Stuey and Roy,
Yes it should be cheap. I understand it to be simply a very large area diode. A big, old-fashioned power transistor would likely work too.
It just occurred to me that modern dynamic RAM, as used in PCs etc, is cheap, and has a truly massive problem with alpha particles unless it is covered with a layer of a compound which does not emit alphas. As we know, you don't need much thickness to stop them. The normal epoxy used for the outer package does contain traces of alpha emitters, which would cause an excessive number of single-bit errors. That is giving me ideas.
I do work with people who can procure bare semiconductor die, fit them to substrates, and package them suitably. I bet they could do a nice thin mica window. If the quantity was right, the price might be too. I will ask next time I see them, in a week or so.
Oh, and thinking about it, the CCD or diode array in a digital camera should also detect alphas quite well. If someone wants to risk their SLR underground, they could take the lens off, to allow alphas in, and take a suitable exposure of darkness. The background will be noisy on a long exposure, but I expect any alphas to leave very bright spots. I have an old Ricoh which is broken, all that is wrong is that is wrong is that the motorised lens covers stick, and neither open nor close fully. I could sacrifice that to a good cause, provided I can find a way of fooling it into taking pictures with no lens fitted, having first found how to remove the lens.
But I saw an inexpensive "solid state beta" detector in about 1972, which was also very good for alphas. I am still trying to track down the source of these.
Funnily enough, my employer, on another site, makes neutron detectors, but as we don't expect much fission in the mines, I doubt that these would be useful. They are not cheap, or small, or robust.
Google shows lots of scientific papers about solid state alpha detectors, but we want a simple semiconductor at a simple semiconductor price, not a lab prototype.
A silicon photocell, for making electricity from sunlight, is basically a large area diode, but I don't know if its characteristics would be suitable. If I had a decent alpha source, I could test one, but it is not too easy to obtain legal alpha sources in the UK. Yet you can legally get things containing a small amount of Polonium in the US. Maybe I need to purchase a specimen of pitchblende.
This link
http://books.google.co.uk/books?id=BXpF3n-OjvEC&pg=PA150&lpg=PA150&dq=geiger+counter&source=web&ots=-DTziKhw9W&sig=OnOMBLbO3PugAAdPvr44ItoWhfE&hl=en&sa=X&oi=book_result&resnum=10&ct=result#PPR15,M1 might be interesting.
Alan