Back in the 1950s, hobbyists made crude germanium transistors. Below are some suggestions...
It is possible to make a transistor using Galena (lead sulfide, PbS).
Galena is often available from rock shops and science museum stores.
You can even make your own by melting sulfur and lead powder over a flame.
Look up keywords such as "cat's whisker diode" and "crystal radio" to find
out more.
The trick to making a transistor is to use a hyper-clean, freshly-cleaved
crystal face,
to sharpen your cat's-whisker contacts by dissolving the tips using
electrolysis, and then to put the tips within 0.05mm of each other (or
preferably within 0.01mm). Obviously the latter is the hardest part.
Better use a microscope! The authors of the following article found that
the base/emitter junction was critical: it HAD to act as a good rectifier.
The base/collector junction wasn't as important. They got some power
gain, but their beta was in the single digits. Others have mentioned that
if you break open a 1N34 glass diode to expose the Germanium chip, you can
make a crude transistor with a similar procedure. Old Germanium audio
power transistors probably do the same, while giving much larger
semiconductor area on which to play.
Crystal Triode Action in Lead Sulphide, P. C. Banbury, H.A. Gebbie, C. A.
Hogarth, pp78-86. SEMI-CONDUCTING MATERIALS, Conference proceedings,
H.K. Henisch (ed), 1951 Butterworth's scientific publications LTD 1951.