This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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. Oneelectron picture Multielectron 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 0bit 790(VIDCI1‘ 313%)
Ram t—ao: Pi (Viit’l/LE) ...
View
Full Document
 Fall '06
 SupriyoDatta
 Electrochemistry, Electron, Fundamental physics concepts, Phonon, SMMLWM mWaJ Mammy

Click to edit the document details