Introduction to Carrier Transport - - Simulation

Lundstrom ECE-656 F11

ECE-656: Fall 2011

Introductionto

Carrier Transport

Professor Mark LundstromElectrical and Computer Engineering

Purdue University, West Lafayette, IN USAEE-310 / [email protected]

18/21/11

Lundstrom ECE-656 F11 2

copyright 2011

This material is copyrighted by Mark Lundstrom under the following Creative Commons license:

Conditions for using these materials is described at

http://creativecommons.org/licenses/by-nc-sa/3.0/us/


the drift-diffusion equation

p p nJ pq qD pµ= − ∇

E

• Where does the DD equation come from?

• How are B-fields and temperature gradients included?

• How is mobility related to material parameters?

• How are the mobility and diffusion coefficient related?

• When does the DD equation fail? How?

• What do we do then?


course objectives

» To introduce students to the fundamentals of charge carrier transport in semiconductor materials and devices.

» To give students a foundation so that they can learn what they need to when confronted with a new problem.

designed for students interested in building, designing, analyzing, and/or simulating electronic devices.

course outline

5

Course Introduction

Preliminaries 1 weekbandstructure, quantum confinement, density-of-states

Part 1: Near-equilibrium transport: 6 weeksgeneral model, conductance, thermoelectric effectsintro to scattering, Boltzmann Transport Eq. (BTE),measurements

Part 2: Carrier scattering 4 weeksscattering and the BTE, Fermi’s Golden RuleII and phonon scatteringscattering in common semiconductors and graphene

Part 3: Far from equilibrium transport 4 weeksmoments of the BTE, Monte Carlo and quantum transporthot carrier transport in bulk semiconductorstransport in devices


carrier transport in bulk semiconductors

I

V I = GV

“low-field” or “near-equilibrium” or “linear” transport

“high-field” or “hot carrier” transport


near-equilibrium, diffusive transport

uniform n-type semiconductor

Lcross-sectional

area, A

“ideal” contacts

−V +

1) random walk with a small bias from left to right

2) electric field

E x = −

dVdx

= −VL

Fe = −qE x

3) force on an electron

I

4) average velocity:

υd = −µnE x


conductance (resistance)

n-type semiconductor

Lcross-sectional

area, A

“ideal” contacts

−V +

I

υd = −µnE x

I = Q tt

Q = nqAL

tt = L υd

I = nqυd A = −nqµnE x A

I = nqµn

AL

V

G = nqµn

AL= σ n

AL

σ n = nqµn G = σ n

AL


more generally

L

W

A

How do we understand conductance in 1D, 2D, or 3D and from the ballistic to diffusive limits?

How do we understand any small conductor?


thermoelectric effects

The Seebeck effect was discovered in 1821 by Thomas Seebeck. It also occurs between the junction of two dissimilar metals at different temperatures. It is the basis for temperature measurement with thermocouples and for thermoelectric power generation. 10

n-type semiconductor

T1 T2 > T1 ∆V = −S∆T

S is the “Seebeck coefficient” in V/K

S < 0 for n-type conduction

S is also called the “thermopower”

I = 0− +

∆V = ?


hot carrier transport

I

V

“high-field” or “hot carrier” transport

G = σ n A L( )

G = σ n E x( ) A L( )?


semi-classical carrier transport in devices

υSAT

Velo

city

(cm

/s)

D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.

µm( )

µm( )


quantum transport in devices

L = 10 nm, double gate, Si N-MOSFET

nanoMOS (www.nanoHUB.org)

EC x( )

n x,E( )


course prerequisites

» Introductory level understanding of semiconductor physics and devices (ECE 606 at Purdue).

» “Fundamentals of Nanoelectronics” (Datta –Purdue) and a course on solid-state physics (e.g. Phys. 545 at Purdue) are helpful, but not essential.

1) Fundamentals ofCarrier Transport, 2nd Ed.Mark Lundstrom

Cambridge Univ. Press, 2000www.cup.cam.ac.uk/

15

course texts

2) Near-equilibrium Transport:Fundamentals and ApplicationsMark Lundstrom and Changwook JeongWorld Scientific, 2011

(a pre-release draft will be provided to ECE-656 students.


lecture format

• ~50 minute (PowerPoint) lectures. Please interrupt with questions.

• Posted on the course webpage shortly before class.

• Recorded and deployed online soon after.

• Office hours immediately after class.

• Online discussion on the course webpage.


course grading

Homework: 25%assigned and collected, but not gradedsolutions posted(will grade only to decide borderline final grades)

Exam 1: 25% (near-equilibrium transport)

Exam 2: 25% (BTE, B-fields, measurements, scattering)

Final Exam: 25% (comprehensive)

course web page

18https://nanohub.org/groups/ece656


some suggestions

1) Do the reading before class.

2) Review lectures after class.

3) Do the homework!

4) Keep up with the field (TED, EDL, APL, JAP, etc. and local seminars.

5) Ask questions.

6) Monitor the course homepage for announcements, handouts, etc.

19


next steps…

2) Familiarize yourself with the course web site and download HW1

https://nanohub.org/groups/ece656

3) View “Bandstructure Review” (L1 ECE 656 F2009)

1) Send an e-mail to Vicki Johnson ([email protected]) requesting membership in the ECE656 group.You will need to supply your nanoHUB login.


questions

Introduction to Carrier Transport - - Simulation

Documents

Transcript of Introduction to Carrier Transport - - Simulation