AM by Probeman »
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Sander

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Re: Duane-Hunt limit
« Reply #55 on: April 13, 2024, 06:21:07 AM »
At least 12 bit is a standard. What kind of a**h**** would make SEM/EPMA EHT with 10bit DAC? EHT is not (can't be) fast changing as i.e. scanning coils - there is absolutely no excuse using lower resolution. Even my grandma would had used 12bit for that...

Wow, are you trying to pick a fight?  Any design is a compromise.  When you tell your electronics department to make a high-voltage supply that goes from a few kV to 30 or so, then their first question will be "how accurate do you want it to be?" and in our case, we specified "max 1V per step, max 1Vpp ripple".  So I suppose we ended up with a 15V DAC.  But that's just because these components are cheap nowadays (and, as you said - it doesn't need to be fast).

Quote
Some of HV PSU supplies filament with AC, but again at middle point of it the added/subtracted filament voltage is going to be near 0V. (The advantage of AC is the equal filament current from both sides - the tungsten evaporates more evenly - no thinning from single side as on DC).

Actually, something like this this was patented quite recently; see https://patents.google.com/patent/JP2023036117A/en?oq=JP2023036117.  Filed 2021-09-02, status is still "pending".

Quote
If electrons can be instantly accelerated (from cathode) why they could not be instantly deaccelerated? Electrons can be instantly deflected why they could not be made to stop? electrons can instantly jump the "band-gap" and can do weird tunneling and other weird weird stuff... From all of weird workings of electrons, indeed, bremstrahlung effect looks the least weird in my opinion.

I don't think many people think that electrons are instantly accelerated from the cathode, and have the "mental model" that there is an electric force acting on the particle which gradually increases its velocity.  The "band-gap jumping" is a quantum mechanical effect that has no macroscopic equivalent.

Of course, if we're talking about the philosophic aspects of "understanding": macroscopic effects are obviously just as weird if you really stop and think about them.  We're just used to them.

Probeman

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Re: Duane-Hunt limit
« Reply #56 on: April 13, 2024, 08:24:52 AM »
At least 12 bit is a standard. What kind of a**h**** would make SEM/EPMA EHT with 10bit DAC? EHT is not (can't be) fast changing as i.e. scanning coils - there is absolutely no excuse using lower resolution. Even my grandma would had used 12bit for that...

Wow, are you trying to pick a fight?  Any design is a compromise.  When you tell your electronics department to make a high-voltage supply that goes from a few kV to 30 or so, then their first question will be "how accurate do you want it to be?" and in our case, we specified "max 1V per step, max 1Vpp ripple".  So I suppose we ended up with a 15V DAC.  But that's just because these components are cheap nowadays (and, as you said - it doesn't need to be fast).

SG sometimes gets a little excited- he means well.    :)

Does anyone know how many bits is the HV DAC on a JEOL EPMA instrument?  In other words, what is the smallest increment one can adjust the high voltage on a JEOL EPMA?
« Last Edit: April 13, 2024, 02:17:26 PM by Probeman »
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sem-geologist

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Re: Duane-Hunt limit
« Reply #57 on: April 14, 2024, 08:16:04 AM »
At least 12 bit is a standard. What kind of a**h**** would make SEM/EPMA EHT with 10bit DAC? EHT is not (can't be) fast changing as i.e. scanning coils - there is absolutely no excuse using lower resolution. Even my grandma would had used 12bit for that...

Wow, are you trying to pick a fight?  Any design is a compromise.  When you tell your electronics department to make a high-voltage supply that goes from a few kV to 30 or so, then their first question will be "how accurate do you want it to be?" and in our case, we specified "max 1V per step, max 1Vpp ripple".  So I suppose we ended up with a 15V DAC.  But that's just because these components are cheap nowadays (and, as you said - it doesn't need to be fast).

SG sometimes gets a little excited- he means well.    :)

Our effort to find the means for precise beam energy estimation is a first step. It would be a waste of time, if we could not do the second step - do the software offset calibration. I.e. We would know that if we set 15kV we see that in real it is 15.075kV, we could then for 15kV set at our programs controlling the probe or SEM 14.925kV to offset those 75V overvoltage. If DAC is 10bit and have 30V step, then we could set the offset value either to 14.94kV or 14.91kV, which would give 15.015 or 14.985kV in real. I think if we find easy way to measure real energy, the second step is really easy to implement in PfS (I am saying this just as side observer aware of that huge list of different calibrations already there). If DAC is 12 bit we can correct it better, and if DAC is 14bit - that even much more better... And if it is 10bit DAC our correction would be kinda still OK at 15kV. But i.e. for 5kV step of 30V (10bit DAC), which s like 0.7% of the set value, - and that is not OK.

The chose of DAC (type, bitdepth, speed) often is kind of compromise of speed, price, stability. High precision DAC (16 and more bits) needs much better PCB design, else the electronic noise present on the PCB renders those additional bit precision useless. Higher bitdepth DAC tends to have larger delay which is important in example for scanning beam control and image acquisition synchronisation (thus for imaging we see 11-14bit DAC used for scanning beam control, also ADC for imaging is often not the 16bit, but 8bit, 10bit, 12bit for the same speed/real-time reason). Also price-wise 10bit and 12 bit DAC often has like 1-2$ difference (often it comes in the same IC package) when looking to models from same vendor with same technology. It makes a lot of sense price-wise to chose 10bit over 12bit when manufacturing kids-toys, in example making 1000000 toys and using cheaper 10bit instead of 12bit DAC will give very huge profit. However even taking into account bus width and its buffers (i.e. Jeol and Cameca EPMA use VME, and cards for column control have internal parallel buses, and DAC use parallel digital interface, 10 bit bus is smaller than 12 bit bus... and saves few mm of PCB space, in case of serial interface there is no difference) price saving of more less 10$ per unit for few to tens of units (costing 0.5 to few millions per unit) produced per year is really ******* ridiculous, and I mean it when I called it being AH originally. Speed reason is non existent there, HV can't be changed many times per second. The DAC for HV control basically produce stable DC signal. So in case of HV control the choice of DAC (between 10-14bit) has no basis for any compromise, and lower bit DACs there has no pros, but just cons. There is no reason to choose less bits in these cases.

Probeman

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Re: Duane-Hunt limit
« Reply #58 on: April 14, 2024, 09:10:57 AM »
I agree that when designing a DAC for high voltage control in an SEM/EPMA, there is no need for less than a 12 bit DAC.

Since the Cameca high voltage power supply goes from 0 to 50 KV (is that still true of more recent Cameca probes?) and if it is a 12 bit DAC as SG claims that means 50,000 / 4096 which is 12.2V. 

But what about JEOL instrumemnts?  Does anyone know what bit DACs JEOL uses to control the HV?  I think their high voltage supply is designed to only go from 0 to 30 KV, correct?

The only concern I have is that when we "read" the HV from the gun, how do we know how accurate that number is? It seems to me that only the over voltage curve method is precise and accurate enough, unless one has access to a NIST traceable high voltage voltmeter...
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sem-geologist

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Re: Duane-Hunt limit
« Reply #59 on: April 15, 2024, 12:58:49 AM »
Since the Cameca high voltage power supply goes from 0 to 50 KV (is that still true of more recent Cameca probes?) and if it is a 12 bit DAC as SG claims that means 50,000 / 4096 which is 12.2V. 
AFAI am aware SXFive has column control board very similar (practically the same) as in SX100, thus DAC's precission are the same. Cameca designed HV tanks are still designed to go up to 50kV. However, SXFive FE (field emission) uses YPS manufactured HV supply (up to 30kV) and it interface with Cameca hardware with serial interface. I guess internally the supply has 14bit DAC, as HV, heat, extractor, suppressor can be changed in very small steps. Set Values and reported values are in 5 digit precision, and reported values react to very small increase in set values.

As for my previous claim about 12.2V step for Cameca HV, I could be wrong (the notes on schematics then also are not precise - misleading). It is very likely only 4000 bits from 4096 is used to scale from 0 to 50kV, and then it is 12.5V per bit or step. Such approach makes possible setting precise round high voltage instead closest to the set value. so i.e. 15kV would be round-bit 1200 integer. The analog signal created by DAC (0-10V) would not be then 3V, but... 2.93V (It is noted to be 0-10V signals, but in reality then it would be only 0-9.765V). And actually that is what can be observed if measuring on that analog control line with voltmeter (Initially I had freaked out that something is wrong with our cables). As for other vendor HV supplies, I am pretty convinced that it is rather common practice to use round (dividable by 10) fraction from full bitdepth of DACs for HV control: thus for 10bit from 1024 steps only 1000, for 12bits --- 4000, or 3000 (in case max HV is 30kV), for 14bit  probably only 15000 (from 16,384). Minimum 14bit DAC for FE emission is a must, as Schottky FE is designed to be usable even down to 0.2kV (analytically it makes no sense, but HV supplies are not manufactured explicitly for microprobes but for SEM and eventually probes). Actually to get such small energy beam many SEM use higher voltages in column and de-accelerate beam at bottom of column before being focused to the sample.

I doubt Jeol would had used 10bit DAC, if LaB6 fillaments can be mounted. Logically it should be at least 12bit so precise low voltage values could be set.
« Last Edit: April 15, 2024, 01:15:09 AM by sem-geologist »