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Unformatted text preview: ECE 495N PRACTICE EXAM I CLOSED BOOK, Sept. 25, 2007 Problem 1 [p. 2,] 8 points
Problem 2 [p. 3] 8 points
Problem 3 [p. 4] 9 points Total 25 points
Problem 1
(a) 5 points Source Channel Drain A channel has a density of states as shown, namely a constant nonzero value for E 2 0
and zero for E < O, that is_._ DUE) 2 D0 6' (E ), where 6' represents the unit step function. It is connected to two contacts with the same electrochemical potential it whjich is m 0. Is
there a current in the extemal 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. (b) 3 points
Which side (the hot side or the cold side) will be positive if we leave the tenninals open'? Problem 2
W e have seen in class that free electrons in the absence of any external potential are
:1 , f 3 :3
described by (in one dimension) 1' it “if = — i— 1” W (1)
:3? 2m 532
whose solutions can be written in the fonn gr/(XJ) : a +" h e ﬁEl m (2)
constant
. . . . '3 .
With E and k related by the dispers1on relation: E : E211" .."2m (3) (:1) 3 points
Can solutions be written in the form of (2) if a sinusoidal external potential U = U0
cos(X."'a) is present (a is a constant)? (1}) 5 points Can you suggest a suitable differential equation to replace (1) if you wanted the
dispersion relation to look like E2 : (Inez) 2 + fracz k2 (3") (111, c, T: are all constants) instead of (3) ‘F’ Problem 3 We wish to calculate the current, I through a channel having two discrete energy levels
with energy 8, but with a vely high interaction energy such that both levels CANNOT be simultaneously occupied in our voltage range of interest. Oneeiectron picture i’lrfuitieieetron picture (a) 6 points
Write rate equations in the nniltielectron picture to obtain an expression for the maximum current I that ﬂows when a voltage V is applied with the polarity as shown. Your answer
should be in terms of the couplings 3/1 and y2 for the two contacts (and fundamental constants like q and Ti). (17) 3 points
Assuming 5/1 = 10 3/3, would you get more current or less current (in magnitude) if you reversed the polarity of the applied voltage? Please explain your reasoning. ...
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 Spring '08
 S.Datta
 Electrochemistry, Electron, Energy

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