The main methods of detecting radiation are by charge separation or light emission. For a semiconductor detector we want a volume without charge carriers. When ionising radiation (the clue is in the name) is absorbed by this volume it generates electron hole pairs. If all the energy of the particle/photon has been absorbed then the amount of charge produced tells us something about the energy it had. Rather than explain everything verbose, here is what Wikipedia has to say,
Practically while we are only interested in a non conducting region, all semiconducting detectors are fabricated like a diode. Why a diode? Simply putting electrodes on a poor conductor produces a flow of charge, new charge carriers flow from the wires and the current maintains. By doping the ends of the detector and reverse biasing it, charges are swept out of the insulating region and new (against the bulk region) charge carriers that go in from the wires are mostly eaten by the majority carriers before they can enter the insulating region - this is diode action. Making it into a diode makes the insulating region perform much better.
There are commercial devices that fit this description - PIN diodes. While PN diodes generally have an insulating (depleted) region that is really too thin to be useful as a radiation detector. PIN diodes are fabricated to have an insulating region often as wide as 0.1mm and some as much as 0.3mm. In terms of physics this can't compete with the millimetre or centimetre thickness of cryogenic detectors, but in parallel with the development of the big boys there is always a need for cheap detectors with lower performance and there is about 45 years of relevant material behind subscription walls of major physics journals.
Selecting a good PIN photodiode for this application is probably impossible from the datasheet, but potential candidates for testing would have low capacitance (a few tens of pf maximum at high reverse voltage) low dark current (I don't know what is acceptable here but certainly no more than a few nA) at high reverse voltage and a wide depletion region (more than 50um is probably enough for spectroscopy).
Depletion width rarely appears on datasheets for optical PIN diodes, but there is a trick. The P and N regions of the device are essentially conductors, and the I region is an insulator so it's possible to estimate the depletion width as a parallel plate capacitor. Knowing the area of the diode and the capacitance of the junction for a given reverse bias (curve in the datasheet) and knowing the permittivity of silicon tells us the depletion width. My rule of thumb is that a PIN diode of 1 pf per square mm has a depletion depth of about 100um, so 2 pf would be 50um and half a pf would be 200um. This approximation works really well on large diodes 10 or 100 square millimetres, but is unhelpful for much smaller.
Breakdown voltage tends to scale with depletion width but this is not that reliable and also related to other aspects of the design and manufacture. 80 or 100um diodes tend to be rated for 30V or less, a 300um diode tends to be above 100V.
The two cheapest diodes I'm planning to try are the BPW34 and SFH206K, under 1 USD each, both around 7 square millimetres, 8 or 9 pf and a dark current in single digit nA. The BPW34 is the go to diode for most people in the hacker community wanting to measure radiation with a semiconductor, it's in the radiation watch project and in the excellent OpenCT2 by Peter Jansen, who is also solving the X-ray licencing problem by using a low level exempt radioisotope source. Science lit suggests the depletion width for this diode is around 150um, but that does not match the estimate. The SFH206K in science lit is stated to have a depletion width around 70um which matches the estimate well, maybe they used the same math. This diode is potentially less sensitive to radiation but no one doing X-ray spectroscopy...
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