{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Week2HWSolutions

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

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: 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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online