Electron

04/15/05 http://www.cs.wisc.edu/~kovar/hall.html #1
Electron BandStructureIn Germanium, My Ass
Abstract: Theexponential dependenceof resistivity on temperaturein germanium is foundtobeagreat biglie.
My careful theoretical modelingandpainstakingexperimentation reveal 1 ) that my equipment is crap, as areall the
availabletexts on thesubject and2) that this wholeexercisewas acompletewasteof my time.
Introduction
Electrons in germanium areconfinedtowell-definedenergy bands that areseparatedby "forbidden regions" of
zerocharge-carrier density. You can readabout it yourself if you want to, although I don' t recommendit. You' ll have
towadethrough an obtuse, convoluteddiscussion about consideringan arbitrary number of non-coupled
harmonic-oscillator potentials andtakinglimits andsoon. Theupshot is that if you heat up asampleof germanium,
electrons will jump from anon-conductiveenergy bandtoaconductiveone, thereby creatingameasurablechangein
resistivity. This relation between temperatureandresistivity can beshown tobeexponential in certain temperature
regimes by wavingyour hands andchanting"tofirst order".
Experiment procedure
I siftedthrough thebox of germanium crystals andchosetheonethat appearedtobetheleast cracked. Then I
solderedwires ontothecrystal in thespots shown in figure2 bof LabHandout 3 2. Doyou haveany ideahow hardit is
tosolder wires togermanium?I' ll tell you: real goddamn hard. Thesolder simply won' t stick, andyou can forget about
gettingany of thegradstudents in thesolidstatelabs tohelp you out.
Oncethewires werein place, I attachedthem as appropriatetothesecond-rateequipment I scavengedfrom the
back of thelab, noneof which workedproperly. I soon wisedup andswipedreplacements from thewell-stocked
research labs. This is how they treat undergrads aroundhere: they giveyou broken tools andthen don' t understand
why you don' t get any results.
In order tocontrol thetemperatureof the
germanium, I attachedthecrystal toacopper rod, the
upper endof which was attachedtoaheatingcoil
andthelower endof which was dippedin athermos of
liquidnitrogen. Midway through theproject, the
thermos began leaking. That' s right: I pay acool ten
grandaquarter tocomehere, andyet they can' t
sparethefivebucks toensurethat I haveaworking
thermos.
Results
Check this shit out (Fig. 1 ). That' s bonafide,
1 00%-real data, my friends. I took it myself over the
courseof twoweeks. Andthis was not aleisurely two
weeks, either; I bustedmy ass day andnight in order
toprovideyou with nothingbut thebest data
possible. Now, let' s look abit moreclosely at this
data, rememberingthat it is absolutely first-rate. Do
you seetheexponential dependence?I suredon' t. I seeabunch of crap.
Christ, this was such awasteof my time.
Bankingon my hopes that whoever grades this will just look at thepictures, I drew an exponential through my
noise. I believetheapparent legitimacy is enhancedby thefact that I usedacomplicatedcomputer program tomake
Fig. 1: Check this shit out.
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thefit. I understandthis is thesameprocess by which thetop quark was discovered.
Conclusion
Goingintophysics was thebiggest mistakeof my life. I should' vedeclaredCS. I still wouldn' t haveany women, but
at least I' dberollingin cash.