14 Covalent Bonds - Fundamentals of Nanoelectronics...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Fundamentals of Fundamentals of Nanoelectronics Nanoelectronics Prof. Supriyo Datta ECE 453 Purdue University Network for Computational Nanotechnology 09.27.2004 Lecture 14: Covalent Bonds Ref. Chapter 3.3
Background image of page 1

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

View Full DocumentRight Arrow Icon
Solution of Schrödinger Equation in 3D 00:03 • Last session we talked about finding energy levels of Hydrogen atom. To find energy levels of any material, the Schrödinger equation is the first step: • Since U(r)~1/r and as the result U does not depend on theta or phi (spherical symmetry), the solution can be written as: • Putting this solution in the Schrödinger equation gives us the energy levels: • “l” can take integer values and “m” can take values from –l to l in steps of 1: Φ + = Φ ) ( 2 2 2 r U m E G = φ ) θ , ( ) ( m l Y r r f = Φ ) ( 2 ) 1 ( ) ( 2 ) ( 2 2 2 2 2 r f mr l l r U dr d m r Ef + + + = = = 0,1,2,. .. = l l l l l m , 1 ,..., 0 ,..., 1 , + =
Background image of page 2
Atomic Energy Levels and Self Consistent Solution 02:13 • Since the potential in Hydrogen atom has the form of 1/r, the levels 2s and 2p are at the same energy. This does not have to be the case for other atoms. In all other atoms, the p levels will be a little higher than s levels and the d levels will be higher than p levels. Equation 1 can be used to solve for the energy levels. The equation can be turned into a matrix equation and the eigenvalues and eigenvectors can be found from there. • Solving 1 for any other atom becomes a lot harder because then it has to be solved self consistently. This is because the potential U(r) has two parts: nuclear potential and the electron cloud potential. Since the potential of each electron affects the other ones, the problem must be solved self consistently. l
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/12/2011 for the course ME 305 taught by Professor Wright,j during the Spring '10 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

Page1 / 11

14 Covalent Bonds - Fundamentals of Nanoelectronics...

This preview shows document pages 1 - 4. Sign up to view the full document.

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