Nanophotonics Atilla Ozgur Cakmak Ph D Unit 2

Nanophotonics Atilla Ozgur Cakmak, Ph. D

Unit 2 Lecture 14: Tight Binding Model-Part 1

Outline • The model • Effective Mass • Group Velocity • Density of States • Fermi Energy

A couple of words… There is another model effectively used for periodic wave propagation, which will be very useful for our understanding. It is called the tight binding approach and it is based on the wave functions which are very much localized at their sites. The wave propagation is in a way akin to hopping from site to site. There are studies which treat periodic configurations within the perspective of tight binding approach as we will see in the upcoming lectures. Suggested reading: Peter Markos, Costas M. Soukoulis Wave Propagation From Electrons to Photonic Crystals and Left-Handed Materials, 5 th Chapter.

The model

The model

The model

The model εn=0

Effective mass

Effective mass εn=0

Effective mass (problem) 1) Reproduce and plot the same effective mass plot in the previous slide.

Effective mass (solution) 1) Reproduce and plot the same effective mass plot in the previous slide.

Group velocity εn=0

Group velocity εn=0

Density of States (problem) 2) a) b) c) d) Which of the following correctly depicts the density of states for the tight binding method?

Density of States (solution) 2) Which of the following correctly depicts the density of states for the tight binding method?

Density of States εn=0

Density of States Kronig-Penney Van hove singularity Tight Binding

Fermi Energy