Hello everyone,
Here is something interesting I was considering about the Drude model: most of today's 'interesting' use of materials in the realm of computer hardware couldn't be modelled with the Drude model because of its ignorance of the boundaries of the substances used. Of course, the Drude model doesn't really lend itself to semiconductors either.... But it is interesting that the leading model of its time would be unable to model some of the most important condensed matter problems of the last century.
I suppose a question could be posed about the historical development of condensed matter: if semiconductors had been discovered earlier, would another model besides the Sommerfeld model replaced the Drude model? Also, was semiconductance discovered before or after a theoretical model suggested it existed?
Josh H
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Hmmm, I don't think that knowledge of semiconductors would have altered the course of science very much. Especially considering that there were already clear problems with the Drude model. It often seems that we make a simple model, and then change/remove assumptions until it is appropriate. From this viewpoint, it seems that the first thing you would do to the Drude model is to put the fermi-dirac distribution in there, regardless of whether or not semiconductors were around.
ReplyDeleteUnlike the Drude model, the Sommerfeld model and Bloch model includes periodic boundary conditions. For Sommerfeld, the wave function has to be has to be continuous at the boundary. Bloch extends this so that the wave function has to have include a term with the periodicity of the Bravais lattice. Even so, everything that we have learnt so far assumes an infinitely extended solid which is fine as long as we are interested in the bulk properties of the material. The interesting surface physics are however neglected.
ReplyDeleteI would like to add that the Bloch model apparently can be extended to include surface physics. To do so, according to A&M we have to forfeit the assumption that the wave vectors, k has to be real which comes from the periodic boundary conditions in an infinite crystal.
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