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- 1. Today’s objectives-Electrical Conduction <ul><li>What are the forms of Ohm’s law? </li></ul><ul><li>What are conductance and resistance and some standard values for materials? </li></ul><ul><li>Know the equation which accounts for scattering. </li></ul><ul><li>Describe the contribution of thermal vibrations, atomic defects, and more macroscopic defects on resistivity/conductivity? </li></ul><ul><li>How do available electron energy states vary for atoms, molecules, large molecules, and solids? </li></ul><ul><li>Sketch the 3 possible metallic band diagrams. </li></ul><ul><li>Sketch a simple metallic, semiconducting, and insulating band diagram. </li></ul><ul><li>How is conductivity described based on metal, semiconductor, and insulating band diagrams? </li></ul>Reading for today Semiconductors and Integrated Circuits Chapter sections: 18.1-9
- 2. Voltages and Electric Fields <ul><li>An electric field exists whenever there is a voltage difference between two points. </li></ul>+ - + - Often, we consider the positive bias to simply be at ‘V’ and the negative pole to be at 0 Volts, or ground. V
- 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:
- 4. Ohm’s Law <ul><li>Voltage source, current meter, resistor. </li></ul><ul><li>Note: current is measured in Amperes. </li></ul>V I I = V / R voltage drop (volts) resistance (Ohms) current (amps) Energy Specimen (R) + -
- 5. Resistivity instead of Resistance <ul><li>R depends on specimen shape—but we need a term that is independent of geometry. </li></ul>R = V / I = Volts/Amps = Ohms Resistivity: current density (Ohm*meters)
- 6. Other geometry independent relationships. <ul><li>Rewriting Ohm’s law (V=IR) using these terms yields a second, more materials friendly version: </li></ul><ul><li>Resistivity or conductivity </li></ul><ul><li>Electric field </li></ul><ul><li>Current density (Amps/m) </li></ul>General rules Conductivity is largest for metals & smallest for insulators. Resistivity is smallest for metals and largest for insulators.
- 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
- 39. Reasons for resistivity/conductivity <ul><li>Why does resistivity vary from one material to the next? </li></ul><ul><ul><li>Electronic Structure (metallic, semiconducting, insulating) </li></ul></ul><ul><ul><li>Scattering Events (characterized by ‘ μ ’) </li></ul></ul>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
- 40. Scattering: origin of resistivity/conductivity <ul><li>Primary Scattering Events </li></ul><ul><ul><li>Thermal defects (k b T at room temperature is about 25 meV). </li></ul></ul><ul><ul><li>Atomic Defects (impurities/dopants) </li></ul></ul><ul><ul><li>2d and/or 3d defects (grain boundaries, particles, dislocations) </li></ul></ul><ul><li>Oxygen free high conductivity copper is usually employed when very low resistivity is required. Al is an adequate substitute. Ag or Au are great, but too expensive. </li></ul>
- 41. Resistivity Components • Resistivity increases with: --temperature --wt% impurity --% deformation
- 42. Strengthening Mechanisms in Metals <ul><li>Grain Boundary Strengthening: Smaller grains result in stronger materials. The GB acts as an obstacle to dislocation motion. </li></ul><ul><li>Work-hardening: As a metal is plastically deformed, the dislocation density increases. Dislocation-dislocation interactions result in reduced mobility of dislocations. </li></ul><ul><li>Alloying: Strain fields of alloying elements (substitutional and interstitial) stop dislocation motion. Plus, they may form secondary phases and the GB between phases may reduce dislocation mobility. </li></ul>How do these mechanisms affect electrical conduction?
- 43. Strengthening Mechanisms in Metals <ul><li>Any defect structure will reduce electron mobility . </li></ul><ul><li>Ideal metallic conductor should be: </li></ul><ul><li>Single-crystal (no grain boundaries, twin boundaries, anti-phase boundaries, vacancies [impossible!!!]… ) </li></ul><ul><li>No defects (dislocations). </li></ul><ul><li>As pure as possible (no impurities, no secondary phasesand phase boundaries). </li></ul>They ALL decrease electrical conductivity!!!
- 44. What about electronic structure <ul><li>To understand the electronic structure of a crystal, we have to consider several steps of increasing complication: </li></ul><ul><ul><li>Atoms </li></ul></ul><ul><ul><li>Molecules </li></ul></ul><ul><ul><li>Crystals </li></ul></ul><ul><ul><ul><li>Metals </li></ul></ul></ul><ul><ul><ul><li>Semiconductors </li></ul></ul></ul><ul><ul><ul><li>Insulators </li></ul></ul></ul>
- 45. Electrons in atoms <ul><li>Electrons in an atom have particular energies (quantized energy states ) depending on which orbital they are in. </li></ul>Pauli exclusion principle H 1s He 1s B 1s 1p Energy
- 46. Electrons in solids <ul><li>In a solid, there are so many electrons with energies very near each other that ‘bands’ of states develop. </li></ul>Isolated atoms Solid All we draw is the “band diagram”
- 47. Energy band structures for various metals <ul><li>Partially filled or empty bands are called ‘conduction bands.’ </li></ul><ul><li>Any band that is totally filled is considered to be a “valence band.” </li></ul><ul><ul><li>We usually ignore ‘deep’ valence bands. </li></ul></ul>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
- 48. Energy band structures for various metals <ul><li>Energy bands overlap differently depending on material and esp. valence electrons. </li></ul>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
- 49. Definition of Conductivity <ul><li>The free-est electron (the electron with the highest energy) defines the position of the “Fermi level.” </li></ul><ul><ul><li>Above E f , all available electron states in the energy bands are empty </li></ul></ul><ul><ul><li>Below E f , they are all filled. </li></ul></ul><ul><li>If there is no gap between filled and empty states, the material is conductive . </li></ul><ul><li>If there is a gap, the material is a semiconductor or insulator. </li></ul>Metal (Cu) partially filled 4s (conduction) Empty 4p (conduction) Band gap Band gap Energy Filled (valence) E f , Fermi level
- 50. Band structures for semiconductors and insulators <ul><li>Semiconductors and Insulators have totally full valence bands and empty conduction bands with a bandgap between them. E f exists in the bandgap . </li></ul><ul><ul><li>The distinction between semiconducting and insulating materials is arbitrarily set to a bandgap of < or > 2 eV, respectively. </li></ul></ul>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
- 51. CONDUCTION & ELECTRON TRANSPORT <ul><li>At room temperature, atoms have kinetic energy = kT, which is approximately 25 meV. </li></ul><ul><li>This is sufficient to jump from a filled state to an empty state in a metal since the Fermi level (topmost electron) has empty states nearby. </li></ul><ul><li>Once in the empty state, an electron can be swept away by an electric field. </li></ul><ul><li>In a metal, nearly any electric field is sufficient to pull a substantial number of electrons into these nearby, empty, conducting states. </li></ul>
- 52. Conduction in insulators/semiconductors • Insulators: --Higher energy states not accessible due to gap. • Semiconductors: --Higher energy states possibly accessible due to smaller gap. <ul><li>Note: Conductivity can sometimes be enhanced by adding: </li></ul><ul><li>Dopants to generate excess charges </li></ul><ul><li>Impurities or defects that create states or bands within the gap. </li></ul>
- 53. Metallic conduction <ul><li>Once an electron has jumped across the Fermi level, or whenever there is not an electron in a site beneath the Fermi level, this is considered a ‘hole.’ </li></ul><ul><li>A hole behaves similar to an electron, but has the opposite charge. It can contribute to conductivity. </li></ul>
- 54. SUMMARY Reading for next class Semiconductors and Integrated Circuits, Chapter sections: 18.10-15 <ul><li>How are conductance and resistance characterized? </li></ul><ul><li>What are the forms of Ohm’s law? </li></ul><ul><li>How does conductivity vary for conductors, semiconductors, and insulators? </li></ul><ul><li>How do available electron energy states vary for atoms, molecules, large molecules, and solids? </li></ul><ul><li>Sketch the 3 possible metallic band diagrams. </li></ul><ul><li>Sketch a simple metallic, semiconducting, and insulating band diagram. </li></ul><ul><li>How is conductivity described based on metal, semiconductor, and insulating band diagrams? </li></ul><ul><li>What are, and what are the equations, for the drift velocity and conductivity with respect to the mobility? </li></ul><ul><li>Describe and be able to calculate the thermal and impurity components of conductivity? </li></ul><ul><li>What kinds of scattering sites contribute to the deformation term of conductivity? </li></ul>

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