homework5

homework5 - Department of Electrical and Computer...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Department of Electrical and Computer Engineering, Cornell University ECE 407: Physics of Semiconductor and Nanostructures Spring 2009 Homework 5 ` Due on Feb. 24, 2009 at 5:00 PM Suggested Readings: a) Lecture notes Problem 5.1 (1D lattice energy bands outside the FBZ) In the last homework, in problem 4.1, you found the exact solution for an electron in a periodic 1D lattice. You will consider the same problem again here. Consider a 1D lattice of lattice constant a equal to 5 Angstroms. Suppose the potential has the form: () + = x a V x a V x V π 4 cos 2 2 cos 2 2 1 Where 1 V equals 0.3 eV and 2 V also equals 0.3 eV. The exact solution for any wavevector k in the FBZ can be written as a superposition of plane waves in the form: = = −∞ = + −∞ = + m x G k i m m G k m k k m m e L G c G c 1 φ ψ Where: a m G m 2 = A good approximation to the exact solution can be obtained by terminating the series above at both ends, as follows: = = + N N m G k m k k m G c Where N is some large number, say 10. The way you hopefully solved the problem in homework 4 was to first choose a value of the wavevector k in the FBZ, then setup a matrix, and then find its three smallest eigenvalues. The question is what if one chooses a value of the wavevector k that is not in the FBZ? Would one end up with some new energy eigenvalues and new energy eigenfunctions? The goal of the problem is to explore this point.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/04/2009 for the course ECE 4070 taught by Professor Rana during the Spring '08 term at Cornell.

Page1 / 3

homework5 - Department of Electrical and Computer...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online