4a sketch or produce a matlab plot of ek vs

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Unformatted text preview: ⎞ × 2 m* ⎜ 3 ⎟ ⎝⎠ 3 ⎛ 2 ⎞ ⎛ k F ⎞ num = ⎜ ⎟ ⎜ * ⎟ ⎝ 3⎠ ⎝ m ⎠ (*) ∞ +π /2 kF + π / 2 kF +π /2 2 kF denom = ∫ ∫ k dk dθ f0 = ∫ ∫ k dk dθ = ∫ k dk ∫ dθ = × π 2 0 −π /2 0 −π /2 0 −π /2 Using (*) and (**) 3 ⎛ 2 ⎞ ⎛ k F ⎞ ⎜ 3 ⎟ ⎜ m* ⎟ ⎝ ⎠⎝ ⎠ num 4 k F 4 + υx = = = = υ F 2 * denom 3π m 3π π kF 2 ECE- 656 5 (**) Fall 2013 Mark Lundstrom 8/24/2013 ECE 656 Homework 2: (Week 2) (continued) 4 υ 3π F Makes sense….. ave. x- directed velocity must be less than the maximum velocity of electrons in the conduction band, υ F . 3b) graphene ∞ +π /2 υ x k f0 ( E ) ∫ ∫ k dk dθ υ x f0 ∑ k x >0 , k y num + − υx = = 0 ∞ π /π2/ 2 = + den ∑ f0 ( E ) k x >0 , k y ∫ ∫ k dk dθ f0 + υx = () 0 −π /2 ∞ +π /2 num = ∫ ∫ 0 −π /2 ∞ +π /2 k dk dθ υ x f0 = ∫ ∫ k dk dθ υ F cosθ f0 0 −π /2 f0 = 1 k < k F ( E < E F ) 2 ⎛ kF ⎞ num = ∫ ∫ k dk dθ υ F cosθ =υ F ∫ k dk ∫ cosθ dθ = υ F ⎜ ⎟ × 2...
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This document was uploaded on 01/15/2014.

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