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CONDUCTORS

CONDUCTORS. M V V K Srinivas Prasad K L University. Electrical Conduction in Metals. Ohm’s Law At constant temperature the current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor. Ohm’s Law: Macroscopic form. Resistance.

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CONDUCTORS

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  1. CONDUCTORS M V V K Srinivas Prasad K L University

  2. Electrical Conduction in Metals • Ohm’s Law • At constant temperature the current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor. • Ohm’s Law: Macroscopic form M V V K Srinivas Prasad, K L University

  3. Resistance • The opposing force offered by the material to the flow of current. • Depends on • Nature of the material (ρ). • Temperature. • Geometry/ dimensions (length L, area of cross section A) R = r (L/A) M V V K Srinivas Prasad, K L University

  4. surface area of current flow current flow path length Resistivity • It is a material property. • It defines how difficult is it for current to flow. • Geometry independent. • Temperature dependent. M V V K Srinivas Prasad, K L University

  5. Examples of Resistivity (ρ) • Ag (Silver): 1.59×10-8 Ω·m • Cu (Copper): 1.68×10-8 Ω·m • Graphite (C): (3 to 60)×10-5 Ω·m • Diamond (C): ~1014 Ω·m • Glass: ~1010 - 1014 Ω·m • Pure Germanium: ~ 0.5Ω·m • Pure Silicon: ~ 2300Ω·m M V V K Srinivas Prasad, K L University

  6. Current Density (J) • It is the current flowing through unit area of cross section. M V V K Srinivas Prasad, K L University

  7. Ohm's Law -- Microscopic Form M V V K Srinivas Prasad, K L University

  8. Experimental verification of ohm’s law M V V K Srinivas Prasad, K L University

  9. Electrical conductivity varies between different materials by over 27 orders of magnitude, the greatest variation of any physical property  (.cm)-1 Metals:  > 107 (.m)-1 Semiconductors: 10-6 <  < 105 (.m)-1 Insulators:  < 10-6 (.m)-1 M V V K Srinivas Prasad, K L University

  10. Energy Band Structures in Solids M V V K Srinivas Prasad, K L University

  11. In most of solids conduction is by electrons. • σ depend on no. of electrons available for conduction. • The no. of electrons available for conduction depends on • Arrangement of electrons states or levels with respect to energy. • The manner in which these states are occupied by electrons. M V V K Srinivas Prasad, K L University

  12. Isolated Atom M V V K Srinivas Prasad, K L University

  13. f02_02_pg18 M V V K Srinivas Prasad, K L University

  14. M V V K Srinivas Prasad, K L University

  15. WHY ENERGY BANDS ARE FORMED? M V V K Srinivas Prasad, K L University

  16. Electrons of one atom are perturbed by the electrons and nuclei of the adjacent atoms. • Results in splitting of atomic states into a series of closely spaced electron states to from what are called ELECTRON ENERGY BAND. • Extent of splitting depends on interatomic separation. M V V K Srinivas Prasad, K L University

  17. Electronic Band Structures From Fig. 17.2 Callister’s Materials Science and Engineering, Adapted Version. M V V K Srinivas Prasad, K L University

  18. Band Structure • Valence band – filled – highest occupied energy levels • Conduction band – empty – lowest unoccupied energy levels Conduction band valence band from Fig. 17.3 Callister’s Materials Science and Engineering, Adapted Version. M V V K Srinivas Prasad, K L University

  19. With in each band the energy states are discrete. • No. of states with in each band will equal the total of all states contributed by the N atoms. • s band consists of N states • p band consists of 3N states • Electrical properties of a solid depends on its electron band structure. M V V K Srinivas Prasad, K L University

  20. M V V K Srinivas Prasad, K L University

  21. Energy Band Structure M V V K Srinivas Prasad, K L University

  22. Energy Band Structure M V V K Srinivas Prasad, K L University

  23. Conductors M V V K Srinivas Prasad, K L University

  24. Conductors M V V K Srinivas Prasad, K L University

  25. M V V K Srinivas Prasad, K L University

  26. Partially filled band Overlapping bands Energy Energy empty band empty GAP band partly filled filled band band filled states filled states filled filled band band Conduction & Electron Transport • Metals (Conductors): -- for metals, empty energy states are adjacent to filled states. • thermal energy excites electrons into empty higher energy states. • two types of band structures for metals - partially filled band - empty band that overlaps filled band M V V K Srinivas Prasad, K L University

  27. Energy Band Structures Metals Semiconductors and Insulators M V V K Srinivas Prasad, K L University

  28. Electron movement An electron moves about randomly in a metal being frequently and randomly scattered by thermal vibrations of the atoms. In the absence of an applied field there is no net drift in any direction. M V V K Srinivas Prasad, K L University

  29. Applied Field – net drift • The electrons scatter by collisions with atoms and vacancies that lose the KE and drastically change their direction of motion. • Electronsmove randomly but with a net drift in the direction opposite to the electric field. • In the presence of an applied field, there is a net drift along the x-direction. • After many scattering events the electron has been displaced by a net distance, Δx, from its initial position toward the positive terminal. M V V K Srinivas Prasad, K L University

  30. Scattering of electrons is because of • Imperfections • Impurity atoms • Vacancies • Interstitial atoms • Dislocations • Thermal vibrations M V V K Srinivas Prasad, K L University

  31. Electron Mobility • Force on electron is -eE, e = charge • No obstacles  electron speeds up in an electric field. Vacuum (TV tube) or perfect crystal • Real solid: electrons scattered by collisions with imperfections and thermal vibrations  friction  resistance  net drift velocity of electrons vd = eE e– electron mobility [m2/V-s]. 1 / Friction Transfers part of energy supplied by electric field into lattice asheat. M V V K Srinivas Prasad, K L University

  32. Electron Mobility • Electrical conductivity proportional to number of free electrons per unit volume, Ne, and electron mobility, e  = Nee e Nmetal >> Nsemi metal < semi metal >> semi M V V K Srinivas Prasad, K L University

  33. Electrical resistivity of metals M V V K Srinivas Prasad, K L University

  34. Total resistivity tot (Matthiessen rule) total = thermal+impurity+deformation Increases with T, with deformation, and with alloying. M V V K Srinivas Prasad, K L University

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