Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010

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

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)

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: Please press buzzer before asking questions in class Email HW PDFs to dincer@virginia.edu or hand in class

Texts

References

Grading info Homeworks Wednesdays 25% 1st midterm M, Oct 05 15% 2nd midterm W, Nov 04 Finals S, Dec 12 35%

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 Class Topics Crystals and Semiconductor Materials Where can the electrons sit? 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) Soft Cover How are they distributed? Semiconductors How do they move? Midterm1 Hard Cover Basic Devices Midterm2 Final

Why do we need this course?

Transistor Switches 1947 2003 A voltage-controlled resistor

Biological incentives Transistors in Biology: Ion channels in axons involve Voltage dependent Conductances Modeled using circuits (Hodgkin-Huxley, ’52)

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

A crisis of epic proportions: Power dissipation ! New physics needed – new kinds of computation

We stand at a threshold in electronics !!

How can we push technology forward?

Better Design/architecture Multiple Gates for superior field control

Better Materials? I Strained Si, SiGe Carbon Nanotubes Bottom Gate Source Drain Top Gate Channel Carbon Nanotubes VG VD INSULATOR I Silicon Nanowires Organic Molecules

New Principles? SPINTRONICS Encode bits in electron’s Spin -- Computation by rotating spins GMR (Nobel, 2007) MRAMs STT-RAMs QUANTUM CELLULAR AUTOMATA Encode bits in quantum dot dipoles BIO-INSPIRED COMPUTING Exploit 3-D architecture and massive parallelism

Where do we stand today?

“Top Down” … (ECE6163) Molecular Electronics Solid State Electronics/ Mesoscopic Physics Molecular Electronics Vd 20 µm Vd 2 nm

“Al-Khazneh”, Petra, Jordan Top Down fabrication Photolithography Top down architecture “Al-Khazneh”, Petra, Jordan (6th century BC)

Modeling device electronics Bulk Solid (“macro”) (Classical Drift-Diffusion) ~ 1023 atoms Bottom Gate Source Channel Drain ECE 663 (“Traditional Engg”) Clusters (“meso”) (Semiclassical Boltzmann Transport) 80s ~ 106 atoms Molecules (“nano”) (Quantum Transport) Today ~ 10-100 atoms ECE 687 (“Nano Engg”)

“Bottom Up” ... (ECE 687) Molecular Electronics Solid State Electronics/ Mesoscopic Physics Molecular Electronics Vd 20 µm Vd 2 nm

Bottom Up fabrication Build pyramidal quantum dots from InAs atoms Bottom up architecture Chepren Pyramid, Giza (2530 BC) Build pyramidal quantum dots from InAs atoms (Gerhard Klimeck, Purdue) 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

How can we model and design today’s devices?

Need rigorous mathematical formalisms

Calculating current in semiconductors V Nonequilibrium stat mech (transport) Drift-diffusion with Generation/ Recombination (Ch 5-6, Pierret) I = q A n v Quantum mech + stat mech Effective mass, Occupation factors (Ch 1-4, Pierret)

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?

Solids Metals: Gates, Interconnects

Solids tend to form ordered crystals Natural History Museum, DC (Rock salt, NaCl)

Describing the periodic lattices

Bravais Lattices Each atom has the same environment Courtesy: Ashraf Alam, Purdue Univ Each atom has the same environment

2D Bravais Lattices Only angles 2p/n, n=1,2,3,4,6 Courtesy: Ashraf Alam, Purdue Univ Only angles 2p/n, n=1,2,3,4,6 (Pentagons not allowed!)

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 lattice with a basis

Irreducible Non-Bravais Lattices MC Escher “Quasi-periodic” (Lower-D Projections of Higher-D periodic systems) Early Islamic art Penrose Tilings

Not just on paper... Pentagons ! (5-fold symmetry not 5-fold diffraction patterns Pentagons ! (5-fold symmetry not possible in a perfect Xal) MoAl6 FeAl6 (Pauling, PRL ’87)

Pentagons allowed in 3D Buckyball/Fullerene/C60

3D Bravais Lattices 14 types

Describing the unit cells

Simple Cubic Structure Coordination Number (# of nearest nbs. = ?) # of atoms/cell = ? Packing fraction = ?

Body Centered Cubic (BCC) Mo, Ta, W CN = ? # atoms/lattice = ? Packing fraction?

Face Centered Cubic (FCC) Al,Ag, Au, Pt, Pd, Ni, Cu CN = ? #atoms/cell = ? Packing fraction = ?

Diamond Lattice C, Si, Ge a=5.43Å for Si CN = ? Packing fraction = ? Two FCC offset by a/4 in each direction or FCC lattice with 2 atoms/site

Web Sites That may be helpful http://jas.eng.buffalo.edu/education/solid/unitCell/home.html http://jas.eng.buffalo.edu/education/solid/genUnitCell

Zincblende Structure III-V semiconductors GaAs, InP, InGaAs, InGaAsP,…….. For GaAs: Each Ga surrounded By 4 As, Each As Surrounded by 4 Ga

Only other type common in ICs Hexagonal Lattice Al2O3, Ti, other metals Hexagonal

Crystal Packing: FCC vs HCP X X

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)

Describing the unit cells

Simple Cubic Structure Coordination Number (# of nearest nbs. = ?) # of atoms/cell = ? Packing fraction = ?

Body Centered Cubic (BCC) Mo, Ta, W CN = ? # atoms/lattice = ? Packing fraction?

Face Centered Cubic (FCC) Al,Ag, Au, Pt, Pd, Ni, Cu CN = ? #atoms/cell = ? Packing fraction = ?

Diamond Lattice C, Si, Ge a=5.43Å for Si CN = ? Packing fraction = ? Two FCC offset by a/4 in each direction or FCC lattice with 2 atoms/site

Web Sites That may be helpful http://jas.eng.buffalo.edu/education/solid/unitCell/home.html http://jas.eng.buffalo.edu/education/solid/genUnitCell

Zincblende Structure III-V semiconductors GaAs, InP, InGaAs, InGaAsP,…….. For GaAs: Each Ga surrounded By 4 As, Each As Surrounded by 4 Ga

Only other type common in ICs Hexagonal Lattice Al2O3, Ti, other metals Hexagonal

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)

Quantifying lattices: 1. Lattice Vectors for directions

Lattice Vectors a = (1,0,0)a b = (0,1,0)a c = (0,0,1)a Simple cubic lattice Three primitive vectors are ‘coordinates’ in terms of which all lattice coordinates R can be expressed R = ma + nb + pc (m,n,p: integers)

Body-centered cube a = a(½, ½, ½ ) b = a(-½,-½, ½ ) c = a(½,-½,-½ ) 8x1/8 corner atom + 1 center atom gives 2 atoms per cell

Face-centered cube a = a(0, ½, ½) b = a(½, 0, ½) c = a(½, ½, 0) 6 face center atoms shared by 2 cubes each, 8 corners shared by 8 cubes each, giving a total of 8 x 1/8 + 6 x 1/2 = 4 atoms/cell

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 are Crystallographically equivalent

Quantifying lattices: 2. Miller Indices for Planes

Planes in a Crystal Crystal Planes denoted by Miller Indices h,k,l

Miller indices of a plane 1. Determine where plane (or // plane) intersects axes: a intersect is 2 units b intersect is 2 units c 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" b c a

Some prominent planes Equivalent planes denoted by {} {100}=(100), (010), (001) For Cubic structures: [h,k,l]  (h,k,l)

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

Reconstruction of surfaces Si(100) 2x1 reconstruction Environments, bonding, defect densities, surface bandstructures different Important as devices scale and surfaces become important

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)

Things we learned today Bravais Lattices Unit cells: Coordination no. No. of atoms/cell Nearest neighbor distances Lattice vectors and Miller Indices