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Today’s objectives-Electrical Conduction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Reading for today Semiconductors and Integrated Circuits Chapter sections: 18.1-9
Voltages and Electric Fields ,[object Object],+ - + - Often, we consider the positive bias to simply be at ‘V’ and the negative pole to be at 0 Volts, or ground. V
ELECTRICAL CONDUCTION 3 •  Ohm's  Law:  V = I R voltage drop (volts) resistance (Ohms) current (amps) •  Resistivity,    and  Conductivity,   : --geometry-independent forms of Ohm's Law E: electric field intensity resistivity (Ohm-m) J: current density conductivity •  Resistance:
Ohm’s Law ,[object Object],[object Object],V I I = V / R voltage drop (volts) resistance (Ohms) current (amps) Energy Specimen (R) + -
Resistivity instead of Resistance ,[object Object],R = V / I = Volts/Amps = Ohms Resistivity: current density (Ohm*meters)
Other geometry independent relationships. ,[object Object],[object Object],[object Object],[object Object],General rules Conductivity is largest for metals & smallest for insulators. Resistivity is smallest for metals and largest for insulators.
CONDUCTIVITY:  COMPARISON Remember that Resistivity is the inverse =1/conductivity, and is thus huge for insulators and very small for conductors. way out there Pluto’s orbital diameter 1/2 mile atom 1E+06 1E+03 1E-07 1E-20 good metal metal Semi-conductor insulator
10 million light years (10 23 m). The distant galaxy is the Milky Way.
1 million light years (10 22 m) The disc becomes visible.
1 light year (10 16 m), within the Milky Way. This is our sun.
1 trillion km (10 15 m) The sun even bigger.
100 billion km (10 14 m) Our solar system…
10 billion Km (10 13 m) Our solar system.
1 billion Km (10 12 m) The orbits of Venus, Earth, Mars.
10 million Km (10 10 m) Orbit of Earth...
1 million Km (10 9 m) Earth and the orbit of Moon.
100.000 Km (10 8 m)  Third rock from the sun…
10.000 Km(10 7 m) The northern hemisphere of Earth. As usual, another wonderful day in CT…
1.000 Km (10 6 m) FLA
10 Km (10 4 m) You start to differentiate buildings.
1 Km (10 3 m)
100 m (10 2 m) An ordinary view from an helicopter.
10 m (10 1 m)
1 m (10 0 m)
10 cm (10 -1 m)
1 cm (10 -2 m) You can see the structure of a leaf.
1  mm (10 -3 m) Even closer.
100 micron (10 -4 m)  you can see the cells.
10 micron (10 -5 m)
1 micron (10 -6 m).  The cell itself.
1.000 angstrom (10 -7 m) You can see the chromosomes.
100 angstrom (10 -8 m) You can see the DNA chain.
1 nm (10 -9 m) The chromosomes.
1 angstrom.  (10 -10 m) The carbon atom.
1 Pico metre (10 -12 m) The orbit of electrons, if we could see it....
100 Fermi (10 -13 m) Inside an atom.
10 Fermi (10 -14 m), protons and neutrons… Too bad we can’t see them…
EX:  CONDUCTIVITY PROBLEM •  Question 18.2, p. 649,  Callister 6e : a) What is the minimum diameter (D) of the wire so that  V < 1.5V, given that sigma=6.07*10 7  /(Ohm*m)?  b) What is R? Solve to get  D > 1.88 mm. With D, R can be determined: 0.59 Ohms or less. < 1.5V 2.5A 6.07 x 10  (Ohm-m) 7 -1 100m
Reasons for resistivity/conductivity ,[object Object],[object Object],[object Object],Note that by convention, electrons move opposite to the field direction. n=number of electrons per volume e=charge on electron (or hole) μ =mobility of electrons in a given material
Scattering: origin of resistivity/conductivity ,[object Object],[object Object],[object Object],[object Object],[object Object]
Resistivity Components •  Resistivity increases with: --temperature --wt% impurity --% deformation
Strengthening Mechanisms in Metals ,[object Object],[object Object],[object Object],How do these mechanisms affect electrical conduction?
Strengthening Mechanisms in Metals ,[object Object],[object Object],[object Object],[object Object],[object Object],They ALL decrease electrical conductivity!!!
What about electronic structure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Electrons in atoms ,[object Object],Pauli exclusion principle H 1s He 1s B 1s 1p Energy
Electrons in solids ,[object Object],Isolated atoms Solid All we draw is the “band diagram”
Energy band structures for various metals ,[object Object],[object Object],[object Object],Metal (Cu) partially  filled 4s (conduction) filled 3d, 3p, 3s, 2p, 2s, 1p, 1s (valence) Empty 4p (conduction) Band gap Band gap Energy Filled 3d (valence) Deep valence-only an issue for optical properties
Energy band structures for various metals ,[object Object],conducting conducting conducting Filled 1p, 1s  (deep valence) E f Metal (Be) Filled  2s (valence) Empty  2p (conduction) Empty 3s (conduction) Band gap Band gap Energy E f , Fermi level Metal (Cu) partially  filled 4s (conduction) filled  3d, 3p, 3s, 2p, 2s, 1p, 1s (valence) Empty 4p (conduction) Band gap Band gap Metal (Mg, 3p and 3s overlap) E f Filled [mostly] 3s (valence) Empty [mostly] 3p (conduction) filled (valence) Empty 4s (conduction) Band gap Band gap
Definition of Conductivity ,[object Object],[object Object],[object Object],[object Object],[object Object],Metal (Cu) partially  filled 4s (conduction) Empty 4p (conduction) Band gap Band gap Energy Filled (valence) E f , Fermi level
Band structures for semiconductors and insulators ,[object Object],[object Object],Energy E f , Fermi level Metal (Cu) partially  filled 4s (conduction) filled  3p, 2p, 2s, 1p, 1s (valence) Empty 4p (conduction) Band gap Band gap Filled  (deep valence) E f Semiconductor (Si) Filled (valence) Empty  (conduction) Band gap Band gap Filled  (deep valence) E f Insulator (Al 2 O 3 ) Filled (valence) Empty  (conduction) Band gap Band gap
CONDUCTION & ELECTRON TRANSPORT ,[object Object],[object Object],[object Object],[object Object]
Conduction in insulators/semiconductors •  Insulators: --Higher energy states  not accessible  due to gap. •  Semiconductors: --Higher energy states  possibly accessible  due to smaller gap. ,[object Object],[object Object],[object Object]
Metallic conduction ,[object Object],[object Object]
SUMMARY Reading for next class Semiconductors and Integrated Circuits, Chapter sections: 18.10-15 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Lecture 14

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  • 3. ELECTRICAL CONDUCTION 3 • Ohm's Law:  V = I R voltage drop (volts) resistance (Ohms) current (amps) • Resistivity,  and Conductivity,  : --geometry-independent forms of Ohm's Law E: electric field intensity resistivity (Ohm-m) J: current density conductivity • Resistance:
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  • 7. CONDUCTIVITY: COMPARISON Remember that Resistivity is the inverse =1/conductivity, and is thus huge for insulators and very small for conductors. way out there Pluto’s orbital diameter 1/2 mile atom 1E+06 1E+03 1E-07 1E-20 good metal metal Semi-conductor insulator
  • 8. 10 million light years (10 23 m). The distant galaxy is the Milky Way.
  • 9. 1 million light years (10 22 m) The disc becomes visible.
  • 10. 1 light year (10 16 m), within the Milky Way. This is our sun.
  • 11. 1 trillion km (10 15 m) The sun even bigger.
  • 12. 100 billion km (10 14 m) Our solar system…
  • 13. 10 billion Km (10 13 m) Our solar system.
  • 14. 1 billion Km (10 12 m) The orbits of Venus, Earth, Mars.
  • 15. 10 million Km (10 10 m) Orbit of Earth...
  • 16. 1 million Km (10 9 m) Earth and the orbit of Moon.
  • 17. 100.000 Km (10 8 m) Third rock from the sun…
  • 18. 10.000 Km(10 7 m) The northern hemisphere of Earth. As usual, another wonderful day in CT…
  • 19. 1.000 Km (10 6 m) FLA
  • 20. 10 Km (10 4 m) You start to differentiate buildings.
  • 21. 1 Km (10 3 m)
  • 22. 100 m (10 2 m) An ordinary view from an helicopter.
  • 23. 10 m (10 1 m)
  • 24. 1 m (10 0 m)
  • 25. 10 cm (10 -1 m)
  • 26. 1 cm (10 -2 m) You can see the structure of a leaf.
  • 27. 1 mm (10 -3 m) Even closer.
  • 28. 100 micron (10 -4 m) you can see the cells.
  • 29. 10 micron (10 -5 m)
  • 30. 1 micron (10 -6 m). The cell itself.
  • 31. 1.000 angstrom (10 -7 m) You can see the chromosomes.
  • 32. 100 angstrom (10 -8 m) You can see the DNA chain.
  • 33. 1 nm (10 -9 m) The chromosomes.
  • 34. 1 angstrom. (10 -10 m) The carbon atom.
  • 35. 1 Pico metre (10 -12 m) The orbit of electrons, if we could see it....
  • 36. 100 Fermi (10 -13 m) Inside an atom.
  • 37. 10 Fermi (10 -14 m), protons and neutrons… Too bad we can’t see them…
  • 38. EX: CONDUCTIVITY PROBLEM • Question 18.2, p. 649, Callister 6e : a) What is the minimum diameter (D) of the wire so that  V < 1.5V, given that sigma=6.07*10 7 /(Ohm*m)? b) What is R? Solve to get D > 1.88 mm. With D, R can be determined: 0.59 Ohms or less. < 1.5V 2.5A 6.07 x 10 (Ohm-m) 7 -1 100m
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  • 41. Resistivity Components • Resistivity increases with: --temperature --wt% impurity --% deformation
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