Post on 04-Feb-2022
Lundstrom ECE-656 F11
ECE-656: Fall 2011
Introductionto
Carrier Transport
Professor Mark LundstromElectrical and Computer Engineering
Purdue University, West Lafayette, IN USAEE-310 / 765-494-3515lundstro@purdue.edu
18/21/11
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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/
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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?
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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
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carrier transport in bulk semiconductors
I
V I = GV
“low-field” or “near-equilibrium” or “linear” transport
“high-field” or “hot carrier” transport
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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
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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
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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?
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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 = ?
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hot carrier transport
I
V
“high-field” or “hot carrier” transport
G = σ n A L( )
G = σ n E x( ) A L( )?
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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( )
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quantum transport in devices
L = 10 nm, double gate, Si N-MOSFET
nanoMOS (www.nanoHUB.org)
EC x( )
n x,E( )
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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.
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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.
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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
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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
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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 (vicki@ecn.purdue.edu) requesting membership in the ECE656 group.You will need to supply your nanoHUB login.
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questions