ECE 874:Physical ElectronicsProf. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

Lecture 13, 11 Oct 12

Finite Potential Well:- to 0a to +0 to a(nm)(eV)Electron energy: E > U0Electron energy: E < U0Regions:

Last section of Chp. 02 is about the Finite Barrier:

A last look at the finite well, for E > U0 too:

Finite barrierAnderson, Modern Physics and Quantum Mechanics

E > Anderson V0 Pierret U0

E > Anderson V0 Pierret U0

E < Anderson V0 Pierret U0This is the expression for T that Pr. 2.8 is referring to.

Which situation is this: to start? When part (a) is finished?coshsinh

To start: situation is: tunnelling through the barriercoshsinh

When part (a) is finished, situation being described is: transport over the barrier region, by using Pr. 2.9s mathematical manipulationsStarting description: E < U0Finish description for: E > U0

Which situation is this?

Transport over the barrier region: E > U0 with transmission coefficient T given by:

Chapter 03: Energy band theory

e-

Next Unit cellDescribe e- as a wave:

e- described as a wave fitting into a periodic U0 situation.What happens?The Block theorem is the end result of boundary condition matching over multiple Unit cells. Result is:Only a phase shift when you get back to a repeat situation.

The repeat situation is not the lattice constant unless you are moving in direction. Variable a = the distance between atomic cores in a particulates transport direction.

Another useful way to describe the same wave function for e-:This emphasizes that the e- is described by a travelling wave expikx that is being modulated by a repetitive environment.

The two descriptions are equivalent.Equation (3.3) p. 54

Next Unit cell

Kronig-Penney model: approximate the real U(x) due to a row of atomic cores (top) by a series of wells and finite barriers (bottom).

Kronig-Penney model;

Kronig-Penney model allowed energy levels: where LHS = RHS

Graphical solution of 2.18b: