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

### Overview

**Fall 2017 ECE 656: **

Electronic Transport in Semiconductors:

**A Modern Approach**

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)

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)

____________________________________________________________________________________________________________________________________________________________

### 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: References and Supplementary Information**

Week 2 References (revised 1/24/18)

____________________________________________________________________________________________________________________________________________________________

### 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 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)

____________________________________________________________________________________________________________________________________________________________

### 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

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)

____________________________________________________________________________________________________________________________________________________________

**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

__________________________________________________________________________________________________________________________________________________________

## 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)

### 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)

### 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)

____________________________________________________________________________________________________________________________________________________________### 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

### 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**

**EXAM 2: November 2, 2017**

Goals for Exam 2

Key Equations for Exam 2 (revised 10/28/17)

Exam 2

Exam 2 Solutions

## 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**

# 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**

### 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**

### 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**

### 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)

___________________________________________________________________________________________________________________________________________________________

### 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)

___________________________________________________________________________________________________________________________________________________________

## Course Announcements

Welcome to ECE 656 Fall 2017, Purdue University. All course materials and announcements will be available here. **Check this page frequently**.

**12/19:** Solution to Extra credit problem

**11/30:** Extra credit available if you solve this problem and turn in your solution by 5:00 PM 12/8

**11/28: Information about wrapping up the course**

**11/10: **Instructions for the **mini-project** can be found here. Your report is due by 5:00 PM on the last day of class, Friday, Dec. 8, 2017.

**11/3: Exam 2 has been graded. Ave. = 75, Max = 93, Min = 46
Quiz 2 will take place in class on Thursday, Nov. 9
Exam 2 Retake will take place in class on Tuesday, Nov. 14**

**11/2: Final Exam date and time have been set. **Tuesday, Dec. 12, 3:30 -5:30 PM in EE-115.

**10/31: Exam 2: Thursday, Nov. 2 2017 10:30 AM in EE-115**

**Class participation:** Send me a few sentence description of the content item - what it is about and why it is relevant to 656. If I approve, I will ask you to post it on Piazza, and you will receive 25 points towards your total course score.