Week2HWSolutions

# assume a non parabolic band described by the so

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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...
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