Practice_Exam1_solutions

Practice_Exam1_solutions - EE 453 EXAM I OPEN BOOK...

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Unformatted text preview: EE 453 EXAM I OPEN BOOK Wednesday Sept. 28, 200? 5 330P -‘ 42/0 P NAME: gOLUTION Please show all work and write your answers clearly. This exam should have five pages. Problem 1 a [p. 2] 6 points Problem 2 [p. 3] 7 points Problem 3 [p. 4, 5] 12 points Total ' 25 points ‘ Problem 1 (6 points) E Density of states, D(E) ---> 1000 K “I 300 K A channel has a density of states as shown, given by D(E) = D0 + D1 (E -— (1)2 where D0 = 0.1 / eV, and D1 = 2 / eV3. It is connected to two contacts with the same electrochemical potential pt. 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 showu (from the cold to the hot contact) ? Explain your reasoning. Problem 2 (7 points) 2 8 __ V242, (912 6x2 where Q and v are constants. Assume a solution of the form (F0 being a constant) 2 A field F(X,t) obeys the one—dimensional wave equation (9 F F(x,r) = F0 e H “(x—‘0’) and find the dispersion relation a)(k). SMMLWM mWaJ Mammy 432 1: -_- VF + off 609‘ := /&2V7’—' 512’ w :: :i: ,ggya £1?“ 92F Problem 3 (12 points) We wish to calculate the current, I through a single discrete energy level a 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. One-electron picture Multi-electron picture l—Hlv—H 0 Your answers to all questions below should be in terms of the Fermi functions in the two contacts and the couplings yl and 3/2 for the two contacts. (a) Equate the rate of transition from ‘0’ to ‘l’and that from ‘1’ to ‘0’ to obtain an expression relating the probabilities PO and PI. ' (b) From your result in (a), find an expression for the average number of electrons, N (0) Obtain an expression for the current I from the rates of transition from ‘1’ to ‘0’ and from ‘0’ to ‘1’. Route 0-bit 790(VIDCI1‘ 313%) Ram t—ao: Pi (Viit’l/LE) ...
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Practice_Exam1_solutions - EE 453 EXAM I OPEN BOOK...

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