1. M V V K Srinivas Prasad K L University

2.  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 University2

3.  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 =  (L/A) M V V K Srinivas Prasad, K L University3

4.  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 University4 surface area of current flow current flow path length

5.  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): ~10 14 Ω·m  Glass: ~10 10 - 10 14 Ω·m  Pure Germanium: ~ 0.5 Ω·m  Pure Silicon: ~ 2300 Ω·m M V V K Srinivas Prasad, K L University

6.  It is the current flowing through unit area of cross section. M V V K Srinivas Prasad, K L University6

7. Ohm's Law -- Microscopic Form M V V K Srinivas Prasad, K L University7

8. Experimental verification of ohm’s law M V V K Srinivas Prasad, K L University8

9. 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 Metals:  > 10 7 ( .m) -1 Semiconductors: 10 -6 <  < 10 5 ( .m) -1 Insulators:  < 10 -6 ( .m) -1  ( .cm) -1

10. Energy Band Structures in Solids M V V K Srinivas Prasad, K L University10

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 University11

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15. M V V K Srinivas Prasad, K L University15 WHY ENERGY BANDS ARE FORMED?

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 University16

17. M V V K Srinivas Prasad, K L University17 From Fig. 17.2 Callister’s Materials Science and Engineering, Adapted Version.

18.  Valence band – filled – highest occupied energy levels  Conduction band – empty – lowest unoccupied energy levels M V V K Srinivas Prasad, K L University18 valence band Conduction band from Fig. 17.3 Callister’s Materials Science and Engineering, Adapted Version.

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 University19

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

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

28. 28 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. M V V K Srinivas Prasad, K L University29 Applied Field – net drift 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. The electrons scatter by collisions with atoms and vacancies that lose the KE and drastically change their direction of motion. Electrons move randomly but with a net drift in the direction opposite to the electric field.

30.  Imperfections  Impurity atoms  Vacancies  Interstitial atoms  Dislocations  Thermal vibrations M V V K Srinivas Prasad, K L University30

31. 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 v d =  e E  e – electron mobility [m 2 /V-s]. 1 / Friction Transfers part of energy supplied by electric field into lattice as heat. M V V K Srinivas Prasad, K L University

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

33. M V V K Srinivas Prasad, K L University33 Electrical resistivity of metals

34. 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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