Duane-Hunt limit

[Probeman]

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:



So exactly what is the Duane_Hunt limit in this spectrum?   I guess I should try again at 5 nA?

[Probeman]

Just for reference I had started the Duane-Hunt measurement at 30 nA and this is what that showed:



That is why I tried 10 nA.  Now I'll try 5 nA.

[Probeman]

Ok, here's an acquisition on Bi metal at 15 keV 5 nA for almost 2000 sec (22% deadtime).



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.

[Probeman]

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%.



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%.

[sem-geologist]

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 , 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.

[Probeman]

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 , 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:



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!).

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:



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://probesoftware.com/smf/index.php?topic=1073.0

[chenderson]

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.

[Probeman]

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?

[chenderson]

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.

[Probeman]

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...

[Nicholas Ritchie]

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.

[sem-geologist]

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://probesoftware.com/smf/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.

[sem-geologist]

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).

[Probeman]

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://probesoftware.com/smf/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:



and also on sp5, LiF:



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.

[sem-geologist]

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.