How is the number of charge carriers set free in an x-ray detector proportional to the energy of the incoming photon?

Question

I'm a chemistry undergrad student and I've been doing some research into the ways light is generated and detected at different parts of the spectrum (for the purposes of better understanding practical spectroscopy). My questions comes from this Wikipedia page on semiconductor detectors, which are used in energy-dispersive X-ray fluorescence spectroscopy.

In ED-XRF, x-ray photons strike the detector, causing a pulse in current driven by an large voltage bias across the detector. The Wikipedia article says that then, the number of charge carriers set free in a give pulse is proportional to the energy of the incident photon. I am a bit confused as to how this is the case. My understanding of quantum mechanics and especially solid-state physics is rudimentary, but my understanding was that a single absorption event corresponds to elevating the energy level of a single electron, not many electrons being elevated such that the sum of the energy change corresponds to the energy of the photon. Why isn't this the case for other kinds of detectors, like photomultiplier tubes? For PMTs, each photon produces a single initial electron, which then has to be multiplied by the rest of the structure, right? And if the number of charge carriers tells us the energy of a photon, then how do we count the intensity of a given energy, like in this XRF spectrum? Do we just count the number of "pulses" with a given energy in a fixed amount of time? But then, I would think that the number of pulses you'd get in a given amount of time would be too many for electronics to differentiate one pulse from the next.

Hopefully this question is phrased well! My background is in chemistry, but I have taken a first quantum chemistry course and I have a lot of interest in spectroscopy, so I really want to more deeply understand how these things work!

Answer 1

You are quite correct that in atomic or molecular spectroscopy a photon is absorbed by exciting a single electron from some initial state to some final state.

However in a semiconductor X-ray detector the energy of the X-ray is vastly higher than the binding energy of the electrons so the X-ray photon completely ejects the electron it hits from the atom, and this high energy electron goes careering through the crystal bashing into and exciting other electrons as it does so. The whole process is somewhat chaotic, but the end result is that the energy of the X-ray photon gets transferred to one electron then spread throughout the crystal as that electron collides with valence electrons in the crystal.

The end result is that the energy of the original X-ray photon ends up promoting many electrons into the conduction band, and to a good approximation the number of electrons promoted is proportional to the photon energy divided by the band gap.