Week2HWSolutions

# ave x directed velocity must be less than the

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Unformatted text preview: Mark Lundstrom 8/24/2013 ECE 656 Homework 2: (Week 2) (continued) 3) Assume T = 0K and work out the average +x- directed velocity for electrons in: 3a) A 2D semiconductor with a parabolic conduction band and 3b) The conduction band (E > 0) of graphene. Your answer should be in terms of the Fermi energy, E F . Solution: 3a) parabolic energy bands ∞ +π /2 υ x k f0 ( E ) ∫ ∫ k dk dθ υ x f0 ∑ k x >0 , k y num + − (DOS in k- space cancels from num υx = = 0 ∞ π /π2/ 2 = + den ∑ f0 ( E ) k x >0 , k y ∫ ∫ k dk dθ f0 () 0 −π /2 and denom) ∞ +π /2 num = ∫ ∫ 0 −π /2 ∞ +π /2 k dk dθ υ x f0 = ∫ ∫ k dk dθ 0 −π /2 k cosθ f0 m* f0 = 1 k < k F ( E < E F ) kF + π / 2 k num = ∫ ∫ k dk dθ * cosθ = * m m 0 −π /2 kF +π /2 0 −π /2 2 ∫ k dk ∫ cosθ dθ = 3 ⎛ kF...
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## This document was uploaded on 01/15/2014.

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