ECE 663-1, Fall ‘09

Solid State Devices

Avik GhoshElectrical and Computer Engineering

University of VirginiaFall 2010

ECE 663-1, Fall ‘09

Outline

1) Course Information2) Motivation – why study semiconductor

devices?3) Types of material systems4) Classification and geometry of crystals5) Miller Indices

Ref: Ch1, ASF

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 (dincer@virginia.edu)

ECE 663-1, Fall ‘09

Distance Learning Info

Coordinator Rita Kostoff, rfk2u@virginia.edu, 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 dincer@virginia.edu or hand in

class

ECE 663-1, Fall ‘09

Texts

ECE 663-1, Fall ‘09

References

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%

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%

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)

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Midterm1

Midterm2

Final

Where can theelectrons sit?

How are they distributed?

How do they move?

ECE 663-1, Fall ‘09

Why do we need this course?

ECE 663-1, Fall ‘09

Transistor Switches

A voltage-controlled resistor

1947 2003

ECE 663-1, Fall ‘09

Biological incentives

Transistors in Biology:

Ion channels in axons involve Voltage dependent Conductances

Modeled using circuits (Hodgkin-Huxley, ’52)

ECE 663-1, Fall ‘09

Economic Incentives

From Ralph Cavin, NSF-Grantees’ Meeting, Dec 3 2008

ECE 663-1, Fall ‘09

A crisis of epic proportions: Power dissipation !

New physics needed – new kinds of computation

ECE 663-1, Fall ‘08

We stand at a threshold in electronics !!

ECE 663-1, Fall ‘08

How can we pushtechnology forward?

ECE 663-1, Fall ‘08

Better Design/architecture

Multiple Gates for superior field control

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

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

ECE 663-1, Fall ‘08

Where do we stand today?

ECE 663-1, Fall ‘08

“Top Down” … (ECE6163)

Vd20 µm

Vd

2 nm

Solid State Electronics/Mesoscopic Physics

Molecular Electronics

ECE 663-1, Fall ‘08

Top Down fabrication

PhotolithographyTop down architecture

“Al-Khazneh”, Petra, Jordan(6th century BC)

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”)

ECE 663-1, Fall ‘08

“Bottom Up” ... (ECE 687)

Vd20 µm

Vd

2 nm

Solid State Electronics/Mesoscopic Physics

Molecular Electronics

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

ECE 663-1, Fall ‘08

How can we model anddesign today’s devices?

Need rigorous mathematical formalisms

27

ECE 663-1, Fall ‘08

V

I

I = q A n vQuantum 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

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?

ECE 663-1, Fall ‘08

Solids

Metals: Gates, Interconnects

ECE 663-1, Fall ‘08

Solids tend to form ordered crystals

(Rock salt, NaCl)

Natural History Museum, DC

ECE 663-1, Fall ‘09

Describing the periodic lattices

ECE 663-1, Fall ‘08

Bravais Lattices

Each atom has the same environment

Courtesy: Ashraf Alam, Purdue Univ

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!)

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

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)

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)

ECE 663-1, Fall ‘08

Pentagons allowed in 3D

Buckyball/Fullerene/C60

ECE 663-1, Fall ‘08

3D Bravais Lattices

14 types

ECE 663-1, Fall ‘09

Describing the unit cells

ECE 663-1, Fall ‘08

Simple Cubic Structure

Coordination Number (# ofnearest nbs. = ?)

# of atoms/cell = ?

Packing fraction = ?

ECE 663-1, Fall ‘08

Body Centered Cubic (BCC)

Mo, Ta, W

CN = ?

# atoms/lattice = ?

Packing fraction?

ECE 663-1, Fall ‘08

Face Centered Cubic (FCC)

Al,Ag, Au, Pt, Pd, Ni, Cu

CN = ?

#atoms/cell = ?

Packing fraction = ?

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

ECE 663-1, Fall ‘08

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

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

ECE 663-1, Fall ‘08

Hexagonal Lattice

Al2O3, Ti, other metals

Hexagonal

Only other type common in ICs

ECE 663-1, Fall ‘09

XX

X

X

X X

Crystal Packing: FCC vs HCP

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)

ECE 663-1, Fall ‘09

Describing the unit cells

ECE 663-1, Fall ‘08

Simple Cubic Structure

Coordination Number (# ofnearest nbs. = ?)

# of atoms/cell = ?

Packing fraction = ?

ECE 663-1, Fall ‘08

Body Centered Cubic (BCC)

Mo, Ta, W

CN = ?

# atoms/lattice = ?

Packing fraction?

ECE 663-1, Fall ‘08

Face Centered Cubic (FCC)

Al,Ag, Au, Pt, Pd, Ni, Cu

CN = ?

#atoms/cell = ?

Packing fraction = ?

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

ECE 663-1, Fall ‘08

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

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

ECE 663-1, Fall ‘08

Hexagonal Lattice

Al2O3, Ti, other metals

Hexagonal

Only other type common in ICs

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)

ECE 663-1, Fall ‘09

Quantifying lattices:1. Lattice Vectors for directions

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)ab = (0,1,0)ac = (0,0,1)a

Simple cubic lattice

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 )

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)

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

ECE 663-1, Fall ‘09

Quantifying lattices:2. Miller Indices for Planes

ECE 663-1, Fall ‘08

Crystal Planes denoted by Miller Indices h,k,l

Planes in a Crystal

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

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

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

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

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)

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