# solid state

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## Presentation Transcript

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

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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

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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

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ECE 663-1, Fall ‘08 Texts

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ECE 663-1, Fall ‘08 References

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ECE 663-1, Fall ‘08 Grading info

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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 ‘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

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

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

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

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

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ECE 663-1, Fall ‘08 Better Materials?

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

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ECE 663-1, Fall ‘08 New Principles?

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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)

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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

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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)

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

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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 Composition of atoms (Si, Ga, As, ..) Spatial Arrangement (crystal structure) Quantifying structures and orientations 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 ‘08 Simple Cubic Structure Lattice Constant=a Length of unit cell Not a common structure Coordination Number (# of nearest neighbors) =6

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

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

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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

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ECE 663-1, Fall ‘08

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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

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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

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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)

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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

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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

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ECE 663-1, Fall ‘08 J.C. Bean

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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

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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

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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

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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 2p/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 Missing atom  not all atoms have the same environment Can reduce to Bravais lattice with 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 periodic systems)

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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 not possible 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 ‘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)

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

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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

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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 are Crystallographically equivalent

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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 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

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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 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 (Ch. 3)