Fall 2017  ECE 656: 
Electronic Transport in Semiconductors: 
A Modern Approach

Course Description: This course is about the flow of charge and heat in semiconductors with an emphasis on transport in novel materials and nanoscale devices. The objective is to develop a broad understanding of basic concepts. In 1990, the first edition of Fundamentals of Carrier Transport was written as a text for this course. The second edition was written in 2000, but much has changed since then. Today, in work at the nanoscale, we encounter ballistic, quasi-ballistic, and quantum transport, but just as often, problems involve traditional transport theory, such as diffusion equations, Hall effect, etc.  Those who work on electronic materials and devices need to understand both traditional and modern transport theory and how to apply it in practice. Covering all this ground in one semester without assuming a long string of prerequisites, requires a new approach. Fortunately, research over the past three decades has provided us with a deep understanding of transport at the nanoscale and with simple, clear, elegant approaches that seamlessly connect transport at the nanoscale to transport at the macroscale. This course is a first draft of a third edition of the book with a new title:  Fundamentals of Carrier Transport: A Modern Approach. This course is designed for experimentalists, device physicists, theorists, and computational experts who work on electronic materials and devices. It is accessible to students with a general, introductory background in semiconductors and addresses the fundamentals of electrothermal transport that every materials and device researcher should understand and be able to apply.

The course consists of three five-week modules:

Part 1 reviews advanced semiconductor fundamentals and addresses new topics such as electron and phonon scattering.

Part 2 examines near-equilibrium transport of electrons and phonons in the presence of small gradients in the electrochemical (quasi-Fermi) potential and/or temperature. The influence of magnetic fields is also discussed. Commonly used characterization methodologies, such as Hall effect measurements, are described. The Landauer approach is used to describe transport from the ballistic to diffusive limits and is related to the traditional Boltzmann Transport Equation approach.

Part 3 focuses on far from equilibrium transport. High-field transport in bulk semiconductors is discussed as are so-called “non-local” transport effects that lead to “velocity overshoot” in nanoscale devices. A gentle introduction to the Non-equilibrium Green’s Function (NEGF) approach to dissipative quantum transport is also presented.  Sophisticated numerical simulations are used to illustrate the effects discussed in this part. Some understanding of the numerical methods is necessary, but our goal is not to learn how to write simulation programs; it is to understand how the simulations work, so that we know when a simulation should be used and how to interpret the results.

ECE 656 Fall 2017:  Course information

Instructor:    M.S.  Lundstrom (lundstro at purdue.edu)

Class meetings:    Tues, Thurs. 10:30 – 11:45 PM       EE-115

Office Hours:    MWF, 11:00-12:00 noon, Wang Hall 3055
                           (or make an appointment for a different time by e-mail.)

In addition to office hours, students are encouraged to make use of the discussion forum.

Discussion Forum: piazza.com/purdue/fall2017/ece656/home

Prerequisites: 
                   ECE 606 or equivalent (basic introduction to
                   semiconductor materials and devices, solid-state
                   physics, and quantum mechanics).  Or consent of
                   instructor.

Texts:
                  Near-equilibrium Transport:  Fundamentals and Applications
                  (NET) Mark Lundstrom, World Scientific (2012). (a draft copy of
                  this text will be distributed to 656 students)
                  Near-Equilibrium Transport Errata

                   Fundamentals of Carrier Transport, 2nd Edition (FCT)
                   Mark Lundstrom, Cambridge University Press (2000)
                   ISBN-13: 9780521637244 (paperback)
                   Fundamentals of Carrier Transport Errata (460 KB)
                   Fundamentals of Carrier Transport HW Solutions (14 MB)

                   Handouts and class notes will also be distributed from time to time.

This course homepage provides complete information about the course and will be used for posting weekly reading assignments, homework assignments and solutions, supplemental material, announcements, etc.).

Complete course information (including grading policies, etc.)

On-line lectures that may be helpful:

    For a review of semiconductor physics and devices, see ECE 606

    For a deeper discussion of some of the fundamentals only touched on in this course, see:
    ECE 50653 Fall 2017:  Fundmentals of Nanoelectronics (Datta)

    For lectures from previous ECE-656 classes, see:
    ECE 656 Fall 2015 
    ECE 656 Fall 2011
    ECE 656 Fall 2009

 

Part 1: Advanced Semiconductor Fundamentals

Week 1: August 21, 2017  Review of Fundamentals

Reading Assignment: FCT 1.1-1.6, 1.8 / NET 1.1-1.6, 9.1, 9.2
 

Week 1: In Class Lectures
Lecture 0: Course Introduction
Lecture 1: Electron and Phonon Dispersion
Lecture 2: Semiclassical Transport
Lecture 3: Heterostructure Fundamentals
Lecture 4: Quantum Confinement
 

Week 1 Quiz (280 KB)
Week 1 Quiz Answers

Week 1 HW Assignment (416 KB)
Week 1 HW Solutions

Week 1: References and Supplementary Information

Week 1 References (revised 1/24/18)

Notes on FD Integrals (214 KB)
Heterostructure Fundamentals (3 MB)
Notes on Effective Masses (revised 1/24/18)
Notes on Thermal Velocities (revised 1/24/18)
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Week 2: August 28, 2017: Introduction to Carrier Scattering

Reading Assignment: FCT 1.7, 2.1-2.3, 5.2 / NET 6.2

Week 2: In Class Lectures
Lecture 5: Density of States
Lecture 6: Sums and Integrals  
Lecture 7: Characteristic Scattering Times
Lecture 8: Fermi's Golden Rule
 

Week 2 Quiz
Week 2 Quiz Answers
 

Week 2 HW Assignment

Week 2 HW Solutions

Week 2: References and Supplementary Information

Week 2 References (revised 1/24/18)

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Week 3: September 4, 2017: II and ADP Phonon Scattering

Reading Assignment: FCT 2.4

Week 3: In Class Lectures

Lecture 9:   II Scattering (Brooks-Herring)
Lecture 10: II Scattering (Conwell-Weisskopf)
Lecture 11: II Scattering (Wrap-up)
Lecture 12: ADP Phonon Scattering

 

Week 3 Quiz
Week 3 Quiz Answers

Week 3 HW Assignment
Week 3 HW Solutions

 

Week 3: References and Supplementary Information

Week 3 References

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Week 4: September 11, 2017: Electron-Phonon and Phonon-phonon Scattering

Reading Assignment: FCT 2.5-2.14 and phonon-phonon scattering handout

Lecture 13: ODP Phonon Scattering
Lecture 14: Phonon Scattering in Polar Semiconductors
Lecture 15: Intervalley Phonon Scattering
Lecture 16: Electron-Phonon Scattering in 1D, 2D, and 3D
Lecture 17: Electron-Electron Scattering
Lecture 18: Electron Scattering in Common Semiconductors
Lecture 19: Phonon Scattering

Week 4 Quiz
Week 4 Quiz Answers

Week 4 HW Assignment
Week 4 HW Solutions

Week 4: References and Supplementary Information

Week 4 References (revised 1/24/18)

Notes on Scattering and Mobility in 1D, 2D, and 3D
Low Bias Transport in Graphene: An Introduction
(see Sec.. 6 on electron scattering in graphene)
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Week 5: September 18, 2017: Introduction to the BTE

Reading Assignment: FCT 3.1-3.4 / NET 7.1-7.4

Lecture 20: The BTE (revised 10/2/17)
Lecture 21: The Collision Integral (revised 10/2/17)
Lecture 22: Solving the BTE: Semiconductors (revised 10/5/17)
Lecture 23: Solving the BTE: Metals

Week 5 Quiz

No HW Assignment this week

Week 5: References and Supplementary Information

Week 5 References (revised 1/24/18)

Online Lecture: The Boltzmann Transport Equation (Fall 2011)
Online Lecture: The BTE: Transport Coefficients (Fall 2011)

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EXAM 1 - September 21, 2017
Goals for Exam 1
Key Equations for Exam 1

Exam 1
Exam1 1 Solutions (revised 10/12/17)

Quiz 1
Quiz 1 Answers
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Part 2:  Near-Equilibrium Transport of Electrons and Phonons

Week 6: September 25, 2017: The Landauer Approach to Electron Transport

Reading Assignment: FCT 9.9-9.11 / NET 2.1-2.7, 3.1-3.5

Lecture 24: The Landauer Approach
Lecture 25: Channels (revised 10/7/17)
Lecture 26: Transmission
Lecture 27: Fermi Window and Current (revised 10/7/17)
Lecture 28:  Resistors at T = 0 K (revised 9/29/17)
Lecture 29: 1D Resistors at T > 0 K
Lecture 30: Applications of the Landauer Approach
Lecture 31: Landauer vs. BTE

Week 6 Quiz (revised 9/30/17)
Week 6 Quiz Answers

Week 6 HW Assignment (revised 9/30/17)
Week 6 HW Solutions

Week 6: References and Supplementary Information

Week 6 References (revised 1/24/18)

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Week 7: October 2, 2017: Near-Equilibrium Transport in the Presence of B-fields

Reading Assignment: NET 3.1-3.5, 7.5, 8.6

Lecture 32: The BTE with a B-field
Lecture 33: Transport in a B-Field: A simple approach
Lecture 34: Hall Effect
Lecture 35: High Magnetic Fields

Week 7 Quiz
Week 7 Quiz Answers (revised 11/9/17)

Week 7 HW Assignment
Week 7 Solutions (revised 11/1/17)

Week 7: References and Supplementary Information

Week 7 References (revised 1/24/18)

Notes on Scattering Times and Hall Factors (revised 1/22/18)

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Week 8: October 9, 2017: Application of Landauer Approach to Phonons

Reading Assignment: NET 9.3-9.5, 9.7, 9.8

Lecture 36: A Landauer Approach to Phonon Transport (revised 10/18/17)

Week 8 Quiz
Week 8 Quiz Answers

Week 8 HW Assignment
Week 8 HW Solutions

Week 8: References and Supplementary Information

Week 8 References (revised 1/24/18)

Online lecture: Phonon Transport (Fall 2011)

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Week 9: October 16, 2017: Thermoelectric Transport

Reading Assignment:  NET 4.1-4.7, 5.1-5.6

Lecture 37: Introduction to Thermoelectricity
Lecture 38: Charge Current
Lecture 39: Heat Current
Lecture 40: Coupled Current Equations
Lecture 41: Thermoelectric Devices (revised 10/31/17)

Week 9 Quiz
Week 9 Quiz Answers

Week 9 HW Assignment
Week 9 HW Solutions

Week 9: References and Supplementary Information

Week 9 References (revised 1/24/18)

Notes on the Wiedemann Franz Law
Notes on bipolar thermal conductivity

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Week 10: October 23, 2017: Experimental Characterization

Reading Assignment: NET 8.1-8.7 / FCT 4.7-4.9

Lecture 42: Electrical Characterization of Materials: I
Lecture 43: Electrical Characterization of Materials: II

Week 10 Quiz
Week 10 Quiz Answers

Week 10 HW Assignment
Week 10 HW Solutions

Week 10: References and Supplementary Information

Week 10 References

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EXAM 2: November 2, 2017
Goals for Exam 2
Key Equations for Exam 2 (revised 10/28/17)

Exam 2
Exam 2 Solutions

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Week 11: October 30, 2017: The BTE Revisited

Reading Assignment: FCT 3.1-3.5, 4.1-4.6 / NET 7.1-7.7

Lecture 44: The BTE Revisited (revised 11/8/17)

Week 11 Quiz
Week 11 Quiz Answers

Week 11 HW Assignment
Week 11 HW Solutions

Week 11: References and Supplementary Information

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Part 3:  Far-from-equilibrium Transport in Materials and Devices

Week 12: November 6, 2017: Balance Equations

Reading Assignment: FCT 5.1-5.3.2 and 5.7

Lecture 45: The Moment Equation Approach (revised 11/7/17)
Lecture 46: The First Four Moment Equations
Lecture 47: The Drift-diffusion Equation
Lecture 48: The Coupled Current Equations (again)

Week 12 Quiz (revised 11/10/17)
Week 12 Quiz Answers

Week 12 HW Assignment
Week 12 HW Solutions

Week 12: References and Supplementary Information

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Week 13: November 13/20, 2017: Hot Carrier Transport Simulation

Reading Assignment: FCT 5.3.3, 5.4, 5.5, 6.1-6.9, 7.1-7.7

Week 13 Quiz
Week 13 Quiz Answers

Lecture 49: The Energy Transport Equations
Lecture 50: Monte Carlo Simulation (revised 11/21/17)

Week 13: References and Supplementary Information

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Week 14: November 27, 2017: Transport in the bulk and in Devices

Reading Assignment: FCT 8.1-8.10

Lecture 51: Hot Carrier Transport in the Bulk
Lecture 52: Non-local Carrier Transport in Devices (revised 12/4/17)

Week 14 Quiz
Week 14 Quiz Answers

Week 14 HW Assignment
Week 14 HW Solutions

Week 14: References and Supplementary Information

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Week 15: December 4, 2017: Ballistic and Quantum Transport in Devices

Reading Assignment: FCT 9.7, 9.8, 9.11

 

Lecture 53:  Transport in Devices: Ballistic BTE

Week 15 Quiz (revised 12/11/17)
Week 15 Quiz Answers

Week 15 HW Assignment
Week 15 HW Solution

Week 15: References and Supplementary Information

Online Lecture:  Introduction to Quantum Transport (Fall 2011)

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Finals Week
Exam 3: Tuesday, Dec. 12, 3:30 - 5:30 PM in EE-115

Goals for Exam 3
Exam 3
Exam 3 Solutions

Key Equations for Exam 3 (revised Dec. 8, 2017)

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