Slide 1:ECE 663-1, Fall ‘08 Solid State Devices Avik Ghosh Electrical and Computer Engineering University of Virginia Fall 2008


Slide 2:ECE 663-1, Fall ‘08 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, Pierret


Slide 3:ECE 663-1, Fall ‘08 Course information Books □ Advanced Semiconductor Fundamentals (Pierret) □ Physics of Semiconductor Devices (Sze and Ng) Website: http://toolkit.virginia.edu/ECE663-1 Office hrs: M 2:30-3:30 Grader: Not yet decided


Slide 4:ECE 663-1, Fall ‘08 Texts


Slide 5:ECE 663-1, Fall ‘08 References


Slide 6:ECE 663-1, Fall ‘08 Grading info


Slide 7: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 8:ECE 663-1, Fall ‘08 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


Slide 9:ECE 663-1, Fall ‘08 The future of Electronics?


Slide 10:ECE 663-1, Fall ‘08 A major problem: Power dissipation! New physics needed – new kinds of computation


Slide 11:ECE 663-1, Fall ‘08 How can we push technology forward?


Slide 12:ECE 663-1, Fall ‘08 Better Design Multiple Gates for superior field control


Slide 13:ECE 663-1, Fall ‘08 Better Materials?


Slide 14:ECE 663-1, Fall ‘08 Higher mobility materials 15 nm < 10 nm 5 nm 2 nm


Slide 15:ECE 663-1, Fall ‘08 New Principles?


Slide 16:ECE 663-1, Fall ‘08 Where do we stand today?


“Top Down” … (ECE663) :ECE 663-1, Fall ‘08 “Top Down” … (ECE663) Solid State Electronics/ Mesoscopic Physics Molecular Electronics


Top Down fabrication :ECE 663-1, Fall ‘08 Top Down fabrication Top down architecture “Al-Khazneh”, Petra, Jordan (6th century BC)


Slide 19:ECE 663-1, Fall ‘08 Modeling device electronics ECE 663 (“Traditional Engg”) ECE 687 (“Nano Engg”)


“Bottom Up” ... (ECE 687) :ECE 663-1, Fall ‘08 “Bottom Up” ... (ECE 687) Solid State Electronics/ Mesoscopic Physics Molecular Electronics


Bottom Up fabrication :ECE 663-1, Fall ‘08 Bottom Up fabrication


Slide 22:ECE 663-1, Fall ‘08 Related Courses Fundamentals ECE309 (EM) PHYS 355/751 (Quantum Phys) MSE 601 (Xal str of mats) ECE 686 (QM for engineers) MAE 692 (Q. Engg: At/Mol) Circuits/Architecture ECE 632 (VLSI design) ECE 564 (IC-Fab) ECE 363 (Digital ICs)


Slide 23:ECE 663-1, Fall ‘08 How can we model and design today’s devices?


Slide 24: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 25:ECE 663-1, Fall ‘08 Calculating Electrons and Velocity Composition of atoms (Si, Ga, As, ..) Spatial Arrangement (crystal structure) Quantifying structures and orientations Where are electronic energy levels?


Slide 26:ECE 663-1, Fall ‘08 Solids Metals: Gates, Interconnects


Slide 27:ECE 663-1, Fall ‘08 Solids tend to form ordered crystals (Rock salt, NaCl) Natural History Museum, DC


Slide 28:ECE 663-1, Fall ‘08 Simple Cubic Structure Lattice Constant=a Length of unit cell Not a common structure Coordination Number (# of nearest neighbors) =6


Slide 29:ECE 663-1, Fall ‘08 Body Centered Cubic (BCC) Mo, Ta, W CN=8


Slide 30:ECE 663-1, Fall ‘08 Face Centered Cubic (FCC) Al,Ag, Au, Pt, Pd, Ni, Cu CN=12


Slide 31:ECE 663-1, Fall ‘08 Diamond Lattice C,Si,Ge A=5.43Å for Si CN=4 Difficult to draw or visualize: Two FCC offset by a/4 in each direction or FCC lattice w/2 atoms/site


Slide 32:ECE 663-1, Fall ‘08


Slide 33:ECE 663-1, Fall ‘08 http://www.people.virginia.edu/~jcb6t http://www.people.virginia.edu/~jcb6t/Research/Explore/explore.htm http://jas.eng.buffalo.edu/ http://jas.eng.buffalo.edu/education/solid/unitCell/home.html Web Sites That may be helpful


Slide 34: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 35:ECE 663-1, Fall ‘08 Hexagonal Lattice Al2O3, Ti, other metals Hexagonal Only other type common in ICs


Semiconductors: 4 valence electrons :ECE 663-1, Fall ‘08 Semiconductors: 4 valence electrons Group IV elements (column IV of periodic table): Si, Ge, C Compound Semiconductors – one from Column III and one from Column V: GaAs, InP, AlAs,…. Tertiary (InGaAs) and Quaternary (InGAsP)


Slide 37:ECE 663-1, Fall ‘08 Semiconductor Materials Group IV: Si – preeminent material, indirect bandgap – poor optical properties, good thermal oxide, native oxide – passivation of surfaces Ge – historically first used, lower bandgap than Si (0.68 vs 1.12 eV), H2O soluable oxide, SiGe C - very high bandgap for diamond, SiC


Slide 38:ECE 663-1, Fall ‘08 Groups III V Direct Bandgap – LEDs Ga Sb lasers, detectors, GaAs Al As high mobility for e- - In P high speed GaAs, InP, InGaAs, InGaAlAs,…………… Mix and match – lattice constant, bandgap Also, II-VI materials: CdTe,HgTe,ZnSe,HgCdTe,… Semiconductor Materials


Slide 39:ECE 663-1, Fall ‘08 J.C. Bean


Slide 40:ECE 663-1, Fall ‘08 Diamond Structure The unit cell contains: 8 corners shared by 8 cells = 8*1/8=1 6 face atoms shared by 2 cells= 6*1/2=3 4 interior atoms not shared= =4 _______ 8 8 atoms in unit cell Si lattice constant, a = 5.43 Å =5.43 x 10–8 cm


Slide 41:ECE 663-1, Fall ‘08 Nearest Neighbors in Si Diamond Structure Lattice is two FCC displaced by a/4 in each dirn Nearest neighbor center to center distance: Å Tetrahedral radius= ½ center to center distance For Si: Rtet=1.18Å Hard Sphere Model: Atom volume4/3  Rtet3


Slide 42:ECE 663-1, Fall ‘08 In Compound Semiconductors, tetraheadral radii are different: In GaAs: a=5.65Å N-N distance= Å rGa=1.26Å rAs=1.18Å 1.26+1.18=2.44


Slide 43:ECE 663-1, Fall ‘08 Bravais Lattices Each atom has the same environment Courtesy: Ashraf Alam, Purdue Univ


Slide 44:ECE 663-1, Fall ‘08 2D Bravais Lattices Courtesy: Ashraf Alam, Purdue Univ Only angles 2p/n, n=1,2,3,4,6 (Pentagons not allowed!)


Slide 45:ECE 663-1, Fall ‘08 2D non-Bravais Lattice – e.g. Graphene Missing atom  not all atoms have the same environment Can reduce to Bravais lattice with a basis


Slide 46: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 47:ECE 663-1, Fall ‘08 MoAl6 FeAl6 (Pauling, PRL ’87) Not just on paper... 5-fold diffraction patterns Pentagons ! (5-fold symmetry not possible in a perfect Xal)


Slide 48:ECE 663-1, Fall ‘08 Pentagons allowed in 3D Buckyball/Fullerene/C60


Slide 49:ECE 663-1, Fall ‘08 3D Bravais Lattices 14 types


Slide 50: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)


Slide 51:ECE 663-1, Fall ‘08 Body-centered cube 8x1/8 corner atom + 1 center atom gives 2 atoms per cell


Slide 52: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


Slide 53: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 54:ECE 663-1, Fall ‘08 Crystal Planes denoted by Miller Indices h,k,l Planes in a Crystal


Slide 55:ECE 663-1, Fall ‘08 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" a b c Miller indices of a plane


Slide 56: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


Slide 57: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


Slide 58:ECE 663-1, Fall ‘08 Reconstruction of surfaces Environments, bonding, defect densities, surface bandstructures different Important as devices scale and surfaces become important


Slide 59: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 (Ch. 3)