nanoHUB-U: Thermal Energy at the Nanoscale

A free self-paced course on the essential physics of thermal energy at the nanoscale.

  1. density of states
  2. energy conversion
  3. Landauer Formalism
  4. materials science
  5. nanoHUB-U
  6. NCN Group - Materials Science
  7. NCN Group - Thermal Properties
  8. phonons
  9. thermal transport


Brought to you by:


This web-based course was developed by Professor Tim Fisher to update content that has been taught previously in regular university courses and through the NCN Summer School. This short course is sponsored by nanoHUB and covers the most important thermal transport fundamentals presented in a semester-long course that has been very popular with on-campus students.

Thermal Energy at the Nanoscale is a self-paced online course that develops a unified framework for understanding essential physics of nanoscale thermal energy and its important applications, trends, and directions. The course is taught at the level of a Purdue graduate course for first-year students, but there are no admission requirements and no need to travel to Purdue. The online course can be taken from anywhere in the world. Each unit contains six 20-minute video lectures covering essential physics, practical considerations, models for simulation, and fundamental limits.

Lessons from Nanoscience Lecture Notes Series

Registered participants will be provided an electronic draft copy of lecture notes being written by Prof. Fisher. These notes are published in a book entitled Thermal Energy at the Nanoscale as part of World Scientific’s Lessons from Nanoscience Lecture Notes Series.

Scientific Overview

Download mp4 video

Course Objectives

The objective for this course is to provide students with an understanding of the essential physics of thermal transport as well as some of the practical technological considerations and fundamental limits. The goal is to do this in a way that is broadly accessible to students with only a very basic knowledge of heat transfer. Students in this course will:

1. Gain an understanding of the fundamental elements of solid-state physics relevant to thermal transport.

2. Develop skills to derive continuum physical properties from sub-continuum principles.

3. Apply statistical and physical principles to describe thermal energy transport in modern small-scale materials and devices.

The list of interesting materials and physical structures is almost endless, and therefore given the subject of nanoscale physics, the course begins with a basic treatment of interatomic bonding and crystal structure but then highlights where possible a compelling structure—the graphene carbon lattice—to illustrate important facets of unique thermal behavior at the nanoscale.

Who Should Take the Course

Anyone seeking a sound, physical, but simple understanding of how heat flows at the thermal carrier level. The study of thermal energy in any material should rightly begin with a description of the material itself. Thermal energy, unlike other forms of energy, such as optical, electronic, and magnetic, is routinely generated, stored, and transported by a diverse set of carriers. The reason for broader context of thermal energy derives from the second law of thermodynamics, which dictates that all forms of energy tend toward disorder (or thermalization). In this course, we will make every reasonable attempt to unify the analysis—i.e., to generalize concepts so that they apply to multiple carriers, but this objective is occasionally elusive. In such cases, we will make clear the relevant restrictions by carrier and material types. The course should be useful for advanced undergraduates, beginning graduate students as well as researchers and practicing engineers and scientists. The goal is to provide a simple, accessible, but sound introduction to the fundamentals of thermal transport.


This course is intended to be broadly accessible to those with a background in the physical sciences or engineering. No familiarity with heat transfer and thermal physics is assumed. A basic familiarity with topics usually covered in a two-semester college course in introductory physics is assumed. Selected topics from upper-division undergraduate courses in electricity and magnetism, thermodynamics, and quantum mechanics will be reviewed when required. A working knowledge of both integral and differential calculus is assumed. A basic understanding of concepts such as Fourier’s Law, Ohm’s Law, etc. will be helpful.

Course Outline

Preview the lectures below, or join the course by clicking the yellow button on the right and entering your nanoHUB login information!

Unit 1: Lattice Structure, Phonons, and Electrons

  • L1.1: Introduction and Atomic Bonding
  • L1.2: Mathematical Description of the Lattice
  • L1.3: Lattice Vibrations and Phonons
  • L1.4: Free Electrons
  • L1.5: Example 1D Atomic Chain with a Diatomic Basis
  • L1.6: Unit 1 Wrap Up

Unit 2: Carrier Statistics

  • L2.1: Statistical Ensembles
  • L2.2: Phonon Density of States
  • L2.3: Electron Density of States
  • L2.4: Example: Derivation of Planck’s Law
  • L2.5: Blackbody Emission Intensity
  • L2.6: Unit 2 Wrap Up

Unit 3: Basic Thermal Properties

  • L3.1: Introduction to Specific Heat
  • L3.2: Acoustic Phonon Specific Heat
  • L3.3: Optical Phonon Specific Heat
  • L3.4: Electron Specific Heat
  • L3.5: Thermal Conductivity from Kinetic Theory
  • L3.6: Unit 3 Wrap Up

Unit 4: Landauer Transport Formalism

  • L4.1: Basic Theory
  • L4.2: Heat Flow Rate
  • L4.3: Thermal Conductance
  • L4.4: Spectral Conductance
  • L4.5: Example: The Quantum of Thermal Conductance
  • L4.6: Unit 4 Wrap Up

Unit 5: Carrier Scattering and Transmission

  • L5.1: Scattering Analysis in the Landauer Formalism
  • L5.2: Boundary Scattering
  • L5.3: Internal Phonon Scattering Fundamentals
  • L5.4: Interfacial Transmission
  • L5.5: Thermionic Electron Emission
  • L5.6: Unit 5 Wrap Up

Course Resources

  • A free account is required to access some course components.
  • Homework exercises with solutions.
  • Online quizzes to quickly assess understanding of material after most video lectures.
  • An online forum, hosted by nanoHUB. Students enrolled in the course will be able to interact with one another.
  • Practice exams.

 Thermal Energy at the Nanoscale first published on nanoHUB-U, July 2013.


Creative Commons BY License


This self-paced course is available at no cost.

nanoHUB-U is powered by, the home for computational nanoscience and nanotechnology research, education, and collaboration.