EMS172-2009-Homework2_Solutions

EMS172-2009-Homework2_Solutions - UNIVERSITY OF CALIFORNIA,...

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

View Full Document Right Arrow Icon
EMS 172 Profs. Y. Takamura and A. Moulé, 2009 UNIVERSITY OF CALIFORNIA, DAVIS Department of Chemical Engineering and Materials Science EMS 172: Electronic, Magnetic, and Optical Properties of Materials Homework 2 - Solutions Due Date: Tuesday, Oct. 13 th , 2009, in-class Note: You must show all the steps you used to obtain your answer in order to receive full credit. 1. Fermi-Dirac Distribution [14 pts] (a) At what temperature can we expect a 10% probability that electrons in a given material have an energy which is 2% above the Fermi energy? (Use E F =5.0 eV) When dealing with probability, we are referring to the Fermi-Dirac distribution. E=E F + 0.02*E F , E-E F =0.02*E F () () 1 / 10 62 . 8 0 . 5 02 . 0 exp 1 10 . 0 1 exp 1 5 + × × × = = + = T K eV eV T k E E E F B F () () () ) 9 ln( / 10 62 . 8 0 . 5 02 . 0 9 / 10 62 . 8 0 . 5 02 . 0 exp 10 . 0 1 1 / 10 62 . 8 0 . 5 02 . 0 exp 5 5 5 = × × × = × × × = + × × × T K eV eV T K eV eV T K eV eV Solving for T = 528 K. [1 pt for eqn, 1 pt for value, 1 pt for trying] (b) We stated that the Fermi-Dirac distribution function can be approximated by classical Boltzmann statistics if the exponential factor in the Fermi-Dirac distribution function is significantly larger than one. Using the relationship E-E F =nK b T for various values of n where n is an integer, calculate the value of the Fermi-Dirac distribution and the Boltzmann distribution. State at which value of n , T k E E B F exp can be considered to be significantly larger than one. Hint : Create a table with the calculated error between the full F(E) expression and the Boltzmann distribution for different values of
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 05/14/2010 for the course EMS 172 taught by Professor Takamura during the Winter '10 term at UC Davis.

Page1 / 4

EMS172-2009-Homework2_Solutions - UNIVERSITY OF CALIFORNIA,...

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