[lfjokes] Electron Band Structure In Germanium, My Ass

[Adam Shand]

note: there is a pretty graph of the data he's talking about at the url :)

From: Lance Ahern <ahernlj at fortnocs.com>
URL:  http://www.cs.wisc.edu/~kovar/hall.html

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.

Introduction

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".

Experiment procedure

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.

Once the wires were in place, I attached them as appropriate to the
second-rate equipment I scavenged from the back of the lab, none of which
worked properly. I soon wised up and swiped replacements from the
well-stocked research labs. This is how they treat undergrads around here:
they give you broken tools and then don't understand why you don't get any
results.

In order to control the temperature of the germanium, I attached the
crystal to a copper rod, the upper end of which was attached to a heating
coil and the lower end of which was dipped in a thermos of liquid
nitrogen. Midway through the project, the thermos began leaking. That's
right: I pay a cool ten grand a quarter to come here, and yet they can't
spare the five bucks to ensure that I have a working thermos.

Results

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.

Christ, this was such a waste of my time.  Banking on my hopes that
whoever grades this will just look at the pictures, I drew an exponential
through my noise. I believe the apparent legitimacy is enhanced by the
fact that I used a complicated computer program to make the fit. I
understand this is the same process by which the top quark was discovered.

Conclusion

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.