By completing the Periodic Potential Lab in ABACUS - Assembly of Basic Applications for Coordinated Understanding of Semiconductors, users will be able a) to understand the Kronig-Penney model and the formation of energy bands and energy gaps due to the underlying periodic interaction potential, b) to understand the concept of the effective mass, and c) to create their own Kronig-Penney solver.

The specific objectives of the Periodic Potentials Lab are:

## Recommended Reading

Users who are new to periodic potentials, bandstructure, or the concept of the effective mass should consult the following resources:

1. D. K. Ferry. (2001). *Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers*. 2nd ed. Bristol (UK): Institute of Physics Publishing.

## Demo

## 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

## Examples

1. Periodic Potential Lab Worked Examples

## Exercises and Homework Assignments

1. Homework Assignment: Periodic Potentials

2. Periodic Potentials and Bandstructure: an Exercise

## Solutions to Exercises

Solutions to exercises are provided only to instructors!

## Evaluation

This resource will evaluate the user’s 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

## Challenge

In this final challenge, users will integrate what they have learned about the Kronig-Penney model.