Homework_7

Homework_7 - EE506 Semiconductor Physics Homework...

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Homework Assignment #7 Prof. Steve Cronin Due December 1, 2011 Phonon Dispersion Relations: In this assignment you will write a program in MatLab that calculates the phonon dispersion relations in graphene using the dynamical matrix approach. As a reference for this, see Chapter 9 of Saito, et al, “Physical Properties of Carbon Nanotubes” which is available on blackboard. 1.) In order to describe all of the vibrational motion of the atoms in graphene, we must consider the four nearest neighbor atoms for each of the two atoms in the unit cell (A and B). a.) Determine values for the radii of the 4 tiers of nearest neighbor atoms. The carbon-carbon distance is 1.44Å. b.) Determine the angle of each atom in the four tiers. There will be 3 in the first tier, 6 in the second tier, 3 in the third tier and 6 in the forth tier. It may be convenient to expresses these angles in a singe matrix with one index referencing the tier number and the second index referencing the atom number within the tier. 2.) Define variables for the force constants of the four nearest neighbor atoms using
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This note was uploaded on 01/29/2012 for the course EE 506 at USC.

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Homework_7 - EE506 Semiconductor Physics Homework...

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