By completing the Periodic Potential Lab in ABACUS - Assembly of Basic Applications for Coordinated Understanding of Semiconductors, you will be able to:

a) understand the Kronig-Penney model and the formation of energy bands and energy gaps due to the underlying periodic interaction potential

b) understand the concept of the effective mass

c) create your own Kronig-Penney solver.

The specific objectives of the Periodic Potentials Lab are:

## Recommended Reading

If you have not had experience with periodic potentials, bandstructure, the concept of the effective mass, etc., listed below are the suggested reading materials:

1. D. K. Ferry, Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Second Edition (Institute of Physics Publishing, 2001).

## Demo

Periodic Potential Lab: First-Time User Guide

## Theoretical descriptions

* Energy Bands In Periodic Potentials

* Periodic Potentials and the Kronig-Penney Model

## Tool Verification

Nanoelectronic Modeling Lecture 14: Open 1D Systems - Formation of Bandstructure

## Worked Examples

1. Periodic Potential Lab Demonstration: Standard Kroenig-Penney Model

## Exercises and Homework Assignments

1. Homework Assignment: Periodic Potentials

2. Periodic Potentials and Bandstructure: an Exercise

## Solutions to Exercises

Solutions to exercises will be provided to Instructors ONLY!

## Take a Test

This test will assess your conceptual understanding of the physical, mathematical and computational knowledge related to periodic potentials and formation of bandstructure in crystals.

ABACUS: Test for Periodic Potential Lab

## Solve the Challenge

In this final challenge you will integrate all what you have learned about the Kronig-Penney model.