Solid State Physics Exam Questions and Answers

ESS 4300 Introduction to Solid State Physics Instructor: Pai-Yi Hsiao, Ph.D.

Final exam 20 June 2005 (130 pts)

1. (a) In the chapter 5 of the text book, Kittel wrote The Einstein model, however, is often used to approximate the optical phonon part of phonon spectrum. . Explain why the Einstein model can be used to approximate optical phonon. (4 pts) (b) In the study of phonon collisions, collision process can be characterized by two different ways, (1) normal process and (2) umklapp process. Give the definition of the two processes. (10 pts) What is the importance of the umklapp process in thermal transport phenomena. (4 pts) 2. (a) Explain the term Fermi energy . (5 pts) (b) Find the expression D( ) for the number of orbitals per unit energy range, so-called density of states, for free electron gas under periodic boundary condition. (5 pts) (c) The probability that an orbital at energy is occupied in an ideal Fermi gas in thermal equilibrium at temperature T is given by Fermi-Dirac distribution:

f( )

exp

1 ) / k BT

1

where the

chemical potential depends on temperature and is often called Fermi level in solid state physics. Explain that at T=0 the Fermi level is equal to Fermi energy. (3 pts) Draw the plot of D( )f( ) versus for the case T=0 and the case T 0. Shadow the filled electron orbitals under the curves of the plots for the above two cases. (4 pts) (d) When the system is heated from absolute zero to T (where 0< kBT