{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Week2HWSolutions

# 4a sketch or produce a matlab plot of ek vs

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}