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Exam1Solution[1]

# Exam1Solution[1] - 1 ECE 453 EXAM I Friday Sept 24 2010...

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1 ECE 453 EXAM I Friday, Sept. 24, 2010 NAME : SOLUTION PUID # : CLOSED BOOK 1 page of notes provided Please show all work and write your answers clearly. This exam should have seven pages. Problem 1 [p. 2] 6 points Problem 2 [p. 3] 6 points Problem 3 [p. 4] 6 points Problem 4 [p. 5, 6] 7 points Total 25 points

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2 Problem 1: The energy-momentum relation for electrons in graphene are written in the form E ( p ) = ν 0 p where is a constant. Consider a large two-dimensional channel with dimensions L, W made of such a material. Find the density of states D(E). ˜ N ( p ) = π WL ( p / h ) 2 ˜ N ( E ) = π WL h 2 ν 0 2 E 2 D ( E ) = 2 π WL h 2 ν 0 2 E
3 Problem 2: At low temperatures, the conductance of a ballistic conductor is given by G = q 2 h ˜ M ( E = μ 0 ) while the electron density is given by n s = N ( E = μ 0 )/ LW , assuming a 2-D conductor with dimensions L, W. Find a general expression relating the conductance per unit width to the electron density, that is valid for any energy-momentum relation.

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Exam1Solution[1] - 1 ECE 453 EXAM I Friday Sept 24 2010...

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