Week2HWSolutions

Ns d e f e de n 2d 0 s ec ece 656

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Unformatted text preview: E 2E (valley degeneracy is 2 for graphene) D2 D ( E ) = gV = 2 2 ( E > 0 ) 22 π υF π υF 2 Aside: Note that if we define the effective mass of graphene by E ≡ m*υ F then we could use the parabolic band DOS and get the right DOS for graphene! ∞ nS = ∫ D ( E ) f ( E ) dE = n 2D 0 S = EC ECE- 656 EF ∫ D ( E )1dE 2D (T = 0 K) 0 1 Fall 2013 Mark Lundstrom 8/24/2013 ECE 656 Homework 2: (Week 2) (continued) nS = EF ∫ 0 E2 2E dE = 2F 2 2 π 2υ F π υF 2 EF nS = 2 2 π υF 1b) In terms of the Fermi wave vector, kF : Case i): parabolic energy bands: DOS: 2k 2 = E − EC = E ( E > EC = 0 ) 2 m* 2 2kF = E F − EC = E F ( E > EC = 0 ) 2 m* 22 2 kF 2 m* 2 m* k F nS = E → nS = × = gV × 2π π 2 F π 2 2 m* 2 2 kF kF nS = gV = 2π π Case ii): graphene: DOS: E = υ F k ( E > 0 ) E F = υ F k F E2 nS = 2F 2 π υF nS = 2 kF π ( E > 0) ( υ k ) → F 2 FF 22 F π υ = 2 kF π (same as for parabolic energy bands) Aside: Why are the two expressions the same? At...
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This document was uploaded on 01/15/2014.

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