Free electron gas Handout

Free electron gas Handout - University of California...

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- 35 - University of California, Berkeley EE230 - Solid State Electronics Prof. J. Bokor Free Electron Gas (Read Kittel Ch. 6) Assume non-interacting particles, mass m, spin 1/2, in a 3-D box periodic boundary conditions: etc. for y,z. plane wave solutions. energy (dispersion relation) momentum velocity Mode counting Each state (mode) occupies volume in k-space. Total # of states N, with wavevector k : total # states N, with energy is: L L L Volume V = L 3 ψ r ( ) Ae ik r = N 2 4 π 3 ------ k 3 2 π L ------ 3 -------------- V 3 π 2 -------- k 3 = = spin E
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