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![Page 1: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/1.jpg)
ECE 663-1, Fall ‘09
Solid State Devices
Avik GhoshElectrical and Computer Engineering
University of VirginiaFall 2010
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ECE 663-1, Fall ‘09
Outline
1) Course Information
2) Motivation – why study semiconductor devices?
3) Types of material systems
4) Classification and geometry of crystals
5) Miller Indices
Ref: Ch1, ASF
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ECE 663-1, Fall ‘09
Course information
Books Advanced Semiconductor Fundamentals (Pierret)
Semiconductor Device Fundamentals (Pierret)
Course Website:http://people.virginia.edu/~ag7rq/663/Fall10/courseweb.html
Grader: Dincer Unluer ([email protected])
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ECE 663-1, Fall ‘09
Distance Learning Info
Coordinator Rita Kostoff, [email protected],
Phone: 434-924-4051.
CGEP/Collab Websites: https://collab.itc.virginia.edu/portal
http://cgep.virginia.edu (UVa) http://cgep.virginia.gov (Off-site) http://ipvcr.scps.virginia.edu (Streaming
Video)
Notes: 1. Please press buzzer before asking questions in class2. Email HW PDFs to [email protected] or hand in
class
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ECE 663-1, Fall ‘09
Texts
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ECE 663-1, Fall ‘09
References
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ECE 663-1, Fall ‘09
Grading info
Homeworks Wednesdays
25%
1st midterm M, Oct 05 15%
2nd midterm W, Nov 04 25%
Finals S, Dec 12 35%
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ECE 663-1, Fall ‘08
Grading Info
• Homework - weekly assignments on website, no late homework accepted but lowest score dropped
• Exams - three exams
• Mathcad, Matlab, etc. necessary for some HWs/exams
• Grade weighting:– Exam 1 ~20%– Exam 2 ~30%– Final ~30%– Homework ~20%
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ECE 663-1, Fall ‘10
ECE 663 Class Topics
• Crystals and Semiconductor Materials• Introduction to Quantum Mechanics (QM101)• Application to Semiconductor Crystals – Energy Bands• Carriers and Statistics• Recombination-Generation Processes• Carrier Transport Mechanisms
• P-N Junctions• Non-Ideal Diodes• Metal-Semiconductor Contacts – Schottky Diodes• Bipolar Junction Transistors (BJT)• MOSFET Operation• MOSFET Scaling• Photonic Devices (photodetectors, LEDs, lasers)
Sem
icon
du
ctors
Basi
c D
evic
es
Soft
Cover
Hard
Cover
Midterm1
Midterm2
Final
Where can theelectrons sit?
How are they distributed?
How do they move?
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ECE 663-1, Fall ‘09
Why do we need this course?
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ECE 663-1, Fall ‘09
Transistor Switches
A voltage-controlled resistor
1947 2003
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ECE 663-1, Fall ‘09
Biological incentives
Transistors in Biology:
Ion channels in axons involve Voltage dependent Conductances
Modeled using circuits (Hodgkin-Huxley, ’52)
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ECE 663-1, Fall ‘09
Economic Incentives
From Ralph Cavin, NSF-Grantees’ Meeting, Dec 3 2008
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ECE 663-1, Fall ‘09
A crisis of epic proportions: Power dissipation !
New physics needed – new kinds of computation
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ECE 663-1, Fall ‘08
We stand at a threshold in electronics !!
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ECE 663-1, Fall ‘08
How can we pushtechnology forward?
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ECE 663-1, Fall ‘08
Better Design/architecture
Multiple Gates for superior field control
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ECE 663-1, Fall ‘08
Better Materials?
Strained Si, SiGe
Bottom Gate
Source DrainTop Gate
Channel
Carbon Nanotubes
VG VD
INSULATOR
I
Silicon Nanowires Organic Molecules
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ECE 663-1, Fall ‘08
New Principles?
SPINTRONICS
Encode bits in electron’s Spin -- Computation by rotating spins
GMR (Nobel, 2007)MRAMsSTT-RAMs
QUANTUM CELLULARAUTOMATA
Encode bits in quantum dot dipoles
BIO-INSPIRED COMPUTING
Exploit 3-D architecture andmassive parallelism
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ECE 663-1, Fall ‘08
Where do we stand today?
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ECE 663-1, Fall ‘08
“Top Down” … (ECE6163)
Vd20 µm
Vd
2 nm
Solid State Electronics/Mesoscopic Physics
Molecular Electronics
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ECE 663-1, Fall ‘08
Top Down fabrication
PhotolithographyTop down architecture
“Al-Khazneh”, Petra, Jordan(6th century BC)
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ECE 663-1, Fall ‘08
Modeling device electronics
Bulk Solid (“macro”)(ClassicalDrift-Diffusion)
~ 1023 atoms
Bottom Gate
Source
Channel
Drain
Clusters (“meso”)
(SemiclassicalBoltzmannTransport)
80s ~ 106 atoms
Molecules (“nano”)(Quantum Transport)
Today ~ 10-100 atoms
ECE 663(“Traditional Engg”)
ECE 687(“Nano Engg”)
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ECE 663-1, Fall ‘08
“Bottom Up” ... (ECE 687)
Vd20 µm
Vd
2 nm
Solid State Electronics/Mesoscopic Physics
Molecular Electronics
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ECE 663-1, Fall ‘08
Bottom Up fabrication
Build pyramidal quantum dots from InAs atoms (Gerhard Klimeck, Purdue)
Bottom up architectureChepren Pyramid, Giza (2530
BC) ECE 587/687 (Spring)
Full quantum theory of nanodevices
• Carbon nanotubes, Graphene• Atomic wires, nanowires,• Point contacts, quantum dots, • thermoelectrics,• molecular electronics• Single electron Transistors (SETs)• Spintronics
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ECE 663-1, Fall ‘08
How can we model anddesign today’s devices?
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Need rigorous mathematical formalisms
27
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ECE 663-1, Fall ‘08
V
I
I = q A n v
Quantum mech + stat mech Effective mass, Occupation factors
(Ch 1-4, Pierret)
Nonequilibrium stat mech (transport) Drift-diffusion with Generation/
Recombination (Ch 5-6, Pierret)
Calculating current in semiconductors
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ECE 663-1, Fall ‘08
Calculating Electrons and Velocity
• What are atoms made of? (Si, Ga, As, ..)
• How are they arranged? (crystal structure)
• How can we quantify crystal structures?
• Where are electronic energy levels?
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ECE 663-1, Fall ‘08
Solids
Metals: Gates, Interconnects
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ECE 663-1, Fall ‘08
Solids tend to form ordered crystals
(Rock salt, NaCl)
Natural History Museum, DC
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ECE 663-1, Fall ‘09
Describing the periodic lattices
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ECE 663-1, Fall ‘08
Bravais Lattices
Each atom has the same environment
Courtesy: Ashraf Alam, Purdue Univ
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ECE 663-1, Fall ‘08
2D Bravais Lattices
Courtesy: Ashraf Alam, Purdue Univ
Only angles 2/n, n=1,2,3,4,6(Pentagons not allowed!)
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ECE 663-1, Fall ‘08
2D non-Bravais Lattice – e.g. Graphene
Epitaxial growth by vapor deposition of CO/hydroC on metals (Rutter et al, NIST)
Chemical Exfoliation of HOPG
on SiO2 (Kim/Avouris)
Missing atom not all atoms have the same environment
Can reduce to Bravais latticewith a basis
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ECE 663-1, Fall ‘08
Irreducible Non-Bravais Lattices
MC Escher
Early Islamic art Penrose Tilings
“Quasi-periodic”(Lower-D Projections of Higher-D periodicsystems)
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ECE 663-1, Fall ‘08
MoAl6 FeAl6(Pauling, PRL ’87)
Not just on paper...
5-fold diffraction patterns
Pentagons !(5-fold symmetry notpossible in a perfect Xal)
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ECE 663-1, Fall ‘08
Pentagons allowed in 3D
Buckyball/Fullerene/C60
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ECE 663-1, Fall ‘08
3D Bravais Lattices
14 types
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ECE 663-1, Fall ‘09
Describing the unit cells
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ECE 663-1, Fall ‘08
Simple Cubic Structure
Coordination Number (# ofnearest nbs. = ?)
# of atoms/cell = ?
Packing fraction = ?
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ECE 663-1, Fall ‘08
Body Centered Cubic (BCC)
Mo, Ta, W
CN = ?
# atoms/lattice = ?
Packing fraction?
![Page 43: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/43.jpg)
ECE 663-1, Fall ‘08
Face Centered Cubic (FCC)
Al,Ag, Au, Pt, Pd, Ni, Cu
CN = ?
#atoms/cell = ?
Packing fraction = ?
![Page 44: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/44.jpg)
ECE 663-1, Fall ‘08
Diamond Lattice
C, Si, Ge
a=5.43Å for Si
CN = ?
Packing fraction = ?
Two FCC offsetby a/4 in eachdirection or
FCC lattice with 2 atoms/site
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ECE 663-1, Fall ‘08
![Page 46: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/46.jpg)
ECE 663-1, Fall ‘08
http://jas.eng.buffalo.edu/education/solid/unitCell/home.html
Web Sites That may be helpful
http://jas.eng.buffalo.edu/education/solid/genUnitCell
![Page 47: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/47.jpg)
ECE 663-1, Fall ‘08
Zincblende Structure
III-V semiconductors
GaAs, InP, InGaAs,InGaAsP,……..
For GaAs:
Each Ga surroundedBy 4 As, Each AsSurrounded by 4 Ga
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ECE 663-1, Fall ‘08
Hexagonal Lattice
Al2O3, Ti, other metals
Hexagonal
Only other type common in ICs
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ECE 663-1, Fall ‘09
XX
X
X
X X
Crystal Packing: FCC vs HCP
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ECE 663-1, Fall ‘08
Semiconductors: 4 valence electrons
• Group IV elements: Si, Ge, C
• Compound Semiconductors : III-V (GaAs, InP, AlAs)II-VI (ZnSe, CdS)
• Tertiary (InGaAs,AlGaAs)
• Quaternary (InGaAsP)
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ECE 663-1, Fall ‘09
Describing the unit cells
![Page 52: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/52.jpg)
ECE 663-1, Fall ‘08
Simple Cubic Structure
Coordination Number (# ofnearest nbs. = ?)
# of atoms/cell = ?
Packing fraction = ?
![Page 53: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/53.jpg)
ECE 663-1, Fall ‘08
Body Centered Cubic (BCC)
Mo, Ta, W
CN = ?
# atoms/lattice = ?
Packing fraction?
![Page 54: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/54.jpg)
ECE 663-1, Fall ‘08
Face Centered Cubic (FCC)
Al,Ag, Au, Pt, Pd, Ni, Cu
CN = ?
#atoms/cell = ?
Packing fraction = ?
![Page 55: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/55.jpg)
ECE 663-1, Fall ‘08
Diamond Lattice
C, Si, Ge
a=5.43Å for Si
CN = ?
Packing fraction = ?
Two FCC offsetby a/4 in eachdirection or
FCC lattice with 2 atoms/site
![Page 56: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/56.jpg)
ECE 663-1, Fall ‘08
![Page 57: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/57.jpg)
ECE 663-1, Fall ‘08
http://jas.eng.buffalo.edu/education/solid/unitCell/home.html
Web Sites That may be helpful
http://jas.eng.buffalo.edu/education/solid/genUnitCell
![Page 58: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/58.jpg)
ECE 663-1, Fall ‘08
Zincblende Structure
III-V semiconductors
GaAs, InP, InGaAs,InGaAsP,……..
For GaAs:
Each Ga surroundedBy 4 As, Each AsSurrounded by 4 Ga
![Page 59: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/59.jpg)
ECE 663-1, Fall ‘08
Hexagonal Lattice
Al2O3, Ti, other metals
Hexagonal
Only other type common in ICs
![Page 60: ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649d205503460f949f4114/html5/thumbnails/60.jpg)
ECE 663-1, Fall ‘08
Semiconductors: 4 valence electrons
• Group IV elements: Si, Ge, C
• Compound Semiconductors : III-V (GaAs, InP, AlAs)II-VI (ZnSe, CdS)
• Tertiary (InGaAs,AlGaAs)
• Quaternary (InGaAsP)
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ECE 663-1, Fall ‘09
Quantifying lattices:1. Lattice Vectors for directions
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ECE 663-1, Fall ‘08
Lattice Vectors
Three primitive vectors are ‘coordinates’ in terms of which all lattice coordinates R can be expressed
R = ma + nb + pc (m,n,p: integers)
a = (1,0,0)a
b = (0,1,0)a
c = (0,0,1)a
Simple cubic lattice
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ECE 663-1, Fall ‘08
Body-centered cube
8x1/8 corner atom + 1 center atom gives 2 atoms per cell
a = a(½, ½, ½ )
b = a(-½,-½, ½ )
c = a(½,-½,-½ )
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ECE 663-1, Fall ‘08
Face-centered cube
6 face center atoms shared by 2 cubes each, 8 cornersshared by 8 cubes each, giving a total of 8 x 1/8 + 6 x 1/2 = 4 atoms/cell
a = a(0, ½, ½)
b = a(½, 0, ½)
c = a(½, ½, 0)
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ECE 663-1, Fall ‘08
Directions in a Crystal: Example-simple cubic
• Directions expressed as combinations of basis vectors a,b,c
• Body diagonal=[111][ ] denotes specific direction
• Equivalent directions use < >[100],[010],[001]=<100>These three directions areCrystallographically equivalent
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ECE 663-1, Fall ‘09
Quantifying lattices:2. Miller Indices for Planes
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ECE 663-1, Fall ‘08
Crystal Planes denoted by Miller Indices h,k,l
Planes in a Crystal
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ECE 663-1, Fall ‘08
1. Determine where plane (or // plane) intersects axes:
a intersect is 2 units b intersect is 2 unitsc intersect is infinity (is // to c axis)
2. Take reciprocals of intersects in order(1/2, 1/2, 1 / infinity) = (1/2, 1/2, 0)
3. Multiply by smallest number to make all integers
2 * (1/2, 1/2, 0) = " (1, 1, 0) plane"
a
bc
Miller indices of a plane
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ECE 663-1, Fall ‘08
• Equivalent planes denoted by {}{100}=(100), (010), (001)
• For Cubic structures:[h,k,l] (h,k,l)
Some prominent planes
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ECE 663-1, Fall ‘08
Why bother naming planes?
Fabrication motivations
• Certain planes cleave easier• Wafers grown and notched on specific planes• Pattern alignment
Chemical/Material Motivations
• Density of electrons different on planes• Reconstruction causes different environments• Defect densities, chemical bonding depend on orientation
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ECE 663-1, Fall ‘08
Si(100) 2x1reconstruction
Reconstruction of surfaces
• Environments, bonding, defect densities, surface bandstructures different• Important as devices scale and surfaces become important
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ECE 663-1, Fall ‘08
Summary
• Current depends on charge (n) and velocity (v)This requires knowing chemical composition and
atomic arrangement of atoms
• Many combinations of materials form semiconductors. Frequently they have tetragonal coordination and form Bravais lattices with a basis (Si, Ge, III-V, II-VI...)
• Crystals consist of repeating blocks. The symmetry helps simplify the quantum mechanical problem of where the electronic energy levels are (Chs. 2-3)
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ECE 663-1, Fall ‘08
Things we learned today
• Bravais Lattices
• Unit cells: Coordination no. No. of atoms/cell Nearest neighbor distances
• Lattice vectors and Miller Indices