Near-Equilibrium Transport: Fundamentals and Applications

By Mark Lundstrom

Electrical and Computer Engineering, Purdue University, West Lafayette, IN



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Engineers and scientists working on electronic materials and devices need a working knowledge of "near-equilibrium" (also called "linear" or "low-field") transport. The term "working knowledge" means understanding how to use theory in practice. Measurements of resistivity, conductivity, mobility, thermoelectric parameters as well as Hall effect measurements are commonly used to characterize electronic materials. Thermoelectric effects are the basis for important devices, and devices like transistors, which operate far from equilibrium, invariably contain low-eld regions (e.g. the source and drain) that can limit device performance. These lectures are an introduction to near-equilibrium carrier transport using a novel, bottom up approach as developed by my colleague, Supriyo Datta. This approach is more rigorous than the Drude approach - and often more physically insightful and less mathematically involved than approaches based on the Boltzmann Transport Equation. It also works for nanoscale as well as for micro and macroscale devices. Using this approach, these lectures will introduce the essential principles of near-equilibrium transport theory needed by scientists and engineers working on electronic materials and devices.

These lectures complement a set of lectures notes published by World Scientific, "Near-Equilibrium Transport: Fundamentals and Applications" which is part of the "Lessons from Nanoscience: A Lecture Note Series."

Sponsored by

"Electronics from the Bottom Up" is an educational initiative designed to bring a new perspective to the field of nano device engineering. It is co-sponsored by the Intel Foundation and the Network for Computational Nanotechnology.

Cite this work

Researchers should cite this work as follows:

  • Mark Lundstrom (2011), "Near-Equilibrium Transport: Fundamentals and Applications,"

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Burton Morgan 121, Purdue University, West Lafayette, IN


  1. low-field mobility
  2. low-field transport
  3. Summer School
  4. bottom up approach
  5. nanoelectronics
  6. nanotransistors
  7. transistors
  8. thermoelectrics
  9. Hall effect
  10. near equilibrium transport
Lecture Number/Topic Online Lecture Video Lecture Notes Supplemental Material Suggested Exercises
Lecture 1: Introduction to Near-equilibrium Transport View HTML
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A short overview of the topics to be discussed in the following nine lectures in this short course on near-equilibrium transport.

Lecture 2: General Model for Transport View HTML
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Datta's model of a nanodevice is introduced as a general way of describing nanodevices as well, as bulk metals and semiconductors.

Lecture 3: Resistance-Ballistic to Diffusive View HTML
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The resistance of a ballistic conductor and concepts, such as the quantum contact resistance, are introduced and discussed. The results are then generalized to treat transport all the way from...

Lecture 4: Thermoelectric Effects-Physical Approach View HTML
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The effect of temperature gradients on current flow and how electrical currents produce heat currents are discussed.

Lecture 5: Thermoelectric Effects - Mathematics View HTML
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Beginning with the general model for transport, we mathematically derive expressions for the four thermoelectric transport coefficients: (i) Electrical conductivity, (ii) Seebeck coefficient...

Lecture 6: An Introduction to Scattering View Flash View Notes (pdf) YouTube
In this lecture, we show how the mean-free-path (mfp) is related to the time between scattering events and briefly discuss how the scattering time is related to underlying physical processes.

Lecture 7: The Boltzmann Transport Equation View Flash View Notes (pdf) YouTube
Semi-classical carrier transport is traditionally described by the Boltzmann Transport Equation (BTE). In this lecture, we present the BTE, show how it is solved, and relate it to the Landauer...

Lecture 8: Measurements View Flash View Notes (pdf) YouTube
A brief introduction to commonly-used techniques, such as van der Pauw and Hall effect measurements.

Lecture 9: Introduction to Phonon Transport View Flash View Notes (pdf) YouTube
This lecture is an introduction to phonon transport. Key similarities and differences between electron and phonon transport are discussed.

Lecture 10: Case study-Near-equilibrium Transport in Graphene View Flash View Notes (pdf) YouTube
Near-equilibrium transport in graphene as an example of how to apply the concepts in lectures 1-8.