p, k, and m Handout - University of California, Berkeley...

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University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor p, k, and m Handout.fm Momentum and effective mass What is the physical significance of k ? Free space has continuous translational invariance. It can be shown this leads to conserva- tion of momentum. For free electrons: is momentum. But in a crystal, momentum is not strictly conserved. Coherent Bragg scattering with the crystal lattice occurs --> any can be added or subtracted to k . Recall the Bloch functions: Consider some scattering process involving a photon or phonon with wavevector The space part of the matrix element has the form: Now the U k functions are periodic: , so the integral vanishes unless: for some This is the modified conservation law for crystal momentum, . ψ k r () e ik r = h _ k G k Ψ k f * r e Ψ k i r dr 3 U k f * r U k i r e ik i kk f + r r 3 d = U k r Ck G e iG r G = G h _ k
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- 64 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor i.e.,
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p, k, and m Handout - University of California, Berkeley...

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