Proper PHA tuning for high accuracy quantitative analysis

[sem-geologist]

What a timely post!

I have a user VERY interested in high precision F and Cl in amphiboles and I am diving headfirst into the PHA settings, a topic which I still haven't had a good explanation of despite running a lab (looks around sheepishly). I think some of the confusion stems from the way PHA is discussed in Cameca vs JEOL software discussions...

I couldn't agree more, maybe we need a good discussion around PHA to make us all understand this a bit better. You're not alone

I've been running a lab for ~40 years and it's only been in the last few years that I think I've finally figured this out!   

I really appreciate spreading this "tuning of PHA for integral mode method" by probeman. However as dawncruth and KerstinGruender had noted - the PHA is confusing. I would not blame the "Cameca vs JEOL software discussions", I would not blame anyone, as PHA issue is multidisciplinary and I believe that even authors of different textbooks about microanalysis had no complete understanding about PHA. I, however, want to urge of using proper and precise terminology.

My grin is on using improperly "photon" vs "electronic pulse" and "cutoff" vs "clipped" terms.

PHA have nothing to do with photons. Photons cease to exist somewhere in between the anode and cathode of G(F)PC (Gas (Flow) Proportional Counter) where its energy is converted into bunch of electrons where their sum of energies is proportional to energy of the x-ray photon. (this is a simplification of 1x initial photoelectron -> initial electron cloud, the part where PHA still does not influence that process). This electron cloud becomes a subject of chain of processes which PHA controls directly and indirectly, so PHA begins with electrons and ends with electrons (electronic signal), there is no more photons. While for some of us, who took long discussions with probeman, is clear what his use of "photons" on these plots mean, for some future generations which have no context of these discussion, this could be a source of confusion.

In short – PHA (of GFCP) is about control of amplification of initial electron cloud into measurable electronic signal (setting the height of pulses) AND (optionally) filtering it by height (which is proportional to initial cloud energy – this is where "Analysis" from PHA part-comes into, that "analysis" can be compared to EDS spectral window (i.e. set for mapping of a particular element) - that is a most close comparable thing). If we use "integral" mode we use only the first part, and if we use differential mode - we then use both parts of PHA. It would be so much better if PHA would be renamed into something what would describe both of these functions. I.e. PH&A (Pulse Height AND Analysis)

Short condensed course on X-ray detection, shared paradigms and differences

I want also to present more generalized context of X-ray detection fundamentals, as hitherto to me known EPMA textbooks introduce confusion often by describing EDS and WDS as completely absolutely cardinally different devices. When comparing EDS and GFPC (skipping the diffraction part of WDS) such broader common context can help to understand the differences and, I hope, will easy up the understanding of whole PHA and its place in microanalysis.

So most (excluding some other, like i.e. µ-calorimeter-based EDS) of X-ray and gamma detectors are based on these 3 fundamental parts:
1. semi-conductive (for electric charge) medium
2. voltage bias (gradient) across the medium with cathode and anode
3. measurement system of electron charge at cathode or anode

1. Medium

As for medium it can be made from all 4 states of matter: gas, solid, liquid and even plasma (although these are still in very early-development). Every of these have its pros and cons and are chosen per application basis (required energy resolution, speed/throughput, robustness, cooling requirements, decay (deterioration with age)/long-term stability, maintenance requirements...). The main purpose of medium is to convert photon into photo-electron and then convert that into initial electron cloud. Other optional medium capabilities depend from other 2 parts described below.

2. Voltage Bias

The required minimal voltage bias (for any detection) depends from medium, its size, and requirements of amplification in the medium, it can start from few V and could be up to hundred of thousands of Volts (if not more). Some of mediums transits into amplification region if bias voltage is sufficiently increased. Such amplification makes it easier to measure electron charge at part 3 of the detection system, also lowering its complicated requirements. GFPC is a good example of such amplification, where bias is set at so called "proportional region". IMHO it would be less confusing if it would be called "bias amplification region" instead.

Classical SDD used in common EDS do no amplification in the medium, albeit there are SDD's in development, which would use much higher bias voltages to do some amplification in the medium, and so that would reduce requirements for part 3 of detection (i.e. no cooling needed).

In GFPC we amplify initial electron cloud utilizing increased bias voltage, with that controlling the extent of Townsend's avalanche – the process which amplifies charge of initial electron cloud into much larger collected (and measured) charge at anode. Townsend's avalanche is quite a violent electronic "discharge"-like event (imagine violent avalanche in the mountains, where it could be started by single small dropped snow ball - that is why it is called avalanche; in our case we have electron avalanche instead of snow). GFPC's gas medium is practically "unimpressed" by such violent events and is capable to "repair"/"reset" its state practically instantly after. Trying to achieve such similar electron avalanches on the solid state detector would destroy such solid medium irreparably. This capability of enormous amplification (few orders of magnitude) is the biggest advantage for gas medium compared to other detection mediums, and makes it much easier at part 3 of detection, dropping-off sophisticated cooling and ultra-low-noise electronic design requirements (which are needed i.e. by SDD, because it has no amplification in its medium).

BTW, with some specific gas mixtures and pressure and much higher bias, the gas bias amplification could be "turned up to 11" into "self-quenching streamer" mode (much more faster AND also much more violent discharge-like event compared to Townsend avalanche; for snow avalanche comparison, replace water snow, with some better rolling snow (i.d.k. maybe ammonia, methane...), and replace earth gravity of 9.8 with gravity of 100, while keeping the same mountain height - imagine the result, also add to the picture displaced air upward, faster and more narrow avalanche, more like meteor strike-like). Also do not confuse it with Geiger-Muller mode - that mode would be like you drop a snow ball on the top and, independently from the size of the ball, all snow from whole the mountain collapses to the base reducing the slope of the mountain, and you need to wait for snow to melt down, and evaporate and snow down on the mountain, so the next avalanche would be possible at all.

To illustrate the biggest drawback of such gas bias amplification, imagine how difficult task would be to use measured volume of avalanche'd snow at base of the mountain and try to reconstruct how big was initial snowball, which had initiated that avalanche. So, The biggest disadvantage of violent avalanche event is a very huge error in such reconstruction of initial cause (of initial photo-electron energy) - and that is the Achilles heal of PHA diff mode for GFPC. However if we would have ideal mountain (no trees, buildings, valleys, roads, rivers...), with ideal same thickness of snow coverage, the statistics could allow us to get very similar sized avalanches depending from size of initial snow ball dropped on the top, and that would be much more closer comparison to processes going inside our GFPCs. By setting bias we are like adjusting "gravity under such imaginable ideal mountain and controlling size of avalanche proportionally to initial dropped ball".

So to conclude this sub-chapter, we have no control on bias in EDS, as SDD (the solid) do no amplification in the medium. We have bias control for WDS GFPC PHA, because the majority of signal amplification is done within the medium (the gas), and control of such amplification is done by tweaking the bias values.

3. measurement system of electron charge

On SDD at point of medium (solid) where charge is collected, directly to that point J-FET (very ultra low noise field emission transistor) needs to be attached to amplify very small charge to measurable amount, for following (in the signal pipeline) pre-amplifier. Such J-FET is either directly attached or embedded in the same silicon substrate (i.e. tear-drop shapped SDD). J-FET needs to be as close as possible to point where charge is being collected to minimize the noise introduction.

J-FET amplification is much more smaller when compared with GFPC bias amplification, and so the pre-amplifier construction is a bit different on EDS. Pre-amplifiers in both cases (GFPC and EDS) integrates the sensed collected charge signal (negative short electronic pulse) producing a "stair" or "cascade"-like signal, where step height is proportional to the initial electron cloud energy. Because J-FET amplification is not enough to bring the signal much above the electronic noise floor, the EDS pre-amplifiers feedback loop can't have a bleeding out resistor, and so the feedback loop of integrating OPAMP charges up with integration steps, and continuously due to leakage current (partly J-FET), and so it needs periodic discharge (which adds additional source of dead time). Bleeding out resistor is not used, as resistor on its own would introduce internal resistor noise which would be bigger than signal incoming from J-FET. J-FET itself needs to be cooled down below room temperature to lower internal noise further down and lower leakage current.

On GFPC, because gas bias amplification is so big compared to SDD+J-FET, there is no need for J-FET, and signal is so big that pre-amplifier can use feedback loop with bleeding-out resistor. That means no dead time introduced at pre-amplifier, no charging up of feedback loop, no need to hold detection for its discharge - pre-amplifier is continuously processing the incoming electron charge pulses. There is no need of ultra-low-noise design, and no need of cooling.

In both cases of GFCP and EDS, pre-amplified stair-like signal is further down passed through Shapping amplifiers, which converts the step into pulse, where its height is a subject for PHA, or EDS.
The difference is that on WDS normally it is a single fixed amplifier (in differentiation configuration), where on EDS systems there are a set of shapping amplifiers each with different shapping time constants, which allows to chose/ balance between either precision and/or throughput, by piping the signal through different shapping amplifiers.

After shapping amplifiers we have the final GAIN amplification which scales the pulse height to fit into specific ADC (analog-digital converter) range. On EDS such GAIN amplification is not accessible directly, it is changed indirectly by calibrating the EDS known line to theoretical position, and after the calibration the GAIN (for given shapping amplifier) stays at that set value during calibration. On WDS GFPC PHA such GAIN is all the time directly accessible and can be set to different values per element or sub-measurement basis. On WDS GFPC gain can be often by default be set smaller than 1.0 (that is the amplitude is downsized). I.e. on CAMECA SX line 1000 equals 1.0. So i.e. when "Auto PHA" sets gain to 350 value it is multiplying previously amplified pulse by 0.35 - shrinking it electronically down.


PHA and pulse counter cutoff and clipping

cutoff - is discarding the signals below or above the some thresholds.
clipping - is modifying signal bringing any of its values outside of threshold-set range to values of lower or higher thresholds.
(clipping: the most easy comparison would be overexposure of the photo - you get white pixels - which is information about intense light at that pixel limited at maximum possible value of pixel. cut off would produce NaN pixel - that is no information in the pixel).

WDS systems has much more simple pulse counters than EDS, because on EDS energy discrimination of pulses is primary means to separate the X-rays into different spectral bins (12bit), and on WDS the PHA plot is a secondary mean of separation of X-rays by energy into some bins (8bit).

Precise Pulse height measurement (so the pulse could be added to correct bin in PHA  histogram-like plot) requires pulse sensing/detection prior. The amplitude measurement needs a trigger. Both Jeol and Cameca pulse sensing hardware clearly have some cutoff around 0V (in case of Cameca it is ~0.5V) - any pulse which peak is below that value does not pass - it is cutoff. In both hardware pulses with their amplitude close to 0V are cutoff - they are not counted – they are not sensed by counter and they are not measured as they are simply invisible to pulse sensing part.
As for higher values than ADC maximum value, they are clipped. They are very easily sensed with pulse sensing part, but they are clipped to the highest ADC value - the maximum pulse size.

But however, for some reason OEM software do not show the last bins of PHA on the graph, and neither expose it through API call for PHA graph, probably as in case of clipping all oversized pulses it would produce very strange plots (all clipped values would end in single last bin, and would produce "_|" - shapped plot). Integral mode at Cameca hardware uses only sensing/detection of pulses, ignoring the followed amplitude measurement. As far I had seen crumbs of information, Jeol use amplitude measurement even in integral mode to cutoff the electronic background near 0V, as its cut-off is lower than at Cameca Hardware (about 0.5V - which BTW is not a fixed value, as Schottky diode forward voltage drop (which do the cutoff) will go closer down to 0V at very low current (low count rates) and move more toward 0.5V at very high count rates (higher current)). This is also why it is so important to bring argon-esc peak fully out to the right with some additional reservation gap between baseline and left wing of Ar-esc pulse distribution (as shown in probemans plots above). When Increasing count rates, it will not only shift the PHA distribution leftward, but it will also shift the cut-off baseline rightward!


To conclude PHA:
BIAS controls the primary electron cloud gas amplification inside GFPC
GAIN scales produced pulses to the PHA plot.
Pulses below 0V (or near it) are cuts-off and does not trigger pulse sensing - can't be counted.
Over-sized pulses are clipped to the max value of ADC are easy to sense, are counted in integral mode.
OEM PHA plots hide last bin(s) from plot and from API PHA value return, and so hide clipped pulses from the user, but pulses from such bin in the integral mode are still counted by hardware.

Just for comparison, EDS i.e. cuts-off at higher bound value (i.e. when range of EDS is set to 10kV, and using 15kV beam, the EDS will be cut at 10kV). It was natural to think that we would loose counts at higher boundary. Fortunately both Jeol and Cameca hardware designs had limited only on API and plotting limitations, using pulse-sensing (without amplitude information) circuit for counting in integral mode. Finding that out (that PHA on WDS on EPMA just clip, and not cut-off at higher bound) required to question and ignore the prior knowledge presented in textbooks and passed by generations of EPMA operators.

BTW, PHA was one of biggest black box part of EPMA the first day I started working on EPMA 11 years ago. With some luck of events (downtime + covid19) and some spare time, hanging oscilloscope to look into "pulse" directly was my "aha" moment.

[Probeman]

I really appreciate spreading this "tuning of PHA for integral mode method" by probeman. However as dawncruth and KerstinGruender had noted - the PHA is confusing. I would not blame the "Cameca vs JEOL software discussions", I would not blame anyone, as PHA issue is multidisciplinary and I believe that even authors of different textbooks about microanalysis had no complete understanding about PHA. I, however, want to urge of using proper and precise terminology.

My grin is on using improperly "photon" vs "electronic pulse" and "cutoff" vs "clipped" terms.

PHA have nothing to do with photons...

Thank-you so much SG for the explanation of these terms. This is a very informative post for those of us (including) myself) that were "lost in the black box". 

And just be to clear to everyone, SG was my original source for utilizing integral PHA mode for best accuracy. It just took me a while to realize that we must also make sure our PHA peak is *completely* above the baseline level at the highest count rate we expect to measure.  This is the key to being able to quantify materials were very different count rates, e.g., using high purity synthetic end member oxides and metals as primary standards and measuring unknowns from major elements all the way down to trace levels, and always obtain the highest accuracy k-ratios.

Perhaps we can refer to this as "pulse counting of x-rays"?  We are after all, counting them one by one!   

[John Donovan]

Note, I decided to split this topic and make the fluorine analysis discussion a separate topic, see here:

https://smf.probesoftware.com/index.php?topic=1855.0

I couldn't agree more, maybe we need a good discussion around PHA to make us all understand this a bit better. You're not alone

I've been running a lab for ~40 years and it's only been in the last few years that I think I've finally figured this out!   

The good news is that now anyone can properly tune their PHA with a few steps, but before I list them let's consider PHA pulse height depression effects, where the PHA shifts to the left with increasing count rates as seen here:

https://smf.probesoftware.com/index.php?topic=1831.msg13978#msg13978

Now imagine that one has tuned their Fe ka PHA on a unknown mineral with under 10 wt% Fe and gets it nice and centered in the PHA voltage range.  When they try to use a primary standard such as magnetite, which has a roughly 10 times the count rate, the peak on the standard shifts to the left, getting vut off by the baseline level, thus yielding a non-linear response from the system. And also obtaining a very inaccurate result.

This in short, is why people have felt compelled to use so called "matrix matched" or what I call "count rate" matched standards for so many years. Thus they rely on problematic natural standards with all their natural variability.  But if they instead:

1. Set their PHA to *integral* mode. This way, all photons to the right of the baseline level are counted. Even those photons that no longer plot in the normal PHA range to the right.

2. Tune their PHA on a primary standard with a high concentration of the element, at the highest beam current they expect to use for that element as seen here:



Then increasing their gain (Cameca) or bias (JEOL) such that the PHA peak on the primary standard is *completely* above the baseline level. This way, all photons will still be counted in integral mode. And they obtain a PHA peak that will provide a linear response at all lower count rates (unknowns, etc.)

3. Of course since your standard and unknown will have different count rates, we also want to be sure that our dead time calibrations are accurate, and that is why I suggest using the constant k-ratio method here:

https://smf.probesoftware.com/index.php?topic=1466.msg11173#msg11173

along with the logarithmic dead time expression which works up to count rates of ~300 kcps to 400 kcps which are not uncommon on modern large area crystals (the traditional dead time correction fails at count rates above ~30 to 40 kcps).

4. And finally, use high purity synthetic end member standard materials as demonstrated in this topic and also the topic "The Limits of EPMA Accuracy":

https://smf.probesoftware.com/index.php?topic=1831.0

Try it., you'll like it!

[Probeman]

Using the new integral-baseline PHA tuning method one can obtain ~1% accuracy extrapolating from pure oxides to other materials, from 10 to 20 keV:

[Probeman]

I obtained some JEOL PHA scans from a JEOL colleague trying out the new integral-baseline PHA tuning method. It appears to work well using JEOL gain steps to adjust the PHA peak. Here are the steps one should follow.

1. On the primary (highest concentration) standard (highest expected count rate), start with a bias scan and adjust the bias to be slightly (10 to 20v) above the bias peak:



2. Do a PHA scan:



3. If the PHA (and escape) peaks are not fully above the baseline, do not change the bias! Instead just bump the gain up to the next level (16 to 32)

4. Do another PHA scan:



5. If the PHA peak is fully above the baseline level, you are golden. If not, bump the gain another step and re-run the PHA scan.

Now please try to analyze Si and Fe using SiO2 and Fe2O3 or Fe3O4 as primary standards (you may need to defocus to the beam 10 um for SiO2) and try analyzing the NIST K-411 and K-412 mineral glasses as secondary standards...

https://smf.probesoftware.com/index.php?topic=40.msg14388#msg14388