{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ECE495N-F08-Exam_1_practice

# ECE495N-F08-Exam_1_practice - ECE 495N PRACTICE EXAM I...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 non-zero 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 53-2 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. One-eiectron picture i’lrfuiti-eieetron 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. ...
View Full Document

{[ snackBarMessage ]}