If I am reading the comments on You tube correctly, the metal foil is 8um beryllium foil. Very fragile. Check my work.
My understanding is that the incoming gamma photon excites multiple electrons in the sample in series until it loses all energy. Many of these are outer orbital electrons and we will not see the low energy emitted from these. However, some of these will be characteristic xrays (k shell) and that is what we are picking out.
The xray tube in that device creates a polychromatic beam with 40kV peak energy. The curve is not Gaussian but is skewed to the higher energies. My guess is the idea behind the silver is to create a monochromatic beam (secondary xrays from silver) so you are bombarding the target with only one (or 2?) discrete energies. Again, this scheme is unnecessarily complex if you have a radionuclide gamma emitter as in your design.
Excellent! Thank you for getting at the detail, and for providing the explanation that an incoming gamma photon can expend it's energy into more than one spin, and more than one shell, and even into more than one atom "in series", if there is enough energy left over.
Beryllium, having only one possible electron shell, has traditionally been the material of choice for X-ray transparent windows. Crude (and hazardous) precipitates cost about $4/gram for element collectors on eBay. Actual metal foils 3/4" diameter, 0.0005" thick I see for $400 for six, not including $16 for shipping. This is maybe not for us!
What might we detect?
Between beryllium and aluminium are several that we would love to get some counts from, these being carbon, oxygen, flourine, sodium, and magnesium, but I don't think those are likely. I think we may have to infer the presence of these if we identify a probable alloy from the bigger returns.
Suppose we go for it, and consider whether we might see aluminium. In theory, we might. One might have to increase the gather time to a couple of minutes or more. The PIN diode response probability for 1.48KeV is down to about 2%, meaning a count of only a couple of hundred out of several thousand incoming smoke detector photons.
Letting the bias become 6.6V (2 lithium cells) instead of 10V (3 cells) lowers the dark current from around 2.5nA to about 2nA, and the capacitance increase is from about 82pF to 100pF. The benefit in dark current noise, is hardly worthwhile. The change in capacitance is not going to lower the signal significantly. From the response of the PIN diode, and with the amplifier hoped-for noise figure, and the 91dB possible SNR from the ADC, we might marginally detect aluminium, sometimes. Magnesium is (just about), theoretically possible. Sodium is at probability 0.1%, would yield a count of about 20, even if 20,000 photons were expended on it. That could take much more than a couple of minutes!
Realistically, I think we can happily re-purpose the Chinese take-away aluminium foil tub after eating the contents, and use it for shielding. If I thought we could ever detect aluminium, magnesium, ans sodium, I would think to a conductive carbon shield window, instead of beryllium.
The more we mull this stuff over, the more I become convinced we have got it exactly right!