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# 18.1 - Week 8 Where Are We By now we should all know What...

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Unformatted text preview: Week 8: Where Are We? By now we should all know: What holds atoms together in groups (bonding) How atoms can group and form different structures Key differences between structures of metals, ceramics & polymers The nature of imperfections (defects) in materials How atoms can move (diffusion) How materials interact with their environment (corrosion & degradation) Next we will discuss: Some important properties of different materials: Electrical (3) Magnetic (1.5) Optical (1.5) Web chapters will be posted (PDF) on BbVista Chapter 18 - 1 Week 8: Where Are We? Scores and Grades: Completed 4 of 5/6 Quizzes Completed in-class project (Wk 3) Completed 2 x midterms (Wks 6 and 8): Midterm 2 Average = TBD HI = ??, LO = ?? These account for 250 out of 350 total points for course Max score possible to date = 58.33 % (D) Still to be Done: 1 Quiz (Week 9) + Attendance (= 1 Quiz) Final Exam (35 % weighting) Note: Monday, 5/31 is a holiday…no lectures! Chapter 18 - 2 Chapter 18: Electrical Properties ISSUES TO ADDRESS... • How are electrical conductance and resistance characterized? • What are the physical phenomena that distinguish conductors, semiconductors and insulators? • For metals, how is conductivity affected by imperfections, Temperature and deformation? • For semiconductors, how is conductivity affected by impurities (doping) and Temp.? Chapter 18 - 3 ANNOUNCEMENTS Reading: Chapter 18: Sections 18.1-18.13 Week 8 Recitations: Problems: 18.1, 18.7, 18.9, 18.12, 18.17, 18.19, 18.27, 18.29, 18.31, 18.D1 No Quiz – Midterm 2 this week Midterm 2: Tuesday, May 18, 8:00-8:50 am, Main Auditorium Accommodations: LeBow 348; 8:00-9:15 (1.5X) or 8:00-9:40 am (2X) Chapters 12, 14, 17 + sprinkling of earlier topics Final Exam: Friday, June 11, 1:00-3:00 pm Accommodations: LeBow 348; 1:00-4:00 pm (1.5X) or 1:00-5:00 pm (2X) Chapter 18 - 4 View of an Integrated Circuit • Scanning electron microscope (SEM) images of an IC: Al Si (doped) (d) (d) (a) 45 μm 0.5 mm • Dot map showing location of Si (a semiconductor): - Si shows up as light regions. (b) • Dot map showing location of Al (a conductor): - Al shows up as light regions. Fig. (d) from Fig. 18.27 (a), Callister 7e. (Fig. 18.27 is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.) (c) Fig. (a), (b), (c) from Fig. 18.0, Callister 7e. Chapter 18 - 5 Measuring Electrical Conduction Chapter 18 - 6 Electrical Conduction • Ohm's Law: V=IR Voltage drop (Volts = J/C) C = Coulomb Resistance (Ohms) Current (Amps = C/s) A e- (cross-sectional area) I V L • Resistivity, and Conductivity, : - geometry-independent forms of Ohm’s Law - Resistivity is a material property & is independent of sample E: Electric Field intensity • Resistance: R= V I = L A Resistivity (Ohm-m) J: Current Density L L = AA Conductivity = 1 Chapter 18 - 7 Electrical Properties • Which wire will conduct more electricity? D 2D • Analogous to flow of water in a pipe • So resistance depends on sample geometry, etc. = RA but since V = IR, then, R = V/I, so = VA I Chapter 18 - 8 Example: Conductivity Problem What is the minimum diameter (D) of the wire so that V < 1.5 V? e- Cu wire - 100 m I = 2.5 A + V 100m D2 4 L V R= = A I Solve to get: < 1.5 V 2.5 A 6.07 x 107 (Ohm-m)-1 D > 1.87 mm Chapter 18 - 9 An Alternate Expression of Ohm’s Law l Area = A = = RA RA V = IR V I= R I Vl lV = = A AR l AR l ll dV J= = AR dx E ------------ (I) Chapter 18 - 10 Definitions Therefore: J= E an alternative way of stating Ohm’s law J = current density (A/m2) = current I = and is indeed a flux X - section area A E = electric field potential = V/ or ( V/ J= Electron flux ( V/ ) = V/m ) conductivity voltage gradient Charge (current) carriers: • electrons in most solids • ions can also carry - particularly in liquid solutions, SOFCs Chapter 18 - 11 Electron Scattering • E-field exerts force on free e-: – Accelerated in direction opposite to E-field… – e- cannot accelerate indefinitely, otherwise I would increase without limit over time • I observed to reach constant value…so what’s going on? • “Frictional forces” counter e- acceleration: – Scattering of e- by lattice imperfections: • impurities, vacancies, interstitials, dislocations, thermal vibrations – e- lose K-E & change direction – But, net e- motion opposite to E-field…current flow Chapter 18 - 12 Electron Scattering • Drift Velocity & Mobility: describe extent of escattering vd = average e- vel. in direction of force due to applied E-field vd = eE e= electron mobility… fn. (frequency of scattering events), units of m2/V-s Chapter 18 - 13 If n electrons flow thru a wire with an average drift velocity vd then the current density, Ji, passing through the wire is: Ji = e v d n ------------ (II) WIRE n = concentration of mobile carriers, (m-3) vd = average drift velocity of mobile carriers (m/s) Electron mobility is defined as: vd vd drift velocity drift velocity μe = = = = dV dx E driving force electric field v Average drift velocity, vd vd time (III) For any given solid and temperature, e is constant! Chapter 18 - 14 Combine Eqs. I, II and III and Show that:‡ J= E J = evdn vd = e E = n e μe Most important equation in this chapter! The link between the macro, i.e. , and the micro, i.e. n and e In order to understand we need to understand how n and vary with composition, temperature and defects. ‡ Better to do it here and now than in the final! Chapter 18 - 15 Conductivity: Comparisons • Room T values (Ohm-m)-1 = ( -m)-1 METALS Conductors CERAMICS -10 Silver 6.8 x 10 7 Soda-lime glass 10 -10-11 Copper 6.0 x 10 7 Concrete 10 -9 Iron 1.0 x 10 7 Aluminum oxide <10-13 POLYMERS SEMICONDUCTORS Polystyrene Silicon 4 x 10 -4 Polyethylene Germanium 2 x 10 0 GaAs 10 -6 Semiconductors -14 <10 10 -15-10-17 Insulators Huge range! And this does not include superconductors Chapter 18 - 16 What Accounts for This Huge Range? Let’s look at the KEY equation for this chapter and decide: = n e μe It certainly doesn’t come from e, it also does not stem from So the KEY is n…to understand n, we need to understand band theory in solids… Chapter 18 - 17 e Band Theory: Background Most Conductors, Insulators, Semiconductors: Conduction due to e- alone Magnitude of depends on n Not all e- will move under applied electric field n related to e- states (levels), their energy & how filled • Quantum Mechanics… Quantum Mechanics Revisited: e- energy states (Ch. 2) discrete energy levels occupied by earranged in shells (1, 2, 3 etc.) & subshells (s, p, d & f), latter with 1, 3, 5, 7 states e- fill states with lowest energies, 2 per state, ±1/2 spins e- configuration for 1 atom e- arrangement in allowed states Chapter 18 - 18 Band Theory: Background Consider Solids: Comprise large # (N) atoms, initially well separated Brought together when crystalline solid formed At large separations, each atom independent At close separations, e- acted on by e- & nuclei of adjacent atoms Atomic states “split” into series of closely spaced estates…electron energy band Chapter 18 - 19 Electronic Band Structures Level of splitting: fn. (interatomic separation) begins with outermost e- shells. Why? Energy states discrete within each band; differences v. small Adapted from Fig. 18.2, Callister 7e. Chapter 18 - 20 Band Structure At =m atom spacing, bands do not form for subshells nearest nucleus • • Valence Band – filled – highest occupied energy levels Conduction Band – empty – lowest unoccupied energy levels Conduction Band Adapted from Fig. 18.3, Callister 7e. Valence band Gaps between adjacent bands. Energies within band gaps not available for e- to occupy Chapter 18 - 21 ...
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