{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ECE495N-F08-Exam_2_solution

# ECE495N-F08-Exam_2_solution - ECE 495N EXAM II CLOSED BOOK...

This preview shows pages 1–7. 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 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 EXAM II CLOSED BOOK Wednesday, Nov.5, 2008 NAME: gOLUTION PUID # : Please show all work and write your answers clearly. This exam should have seven pages. Problem 1 [p. 2, 3] 8 points Problem 2 [p. 4, 5] 9 points Problem 3 [p. 6, 7] 8 points Total 25 points Useful Relations: f (E ) = ———1—-—— Fermi function 1+ exp(E — M)/kT Pa = % exp(-— (Ea —— “Na )/kT) Law of equilibrium [h(/E)]= 2[Hm]exp(ii€.(&m—&n)) Bandstructure m D(E) = 2 6(E — so?» Density of States k a h M(E)= ENE—8%))” k ~ -1 (9802) v"(k)_h é’kx w?) -—-———| Density of modes Problem 1: A channel has two energy levels with the same energy 8, but the interaction energy is so high that no more than one of these levels can be occupied at the same time. What is the average number of electrons in the channel if it is in equilibrium with chemical potential 14 and temperature T? Your answer should be in terms of 8 ,y and T. t) W “a“ : 26% .1, Problem 2: Benzene molecule consists of six carbon atoms arranged at the corners of a regular hexagon of side ‘a’. Assume (1) one orbital per carbon atom as basis function ; (2) the overlap matrix [S] is a (6x6) identity matrix; and (3) the Hamiltonian matrix is given by H n n = a (site energy) H n m = t if n, m are neighboring atoms H n m = 0 if n, m are NOT nearest neighbors (a) What are the six energy eigenvalues in terms of ‘ 8’ and ‘t’? <__ a __> (b) What are the corre3ponding eigenvectors? E: 8+ 2ft 6/9955 t%[o,t1,tzizj =€+ 2t, 2+t, 5’17; 3"“7 C1) (2) U") 1 i HHHt—xr—xx—s Problem 3: Suppose a large two—dimensional conductor has an 806.) relationship given where Derive an ex Your by: db= AH A is a constant and k2 = k: + kyz. pression for the density of states, D(E). answer should be in terms of the energy E, A, Width W and length L. ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

ECE495N-F08-Exam_2_solution - ECE 495N EXAM II CLOSED BOOK...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online