Slide 1 ECE 663-1, Fall ‘09 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2010 Slide 2 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 Slide 3 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]) Slide 4 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 class 2.Email HW PDFs to
[email protected] or hand in class Slide 5 ECE 663-1, Fall ‘09 Texts Slide 6 ECE 663-1, Fall ‘09 References Slide 7 ECE 663-1, Fall ‘09 Grading info Homeworks Wednesdays25% 1 st midtermM, Oct 0515% 2 nd midtermW, Nov 0425% FinalsS, Dec 1235% Slide 8 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% Slide 9 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) Semiconductors Basic Devices Soft Cover Hard Cover Midterm1 Midterm2 Final Where can the electrons sit? How are they distributed? How do they move? Slide 10 ECE 663-1, Fall ‘09 Why do we need this course? Slide 11 ECE 663-1, Fall ‘09 Transistor Switches A voltage-controlled resistor 19472003 Slide 12 ECE 663-1, Fall ‘09 Biological incentives Transistors in Biology: Ion channels in axons involve Voltage dependent Conductances Modeled using circuits (Hodgkin-Huxley, ’52) Slide 13 ECE 663-1, Fall ‘09 Economic Incentives From Ralph Cavin, NSF-Grantees’ Meeting, Dec 3 2008 Slide 14 ECE 663-1, Fall ‘09 A crisis of epic proportions: Power dissipation ! New physics needed – new kinds of computation Slide 15 ECE 663-1, Fall ‘08 We stand at a threshold in electronics !! Slide 16 ECE 663-1, Fall ‘08 How can we push technology forward? Slide 17 ECE 663-1, Fall ‘08 Better Design/architecture Multiple Gates for superior field control Slide 18 ECE 663-1, Fall ‘08 Better Materials? Strained Si, SiGe Bottom Gate Source Drain Top Gate Channel Carbon Nanotubes VGVG VDVD INSULATOR I Silicon Nanowires Organic Molecules Slide 19 ECE 663-1, Fall ‘08 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 Slide 20 ECE 663-1, Fall ‘08 Where do we stand today? Slide 21 ECE 663-1, Fall ‘08 “Top Down” … (ECE6163) Vd 20 µm Vd 2 nm Solid State Electronics/ Mesoscopic Physics Molecular Electronics Slide 22 ECE 663-1, Fall ‘08 Top Down fabrication Photolithography Top down architecture “Al-Khazneh”, Petra, Jordan (6 th century BC) Slide 23 ECE 663-1, Fall ‘08 Modeling device electronics Bulk Solid (“macro”) (Classical Drift-Diffusion) ~ 10 23 atoms Bottom Gate Source Channel Drain Clusters (“meso”) (Semiclassical Boltzmann Transport) 80s ~ 10 6 atoms Molecules (“nano”) (Quantum Transport) Today ~ 10-100 atoms ECE 663 (“Traditional Engg”) ECE 687 (“Nano Engg”) Slide 24 ECE 663-1, Fall ‘08 “Bottom Up”... (ECE 687) Vd 20 µm Vd 2 nm Solid State Electronics/ Mesoscopic Physics Molecular Electronics Slide 25 ECE 663-1, Fall ‘08 Bottom Up fabrication Build pyramidal quantum dots from InAs atoms (Gerhard Klimeck, Purdue) Bottom up architecture Chepren 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 Slide 26 ECE 663-1, Fall ‘08 How can we model and design today’s devices? Slide 27 Need rigorous mathematical formalisms 27 Slide 28 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 Slide 29 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? Slide 30 ECE 663-1, Fall ‘08 Solids Metals: Gates, Interconnects Slide 31 ECE 663-1, Fall ‘08 Solids tend to form ordered crystals (Rock salt, NaCl) Natural History Museum, DC Slide 32 ECE 663-1, Fall ‘09 Describing the periodic lattices Slide 33 ECE 663-1, Fall ‘08 Bravais Lattices Each atom has the same environment Courtesy: Ashraf Alam, Purdue Univ Slide 34 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!) Slide 35 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 lattice with a basis Slide 36 ECE 663-1, Fall ‘08 Irreducible Non-Bravais Lattices MC Escher Early Islamic art Penrose Tilings “Quasi-periodic” (Lower-D Projections of Higher-D periodic systems) Slide 37 ECE 663-1, Fall ‘08 MoAl 6 FeAl 6 (Pauling, PRL ’87) Not just on paper... 5-fold diffraction patterns Pentagons ! (5-fold symmetry not possible in a perfect Xal) Slide 38 ECE 663-1, Fall ‘08 Pentagons allowed in 3D Buckyball/Fullerene/C60 Slide 39 ECE 663-1, Fall ‘08 3D Bravais Lattices 14 types Slide 40 ECE 663-1, Fall ‘09 Describing the unit cells Slide 41 ECE 663-1, Fall ‘08 Simple Cubic Structure Coordination Number (# of nearest nbs. = ?) # of atoms/cell = ? Packing fraction = ? Slide 42 ECE 663-1, Fall ‘08 Body Centered Cubic (BCC) Mo, Ta, W CN = ? # atoms/lattice = ? Packing fraction? Slide 43 ECE 663-1, Fall ‘08 Face Centered Cubic (FCC) Al,Ag, Au, Pt, Pd, Ni, Cu CN = ? #atoms/cell = ? Packing fraction = ? Slide 44 ECE 663-1, Fall ‘08 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 Slide 45 ECE 663-1, Fall ‘08 Slide 46 http://jas.eng.buffalo.edu/education/solid/unitCell/home.html Web Sites That may be helpful http://jas.eng.buffalo.edu/education/solid/genUnitCell Slide 47 ECE 663-1, Fall ‘08 Zincblende Structure III-V semiconductors GaAs, InP, InGaAs, InGaAsP,…….. For GaAs: Each Ga surrounded By 4 As, Each As Surrounded by 4 Ga Slide 48 ECE 663-1, Fall ‘08 Hexagonal Lattice Al 2 O 3, Ti, other metals Hexagonal Only other type common in ICs Slide 49 ECE 663-1, Fall ‘09 X X X X X X Crystal Packing: FCC vs HCP Slide 50 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) Slide 51 ECE 663-1, Fall ‘09 Describing the unit cells Slide 52 ECE 663-1, Fall ‘08 Simple Cubic Structure Coordination Number (# of nearest nbs. = ?) # of atoms/cell = ? Packing fraction = ? Slide 53 ECE 663-1, Fall ‘08 Body Centered Cubic (BCC) Mo, Ta, W CN = ? # atoms/lattice = ? Packing fraction? Slide 54 ECE 663-1, Fall ‘08 Face Centered Cubic (FCC) Al,Ag, Au, Pt, Pd, Ni, Cu CN = ? #atoms/cell = ? Packing fraction = ? Slide 55 ECE 663-1, Fall ‘08 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 Slide 56 ECE 663-1, Fall ‘08 Slide 57 http://jas.eng.buffalo.edu/education/solid/unitCell/home.html Web Sites That may be helpful http://jas.eng.buffalo.edu/education/solid/genUnitCell Slide 58 ECE 663-1, Fall ‘08 Zincblende Structure III-V semiconductors GaAs, InP, InGaAs, InGaAsP,…….. For GaAs: Each Ga surrounded By 4 As, Each As Surrounded by 4 Ga Slide 59 ECE 663-1, Fall ‘08 Hexagonal Lattice Al 2 O 3, Ti, other metals Hexagonal Only other type common in ICs Slide 60 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) Slide 61 ECE 663-1, Fall ‘09 Quantifying lattices: 1. Lattice Vectors for directions Slide 62 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 Slide 63 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 ) Slide 64 ECE 663-1, Fall ‘08 Face-centered cube 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 a = a(0, ½, ½) b = a(½, 0, ½) c = a(½, ½, 0) Slide 65 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]= These three directions are Crystallographically equivalent Slide 66 ECE 663-1, Fall ‘09 Quantifying lattices: 2. Miller Indices for Planes Slide 67 ECE 663-1, Fall ‘08 Crystal Planes denoted by Miller Indices h,k,l Planes in a Crystal Slide 68