ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Lecture 12, 09 Oct 12 VM Ayres, ECE874, F12

Finite Potential Well: (eV) Electron energy: E > U0 Electron energy: E < U0 (nm) Regions: -∞ to 0 0 to a a to +∞ VM Ayres, ECE874, F12

Infinite Potential Well: U (eV) = +∞ U (eV) = +∞ Electron energy: E < U0 (nm) Regions: -∞ to 0 0 to a a to +∞ VM Ayres, ECE874, F12

For these two situations, found: - y(x) - En VM Ayres, ECE874, F12

A) U0 = 0.7 eV = half the size of the bandgap Lecture 11 Example problem: Find energy levels in a finite model for a SQW: Consider a SQW of width a = 10 nm that is fabricated in GaAs that operates at 300K. The SQW is modelled as a finite well. How many energy levels for an e- exist for: A) U0 = 0.7 eV = half the size of the bandgap B) U0 = 1.4 eV = just under the size of the bandgap C) What is the practical meaning of the limit: x = E/U0, 0 < x < 1? VM Ayres, ECE874, F12

Finite Potential Well Advantage is: you scale to important parameters: the height U0 and width a. Note: Width a only affects the LHS: the number/spacing of tan curves. Height U0 affects both sides but practical advantage on RHS plot.. VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

Discussion of Matlab solutions for: ECE874_FiniteWellEnergyLevels_Lec11.m Lecture 11 example problem: examples of two different well heights: U0 = 0.7 ev and U0 = 1.4 eV for a fixed well width and electron energy up to same value as U0 ECE874_FiniteWellEnergyLevels_ThreeVariables.m General three variable set-up allows you to change: well height U0 well width a energy “of” electron compared to well height: z = E/U0 VM Ayres, ECE874, F12

Last section of Chp. 02 is about the Finite Barrier: VM Ayres, ECE874, F12

VM Ayres, ECE874, F12

Finite barrier Anderson, Modern Physics and Quantum Mechanics VM Ayres, ECE874, F12

E > Anderson V0  Pierret U0 VM Ayres, ECE874, F12

A last look at the finite well, for E > U0 too: VM Ayres, ECE874, F12