Quote for the Day
You've come to Doug Aberdeen's old pages. In 5 seconds you will taken to my new pages http://sml.nicta.com.au/~daa/
Electron Band Structure In Germanium, My Ass
Abstract: The exponential dependence of resistivity on temperature in germanium is found to be a great big lie. My careful theoretical modeling and painstaking experimentation reveal 1) that my equipment is crap, as are all the available texts on the subject and 2) that this whole exercise was a complete waste of my time.
Electrons in germanium are confined to well-defined energy bands that are separated by "forbidden regions" of zero charge-carrier density. You can read about it yourself if you want to, although I don't recommend it. You'll have to wade through an obtuse, convoluted discussion about considering an arbitrary number of non-coupled harmonic-oscillator potentials and taking limits and so on. The upshot is that if you heat up a sample of germanium, electrons will jump from a non-conductive energy band to a conductive one, thereby creating a measurable change in resistivity. This relation between temperature and resistivity can be shown to be exponential in certain temperature regimes by waving your hands and chanting "to first order".
I sifted through the box of germanium crystals and chose the one that appeared
to be the least cracked. Then I soldered wires onto the crystal in the spots shown in figure 2b of Lab Handout
32. Do you have any idea how hard it is to solder wires to germanium? I'll tell you: real goddamn hard. The
solder simply won't stick, and you can forget about getting any of the grad students in the solid state labs to
help you out.
Check this shit out (Fig. 1). That's bonafide, 100%-real data, my friends. I took it
myself over the course of two weeks. And this was not a leisurely two weeks, either; I busted my
ass day and night in order to provide you with nothing but the best data possible. Now, let's look a bit more closely
at this data, remembering that it is absolutely first-rate. Do you see the exponential dependence? I sure don't. I see a bunch of crap.
Going into physics was the biggest mistake of my life. I should've declared CS. I still wouldn't have any women, but at least I'd be rolling in cash.
This research has been accepted for publication in the May/June issue of the Annals of Improbable Research.