1. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 45 Electrical Properties-1

2. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 2 Bruce Mayer, PE Engineering-45: Materials of Engineering Learning Goals – Elect. Props  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, Temp, and Deformation?  For Semiconductors, How Is Conductivity Affected By Impurities (Doping) And Temp?

3. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 3 Bruce Mayer, PE Engineering-45: Materials of Engineering Electrical Conduction  Georg Simon Ohm (1789-1854) First Stated a Relation for Electrical Current (I), and Electrical Potential (V) in Many Bulk Materials  The Constant of Proportionality, R, is Called the Electrical RESISTANCE Has units of Volts/Amps, a.k.a, Ohms (Ω)  This Expression is known as Ohm’s Law Battery Bulk Matl Volt Meter Amp Meter I ()()

4. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 4 Bruce Mayer, PE Engineering-45: Materials of Engineering Electrical Conduction cont.  Fluid↔Current Flow Analogs  Think of Voltage as the “Electrical Pressure” Current as the “Electrical Fluid” Wire as the “ Electrical Pipe”  Just as a Small Pipe “Resists” Fluid Flow, A Small Wire “Resists” current Flow Thus Resistance is a Function of GEOMETRY and MATERIAL PROPERTIES –Next Discern the Resistance PROPERTY

5. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 5 Bruce Mayer, PE Engineering-45: Materials of Engineering Electrical Resistivity  Consider a Section of Physical Material, and Measure its Resistance Geometry –Length –X-Section Area  Thinking Physically, Since R is the Resistance to Current Flow, expect  R↑ as L↑ R  L  R↑ as A↓ R  1/A Area, A Length, L Matl Prop → “  ” Resistance, R

6. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 6 Bruce Mayer, PE Engineering-45: Materials of Engineering Electrical Resistivity cont.  Thus Expect  This is, in fact, found to be true for many Bulk Materials  Convert the Proportionality (  ) to an Equality with the Proportionality Constant, ρ  Units for  ρ → [Ω-m 2 ]/m ρ → Ω-m Area, A Length, L Matl Prop → “  ” Resistance, R

7. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 7 Bruce Mayer, PE Engineering-45: Materials of Engineering Electrical Conductivity  conductANCE is the inverse of resistANCE  Similarly, conductIVITY is the inverse of resistIVITY  Units for   = 1/ρ → 1/ Ω-m  Now Ω − 1 is Called a Siemens, S σ → S/m Area, A Length, L Matl Prop → “  ” Conductance, G

8. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 8 Bruce Mayer, PE Engineering-45: Materials of Engineering Ohm Related Issues  Recall Ohm’s Law  E =  J is the NORMALIZED, Resistive, Version of Ohm’s Law  J  Current Density in A/m 2  E  Electric Field in V/m In the General Case L VV

9. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 9 Bruce Mayer, PE Engineering-45: Materials of Engineering Normalized, Conductive Ohm  Recall Ohm’s Law  G is Conductance  Recall also  Rearranging L VV J = σ E is the Normalized, Conductive Version of Ohm’s Law

10. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 10 Bruce Mayer, PE Engineering-45: Materials of Engineering Some Conductivities in S/m  Metals  10 7  SemiConductors Si (intrinsic)  10 -4 Ge  10 0 = 1 GaAs  10 -6 InSb  10 4  Insulators SodaLime Glass  10 -11 Alumina  10 -13 Nylon  10 -13 Polyethylene  10 -16 PTFE  10 -17 Conductivity (10 7 S/m) Metals

11. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 11 Bruce Mayer, PE Engineering-45: Materials of Engineering Conductivity Example  Recall  What is the minimum diameter (D) of a 100m wire so that ΔV < 1.5 V while carrying 2.5A? 100m Cu wire I = 2.5A - + e - VV  Also G by σ & Geometry  For Cu: σ = 6.07x10 7 S/m

12. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 12 Bruce Mayer, PE Engineering-45: Materials of Engineering Conductivity Example cont  Solve for D  What is the minimum diameter (D) of a 100m wire so that ΔV < 1.5 V while carrying 2.5A? 100m Cu wire I = 2.5A - + e - VV  Sub for Values

13. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 13 Bruce Mayer, PE Engineering-45: Materials of Engineering Electronic Conduction  As noted In Chp2 Electrons in a FREE atom Can Reside in Quantized Energy Levels The Energy Levels Tend to be Widely Separated, Requiring significant Outside Energy To move an Electron to the next higher level  In The SOLID STATE, Nearby Atoms Distort the Energy LEVELS into Energy BANDS Each Band Contains MANY, CLOSELY Spaced Levels

14. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 14 Bruce Mayer, PE Engineering-45: Materials of Engineering Solid State Energy Band Theory  Consider the 3s Energy Level, or Shell, of an Atom in the SOLID STATE with EQUILIBRIUM SPACING r 0 By the Pauli Exclusion Principle Only ONE e − Can occupy a Given Energy Level

15. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 15 Bruce Mayer, PE Engineering-45: Materials of Engineering Band Theory, cont.  The N atoms per m 3 with Spacing r 0 produces an Allowed-Energy BAND of Width ΔE  Most Solids have N = 10 28 -10 29 at/m 3  Thus the ΔE wide Band Splits into  10 29 /m 3 Allowed E-Levels  Leads to a band of energies for each initial atomic energy level e.g., 1s energy band for 1s energy level

16. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 16 Bruce Mayer, PE Engineering-45: Materials of Engineering Energy Band Calc  Given ΔE  15 eV N  5 x 10 28 at/cu-m  Then the difference between allowed Energy Levels within the Band,  E  The Thermal Energy at Rm Temp is  25 meV/at, or about 10 26 times  E Thus if bands are Not Completely Filled, e- can move easily between allowed levels

17. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 17 Bruce Mayer, PE Engineering-45: Materials of Engineering Electronic Conduction - Metals  In Metals The Electronic Energy Bands Take One of Two Configurations 1.Partially Filled Bands e - can Easily move Up to Adjacent Levels, Which Frees Them from the Atomic Core 2.Overlapping Bands e - can Easily move into the Adjacent Band, Which also Frees Them from the Atomic Core Energy filled band filled valence band empty band filled states filled band Energy partly filled valence band empty band GAP filled states

18. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 18 Bruce Mayer, PE Engineering-45: Materials of Engineering Metal Conduction, Cont.  Atoms at Their Lowest Energy Condition are in the “Ground State”, and are Not Free to Leave the Atom Core  In Metals, the Energy Supplied by Rm Temp Can move the e − to a Higher Level, making them Available for Conduction  Metallic Conduction Model → Electron- Gas or Electron-Sea Net e - Flow Current Flow E -Field V- V+ Note: e - ’s Flowing “UPhill” constitutes Current Flowing DOWNhill

19. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 19 Bruce Mayer, PE Engineering-45: Materials of Engineering Insulators & Semiconductors  Insulators: Higher energy states not accessible due to lg gap –E g > ~3.5 eV  Semiconductors: Higher energy states separated by smaller gap –E g < ~3.5 eV Energy filled band filled Valence band empty band filled states GAP Conductio n Band 7 Energy filled band filled valence band empty band filled states GAP ? Conduction Band

20. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 20 Bruce Mayer, PE Engineering-45: Materials of Engineering Metals -  vs T,  vs Impurities  The Two Basic Components of Solid-St Electronic Conduction The Number of FREE Electrons, n The Ease with Which the Free e - ’s move Thru the Solid –i.e. the electron Mobility, µ e  Consider The ρ Characteristics for Cu Metals T (°C) -200-1000 Cu + 3.32 at%Ni Cu + 2.16 at%Ni deformed Cu + 1.12 at%Ni 1 2 3 4 5 6 Resistivity,  (10 -8  -m) 0 Cu + 1.12 at%Ni “Pure” Cu

21. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 21 Bruce Mayer, PE Engineering-45: Materials of Engineering Metals -  vs T, Impurities cont  Since “Double Ionization” of Atom Cores is difficult n(Hi-T)  n(Lo-T)  Thus T, Impurities and Defects must Cause Reduced µ e These are all e- Scattering Sites –Vacancies –Grain Boundaries T (°C) -200-1000 Cu + 3.32 at%Ni Cu + 2.16 at%Ni deformed Cu + 1.12 at%Ni 1 2 3 4 5 6 Resistivity,  (10 -8  -m) 0 Cu + 1.12 at%Ni “Pure” Cu –Impurities; e.g., Ni above –Dislocations; e.g., deformed

22. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 22 Bruce Mayer, PE Engineering-45: Materials of Engineering Metal  - Mathiessen’s Rule  The Data Shows The Factors that Reduce σ Temperature Impurities Defects  These Affects are PARALLEL Processes i.e., They Act Largely independently of each other  The Cumulative Effect of ||-Processes is Calculated by Mathiessen’s Rule of Reciprocal Addition

23. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 23 Bruce Mayer, PE Engineering-45: Materials of Engineering Resistivity Relations for Metals  Temperature Affects may be approximated with a Linear Expression Where –  0 is the Resisitivity at the Baseline Temperature, Ω-m –a is the Slope of ρ vs T Curve, Ω-m/K  For A Single Impurity That Forms a Solid-Solution Where –A is an Alloy-Specific Constant, Ω-m/at-frac –c i is the impurity Concentration in in the atomic-fraction Format  At-frac = at%x(1/100%)

24. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 24 Bruce Mayer, PE Engineering-45: Materials of Engineering ρ Relations for Metals cont  In alloys where the impurity results, not in Solid-Solution, but in the Formation of a 2 nd Xtal Structure, or Phase, Use a Rule-of-Mixtures Relation for ρ i Use Vol-Fractions as the Weighting Factor Where –ρ k is the Resistivity of phase-k –V k is the Volume- Fraction of phase-k  Plastic Deformation There is no Simple Relation for This –Consult individual metal or alloy data

25. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 25 Bruce Mayer, PE Engineering-45: Materials of Engineering Example  Estimate σ  Est. σ for a Cu-Ni alloy with yield strength of 125 MPa From Fig 7.19 Find Composition for S y = 125 MPa  So need 21 wt% Ni Find ρ from Fig 18.9 Yield strength (MPa) wt. %Ni, (Concentration C) 01020304050 60 80 100 120 140 160 180 21 wt%Ni wt. %Ni, (Concentration C) Resistivity,  (10 -8 Ohm-m) 10203040 50 0 10 20 30 40 50 0    30x10 -8 Ω-m And σ = 1/ρ   σ = 3.3x10 6 S/m

26. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 26 Bruce Mayer, PE Engineering-45: Materials of Engineering All Done for Today Using BandGaps To Make LEDs

27. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 27 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Chabot Engineering Appendix

28. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 28 Bruce Mayer, PE Engineering-45: Materials of Engineering http://www.chemistry.wustl.edu/~edudev/LabTutorials/PeriodicPro perties/MetalBonding/MetalBonding.html

29. BMayer@ChabotCollege.edu ENGR-45_Lec-08_ElectProp-Metals.ppt 29 Bruce Mayer, PE Engineering-45: Materials of Engineering WhiteBoard Work  Derive Relation for e - Drift Velocity, v d  Calculate the Drift Velocity in a 20 foot Gold Wire Connected to a 9Vdc Batt Assume Au Atoms in the Solid Are Singly Ionized, contributing 1 conduction-e - per atom (monovalent)  Compare (random) THERMAL Velocity