Mechanics behind counting of X-rays on solid state and gas proportional counters

[sem-geologist]

Introduction

I had witnessed many misconceptions being born out from lack of knowledge and work-around being developed to address these. Trying to improve the situation I decided to open this topic. This topic is going to look very closely to pipelines of X-ray counting while comparing EDS (Bruker) with WDS (Cameca), as these are detectors which (counting) working principles I could study closely (topic is going to be very lengthy). Additionally I will link here some other public available materials. In case anyone would be able to study other detectors or have public information on that, please, do not hesitate to add it to this topic (i.e. other vendor EDS, or some details on WDS of JEOL or some SEM-WDS).

Why this topic? Someone would say that there are some brief introductions on topic of x-ray counting in older books (i.e. Goldstein et al's "SEM and X-ray µ-analysis 3rd ed."; Reed's "EMPA and SEM in Geology"). I understand that those are written by experienced credible authors. However, I find lots of mental-shortcuts in these books. Those mental shortcuts were OK then (as books are more "how to use", not "how exactly it works") these texts were written, but currently (after some important technological leaps such as large or very large diff crystals or SDD detectors) those mental-shortcuts lead many into wrong interpretation of how modern detectors work, and thus I will point to these inconsistencies when going through pipelines. This topic is in particularly looking at how these pipelines behave when pushed to its very limits (very high count rates) revealing the limitation points which every micro analyst should be aware.

What is the pipeline? "Pipeline" meaning used here by me is "a set of chained processes". Every process has its input(s) and output(s) and chain of these processes as a whole has its input (in our case X-rays) and output(s) (electronic pulses). These processes are altering (processing) the signal to the shape expected by the input of consecutive process in the chain. So this topic is going to look into "X-ray detector Signal Processing Pipeline", but for making text shorter I am simply further using the single word "pipeline". The processes are run on analog and digital electronic devices. In all of the detector implementations the signal starts with analog processing part which depending from implementation at different part of pipeline is switched into digital part (closer to output). All pipelines of detectors from last few decades have analog input and digital output.

Subtopics which this topic is going to address at different parts of pipelines:

• pulse-pileup (probability at given process, the limiting factors)
• PHA (historical considerations, limiting factors, why it shifts or gets distorted)
• dead-time (how, where, why, historical considerations, limiting factors)
• ...

The Setup:

• digital 50MHz oscilloscope
• Cameca SX100, and SXFiveFE WDS'es
• Bruker XFlash Nano, XFlash 6|10, XFlash 6|30 detectors and 3rd and 4th generation Bruker Signal processing Units.

The used oscilloscope is not high-end and pretty slow, but its capabilities is enough to look into relevant parts of two different pipelines. As we will look further we can conveniently look with oscilloscope at a bit different parts of pipelines, but those conveniently exposed pipeline points are relevant parts for explaining observed peculiarities on EDS and WDS, and missing picture can be filled with other publicly available material. What is also not clear from the books is why in some parts these pipelines differ so much, but considering of "borrowing" part from one pipeline to the other and understanding the downsides of such theoretical exchange will clear-up why WDS and EDS has different pipelines and is as it is. Some processing parts will be initially only briefly described, but revisited later as direct signal measurement is not easy or financially (for me) feasible, but its working principles (and contribution to sub-topic parts) can be easy understood looking at output signal of consecutive process. Please mind also that I had not engineered any of those devices, and some of information can be not precise, albeit it is logic. Also I am going into waters, which device manufactures would not like probably to show. But this is necessary to understand detection of X-rays with solid and gas proportional counters more fully and particularly dead-time and PHA.

Before we start with the pipeline, there are few electronics topics which needs to be understood before we start, as those are pivotal points in the pipeline:

• Charging and discharging of capacitor through resistor (curves of charge and discharge voltage vs time)
• what is OPAMP and what it can do (its basic principles; I think one of the best introduction is on youtube EEVblog channel: EEVBlog #600)

The most important thing about capacitors being charged and discharged through resistor is that voltage vs time curve will have exponential shape, where charging of capacitor is fastest at near empty state and slows down exponentially toward being charged up, and discharging from fully charged capacitor is much faster than discharging near-empty capacitor (decay exponentially). That brings some interesting consequences depending from counting rate, and sheds light into some of interesting design decisions of some of EDS detectors, and explains some observations on WDS proportional counter behavior.

I also hope this Topic will bring some directions for future improvements of detection systems.

P.S. I am going to add to this post step by step in a slow pace.