ECE495N-F08-HW_3 - ECE 495N Fall08 ME118 MWF 1130A 1220P...

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9/10/08 ECE 495N, Fall’08 ME118, MWF 1130A – 1220P HW#3: Due Friday Sept.26 in class. Problem 1: A sheet of graphene (Width: W, Length: L) has a density of states given by 2 ( ) | | /( ) f D E LW E ν = where v f 10 6 m / s . The equilibrium electrochemical potential μ = 0 eV, k B T 1 = 2 = 0.025 eV and assume escape rates 12 ( /) / ff L vL L λ γγ = = +  , for ballistic transport L << . (a) Plot (N-N 0 )/LW versus U for -0.5 eV < U < +0.5 eV (Note: N 0 = N(U=0)) using the equation N = dED ( E U ) −∞ +∞ γ 1 1 ( ) + 2 2 ( ) 1 + 2 (1) assuming 1 2 (close to equilibrium), and (b) G versus U, using the equation 2 1 () f q G dED E U E +∞ −∞  =  +  (2) Compare your plots with the expressions (a) 2 0 ( ) / 0.5( / ) , 0 f N N LW U U −= > 2 0 ( ) / 0.5( / ) , 0 f N N LW U U (3) and (b) 2 / | |/ 2 f q GW U = (4) D(E) µ E 1 2 Source Channel Drain
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9/10/08 Show how you could obtain the approximate expressions (3) and (4) from Equations (1) and (2). For Problems 2,3 you can use the MATLAB code at the end of the text as a guide, but the code you turn in should be your own work, not copied from the text.
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ECE495N-F08-HW_3 - ECE 495N Fall08 ME118 MWF 1130A 1220P...

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