8/28/2015PHY 752 Fall Lecture 21 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 103 Plan for Lecture 2: Reading: Continue reading Chapter 1 in GGGPP; Electrons in one-dimensional periodic potentials 1.Review of Bloch’s Theorem 2.Kronig-Penny model potential from the viewpoint of scattering or tunneling

8/28/2015PHY 752 Fall Lecture 22

8/28/2015PHY 752 Fall Lecture 23

8/28/2015PHY 752 Fall Lecture 24 Li 2 SnO 3

8/28/2015PHY 752 Fall Lecture 25 Li 2 SnS 3

8/28/2015PHY 752 Fall Lecture 26 Bloch theorem:

8/28/2015PHY 752 Fall Lecture 27 Eigenvalue solutions to Kronig-Penny model

8/28/2015PHY 752 Fall Lecture 28

8/28/2015PHY 752 Fall Lecture 29 From wavefunction matching conditions: Condition for non-trivial solution: Simplified result:

8/28/2015PHY 752 Fall Lecture 210

8/28/2015PHY 752 Fall Lecture 211 v v Forbidden states f

8/28/2015PHY 752 Fall Lecture 212 f ka/  Band gap

8/28/2015PHY 752 Fall Lecture 213 Treatment of same problem in terms of transmission and reflection from a periodic barrier. First consider a single barrier: Matrix for determining coefficients:

8/28/2015PHY 752 Fall Lecture 214 Matching conditions for wavefunction coefficients:

8/28/2015PHY 752 Fall Lecture 215 Solving for transfer matrix elements:

8/28/2015PHY 752 Fall Lecture 216 Transmittance

8/28/2015PHY 752 Fall Lecture 217 After some algebra:

8/28/2015PHY 752 Fall Lecture 218 Electron transmission through a one-dimensional periodic barrier Because of Bloch theorem:

8/28/2015PHY 752 Fall Lecture 219 Bloch theorem & transmission coefficients: Condition for solution: