When we bought the instrument in 2006 we specified that Cameca test the accelerating voltage using a high voltage reference and they did and it looked excellent at that time. Unfortunately the installation engineer from France accidentally set the water chiller too cold and condensation shorted out the HV tank before he had even finished installing the instrument.
Recently on our Cameca SX100 if I set the keV to 15 and read the operating value back from the instrument I get something like 14.88 keV. Now this could be just an A-D calibration issue, so I calibrated our Thermo EDS system using the Cu La and Ka lines and when I acquired a long (1000 sec) acquisition on Bi metal at 15 keV and 10 nA (to minimize coincidence counts above the accelerating voltage) I see this:
(https://smf.probesoftware.com/gallery/395_11_04_18_12_04_23.png)
So exactly what is the Duane_Hunt limit in this spectrum? I guess I should try again at 5 nA?
Just for reference I had started the Duane-Hunt measurement at 30 nA and this is what that showed:
(https://smf.probesoftware.com/gallery/395_11_04_18_12_59_31.png)
That is why I tried 10 nA. Now I'll try 5 nA.
Ok, here's an acquisition on Bi metal at 15 keV 5 nA for almost 2000 sec (22% deadtime).
(https://smf.probesoftware.com/gallery/395_11_04_18_1_48_37.png)
It sure looks like the electron beam is more than 15 keV, whereas I would expect 15 keV or a smidgem less. Particularly since this is a carbon coated sample and from CalcZAF we should see a loss of about 8 eV for 20 nm of carbon and 15 keV electrons.
Ok, I think I figured this out. I again acquired a spectrum (4000 sec) on Bi metal at 15 keV, but this time at 2 nA which gives a deadtime of about 16%.
(https://smf.probesoftware.com/gallery/395_17_04_18_2_58_15.png)
Now that the coincidence continuum x-rays are further reduced, I can convince myself that my high voltage on my gun is actually quite close to 15 keV.
So I guess the lesson is that if one wants to see the Duane-Hunt limit clearly, you should keep the deadtime below 20%.
Quote from: Probeman on April 11, 2018, 12:05:40 PM
So exactly what is the Duane_Hunt limit in this spectrum? I guess I should try again at 5 nA?
My short answer is - it is closer to 14.88 kV than to 15 kV :o, and I also have a long and very convoluted answer and proofs to that. It is not so straight forward as it seems to be. But before I go into lengthy details let me ask:
What analytical consequences would be there if it is indeed 14.88 kV, but calculations would use 15 kV; 0.12kV offset is a bit less than 1%, I guess that will make nearly no difference for low energies. Albeit I think it could cause some significant enough differences with too weak over-voltage (i.e. Cu Ka, Zn Ka... at 15kV beam)?
P.S. (actually I find this as potentially nice topic for upcoming regional EMAS meeting at Czech Brno in May; As it seems more SEM-centric even I think that would particularly fit there.)
P.S.S. I was looking through documentations of new HV generators (different vendors different models), where HV accuracy'ies were listed ranging from 1 to 2 % of the set value. Initially I thought - "This is outrageously enormous! We know the Duane-Hunt method and I can implement some calibration routines to lower this to tenth of %". But after digging into the problem changed my opinion that such accuracy is indeed decent.
Quote from: sem-geologist on January 14, 2024, 01:58:00 PM
Quote from: Probeman on April 11, 2018, 12:05:40 PM
So exactly what is the Duane_Hunt limit in this spectrum? I guess I should try again at 5 nA?
My short answer is - it is closer to 14.88 kV than to 15 kV :o, and I also have a long and very convoluted answer and proofs to that. It is not so straight forward as it seems to be.
I'd be interested in seeing your "long and very convoluted answer and proofs to" why you think the D-H limit is only 14.88 kV. If I take a very simple minded approach and just extrapolate a rough fit to the bremsstrahlung, this is what I see for the electron beam energy in this plot:
(https://smf.probesoftware.com/gallery/395_15_01_24_1_26_19.png)
At the very least, the electron beam energy seems to be a bit above 15 keV (of course we are ignoring the small tail of continuum coincidence events!).
Quote from: sem-geologist on January 14, 2024, 01:58:00 PM
But before I go into lengthy details let me ask: What analytical consequences would be there if it is indeed 14.88 kV, but calculations would use 15 kV; 0.12kV offset is a bit less than 1%, I guess that will make nearly no difference for low energies. Albeit I think it could cause some significant enough differences with too weak over-voltage (i.e. Cu Ka, Zn Ka... at 15kV beam)?
Indeed, the analytical consequences are small so long as the overvoltages of the emission lines are greater than 1.5 or 2. For example here is a plot of Si Ka ionization efficiency as a function of overvoltage:
(https://smf.probesoftware.com/gallery/395_15_01_24_1_26_36.png)
The ionization efficiency curve for Fe Ka is a little less steep but still pretty nasty as one drops below an overvoltage of 1.5 or so. And of course, as you know, at low overvoltages there are the issues of surface coating/oxidation/contamination as one can lose a few hundred eV in the electron beam landing energy just from the carbon coating.
In fact, one might say that when performing low overvoltage (or low voltage) analyses, one is mostly measuring the surface coating/oxidation/contamination layers! Which is why we need this:
https://smf.probesoftware.com/index.php?topic=1073.0
You can also measure the Duane-Hunt limit on WDS using a standard LiF, if you are using high voltages less than 13 kV.
For the SX100 and SX Five, the measured value read from the HV regulation board can be adjusted using R307. This only affects the measured (feedback) value and doesn't change the gun voltage.
Quote from: chenderson on January 17, 2024, 08:27:26 AM
You can also measure the Duane-Hunt limit on WDS using a standard LiF, if you are using high voltages less than 13 kV.
I don't understand. Do you mean check the DH limit on an LiF beam incident material? Why would you not utilize a high Z material which will produce an abundance of continuum x-rays?
I meant you can also check the Duane-Hunt limit using WDS. You can use any material.
The common LiF [200], 2d of 4.0267 Angstroms, will cover out to about 13kV, at least on CAMECA WDS. If you're fortunate enough to have an LiF [220], 2d of 2.848 Angstroms, you can get out to about 19kV.
Attached is an example at 10 kV beam voltage on Zr metal using LiF [200]. X-axis is plotted in HV.
Quote from: chenderson on January 18, 2024, 11:53:26 AM
I meant you can also check the Duane-Hunt limit using WDS. You can use any material.
The common LiF [200], 2d of 4.0267 Angstroms, will cover out to about 13kV, at least on CAMECA WDS. If you're fortunate enough to have an LiF [220], 2d of 2.848 Angstroms, you can get out to about 19kV.
Attached is an example at 10 kV beam voltage on Zr metal using LiF [200]. X-axis is plotted in HV.
OK, that is a very cool suggestion as it should provide much better energy resolution for determining the DH limit. But yeah, without an LiF220 one cannot get up to 15 keV.
Again, I would use a high Z material to improve the continuum statistics. I'm going to try this when I get back in the lab...
Coincidence events (pulse pileup) are making it difficult to extract the Duane-Hunt limit from the spectrum. Lower the beam current and measure again.
Extracting the Duane-Hunt limit is always a challenge because, by definition, the counts go to zero - so zero signal. You can't expect too much precision in the estimate. However, the best approach is to count for a long time at a low count rate and fit the signal to a continuum model in the range of energies right below the DH limit. This is the approach that DTSA-II takes.
Quote from: Nicholas Ritchie on January 19, 2024, 06:06:00 AM
Coincidence events (pulse pileup) are making it difficult to extract the Duane-Hunt limit from the spectrum. Lower the beam current and measure again.
Extracting the Duane-Hunt limit is always a challenge because, by definition, the counts go to zero - so zero signal. You can't expect too much precision in the estimate. However, the best approach is to count for a long time at a low count rate and fit the signal to a continuum model in the range of energies right below the DH limit. This is the approach that DTSA-II takes.
I appreciate how DTSA-II and NeXL(Spectrum) takes care of that. The method as is implemented in those are robust to find out sample charging effects as these will be always strong enough to show the difference. What accuracy and precision does it have? I think we don't know, and that is what I want to try to find out. Accuracy is not so much influential for detection of charging of the sample as it will influence D-H a lot.
However, the accuracy and precision need to be well understood if method is used for checking or calibrating of HV voltage as proposed there by Probeman, and also here :https://smf.probesoftware.com/index.php?topic=1535.msg11937#msg11937 (https://smf.probesoftware.com/index.php?topic=1535.msg11937#msg11937) (the point 4). I actually got influenced by reasoning of this post and without a second thought I was insisting on doing such tests last year when acquiring a new SEM for our lab. I got aware about the problem only recently when being forced to dig deeper into how HV tension is produced and what other vendor power supply provides. WDS method indeed provides better means for defining Duane-Hunt limit... but still, how much precise and accurate it is? You can increase precision by decreasing count rate and increasing time, but what about accuracy? The fundamental question is Can an electron be halted to 0 velocity? will that energy difference will be exactly the energy of electron before impact?
The first fundamental question: Does perfectly defined D-H will be exactly same as beam energy? Or is there some substantial energy always left in slowed down electron and thus D-H should be a bit (how much) smaller than beam energy? Is there some fundamental difference?
Then next question is how accurate our measurement is (for precision we know and agree already for some tricks). EDS, especially SDD type will loose efficiency over 10keV. In general Bremstrahlung going toward higher energy on EDS seems diminishing. Thus Probeman suggests of using heavy (Bismuth metal?) standard for increasing the continuum before and thus the interpolation down to 0 would be easier. WDS naturally has increasing intensity toward higher energies (or lower sin theta) - thus the problem of low counts transiting into 0 being not very well pronounced is not there, which is nicely illustrated by example from chenderson. Also WDS pulse-pile-ups do not show up in the spectral (wavescan) form (they affect measurements at single static spectrometer position), thus also there is advantage compared with using EDS for D-H. But I disagree it is accurate - if line is fitted to section before getting to 0 of such wavescan. Also at low sin theta the spectral resolution is not so much different form EDS. But why the spectral resolution was at all mentioned before?
The missing piece is "deconvolution" - the ability to deconvolve that continuum wedge going to 0 will define the real D-H, and will show that D-H is always smaller than set HV beam energy. On WDS it is easy as the wedge is pretty steep, and thus simple half length at the (supposed at given spectral position) peak bottom (i.e. in my case that is about 0.1keV at 10kV for LIF) needs to be subtracted. For EDS due to more complicated Gaussian shape and shallow-angled wedge such retraction is not giving anything, as like Ritchy said - it is complicated with pile-up continuum.
Now I did a small experiment on DTSA-II, I made a MC at 14.88 kV and 15kV - for Bi metal. visually they show sigmoidal edge - where clearly the curve hits 0 intensity just a bit above 15kV and a bit more. Due to lack of deconvolution of that edge when using built-in D-H function it gives about 15kV and 15.1kV, so the method highly overestimates D-H. Going with lighter elements can make underestimated D-H. In heaver element spectra there is temptation of subtracting 3 sigmas equivalent calculated for FWHM at given initially estimated D-H position. However at lighter materials this will highly underestimates (shifts down) the DH.
Then again, HV supply can be calibrated at factory, but HV cable length and other factors will influence final acceleration, column geometry - those will influence the final electron landing energy. The more I dig into this the more I am convinced that 1-2% uncertainty of acceleration voltage is hard to improve.
Additional considerations for WDS vs EDS for estimating DH for generated HV acceleration voltage validation and calibration.
Yes, in case there is no LIF220 the 13kV would look like some kind of limitation. I agree 13kV is not 15kV (probably most commonly used voltage for EPMA as it has this sweet spot for most of common analytical requirements.), however HV generators in EPMAs are pretty continoues and linear (there is no discontinuous circuit switching for specific ranges of voltages, like in contrast to i.e. picoamperometer with different OPAMPS for different beam current measurement ranges; HV generator uses single circuit for whole range from 0 to 30 (or 50) kV). Thus if HV generator is calibrated well at 13kV - it should stay calibrated also at 15kV and casual LIF is absolutely enough to check the D-H limit. Personally I would check it for 10kV instead of 13kV, as spectral resolution decreases a lot at the lowest sin theta (the spectral peak broadening effect increases - the so the DH boundary would be washed out too).
Quote from: sem-geologist on January 22, 2024, 08:58:15 AM
Additional considerations for WDS vs EDS for estimating DH for generated HV acceleration voltage validation and calibration.
Yes, in case there is no LIF220 the 13kV would look like some kind of limitation. I agree 13kV is not 15kV (probably most commonly used voltage for EPMA as it has this sweet spot for most of common analytical requirements.), however HV generators in EPMAs are pretty continoues and linear (there is no discontinuous circuit switching for specific ranges of voltages, like in contrast to i.e. picoamperometer with different OPAMPS for different beam current measurement ranges; HV generator uses single circuit for whole range from 0 to 30 (or 50) kV). Thus if HV generator is calibrated well at 13kV - it should stay calibrated also at 15kV and casual LIF is absolutely enough to check the D-H limit. Personally I would check it for 10kV instead of 13kV, as spectral resolution decreases a lot at the lowest sin theta (the spectral peak broadening effect increases - the so the DH boundary would be washed out too).
I think checking the DH limit at 10 keV is a great idea given the improvement in spectral resolution. Here's a plot that demonstrates this nicely:
https://smf.probesoftware.com/index.php?topic=837.msg5476#msg5476
I'll definitely try 10 keV next.
Meanwhile over the weekend I ran some wavescans on my two LiF crystals at 13 keV, 10 nA, on Ge, Ta and Pt standards, first on my sp3, LLIF:
(https://smf.probesoftware.com/gallery/395_22_01_24_11_03_15.png)
and also on sp5, LiF:
(https://smf.probesoftware.com/gallery/395_22_01_24_11_08_31.png)
Even with some "hand drawn" lines, we can see that the continuum zeros out above 13 keV. However there is still some difference of around a few hundred volts between the two spectrometers.
Question: why does the background seem to increase at the highest energies? Does this indicate a misalignment of the spectrometers?
Next I'll show the EDS spectra.
Quote from: Probeman on January 22, 2024, 11:15:30 AM
Question: why does the background seem to increase at the highest energies? Does this indicate a misalignment of the spectrometers?
Thank You for this example. It explains me a lot: now I can conclude that this is universal thing seen not only on our spectrometrs with LIF.
Higher energy -> lower sin theta. At two different machines (SX100 and SXFiveFE) we observe very funky behaviour at these "over 13keV" (or starting portion of lowest sin theta region) near edge regions. I am aware about these funky behavior already at 15 keV for all our (L)LIF, where bremstrahlung intensity starts to decrease going over 10keV (as it is getting closer to 15keV) and then shots up near low sin theta limits of spectrometers. I mentioned previously only worse resolution, but now it is clear 13keV for DH limit should be also avoided due to funkiness of these.
2nd thought (a little detour from main subject): When seeing the wavescans fo LIF acq at beam energy of 25keV that spectrometer edge anomaly is hidden behind the general exponential behavior of background. Maybe this is not XTAL specific, but Cameca spectrometer specific behavior. This adds yet another interesting experiment to my to-do list (TODO #1: setting lower voltages than PET highest, and same for TAP and look if there are similar "hockey-stick" background shapes present). The side-effect of this is that probably "exponential-like" background intensity shape, which we are so familiar with, is made by two and not one process - that is why same exponential equation does not fit well the background for different spectrometer sin theta regions... What exactly could go on?:(1) XTAL gets closer to the X-ray-entry-Chamber-hole - more 2ndary Fluorescence background diffracted at wrong angles? (X-ray energy <beam-energy, but due to different entry angle to XTAL the diffraction would overlap the region with higher energies?); (2) as counter gets very close to the XTAL it starts to register other diffraction orders, or maybe... other orders enters the GFPC chamber and while it can't directly initiate townsend avalanches (interacts with gas further away (more than 1-2mm) from the tungsten wire) maybe it ionizes critical volume of gas chamber... or maybe it could directly cause townsend avalanches from larger distance? TODO #2: hook up the oscilloscope and see how pulses changes going to these low sin theta regions. I always was avoiding those lowest theta regions by my intuition - there is something funky there. Relooking to huge base of Wavescans and how this low sin theta region behaves - puzzle pieces finally starts to fit - it rather universal thing for Cameca spectrometers. Ouch! TODO #3: check at which Acceleration voltage wavescans will have no "hockey stick" - that will let to re-define lowest (analytically-safe) sin theta boundary for all Cameca spectrometers.
The other challenge I didn't mention when fitting the Duane-Hunt to an EDS spectrum (or, presumably, a wavescan) is that, when the issue is charging, the charging is dynamic and the Duane-Hunt isn't a single number. When you model the continuum to fit the D-H, you assume a nominal continuum shape. However, dynamic charging can lead to a very strange looking continuum particularly near the limit. I wouldn't trust the DH where there is charging. It is probably better than assuming the nominal beam energy but... :o
Adding to my previous checks on the DH limit at 13 keV on WDS (see above), I also acquired EDS spectra at the same time as the WDS scans (~4.4 hours each). Here is the energy calibration check on Ge metal:
(https://smf.probesoftware.com/gallery/395_27_01_24_1_08_09.png)
Pretty good looking. Next a zoom in on the DH limit on Ge:
(https://smf.probesoftware.com/gallery/395_27_01_24_1_08_27.png)
Now on Ta:
(https://smf.probesoftware.com/gallery/395_27_01_24_1_08_43.png)
And finally on Pt:
(https://smf.probesoftware.com/gallery/395_27_01_24_1_08_57.png)
I think it's safe to conclude that our high voltage source is calibrated a bit too high... the irony of course is that when I purchased this instrument back in 2005 (so I guess it could have drifted since then), I had included in my purchase specifications that Cameca provide calibration data showing that the high voltage source was calibrated (prior to shipping) to within our specifications:
Quoteb) absolute accuracy of accelerating voltage at 3, 5, 10, 15 and 20 KeV must be less than 0.5 % (+/- 0.25%) from the nominal accelerating voltage or within 7.5 volts at 3 KeV, 12.5 volts at 5 KeV, 25 volts at 10 KeV, 37.5 volts at 15 KeV and within 50 volts of 20 KeV as determined using the Duane-Hunt limit test on EDS (when calibrated on known x-ray line energies, Eg, Cu Ka, Cu La)
https://epmalab.uoregon.edu/reports/UofO-SPEC_EPMA-2004.pdf
Sounds like a good plan, right? Well a week after installing the high voltage source and hooking it up to the chiller, the Cameca engineer accidentally left the chiller on with the thermostat set so low that condensation starting occurring in the HV tank, then there a loud bang and that was the end of that HV transformer!
So they shipped another HV transformer, and did they test it before they shipped the new transformer? I don't remember, but it's certainly not within specifications any longer!
Does anyone have a procedure for adjusting the HV transformer in a Cameca?
I should apologize as I had not found enough time to make a proper explanation. Two probes are down at our lab, and troubleshooting and getting at least one on-line took my time and attention.
Quote from: Probeman on January 27, 2024, 01:22:27 PM
Does anyone have a procedure for adjusting the HV transformer in a Cameca?
I am aware there is potentiometer for exactly that purpose there kind-of "accessible" from outside of HV tank case, but I firmly believe !!! This should not be attempted at customer-site as these voltages (together with current storage in the tank) are absolutely lethal!!!
While it is at low Voltage side of tank it is better not take the risk. Also see my rambling below, as I am pretty sure You don't need to do any of that. Also HV tank calibration should be attempted only and only if problem is not somewhere else. I.e. fatique of cable isolation, breakage of terminating clam diodes (can pull up or down reference voltage). System (software) shows what HV voltage were set by reading reference voltage at output of DAC output, before it is terminated, transported by cable, received by HV regulation board, converted into voltage/current for supplying HV transformer - there is many steps where it could go wrong. Especially I would suspect that at first if requesting HV values at software return something else than what is set (In your case it was previously reported 14.88kV instead of 15kV).
Quote from: Probeman on January 27, 2024, 01:22:27 PM
I think it's safe to conclude that our high voltage source is calibrated a bit too high... the irony of course is that when I purchased this instrument back in 2005 (so I guess it could have drifted since then), I had included in my purchase specifications that Cameca provide calibration data showing that the high voltage source was calibrated (prior to shipping) to within our specifications:
I would risk to say that it is very probably contrary to what you think, if the DH limit measurements were done exactly as You demonstrate here above, - it is most probable that initial HV tank was unintentionally miss-regulated and thus unintentionally was set out of specs, and your current HV tank is actually within specs.
The key point (the missing piece in yours (and other's) fitting method) is this:
the count distribution of X-ray energies, as we see acquired by X-ray detectors, are the real (energetically very narrow) X-ray distributions convoluted enormously by detection processes. Thus, DH limit estimation needs to take into account that background is affected by such convolution exactly in the same manner as the characteristic X-ray peaks (which are initially lines).Had You tried to replicate my DTSA-II MC experiment? I highly recommend that:
1. simulate some low Z EDS: i.e. MgO; medium Z: ZrO, ZnAs2, heavy Z: Bi, Th....
2. use .duaneHunt() function in scripting tab for these simulated spectras; (optionally (or maybe mandatory): look and witness on the EDS plots how these simulated spectra go over set acceleration voltages ... and No, DTSA-II does not simulate peak pile-ups - that effect is there is purelly due to convolution by simulated detector on properly simulated initial X-ray spectrum)
3. notice that DH will be not the same than defined landing energy defined in simulation parameters:
* lowest Z materials will get closest to the defined HV, heaviest materials will have very much overestimated DH than HV.
Why is that like that? I believe DTSA-II does no deconvolution before fitting the line for getting the interference with 0 intensity. The deconvolution is more important the steeper the slope is, thus that is why D-H kinda works for very low Z materials (in DTSA-II), but it is severely overestimated with very high Z materials. In real-life EDS there is also these pileup peaks of continuum. The caveat is that pileup tail does not start where real "non-pile-up'ed" spectra finishes (D-H) and spreads to higher energies from there, but it spreads practically from low energy (2x lowest channel) of spectra to 2x energies of DH. (also there can be 3x and 4x, but those are extremely rare events). Overlapping pileuped continuum counts will shift whole slope (which is fitted for D-H) to higher energies. EDS as means for precise DH estimation for acceleration voltage validation or calibration is absolutely unreliable.
As for WDS, I suggest to repeat the experiment at lower energy (we saw in Henderson example that 10kV works ok) - and even there the same - "3 sigma" (half width at base of the peak) of peak will need to be subtracted from interpolated 0 intensity intersection point (The peak width can be determined at first at higher acceleration voltage making a wavescan of some element with its characteristic X-ray line near that aimed limit; i.e. near 10keV is Ge Ka; in my case half width at base of Voigt-shaped peak of Ge Ka on one of LLIF (actually aglomeration of Ka1, Ka2, and Ka3) is about 150keV, thus 150keV needs to be subtracted then from interpolated at 0 intensity point for get correct D-H estimation).
P.S. I would demonstrate this WDS experiment myself, but I still am at the path of switching back our SXFiveFE online. And BTW, I got aware about this D-H problem due to problems with HV tank on our SX100 and looking for alternatives (manufacturers of HV supplies gives 2% to 1% accuracy for HV). Testing HV on SXFiveFE is also different beast, as it is no more Cameca designed and in-house manufactured HV tank, but a third party, YPS FEG power supply - I am aware that there is some minor difference between set and get voltage readings there already. I am waiting for some time gap to do some experiments.
Quote from: sem-geologist on January 28, 2024, 05:48:16 AM
I should apologize as I had not found enough time to make a proper explanation. Two probes are down at our lab, and troubleshooting and getting at least one on-line took my time and attention.
No need to apologize as it gave me some time to do these measurements! ;D
Quote from: sem-geologist on January 28, 2024, 05:48:16 AM
Quote from: Probeman on January 27, 2024, 01:22:27 PM
Does anyone have a procedure for adjusting the HV transformer in a Cameca?
I am aware there is potentiometer for exactly that purpose there kind-of "accessible" from outside of HV tank case, but I firmly believe !!! This should not be attempted at customer-site as these voltages (together with current storage in the tank) are absolutely lethal!!!
Don't worry, I will leave this to our in-house instrument engineer, he is used to dealing with high voltages!
Quote from: sem-geologist on January 28, 2024, 05:48:16 AM
Quote from: Probeman on January 27, 2024, 01:22:27 PM
I think it's safe to conclude that our high voltage source is calibrated a bit too high... the irony of course is that when I purchased this instrument back in 2005 (so I guess it could have drifted since then), I had included in my purchase specifications that Cameca provide calibration data showing that the high voltage source was calibrated (prior to shipping) to within our specifications:
I would risk to say that it is very probably contrary to what you think, if the DH limit measurements were done exactly as You demonstrate here above, - it is most probable that initial HV tank was unintentionally miss-regulated and thus unintentionally was set out of specs, and your current HV tank is actually within specs. The key point (the missing piece in yours (and other's) fitting method) is this: the count distribution of X-ray energies, as we see acquired by X-ray detectors, are the real (energetically very narrow) X-ray distributions convoluted enormously by detection processes. Thus, DH limit estimation needs to take into account that background is affected by such convolution exactly in the same manner as the characteristic X-ray peaks (which are initially lines).
...
As for WDS, I suggest to repeat the experiment at lower energy (we saw in Henderson example that 10kV works ok) - and even there the same - "3 sigma" (half width at base of the peak) of peak will need to be subtracted from interpolated 0 intensity intersection point (The peak width can be determined at first at higher acceleration voltage making a wavescan of some element with its characteristic X-ray line near that aimed limit; i.e. near 10keV is Ge Ka; in my case half width at base of Voigt-shaped peak of Ge Ka on one of LLIF (actually aglomeration of Ka1, Ka2, and Ka3) is about 150keV, thus 150keV needs to be subtracted then from interpolated at 0 intensity point for get correct D-H estimation).
You know, I think you may be correct on this.
So I took my Ge metal scan and roughly obtained a base width of ~160 eV or 80 eV for half that. Not sure why my LLIF crystal seems to have better resolution than yours. My normal size LiF looks exactly the same interestingly enough:
(https://smf.probesoftware.com/gallery/395_28_01_24_2_51_43.png)
Now if I apply that 80 eV offset I do indeed get closer to 13 keV, but maybe still a little above?
(https://smf.probesoftware.com/gallery/395_28_01_24_2_52_03.png)
So now I need to re-run at 10 keV... and see what that reveals for WDS (and EDS).
But I'm still thinking about why DH limit would be different for different atomic numbers. There does indeed seem to be a small effect in the above plot. Have you also measured this?
This 80eV would be closer to correct value to subtract if HV was 10keV. At 13keV it should be wider as intensities and peak width increases, especially close to the smallest sin theta (highest energy on spectrometer). Ge Ka half base width is applicable for 10keV DH experiments.
Quote from: Probeman on January 28, 2024, 03:03:12 PM
But I'm still thinking about why DH limit would be different for different atomic numbers. There does indeed seem to be a small effect in the above plot. Have you also measured this?
It is not real physical DH limit which differ, it is perceived limit on spectra. Why? Because convolution by same function makes different impact on different slopes. We know convolution (or rather use it maybe even not knowing it) from image processing, i.e. smoothing algorithms is nothing else as convolution. Convolution will smooth high gradients and keep already smooth graditients intact in the image (i.e. Gaussian blurring works like that). And in convolving 1D array (spectra) is exactly the same as in 2D convolution - steep slope will be made more shallow, but shallow slope will be left as is. And so perceived DH for heavier elements has its slope pointing toward real DH after convolution made more shallow which leads to shifting of its interference with 0 point toward the higher energies. For low Z material the slope will be already so shallow that smoothing by convolution won't change the slope and thus it will still point to the real DH position. This applies for EDS. WDS is more simple as slope will be steep enough for "peak-base half width" be applicable despite different Z of material. There is also important question and point of individual perception at measuring base of the peak, maybe our LLIF have similar FWHM, but I get wider base as I am more pessimistic :P ?
What is the uncertainty of my eyes? I guess about 50% plus/minus content in my drink... But getting more serious - how do we measure the base of the peak - that is huge ground for uncertainty on DH estimation even with WDS.
Quote from: sem-geologist on January 28, 2024, 04:13:52 PM
This 80eV would be closer to correct value to subtract if HV was 10keV. At 13keV it should be wider as intensities and peak width increases, especially close to the smallest sin theta (highest energy on spectrometer). Ge Ka half base width is applicable for 10keV DH experiments.
Quote from: Probeman on January 28, 2024, 03:03:12 PM
But I'm still thinking about why DH limit would be different for different atomic numbers. There does indeed seem to be a small effect in the above plot. Have you also measured this?
It is not real physical DH limit which differ, it is perceived limit on spectra. Why? Because convolution by same function makes different impact on different slopes. We know convolution (or rather use it maybe even not knowing it) from image processing, i.e. smoothing algorithms is nothing else as convolution. Convolution will smooth high gradients and keep already smooth gradients intact in the image (i.e. Gaussian blurring works like that). And in convolving 1D array (spectra) is exactly the same as in 2D convolution - steep slope will be made more shallow, but shallow slope will be left as is. And so perceived DH for heavier elements has its slope pointing toward real DH after convolution made more shallow which leads to shifting of its interference with 0 point toward the higher energies. For low Z material the slope will be already so shallow that smoothing by convolution won't change the slope and thus it will still point to the real DH position. This applies for EDS. WDS is more simple as slope will be steep enough for "peak-base half width" be applicable despite different Z of material. There is also important question and point of individual perception at measuring base of the peak, maybe our LLIF have similar FWHM, but I get wider base as I am more pessimistic :P ?
What is the uncertainty of my eyes? I guess about 50% plus/minus content in my drink... But getting more serious - how do we measure the base of the peak - that is huge ground for uncertainty on DH estimation even with WDS.
Not sure what you mean by "perceived" Duane-Hunt. Can you show some us graphical examples?
Yes, I agree the 80 eV half base width offset applies more appropriately to 10 keV DH measurements, and yes, I look forward to trying that next. But I won't be able to check the energy calibration using Ge Ka so I will use Zn Ka I guess.
I really appreciate your comments on this topic. Can you share some of your own measurements of Duane-Hunt limit tests?
Recently I just came across something so obvious and big (The really big Elephant in the room) that we could absolutely missed it in these attempts of precise DH estimation.
Let me quote a paragraph from Ritchie et al 2020 (Proposed practices for validating the performance of instruments used for automated inorganic gunshot residue analysis https://doi.org/10.1016/j.forc.2020.100252 (https://doi.org/10.1016/j.forc.2020.100252)), section on Duane-Hunt limit difference (4.1.3. Diagnosis), at point 1e we see this (emphasis is mine):
Quote(c) The beam energy on some tungsten-filament SEMs is always a few hundred volts less than the set voltage due to a bias on the Wehnelt, a component of the electron gun assembly. A Duane-Hunt limit that is consistently low by a few hundred volts is not a problem so long as the over-voltage, U, on the lead L-lines is sufficient that they remain visible ( U > 1.5 20 keV/13.0 keV ).
While context about Pb L-lines is not relevant for us here, what is relevant is bias on the Wehnelt. First of all Bias voltage can be not just few hundred of volts but up to over one thousand! Let me show some quick summary of bias provided by different commercial HV supplies (SEM/EPMA dedicated) (aggregated from publicly available datasheets from manufacturer sites):
Manufacturer; model(s) | | Max bias (kV) |
Matsusada; SEM-30 & SEM-15 | 3.5 kV |
CPS; 3604 & 3603 | 2kV |
SpellmanHV, EBM20N5/24 | 1.5kV (alt 2 kV) |
SpellmanHV, EBM-TEG | 3.5 kV |
SpellmanHV, EBM-TEGR | 1.65 kV |
Operational bias depends a lot from geometry of W-hairpin and Wehnelt aperture assembly (i.e. diameter of aperture, thickness of W wire). In case of small Wehnelt aperture and close proximity to the W-wire, the bias voltage for proper operation will need to be small, where setting too huge bias would "pinch-off" the emission (it is over-generalization, and "pinch-off" is possible on some of designs and impossible on other. See below). On the other hand, if Wehnelt aperture is large, then 3kV of bias voltage could be just barely enough to get a beam crossover. All geometry/bias voltage approaches have it's pros and cons. But what matters for us here is actually how bias and acceleration voltage is regulated and I think it can be summarized in 3 possible types. The main emphasis there is how bias voltage difference is created, and where high voltage feedback is measured for regulation.
1. Classical
(https://smf.probesoftware.com/gallery/1607_02_02_24_1_17_06.png)
Pros: most simple
Cons: Voltage set and regulated on Wehnelt, voltage cathode (thus electron acceleration voltage, thus landing energy) always lower than set voltage.
Characteristics: fixed stable voltage, Bias voltage is regulated by regulating the resistance of bias resistor. 2 power transformers (heat, tension). Bias voltage is affected by emission current thus it has a minimal emission current limit thus which is not possible to go below and to pinch-off the emission.
2. Classical-alternative
(https://smf.probesoftware.com/gallery/1607_02_02_24_1_25_09.png)
Pros: still simple; Voltage is set and regulated on cathode
Cons: stability?
Characteristics: Bias is regulated by changing Resistance of Bias resistor, HV increases to compensate the voltage drop on the cathode, some limited possibilities for oscillations. 2 power transformers (heat, high tension). It has a minimal emission limit thus it is not possible to go below and pinch-off the emission.
3. Active Bias supply
(https://smf.probesoftware.com/gallery/1607_02_02_24_1_39_45.png)
Pros: Voltage of cathode is regulated independently from bias, It is possible to get smaller emission areas which would be not possible with resistive bias.
Cons: more complex built (3 power transformers instead of 2)
Characteristics: Bias is regulated independently from cathode voltage, bias is independent from emission - no self oscillation possible. It is possible to set bias voltage huge enough to "pinch-off" emission.
So Those SEM (and EPMA) which are affected by e) in quote from Ritchy'ies publication are some older generation instruments with type 1. HV supply.
At first glance Cameca SX100 HV tank is implemented like type 1. However it is not so very bad as cathode voltage can be calibrated for particular emission current, or tabulated and applied as corrections for different emission currents. Single potentiometer calibration in this case can help only temporary with single emission current, running with other emission currents than HV got calibrated with will provide some offset in read HV values from the tank. (I guess that is 100uA). The question is also if Cameca firmware does not do corrections behind the back (maybe thats why few year ago when set 15kV it was reporting 14.88kV?), and if Probe Software does not ignore that. Are Probe Software saving "setted" or "getted" HV values? or both? Which one is used in calculations?
Are someone familiar with HV system on Jeol (W-based) Probe? Could anyone comment which type it is?
I will soon share some DH limit experiments from our SXFiveFE. FE advantage is that it is more like type 3, thus I suspect the landing energy should be very close to the set voltage.
Quote from: Probeman on April 11, 2018, 01:59:14 PM
It sure looks like the electron beam is more than 15 keV, whereas I would expect 15 keV or a smidgem less. Particularly since this is a carbon coated sample and from CalcZAF we should see a loss of about 8 eV for 20 nm of carbon and 15 keV electrons.
Just a small comment on that.
Coating layer should not slow down every beam electron, but only just some small portion of electrons, which gets into interaction with coating material atoms. Bremstrahlung radiation is due to electron acceleration or slowing down ( depends from space frame we are looking from, slowing down is negative acceleration looking from our space frame, or braking) - not because of direct interaction with the matter (albeit matter makes it possible to halt the electron in hard way, like near instant slow down, where electric field would do kind of soft continuous breaking (slowing down)). A fun fact: Bremstrahlung radiation is also generated near gun where electrons are accelerated (will generate kind of soft Bremstrahlung), near lenses where they are deflected. Unfortunately the German-originating name of this radiation meaning "braking" radiation brings in some mind-shortcuts and confusion, it should be called "acceleration radiation" or "inertia breaking radiation".
Here, I find this material quite complementing my understanding on Bremstrahlung:
https://physics.stackexchange.com/questions/186361/why-does-accelerating-electron-emits-photons (https://physics.stackexchange.com/questions/186361/why-does-accelerating-electron-emits-photons)
and especially this animated particle acceleration looks like a picture worth many thousand words:
(https://smf.probesoftware.com/proxy.php?request=http%3A%2F%2Fwww.tapir.caltech.edu%2F%7Eteviet%2FWaves%2Ffield_a.gif&hash=d68a046e35a706891b547b372f16ad49c8df8bfc)
The red dot represents a charged particle, where lines represent the field, the ripple in field is seen by us as some electromagnetic radiation.
Source and further explanations: http://www.tapir.caltech.edu/~teviet/Waves/empulse.html (http://www.tapir.caltech.edu/~teviet/Waves/empulse.html)
DH limit depends on electron "completely" deaccelerating to halt in a single momentary step and for that some "hard" obstacle is required. While statistically carbon coating will influence the spectral distribution, the DH limit stays the same. It is only that denser matter has more chances to instantly stop the electron, than not dense matter (and thus the slope in the EDS approaching the DH limit of those are much more steeper compared to the light materials). Carbon coating for these kind of experiments actually help as it prevents the charge build up. Charge build up is much worse for precise DH estimation, as its electric field slows down every single electron in the beam approaching the surface (there should be increase in background at low energies when surface is charged) - then whole DH lowers down. There of course is few modes: a) unintentional surface charge by the beam electrons, when there is no well grounded electron return path or surface is not conductive - such charge tends to get into oscillations and thus as Ritchy mentioned DH will be highly dynamic.
And b) - intentional bias of surface charge potential - that is available on some new SEM - that is stage instead being connected to ground is connected to some bias voltage and so it would make well coated surface of sample to produce uniform negative or positive electric field which would increase or decrease the landing energy of all landing electrons. I still don't get complete understanding of its benefits, but I had not much opportunity to play around with that.
Quote from: sem-geologist on February 02, 2024, 03:27:05 AM
At first glance Cameca SX100 HV tank is implemented like type 1. However it is not so very bad as cathode voltage can be han HV got calibrated with will provide some offset in read HV values from the tank. (I guess that is 100uA).
This is fascinating reading, thank-you for documenting this. I think your results from 10 keV LiF WDS measurements will be very interesting. I was going to try this weekend, but the lab power may be down.
Quote from: sem-geologist on February 02, 2024, 03:27:05 AM
The question is also if Cameca firmware does not do corrections behind the back (maybe thats why few year ago when set 15kV it was reporting 14.88kV?), and if Probe Software does not ignore that. Are Probe Software saving "setted" or "getted" HV values? or both? Which one is used in calculations?
And here we thought we recorded everything! Right now we are only utilizing the "set" HV values. We will look into recording the "get" HV values also.
The problem I see is what do we believe in terms of the electron landing energy? We don't know the accuracy of the set HV values, nor do we know the accuracy of the "read" HVC value.
The Duane-Hunt limit should help us to decide this.
Note also that even with the same coating on both standards and unknowns once can apply a "coating correction" in Probe for EPMA to account for the electron landing energy loss as described here:
https://smf.probesoftware.com/index.php?topic=23.msg1258#msg1258
This coating correction is in two parts, one for x-ray absorption which mainly affects low energy emission lines and another coating correction for electron energy loss, which really only matters at low overvoltages.
Quote from: chenderson on January 18, 2024, 11:53:26 AM
I meant you can also check the Duane-Hunt limit using WDS. You can use any material.
The common LiF [200], 2d of 4.0267 Angstroms, will cover out to about 13kV, at least on CAMECA WDS. If you're fortunate enough to have an LiF [220], 2d of 2.848 Angstroms, you can get out to about 19kV.
Attached is an example at 10 kV beam voltage on Zr metal using LiF [200]. X-axis is plotted in HV.
Thank-you!
This is a great suggestion (see my tests at 13 keV below) and I want to try again at 10 keV, but our instrument is down for the moment...
In the meantime can you explain how Cameca (or JEOL) handles the issue of bias voltage in calibrating the high voltage power supply to ensure that the electron landing energy takes the bias voltage offset into account?
Also do you know of any tests that can characterize the degree of electron energy spread in the electron beam? That is, how non monochromatic are our electron beams?
Quote from: Probeman on February 10, 2024, 12:54:42 PM
Also do you know of any tests that can characterize the degree of electron energy spread in the electron beam? That is, how non monochromatic are our electron beams?
We know from electron energy loss spectroscopy (EELS) that the electron source is essentially monochromatic from the perspective of X-ray analysis. Today, monochromated cold field emission beams are used which can produce beams with milli-eV energy spreads. However, early EELS was performed with thermal sources which had resolutions on the order of 1 eV. This is the number we should compare to.
Quote from: Nicholas Ritchie on February 11, 2024, 06:53:07 AM
We know from electron energy loss spectroscopy (EELS) that the electron source is essentially monochromatic from the perspective of X-ray analysis. Today, monochromated cold field emission beams are used which can produce beams with milli-eV energy spreads. However, early EELS was performed with thermal sources which had resolutions on the order of 1 eV. This is the number we should compare to.
1 eV or less? OK, that is good to know. So even tungsten electron sources, as used here:
https://smf.probesoftware.com/index.php?topic=1063.msg12312#msg12312
cannot seemingly explain the extent to which continuum seems to be produced past the assumed electron beam energy. So that leaves the FWHM of the detector convolution and the gun bias voltage differential as other culprits... assuming the high voltage supply is accurate of course!
I'm beginning to think that the Duane-Hunt limit test is more *limited* than we originally suspected! :D
Quote from: Nicholas Ritchie on February 11, 2024, 06:53:07 AM
We know from electron energy loss spectroscopy (EELS) that the electron source is essentially monochromatic from the perspective of X-ray analysis. Today, monochromated cold field emission beams are used which can produce beams with milli-eV energy spreads. However, early EELS was performed with thermal sources which had resolutions on the order of 1 eV. This is the number we should compare to.
Do you have any literature references for the thermal sources that you can share with us?
Quote from: chenderson on January 17, 2024, 08:27:26 AM
You can also measure the Duane-Hunt limit on WDS using a standard LiF, if you are using high voltages less than 13 kV.
For the SX100 and SX Five, the measured value read from the HV regulation board can be adjusted using R307. This only affects the measured (feedback) value and doesn't change the gun voltage.
Carl,
How does Cameca ensure that the electron landing energy (high voltage power supply) is accurately calibrated?
On the Cameca Shallow Probe (which it appears they no longer manufacture?), because it is based on the principle of minimum overvoltage (for detection of trace elements in very thin films), it seems this would be a critically important calibration. See product literature attached below.
This Shallow Probe high voltage power supply could apparently operate only at relatively low electron beam energies, e.g., "The EX-300 covers an
implant energy range from a few hundred eV up to 5keV/10keV for Boron and up to 70keV for Phosphorus and Arsenic." Also mentioned is "In LEXES, soft X-rays are generated by an electron beam, then analyzed by spectrometers. A special electron column was designed by CAMECA to deliver focused beam carrying high electron current at low impact energies (up to 30μA and down to 0.3 keV)."
So from 300 eV up to what? What was the highest electron energy it could deliver? And how was the gun electron voltage calibration accomplished?
Quote from: Probeman on February 11, 2024, 05:24:20 PM
Quote from: Nicholas Ritchie on February 11, 2024, 06:53:07 AM
We know from electron energy loss spectroscopy (EELS) that the electron source is essentially monochromatic from the perspective of X-ray analysis. Today, monochromated cold field emission beams are used which can produce beams with milli-eV energy spreads. However, early EELS was performed with thermal sources which had resolutions on the order of 1 eV. This is the number we should compare to.
Do you have any literature references for the thermal sources that you can share with us?
K. Kimoto, G. Kothleitner, W. Grogger, Y. Matsui, F. Hofer Micron, 36 (2005), p. 185
Quote
The bandgap is one of the principal properties of electronic materials. Electron energy-loss spectroscopy (EELS) in transmission electron microscopy (TEM) gives information on the direct and indirect transitions with high spatial resolution (Egerton, 1996). There are several reports on bandgap measurements of insulators and semiconductors (Batson et al., 1986, Bangert et al., 1997, Rafferty and Brown, 1998, Batson, 1999). Since a bandgap measurement requires high energy resolution, the previous authors employed a cold field-emission gun (CFEG), whose energy spread (>0.25 eV) is smaller than that of a Schottky emitter (>0.5 eV) and those of other thermionic electron sources (>1 eV). Recently, several types of monochromator for a TEM have been developed to reduce the energy spread (Terauchi et al., 1999, Tiemeijer, 1999a, Kahl and Rose, 2000, Mook and Kruit, 2000, Tanaka et al., 2002), and some of them are now commercially available. Several authors have demonstrated the efficiency of monochromators (Terauchi et al., 1998, Terauchi and Tanaka, 1999, Mitterbauer et al., 2003). There is a pioneering study for bandgap measurements (Lazar et al., 2003), but the previous papers mainly focused on core-loss spectroscopy or valence-band spectroscopy.
I just thought I would follow up with some WDS and EDS measurements I did last weekend on Si, Ge and W at 10 keV, looking specifically at the Duane-Hunt limit.
Each of these scans (simultaneous WDS and EDS) took ~7 hours (300 points at 80 sec) for each sample. The EDS had a dead time of ~28% at a 2000 nsec pulse processing time.
Here's the EDS data:
(https://smf.probesoftware.com/gallery/395_06_03_24_9_13_40.png)
And here's the WDS data:
(https://smf.probesoftware.com/gallery/395_06_03_24_9_14_04.png)
Due to the convolution by the detector spectral resolution (as mentioned previously by SEM-geologist) the extrapolated Duane-Hunt limit appears to be higher than the expected value of 10 keV.
Of course it could be that our high voltage power supply is also not calibrated accurately.
We need a better method to determine the actual value of of electron beam energy, perhaps using the method suggested by Nicholas Ritchie where we measure a characteristic emission line at various over voltages from 1.5 and down close to the edge energy and see where that trend approaches zero as shown here (from Edax):
(https://smf.probesoftware.com/gallery/395_06_03_24_9_22_40.png)
For example, for calibrating our beam energy at say 5 keV we could use Ti K edge at 4.967 keV and measure the Ti Ka emission intensities at say 8 keV, 7 keV, 6 keV and 5 keV (the last one being problematic to say the least!).
For calibrating at 10 keV we could utilize Zn Ka (edge energy 9.66 keV) and at 15 keV we'd have to use EDS and perhaps the Rb Ka (in RbTiOPO4 synthetic) with an edge energy of 15.2 keV.
I think we can explain what we are seeing in the above Duane-Hunt limit measurements.
Here are some continuum models using PENEPMA which show two different artifacts which occur together in our empirical measurements. First a "binning" effect where the last several bins (just under the electron beam energy) will always have positive intensities (with a long enough integration time), so the trend never extrapolates exactly to zero at the beam energy as seen here:
(https://smf.probesoftware.com/gallery/395_13_03_24_9_07_18.png)
And second a convolution effect due to detector spectral resolution (which spreads out the photon energies) as seen here using the same model data as above:
(https://smf.probesoftware.com/gallery/395_13_03_24_9_07_41.png)
So here's the basic problem with trying to determine the accuracy of one's electron beam energy using the Duane-Hunt limit:
First, even with WDS, the spectral resolution using an LiF crystal (using the Ge Ka emission line of ~9.87 keV), is still around 100 eV (FWHM) as seen here measured at 15 keV in Ge metal:
(https://smf.probesoftware.com/gallery/395_24_03_24_1_15_53.png)
Running the same region at 10 keV (below the Ge K edge energy of 11.1 keV), we see both the binning artifact and the spectra resolution artifact imposed on the continuum (100 nA, 120 sec per wavescan point):
(https://smf.probesoftware.com/gallery/395_24_03_24_1_16_25.png)
Compare this measurement to the continuum intensities modeled using PENEPMA in the previous post above.
This is why we need a better method to estimate our electron beam energy accuracy. Here are some preliminary measurements I performed on Zn metal using a range of accelerating voltages from 10 to 15 keV this weekend (three points per keV):
(https://smf.probesoftware.com/gallery/395_24_03_24_1_27_53.png)
Extrapolating the curve it appears the net intensity does *not* intercept zero exactly at the Zn Ka edge energy... is this evidence that our electron beam energy is slightly higher than the nominal value reported by the instrument?.
Quote from: Probeman on March 24, 2024, 01:34:13 PM
Running the same region at 10 keV (below the Ge K edge energy of 11.1 keV), we see both the binning artifact and the spectra resolution artifact imposed on the continuum (100 nA, 120 sec per wavescan point):
(https://smf.probesoftware.com/gallery/395_24_03_24_1_16_25.png)
Compare this measurement to the continuum intensities modeled using PENEPMA in the previous post above.
What intrigues me is that on WDS we see some background much above 10.1kV (ignoring the questionable region where Duane-Hunt limit could be). Then I see that Your data (which You had sent in mail thread) and mine WDS scans shows that this faint background over Duane-Hunt limit seems clearly dependant on average atom number. The higher atom number - the higher this fain background intensity is. Differently to EDS there (on WDS) is no pulse pile-up to blame. I see no physical possibility to create such artifact, and maybe we should consider it is not artifact, but a tiny window showing what some rare electrons (from massive stream of electrons in the beam) goes through. Another clue is PENEPMA simulations. Abrupt cutoff at set beam energy is probably artificial implemented limitation in the modeling to not produce any X-rays above Duane-Hunt limit. But intensities at last channel below Duane-Hunt limit in those simulations, and its clear dependency to material average atom number, hints that this cut off at Duane-Hunt is rather artificially forced in the modeling.
So are there some electrons accelerated more than set acceleration voltage - I doubt it. But I think there is important concept missed here:
1) Bremstrahlung is not just from breaking (Stopping) of electron - it is inertia breaking radiation - be it acceleration, de-acceleration or
deflection. Observed bremstrahlung radiation does not directly map to the kinetic electron energy
2) if deflection of electron is more than 90 degree (thus a bit backwards than initial trajectory) - the difference in ripple of updated electric field radiating from the charged particle will have shorter wavelength than it would be if halted to 0 velocity (in such complete halt case giving bremstrahlung radiation at Duane-Hunt limit). In case the electron would be ricochet in perfect 180 degrees - the wavelength of ripple would be double to that of halting it to 0 velocity. What Do I mean with
ripple in changed electric field? Such ripple would be virtual photons as I had shared some interesting concept found in internet in some previous post:
Quote from: sem-geologist on February 02, 2024, 06:09:10 AM
Here, I find this material quite complementing my understanding on Bremstrahlung:
https://physics.stackexchange.com/questions/186361/why-does-accelerating-electron-emits-photons (https://physics.stackexchange.com/questions/186361/why-does-accelerating-electron-emits-photons)
and especially this animated particle acceleration looks like a picture worth many thousand words:
(https://smf.probesoftware.com/proxy.php?request=http%3A%2F%2Fwww.tapir.caltech.edu%2F%7Eteviet%2FWaves%2Ffield_a.gif&hash=d68a046e35a706891b547b372f16ad49c8df8bfc)
The red dot represents a charged particle, where lines represent the field, the ripple in field is seen by us as some electromagnetic radiation.
Source and further explanations: http://www.tapir.caltech.edu/~teviet/Waves/empulse.html (http://www.tapir.caltech.edu/~teviet/Waves/empulse.html)
In most of our cases electron has many small deflections (As we know from MC simulations) before loosing completely its velocity and thus many much lower (than set beam energy) continuum radiation will be observed from those numerous deflections. But if we send millions of electrons in short time-span to relatively same spot, some will have opportunity to get deflected backwards at the first interaction with matter which (following the pseudo-photon/e-field ripple concept) will produce higher energy pseudo-photon than energy of the beam electron. The denser the matter - the greater the chance to get such first-interaction backward deflected electrons. Additionally - lets remember that other electrons from the beam do not instantaneously magically dissapear after hitting the matter, but after loosing its velocity (energy) they need to be drained from the hit sample surface back to the HV generator, but as there is resistance on the surface - it takes some time (impedance all the way from the spot-coated conductive surface of the sample, stage contacts, wires, picoamp, HV generator...)... and so some "unlucky" electrons from the beam with full velocity has higher chances to hit such "free" drifting electrons which are traveling outward to ground and in some rare circumstanced such beam electron can be deflected backwards.
One more detail to not overlook - Electron has nearly no mass and reacts to electric field near instant (that is why waveguide - aka conductor wire and its dialectric space allows sending signals nearly at speed of light, where electrons travel only some cm/s on conductor surface). Such stunts are much harder to make with positive ions which have mass (i.e. FIB) (PIXE- needs few MeV acceleration).
....
I just got one big extremely crazy idea, which probably wont work miserably...
Last weekend I again did some overvoltage measurements on some pure metal standards, but this time using 0.2 keV increments above the edge energies as proposed by Nicholas Ritchie (using the net intensities avoids the detector convolution issues of the Duane Hunt limit determinations we have seen in this topic). Here are Ti K edge net intensity measurements:
(https://smf.probesoftware.com/gallery/395_30_03_24_3_13_55.png)
Can we say something about the accuracy of the electron beam energy at 5 keV on this instrument? :-\
I think next I need to try 0.1 keV increments and this time I will polish the metal standards to remove the carbon coating which at very low overvoltages could affect this measurement.
By the way, Donovan mentioned to me that there is now a new right click menu item in Probe for EPMA for easy export of these over voltage measurements which do not require primary standards:
(https://smf.probesoftware.com/gallery/395_30_03_24_3_14_25.png)
I wanted to weigh in on this discussion, if only to sharpen my own understanding of things.
First, the Wehnelt voltage. I don't think this should really be subtracted from the initial HV. I think the Wehnelt determines how many electrons emerge from the gun and from which part of the crystal/tungsten filament, but not their final energy. Typically, the Wehnelt voltage is relative to the emitter, so whereas the electrons emerging from the filament see a decelerating field on their way towards the Wehnelt, they are accelerated again by the same amount after leaving the Wehnelt aperture. I think of it this way: When you consider the whole gun module as a "closed system" ensemble which is at voltage E0, then electrons coming out of it will have that potential, regardless of what's happening inside that ensemble.
I tried to do some bookkeeping of all the energy deltas. Here's my list, feel free to comment.
First, the E0 itself (as set by the microscope) will likely have some (systematic) "setpoint error", for example because the voltage entering the HV cascade is determined by some DAC with a finite number of steps. The "problem" here is that this will then be a fixed percentage of the "full range", so if your HV subsystem can go up to 30kV and uses a 10-bit DAC to set the value, you're looking at a discretization error of ~30V just from this. The HV supply should also specify a certain maximum "ripple", which is typically an order of magnitude better than this (because it would otherwise give bad ("fluctuating") imaging results).
There may be a small voltage that needs to be subtracted from the supplied HV because that's applied to the filament itself to heat it up, but that would be just a few volts.
Then, there will be a spread in the energy with which the electrons escape from the filament or crystal. This is worst for tungsten (because you typically heat it up the most) and best for a cold FEG. Regardless, it will also be only a few eV, so I don't think this should worry us. This is one of the causes of chromatic aberration which is why microscope builders try to keep it as small as possible, or even insert monochromators for ultimate imaging performance (at the cost of intensity, so I suppose nobody here would use them unless you're also doing EELS).
Then, electrons can also undergo further ("perpendicular") acceleration inside the scanning column, so that increases their energy as a function of their final distance from the optical center. In case you're scanning a big field of view, this may be significant. Speaking for the microscope my team is producing, we're scanning electrostatically with a few hundred volts on the scanning poles, so my guess is that electrons aimed for the edges of the maximum field of view have their energy increased by the same amount (and worse: that means the electron energy varies over the image - interesting when doing mapping!)
Finally, I think in many cases there will be some charging happening at the sample surface. This is the hardest to quantify. But unless you're analyzing some piece of perfectly grounded metal, I'm sure there will be some equilibrium between the electrons you're blasting onto a single tiny point on the sample and them flowing away to earth again.
And when the X-rays are finally being created in the sample, there is (as already mentioned here) the gaussian spread in the detector itself (and the resulting "convolution" of the measurement) and I think that should not be underestimated. After all, even for a perfect SDD with a MnKa FWHM of 119 eV, the FWHM of a 15kV peak would be something like 190eV. So, I think that even if "perfect" 15000.0eV electrons are hitting your specimen, you should not be surprised to find some signal in your spectra a few hundred eV higher than that.
By the way, this is all not to say that I don't find the whole bremsstrahlung phenomenon super weird. Since we are seeing photons with energies up to E0 in our spectra, that means that these were emitted by electrons losing all their energy during deceleration (so far, I'm nodding) but since each photon corresponds to a single quantum mechanical event, that must mean that some electrons come to an abrupt stop from full speed in one infinitesimal event. How?!
Wasn't it Bohr himself who said "Anyone who is not shocked by quantum theory has not understood it" - I'm definitely still in the "shocked" phase.
Quote from: Sander on April 06, 2024, 01:50:09 AM
I wanted to weigh in on this discussion, if only to sharpen my own understanding of things.
I'm with you here. I still consider myself a student because I try and learn something new every day!
Quote from: Sander on April 06, 2024, 01:50:09 AM
And when the X-rays are finally being created in the sample, there is (as already mentioned here) the gaussian spread in the detector itself (and the resulting "convolution" of the measurement) and I think that should not be underestimated. After all, even for a perfect SDD with a MnKa FWHM of 119 eV, the FWHM of a 15kV peak would be something like 190eV. So, I think that even if "perfect" 15000.0eV electrons are hitting your specimen, you should not be surprised to find some signal in your spectra a few hundred eV higher than that.
Yes, this convolution effect is the main reason we don't see the so-called photon "shelf" or "cliff" artifact that we've been seeing in PENEPMA I think. Here is a simulation from PENEPMA that is not convolved to the detector resolution:
(https://smf.probesoftware.com/gallery/395_13_03_24_9_07_18.png)
And here convolved:
(https://smf.probesoftware.com/gallery/395_13_03_24_9_07_41.png)
The photon cliff is completely obscured. Yes, yet one more reason not to trust the Duane-Hunt limit to check the accuracy of one's electron beam energy!
Quote from: Sander on April 06, 2024, 01:50:09 AM
By the way, this is all not to say that I don't find the whole bremsstrahlung phenomenon super weird. Since we are seeing photons with energies up to E0 in our spectra, that means that these were emitted by electrons losing all their energy during deceleration (so far, I'm nodding) but since each photon corresponds to a single quantum mechanical event, that must mean that some electrons come to an abrupt stop from full speed in one infinitesimal event. How?!
Wasn't it Bohr himself who said "Anyone who is not shocked by quantum theory has not understood it" - I'm definitely still in the "shocked" phase.
Yeah, I'm always shocked! And it is weird that an electron could come to a complete halt. Here is a figure that a colleague of mine in the Physics Department at the University of Oregon , Andrew Ducharme, wrote me recently in discussing the above photon "cliff":
QuoteThe established physics is that bremsstrahlung cross-sections are nonzero for complete energy losses, or for production of photons with the beam energy E (see figure from Penelope manual), while the probability of producing a photon with energy E + 1 eV is 0. Wait long enough (assuming ideal detector, electron source) and you will count photons at the Duane-Hunt limit while never getting counts in the energy bin of E + 1 eV. The longer you wait, the more DH-energy photons, and the higher the cliff.
(https://smf.probesoftware.com/gallery/395_06_04_24_8_24_59.png)
I think of it in the sense that the coulombic field of an atom is actually a pretty big target, so a few electrons are going to hit some atoms directly right at the surface...
Here's a question I have: I was recently chatting with someone from the industry and they said that they only use the DH limit as a crude measure of the electron beam energy, say to check for sample charging (as you mentioned). And that in fact, on their high end FEG electron beam instruments they utilize a special electron detector situated inside the electron column (gun?) so that when the objective lens is adjusted to reflect electrons back up the column, they use this detector to measure the electron energy with extreme precision and accuracy. He mentioned that it was based on a "Wine" detector (pronounced "vine" in German?) but as it's a trade secret he couldn't say more.
Does anyone here know anything more about this electron beam energy measurement system?
Wien filter?
It is used as monochromater in TEM.
Quote from: yuji on April 07, 2024, 06:33:24 AM
Wien filter?
It is used as monochromater in TEM.
Wien filter pronounced like "vine" in German? That sounds about right.
This person mentioned that this Wien (he called it a detector) could be used to calibrate the electron beam energy of an SEM (and possibly a microprobe). Does that sound right?
Looking through the literature I can't find anything specific to using Wien device for electron beam energy calibration except maybe for very low beam energies...
Quote from: Sander on April 06, 2024, 01:50:09 AM
Then, there will be a spread in the energy with which the electrons escape from the filament or crystal. This is worst for tungsten (because you typically heat it up the most) and best for a cold FEG. Regardless, it will also be only a few eV, so I don't think this should worry us. This is one of the causes of chromatic aberration which is why microscope builders try to keep it as small as possible, or even insert monochromators for ultimate imaging performance (at the cost of intensity, so I suppose nobody here would use them unless you're also doing EELS).
Here is a reference Nicholas Ritchie posted above for the energy spread of an electron beam:
K. Kimoto, G. Kothleitner, W. Grogger, Y. Matsui, F. Hofer Micron, 36 (2005), p. 185
By the way, here is one (quite old) paper for measuring electron beam energies:
Schulson, E. M. "Method for Measuring the Incident‐Beam Energy in Scanning Electron Microscopy Using Electron Channelling Patterns." Journal of Applied Physics 42.10 (1971): 3894-3899.
I wanted to try and push the envelope this last weekend and see if we can evaluate this overvoltage method for attempting to check our electron beam energy accuracy by utilizing 0.1 keV increment intervals for the Ti K edge (~5 keV) and the Ge K edge (~11 keV).
I finally realized that this overvoltage method is essentially a trace element problem because the net intensity approaches zero asymtotically. And zero intensity is presumably where our overvoltage is 1.0 for the edge energy. Therefore I tuned up at 100 nA using 120 seconds on-peak and 60 seconds on each off-peak, carefully selected my backgrounds.
I also carefully re-polished (removed the carbon coat) on our Ti and Ge standards to avoid any electron energy loss from a coating or oxide layer, and immediately put them in the instrument (yeah, this old man ran from the polishing lab to the microprobe lab!).
Here is the first attempt using Ge Ka starting at 11.2 keV and increasing 0.1 keV to 12.2 keV using a 2nd order polynomial extrapolation:
(https://smf.probesoftware.com/gallery/395_08_04_24_8_49_21.png)
The red arrow is approximately where we would like to see the intercept cross zero on the Y axis (11.103 keV), but maybe we are underfitting, so let's try a 3rd order polynomial:
(https://smf.probesoftware.com/gallery/395_08_04_24_8_49_44.png)
Hmmm, well now we're clearly overfitting, as we never cross zero intensity! OK let's try again with a second dataset, once more with a 2nd order polynomial:
(https://smf.probesoftware.com/gallery/395_08_04_24_8_50_02.png)
OK, and now with a 3rd order polynomial:
(https://smf.probesoftware.com/gallery/395_08_04_24_8_50_20.png)
Well so what can we conclude from this? The high voltage at 11.2 keV is not too far from the nominal voltage I would guess...
It sure would be nice to test at around 15 keV (where most users tend to run), but then we would need an LiF220 Bragg crystal and use the Rb K edge or Sr K edge, but those aren't great as pure metals (I think we need to use pure metals without a conductive coating or oxide layer for best accuracy...).
Maybe we need to use 0.05 keV increments? Does anyone know what the minimum high voltage step sizes on a Cameca SX100 are?
Quote from: Probeman on April 08, 2024, 09:10:47 AM
Maybe we need to use 0.05 keV increments? Does anyone know what the minimum high voltage step sizes on a Cameca SX100 are?
I think I know. SX100 HV control board is controlled by analog DC signal of 0-10V. As for EHT that correspond to range of acceleration voltages 0-50kV. i.e. for 30kV it will be 6V DC, for 15kV it will be 3V. Analog DC signal is created at Column Control board with 12bit DAC, thus one bit is 50kV/2^12 = 12.20703125V, so theoretically that would be minimal step...
...which brings me to point that 15kV would require 1228.8 bit, where closest round bit would give 15002.7V - essentially close enough to the 15kV.
Quote from: Sander on April 06, 2024, 01:50:09 AM
First, the E0 itself (as set by the microscope) will likely have some (systematic) "setpoint error", for example because the voltage entering the HV cascade is determined by some DAC with a finite number of steps. The "problem" here is that this will then be a fixed percentage of the "full range", so if your HV subsystem can go up to 30kV and uses a 10-bit DAC to set the value, you're looking at a discretization error of ~30V just from this.
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...
Some HV PSU use even 14bit for EHT.
Quote from: Sander on April 06, 2024, 01:50:09 AM
The HV supply should also specify a certain maximum "ripple", which is typically an order of magnitude better than this (because it would otherwise give bad ("fluctuating") imaging results).
It is kind of ironic that HV tank is powered with high frequency AC which we don't see (on images) thanks to smoothing properties of Cockcroft–Walton voltage multiplier on its own (often on SEM/Probe there is up to 10 multiplication stages) and additional RC filtering stages just takes any residual ripple out of equation. The HV ripple is order of magnitude smaller than accuracy of HV, because it is few orders of magnitude easier technically to achieve (basically - no effort, and accuracy as we see here is enormously challenging to keep in check).
Quote from: Sander on April 06, 2024, 01:50:09 AM
There may be a small voltage that needs to be subtracted from the supplied HV because that's applied to the filament itself to heat it up, but that would be just a few volts.
Subtracted or added? If it is DC used to heat the filament, mostly those are up to 5V. As example, lets say filament is supplied with 5V - the HV is applied through symmetric matched resistors to plus and minus rail of that filament circuit, lest say 10kV (this is biasing the filament). The negative rail of filament then has -10002.5V and positive rail of filament then have -9997.5V. So as current in ampere range flows through filament, what voltage (relative to anode) will be at the middle (the electron emitting) point of the filament? At center point the filament will be 10kV - there is nothing to be subtracted or added. Well... unless some SEM manufacturer would bias filament not symmetrically, but directly to the single filament supply rail... 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).
Quote from: Sander on April 06, 2024, 01:50:09 AM
Then, electrons can also undergo further ("perpendicular") acceleration inside the scanning column, so that increases their energy as a function of their final distance from the optical center. In case you're scanning a big field of view, this may be significant. Speaking for the microscope my team is producing, we're scanning electrostatically with a few hundred volts on the scanning poles, so my guess is that electrons aimed for the edges of the maximum field of view have their energy increased by the same amount (and worse: that means the electron energy varies over the image - interesting when doing mapping!)
this! This is very interesting concept. Would this be able to recognize with Duane-Hunt limit on EDS? The limit should be shifted I guess?
Quote from: Sander on April 06, 2024, 01:50:09 AM
By the way, this is all not to say that I don't find the whole bremsstrahlung phenomenon super weird. Since we are seeing photons with energies up to E0 in our spectra, that means that these were emitted by electrons losing all their energy during deceleration (so far, I'm nodding) but since each photon corresponds to a single quantum mechanical event, that must mean that some electrons come to an abrupt stop from full speed in one infinitesimal event. How?!
That's the whole point of D-H limit, to catch these electrons which get to an abrupt stop from full speed in one infinitesimal event. And one of challenging part of D-H is that these are very very rare as most of them are stopped in few or many many steps (thus we get 0 to E0 continuum). 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.
Quote from: SandThe question is if it infinitesimal event?er on April 06, 2024, 01:50:09 AM
Wasn't it Bohr himself who said "Anyone who is not shocked by quantum theory has not understood it" - I'm definitely still in the "shocked" phase.
But do we need quantum theory at all in this case? (probably I am the one who do not fully understand it (or completely don't understand) as I don't feel shocked :D)
Quote from: sem-geologist on April 09, 2024, 12:56:20 AM
Quote from: Probeman on April 08, 2024, 09:10:47 AM
Maybe we need to use 0.05 keV increments? Does anyone know what the minimum high voltage step sizes on a Cameca SX100 are?
I think I know. SX100 HV control board is controlled by analog DC signal of 0-10V. As for EHT that correspond to range of acceleration voltages 0-50kV. i.e. for 30kV it will be 6V DC, for 15kV it will be 3V. Analog DC signal is created at Column Control board with 12bit DAC, thus one bit is 50kV/2^12 = 12.20703125V, so theoretically that would be minimal step...
Very good! OK so 12.2 eV (0.012 keV) would be the smallest step size? I'll give 50 eV increments a try next weekend. So far the overvoltage plots (above) seem very smooth using 100 eV steps:
https://smf.probesoftware.com/index.php?topic=1063.msg12536#msg12536
Quote from: sem-geologist on April 09, 2024, 12:56:20 AM
Quote from: Sander on April 06, 2024, 01:50:09 AM
Then, electrons can also undergo further ("perpendicular") acceleration inside the scanning column, so that increases their energy as a function of their final distance from the optical center. In case you're scanning a big field of view, this may be significant. Speaking for the microscope my team is producing, we're scanning electrostatically with a few hundred volts on the scanning poles, so my guess is that electrons aimed for the edges of the maximum field of view have their energy increased by the same amount (and worse: that means the electron energy varies over the image - interesting when doing mapping!)
this! This is very interesting concept. Would this be able to recognize with Duane-Hunt limit on EDS? The limit should be shifted I guess?
Based on the D-H testing we've performed above:
https://smf.probesoftware.com/index.php?topic=1063.msg12442#msg12442
due to convolution effects of the EDS detector on the photon "cliff" binning artifact, I don't think we can do better than +/- 100 or 150 eV using the Duane-Hunt limit test:
https://smf.probesoftware.com/index.php?topic=1063.msg12472#msg12472
Therefore I think the overvoltage method on the characteristic net intensity, suggested by Nicholas Ritchie, is the only way forward for absolute determinations of electron beam energies at high voltages:
https://smf.probesoftware.com/index.php?topic=1063.msg12536#msg12536
A blind test I've thought about trying someday is to acquire some EDS spectra at say 15.2 keV or 14.9 keV and see if anyone can actually back out the correct accelerating voltage- I think if we didn't already know what the high voltage was we couldn't do it...
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.
(https://smf.probesoftware.com/gallery/399_10_04_24_11_37_58.png)
When I compared the measured spectra with simulations from PENEPMA and DTSA-II, both were capable of modeling the general shape of the continuum quite well. Red is measured, blue is penepma, and green is DTSA-II. All are scaled such that the continuum intensity near 5 keV is the same.
(https://smf.probesoftware.com/gallery/399_10_04_24_11_38_49.png)
However, at the highest energies (within a couple hundred eV of the D-H) PENEPMA did a more realistic job. It has been suggested that the continuous slowing down model underestimates the intensity at energies just below the D-H. This seems credible.
Red is measured, blue is penepma, and green is DTSA-II. All are scaled such that the continuum intensity near 5 keV is the same.
(https://smf.probesoftware.com/gallery/399_10_04_24_11_39_44.png)
If you are curious about the details, I've attached a Jupyter notebook as a self-contained HTML file. (I had to ZIP it to fit within the site's file size constraints.)
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'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.
Quote from: Nicholas Ritchie on April 10, 2024, 11:51:26 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.
(https://smf.probesoftware.com/gallery/399_10_04_24_11_37_58.png)
Very nice work.
These plots will be perfect for our Duane-Hunt limit presentation at M&M this summer.
Quote from: xllovet 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.
I was just going to post the same comment!
I did convolve the PENEPMA photon cliff in this post above:
https://smf.probesoftware.com/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.
Quote from: Nicholas Ritchie 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.
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.
Quote from: Nicholas Ritchie on April 11, 2024, 05:58:52 AM
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:
C **** Example of FWHM(E) function for a Si(Li) detector.
FWHM=DSQRT(7849.255D0+2.237253D0*E)
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:
(https://smf.probesoftware.com/gallery/395_11_04_24_7_34_50.png)
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://smf.probesoftware.com/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?
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.
Quote from: Nicholas Ritchie 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.
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://smf.probesoftware.com/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:
(https://smf.probesoftware.com/gallery/395_11_04_24_10_43_11.png)
And here is the 2nd effort:
(https://smf.probesoftware.com/gallery/395_11_04_24_10_43_32.png)
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...
It depends upon what you want out of the measurement. The Duane-Hunt remains the best way to determine if your sample is charging.
Quote from: Nicholas Ritchie 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.
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://smf.probesoftware.com/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?
Quote from: sem-geologist on April 09, 2024, 12:56:20 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 (https://patents.google.com/patent/JP2023036117A/en?oq=JP2023036117). Filed 2021-09-02, status is still "pending".
QuoteIf 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.
Quote from: Sander on April 13, 2024, 06:21:07 AM
Quote from: sem-geologist on April 09, 2024, 12:56:20 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?
Quote from: Probeman on April 13, 2024, 08:24:52 AM
Quote from: Sander on April 13, 2024, 06:21:07 AM
Quote from: sem-geologist on April 09, 2024, 12:56:20 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.
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...
Quote from: Probeman on April 14, 2024, 09:10:57 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.
At the end of the day, reproducibility is more important than accuracy. While beam energy is an important parameter in our matrix corrections, if the true beam energy is 10.25 keV when we've set it to 10 keV, the difference is probably buried within the uncertainty in the matrix correction so long as all data is collected at the 10.25 keV.
Quote from: Nicholas Ritchie on April 15, 2024, 06:08:55 AM
At the end of the day, reproducibility is more important than accuracy. While beam energy is an important parameter in our matrix corrections, if the true beam energy is 10.25 keV when we've set it to 10 keV, the difference is probably buried within the uncertainty in the matrix correction so long as all data is collected at the 10.25 keV.
Well, I for one sure would like to know if my high voltage was off by 250V! :)
As I said previously the whole point of this topic is to determine the accuracy of our electron beam energy. Yes, I agree that most of the time at sufficiently high over voltages the beam energy accuracy isn't too critical. But we at UofO often run at low over voltages in order to attain high spatial resolution analyses, so the question has concerned me enough to have started a thread to look into this.
And now we've made significant progress in learning about the convolution of the photon "cliff" at the Duane-Hunt limit... which no one had even suspected existed previously! I think this has been a fun and interesting exercise and appreciate all the help and support! :)
The good news is that the over voltage curve method is also good for determining our beam energy precision/reproducibility...
I made some very low over voltage measurements over the weekend on Ti Ka (~ 5 keV) and Ge Ka (~11 keV) and the results are very encouraging.
The Ti K edge energy is 4.964 (or 4.967 in another tabulation), so I started with a beam energy of 4.98 kV and went up from there. At 4.98 kV, I obtained a count rate of 0.05 cps/nA with a variance of less than 0.0003!
I then increased the beam energy in increments of 0.04 KV, so the next measurement at 5.02 kV I obtained a count rate of 0.33 cps/nA +/- 0.02.
These were at 100 nA and counting 120 sec on-peak and 60 seconds on each off-peak. I'm plotting them up now...
This over voltage curve method is working better than I initially thought possible.
Unfortunately the instrument failed with a vacuum error about halfway through so the second data sets didn't get acquired, but here is the first attempt using 0.04 KV increments just about the TI K edge:
(https://smf.probesoftware.com/gallery/395_15_04_24_7_32_34.png)
Looking at the counting scatter, this plot shows how reproducible this method is. One can also conclude that the instrument is producing a fairly smooth curve in the high voltages... so perhaps we can conclude that the electron beam energy on my SX100 is very slightly lower than the nominal value at ~5 kV since the zero intercept is very slightly higher than the Ti K edge energy?
And here is the dataset for Ge Ka:
(https://smf.probesoftware.com/gallery/395_15_04_24_7_49_39.png)
This plot causes me to suspect that the electron beam energy on my Cameca SX100 at ~11 kV is slightly higher than the nominal value would indicate... what do you all think?
Again, both the Ti and Ge pure metals were freshly polished and uncoated (though well grounded).
Here's a zoom of of the D-H limit photon cliff in PENEPMA using continuum forcings:
(https://smf.probesoftware.com/gallery/395_16_04_24_8_18_12.png)
These continuum forcings are seen here:
>>>>>>>> Interaction forcing.
IFORCE 1 1 4 -100 0.9 1.0 [KB,KPAR,ICOL,FORCER,WLOW,WHIG]
IFORCE 1 1 5 -10 0.9 1.0 [KB,KPAR,ICOL,FORCER,WLOW,WHIG]
Interestingly if I run the same simulation but using characteristic forcings we see an even more prominent photon cliff:
(https://smf.probesoftware.com/gallery/395_16_04_24_8_15_52.png)
The characteristic forcings used are here:
>>>>>>>> Interaction forcing.
IFORCE 1 1 4 -10 0.9 1.0 [KB,KPAR,ICOL,FORCER,WLOW,WHIG]
IFORCE 1 1 5 -100 0.9 1.0 [KB,KPAR,ICOL,FORCER,WLOW,WHIG]
I do not have an explanation for this.
Looking at the data in replies #63 and #64 above, it is interesting (to me anyway) how quickly the statistics improve at such low over voltages!
Here is the raw data from the Ti Ka measurements (K edge is 4.964 kV):
Ti Ka kV cps/100nA STD DEV %STD DEV
4.98 4.80 0.30 7.23
5.02 33.2 1.70 5.04
5.06 67.8 3.90 5.80
5.10 125.0 2.30 1.85
5.14 190.4 2.90 1.54
5.18 287.7 1.60 1.89
5.22 370.6 9.00 2.42
5.26 481.9 6.20 1.28
5.30 624.6 9.20 1.47
5.34 732.9 11.60 1.59
And here are the Ge Ka measurements (K edge is 11.103 kV):
Ge Ka kV cps/100nA STD DEV %STD DEV
11.12 21.9 1.20 5.49
11.16 49.9 2.30 4.63
11.20 78.3 1.20 1.57
11.24 115.3 1.40 1.17
11.28 162.0 2.00 1.22
11.32 229.7 1.00 0.44
11.36 288.6 2.20 0.78
11.40 354.8 1.80 0.51
11.44 422.8 3.50 0.83
11.48 530.2 3.60 0.69
We're at less than 1/2 kV above the edge energy and getting excellent statistics!
I drafted these schematics in an attempt to explain how the photon "cliff" forms near the Duane Hunt limit (see previous post above).
But the short answer is: if one is acquiring (or simulating) photons near the Duane-Hunt limit, one will accumulate photons below the electron beam energy, but one will NOT accumulate photons above the electron beam energy (aide from coincidence (continuum sum) photons of course). So the appearance of this so-called photon cliff should not surprise us.
Here is my schematic when accumulating photons into non-zero wide bins (assuming a detector with an energy resolution equal or better than the bin width:
(https://smf.probesoftware.com/gallery/395_29_04_24_2_23_05.png)
The photons simply accumulate from zero. And here is the schematic for Monte Carlo simulations when the photon count is normalized to the number of incident electrons:
(https://smf.probesoftware.com/gallery/395_29_04_24_2_23_29.png)
The difference being that the integer accumulation will show the photon cliff rising from a zero level with improving precision over time, while the simulated photon cliff stays at a constant value but also improves in precision over simulation time.
Of course since our EDS detector spectral resolutions are around 130 eV or more, we'd have to utilize 100 to 200 eV bins in order to see this photon cliff with actual spectra.
Two questions: first, can anyone suggest any improvements for these schematics? We'll be presenting this at M&M this summer. And second, does anyone have access to a photon detector with at least an order of magnitude better spectral resolution (say, 10 eV or better), where we might be able to actually see this photon cliff using our typical 10 eV per channel EDS acquisition software?
Quote from: Probeman on April 29, 2024, 02:38:18 PM
... So the appearance of this so-called photon cliff should not surprise us.
... it had surprised me the first time I saw it from simulation and it still surprises me, even if it should not. I highly suspect it to be an artifact of modeling. I have doubt about the sharp cliff as WDS Duane-Hunt experiments show the region above the beam energy has some faint continuum and the level of continuum is clearly dependent from (electron) density of material. Cosmic radiation can be ruled out, and photon coincidence too as it is WDS not EDS, and if it would be for some weird reason coincidence or other orders - it could be cached with PHA, but it is not. If this sharp "cliff" could be proven to exist with higher spectral resolution detector (would that fancy calorimetric-EDS be any help here?) - then knowing that would give an advantage as such "cliff" position could be then resolvable by deconvolution and could provide the closest estimation of beam energy.
Quote from: sem-geologist on April 30, 2024, 01:47:37 PM
Quote from: Probeman on April 29, 2024, 02:38:18 PM
... So the appearance of this so-called photon cliff should not surprise us.
... it had surprised me the first time I saw it from simulation and it still surprises me, even if it should not. I highly suspect it to be an artifact of modeling.
We already know it is not an artifact of modeling, according to Llovet, Ducharme, Ritchie and Rohde (it's actually a "binning" artifact if we assume non-zero width bins), and it should not surprise you because of what was posted previously:
Quote from: Probeman on April 06, 2024, 08:34:49 AM
Yeah, I'm always shocked! And it is weird that an electron could come to a complete halt. Here is a figure that a colleague of mine in the Physics Department at the University of Oregon , Andrew Ducharme, wrote me recently in discussing the above photon "cliff":
QuoteThe established physics is that bremsstrahlung cross-sections are nonzero for complete energy losses, or for production of photons with the beam energy E (see figure from Penelope manual), while the probability of producing a photon with energy E + 1 eV is 0. Wait long enough (assuming ideal detector, electron source) and you will count photons at the Duane-Hunt limit while never getting counts in the energy bin of E + 1 eV. The longer you wait, the more DH-energy photons, and the higher the cliff.
(https://smf.probesoftware.com/gallery/395_06_04_24_8_24_59.png)
I think of it in the sense that the coulombic field of an atom is actually a pretty big target, so a few electrons are going to hit some atoms directly right at the surface...
Note that the cross sections at complete loss of energy by the electron (at 1.0 on the x axis) are non-zero. The implication of this is that it is possible to produce continuum photons up to and at the electron beam energy, but impossible to produce photons above the electron beam energy. That means that
if we collect photons into bins of a non-zero width, the appearance of a photon cliff is inevitable, even if that photon cliff is obscured by the (limited) spectral convolution of our photon detector. This is the reason why we only observe the photon cliff in unconvolved simulations and when not using a continuous slowing down model (CSDA). PENEPMA uses a discrete energy loss model so the photon cliff becomes apparent in simulations with sufficient electron trajectories.
However as you suggest, using a micro-calorimeter EDS could be a good idea as the authors claimed an ~10 eV spectral resolution:
D. A. Wollman, G. C. Hilton, K. D. Irwin, L. L. Dulcie, N. F. Bergren, Dale E. Newbury, Keung-Shan Woo, Benjamin Y. H. Liu, Alain C. Diebold, John M. Martinis; High-resolution microcalorimeter energy-dispersive spectrometer for x-ray microanalysis and particle analysis. AIP Conf. Proc. 24 November 1998; 449 (1): 799–804. https://doi.org/10.1063/1.56867
But I'm not sure who still has one up and running? But if anyone does it would be an easy (and cool!) measurement, just use 10 eV wide energy channels and the photon cliff should appear given enough acquisition time.
Quote from: Probeman on April 15, 2024, 07:52:14 AM
And here is the dataset for Ge Ka:
(https://smf.probesoftware.com/gallery/395_15_04_24_7_49_39.png)
This plot causes me to suspect that the electron beam energy on my Cameca SX100 at ~11 kV is slightly higher than the nominal value would indicate... what do you all think?
Again, both the Ti and Ge pure metals were freshly polished and uncoated (though well grounded).
Somebody asked about the counting times and beam current for these over voltage curve measurements and so I checked and they were 120 seconds on-peak and and 120 seconds off-peak at 100 nA.
Note that I used freshly polished pure metal standards for these tests, but in case ones samples are carbon coated, one can calculate the electron beam energy loss with a 20 nm carbon using the CalcZAF app and here is is for 5 keV:
(https://smf.probesoftware.com/gallery/395_16_05_24_10_21_04.png)
So we're losing about 14 volts out of 5 KV. And here at 12 KV:
(https://smf.probesoftware.com/gallery/395_16_05_24_10_21_24.png)
So only about 8 volts at 12 KV. But I would still stick with freshly polished pure metals for these over voltage curve tests...
I'm about to go mount our "Considerations for Determining Duane-Hunt Limits on Electron Beam Instruments" poster at M&M, so I thought I'd also share it here for those not at the conference (see attached):
John Donovan1*, Petras Jokubauskas2, Nicholas Ritchie3, John Fournelle4 and Andrew Ducharme5 1. Center for Advanced Materials Characterization in Oregon, University of Oregon, Eugene, OR, USA (0000-0002-6187-5041) 2. Faculty of Geology, University of Warsaw, Warsaw, Poland (0000-0002-1099-4497) 3. National Institute of Standards and Technology, Gaithersburg, MD, USA (0000-0001-5734-5729) 4. Department of Geoscience, University of Wisconsin-Madison, Madison, WI, USA (0000-0001-96898852) 5. Department of Physics, University of Oregon, Eugene, OR, USA (0000-0003-2765-1455)
This poster explains why the Duane-Hunt limit for determination of the electron beam energy is not accurate due to the presence of a "photon cliff" that is convolved by the EDS detector, and therefore not visible but still present.
See replies above for more explanation.