495wPracticeExam1

# 495wPracticeExam1 - v 2 2 F x 2 + Ω 2 F where Ω and v are...

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1 EE 453 EXAM I OPEN BOOK Wednesday Sept.28, 2002 NAME : SS # : Please show all work and write your answers clearly. This exam should have five pages. Problem 1 [p. 2] 6 points Problem 2 [p. 3] 7 points Problem 3 [p. 4, 5] 12 points Total 25 points

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2 Problem 1 (6 points) A channel has a density of states as shown, given by D ( E ) = D 0 + D 1 ( E μ ) 2 where D 0 = 0.1 / eV, and D 1 = 2 / eV 3 . It is connected to two contacts with the same electrochemical potential μ. Is there a current in the external circuit ? If so, is it in the direction shown (from the hot to the cold contact) or opposite to the direction shown (from the cold to the hot contact) ? Explain your reasoning. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1000 K 300 K Density of states, D(E) ---> E
3 Problem 2 (7 points) A field F(x,t) obeys the one-dimensional wave equation 2 F t 2 =

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Unformatted text preview: v 2 2 F x 2 + Ω 2 F where Ω and v are constants. Assume a solution of the form ( F being a constant) F ( x , t ) = F e + i ( kx − ω t ) and find the dispersion relation (k). 4 Problem 3 (12 points) We wish to calculate the current, I through a single discrete energy level ε and the average number of electrons, N using the multielectron picture where we have two levels ‘0’ and ‘1’ corresponding to the one-electron level being empty or full respectively. Your answers to all questions below should be in terms of the Fermi functions in the two contacts and the couplings γ 1 and 2 for the two contacts. (a) Equate the rate of transition from ‘0’ to ‘1’and that from ‘1’ to ‘0’ to obtain an expression relating the probabilities P and P 1 . (b) From your result in (a), find an expression for the average number of electrons, N (c) Obtain an expression for the current I from the rates of transition from ‘1’ to ‘0’ and from ‘0’ to ‘1’. μ 2 μ 1 Drain Source I V I ε 1 One-electron picture Multi-electron picture 5...
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## This note was uploaded on 02/19/2012 for the course ECE 495w taught by Professor Supriyodatta during the Fall '06 term at Purdue.

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495wPracticeExam1 - v 2 2 F x 2 + Ω 2 F where Ω and v are...

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