Week2HWSolutions

assume a non parabolic band described by the so

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ⎝ 2⎠ 0 −π /2 0 −π /2 2 num = υ F k F (*) kF + π / 2 ∞ +π /2 den = ∫ ∫ k dk dθ f0 = 0 −π /2 kF kF + π / 2 ∫∫ 0 −π /2 +π /2 kF +π /2 0 −π /2 k dk dθ = ∫ k dk From (*) and (**), we find: 2 num υ F k F 2 + υx = =2 = υ F den k F π 2 π ∫ dθ = 2 kF × π 2 (**) + υx = 2 υ πF ECE- 656 6 Fall 2013 Mark Lundstrom 8/24/2013 ECE 656 Homework 2: (Week 2) (continued) 4) Assume a nonparabolic, 1D energy bandstructure described by: 2 kx2 E ( kx ) ⎡1 + α E ( kx ) ⎤ = ⎣ ⎦ 2 m* ( 0 ) . where 1 m* ( 0 ) = 2 1 d E ( kx ) 2 2 dkx k x =0 . 4a) Sketch (or produce a Matlab plot) of E(k) vs. k for two cases: i) α = 0 and ii) α > 0 . If you are producing a Matlab plot, the energy range should be from 0 to 1 eV, and you can assume α = 0.5 eV. Solution: We can see from the equation, that for a given E, the left hand side will be bigger than for a parabolic energy band, so it will take a bigger kx for...
View Full Document

Ask a homework question - tutors are online