handout10 - 1 ECE 407 Spring 2009 Farhan Rana Cornell...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 ECE 407 Spring 2009 Farhan Rana Cornell University Handout 10 The Tight Binding Method (Contd) In this lecture you will learn: The tight binding method (contd) The -bands in conjugated hydrocarbons Energy k a a s E ss V 4 ECE 407 Spring 2009 Farhan Rana Cornell University Tight Binding for a Square Lattice with a Two-Atom Basis Consider a 2D square lattice with a two-atom basis: y a d x a d y a a x a a 2 2 2 1 2 1 = = = = r r r r The primitive vectors and basis vectors are as follows: Each basis atom contributes one s-orbital that participates in bonding Each primitive cell contributes two s-orbitals that participate in bonding a a 1 d r 1 a r 2 a r 2 d r A B ( ) ( ) ( ) ( ) ( ) [ ] + = m m SB d k i SB m SA d k i SA R k i k d R r e k c d R r e k c N e r m 2 . 1 . . 2 1 r r r r r r r r r r r r r r r v One can write the trial tight-binding solution for wavevector as: k r ( ) ( ) SB SB SA SA E r E r r r 2 ECE 407 Spring 2009 Farhan Rana Cornell University Analysis of the Tight Binding Solution a a 1 d r 1 a r 2 a r 2 d r A B ( ) ( ) ( ) ( ) ( ) [ ] + = m m SB d k i SB m SA d k i SA R k i k d R r e k c d R r e k c N e r m 2 . 1 . . 2 1 r r r r r r r r r r r r r r r v (1) Summation over all primitive cells (2) Common phase factor for each primitive cell (4) A phase factor for each orbital that is related to the position of the orbital within the primitive cell w.r.t. lattice point (3) Summation over all orbitals within a primitive cell with undetermined coefficients ECE 407 Spring 2009 Farhan Rana Cornell University Tight Binding Solution a a 1 d r 1 a r 2 a r 2 d r A B Plug the solution into the Schrodinger equation: ( ) ( ) ( ) r k E r H k k r...
View Full Document

Page1 / 7

handout10 - 1 ECE 407 Spring 2009 Farhan Rana Cornell...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online