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Unformatted text preview: terms of k x and other relevant quantum numbers. (d) For an electron in the conduction band of Silicon, the Hamiltonian that describes the quantum mechanical motion of electron described by ) ~ ~ ~ ( 2 1 ~ 2 2 2 z y x eff p p p m H + + = where m eff is the effective mass that is about 20% of the real electron mass. Now we put an electron in a Silicon nanowire whose cross section is 10 x 10 nm 2 . Assume that this nanowire can be reasonably described by the model in (c). Now at a temperature T , the electron has a total energy k B T where k B is Boltzmann constant. Find the upper limit of the temperatures that the electron behaves as if it is confined in 1-dimensional box (i.e., the energy is small enough that the quantum numbers other than k x is fixed to their lowest value). 2. Problem 4.38 3. Problem 4.19 4. Problem 4.24 5. Problem 4.9 6. Problem 4.13 1...
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This note was uploaded on 02/23/2010 for the course PHYS 4021 taught by Professor Kim during the Fall '08 term at Columbia.
- Fall '08