2.57 | Spring 2012 | Graduate

Nano-to-Macro Transport Processes


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


Parallel treatments of photons, electrons, phonons, and molecules as energy carriers, aiming at fundamental understanding and descriptive tools for energy and heat transport processes from nanoscale continuously to macroscale. Topics include the energy levels, the statistical behavior and internal energy, energy transport in the forms of waves and particles, scattering and heat generation processes, Boltzmann equation and derivation of classical laws, deviation from classical laws at nanoscale and their appropriate descriptions, with applications in nano- and microtechnology.


Chen, Gang. Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons. Oxford University Press, 2005. ISBN: 9780195159424. [Preview with Google Books]


Students are required to complete weekly homework, due on the second session of each week. For graduate students: complete homework plus weekly paper reading. For undergraduate students: complete homework (sometimes less than graduate assignment) and no weekly paper report.


There is no final exam.

For undergraduate Students: 10% Bonus will be given for undergraduate students following graduate assignments.

Homework 50%
Two Midterms 25% each

For graduate Students:

Homework 40%
Two Midterms 25% each
Final Project 10%


1 Intro to Nanotechnology and Nanoscale Transport Phenomena  
2 Characteristic Time and Length, Simple Kinetic Theory  
3 Schrödinger Equation and Material Waves  
4 Solution of Schrödinger Equation, Energy Quantization  
5 Electronic Levels in One-Dimensional Lattice Chain Homework 1 due
6 Crystal Bonding and Electronic Energy Levels in Crystals  
7 Phonon Energy Levels in Crystal and Crystal Structures Homework 2 due
8 Density of States and Statistical Distributions  
9 Specific Heat and Planck’s Law Homework 3 due
10 Fundamental of Statistical Thermodynamics  
11 Energy Transfer by Waves: Plane Waves Homework 4 due
12 Electromagnetic Waves: Reflection at a Single Interface  
13 EM Wave Propagation Through Thin Films and Multilayers Homework 5 due
14 Wave Phenomena and Landauer Formalism  
  Midterm 1 Homework 6 due
15 Particle Description, Liouville and Boltzmann Equations  
16 Fermi Golden Rule and Relaxation Time Approximation  
17 Solutions to Boltzmann Equation: Diffusion Laws Homework 7 due
18 Electron Transport and Thermoelectric Effects  
19 Classical Size Effects, Parallel Direction Homework 8 due
20 Classical Size Effects, Perpendicular Direction  
21 Slip Condition, Coupled Energy Transport and Conversion Homework 9 due
22 PN junction, Diode and Photovoltaic Cells Take-home midterm 2 out
23 Liquids: Brownian Motion and Forces in Liquids Take-home midterm 2 due in class
24 Electrical Double Layer, Size Effects in Phase Change  
25 Statistical Foundation for Molecular Dynamics Simulation Final project report due

Course Info

As Taught In
Spring 2012
Learning Resource Types
Lecture Videos
Problem Sets
Lecture Notes
Projects with Examples