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Chapter18

# Chapter18 - Electrical properties Electrical conduction How...

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1 MSE 2090: Introduction to Materials Science Chapter 18, Electrical Conductivity Electrical properties ¾ Electrical conduction How many moveable electrons are there in a material (carrier density) ? How easily do they move (mobility) ? ¾ Semiconductivity Electrons and holes Intrinsic and extrinsic carriers Semiconductor devices: p-n junctions and transistors ¾ Conduction in polymers and ionic materials ¾ Dielectric behavior Optional reading: 18.14, 18.15, 18.21, 18.23-18.25

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Basic laws and electrical properties of metals (I) When an electrical potential V [volts, J/C] is applied across a piece of material, a current of magnitude I [amperes, C/s] flows. In most metals, at low values of V, the current is proportional to V, and can be described by Ohm's law : I = V/R where R is the electrical resistance [ohms, : , V/A]. R depends on the intrinsic resistivity U of the material [ : - m] and on the geometry (length l and area A through which the current passes): R = U l/A In most materials (e.g. metals), the current is carried by electrons ( electronic conduction ). In ionic crystals, the charge carriers are ions ( ionic conduction ).
3 MSE 2090: Introduction to Materials Science Chapter 18, Electrical Conductivity Basic laws and electrical properties of metals (II) The electrical conductivity (the ability of a substance to conduct an electric current) is the inverse of the resistivity: V = 1/ U Since the electric field intensity in the material is E = V/l, Ohm's law can be rewritten in terms of the current density J = I/A as: J = V E Electrical conductivity varies between different materials by over 27 orders of magnitude , the greatest variation of any physical property Metals: V > 10 5 ( : .m) -1 Semiconductors: 10 -6 < V < 10 5 ( : .m) -1 Insulators: V < 10 -6 ( : .m) -1 V ( : .cm) -1

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4 MSE 2090: Introduction to Materials Science Chapter 18, Electrical Conductivity
5 MSE 2090: Introduction to Materials Science Chapter 18, Electrical Conductivity Energy Band Structures in Solids (I) In an isolated atom electrons occupy well defined energy states, as discussed in Chapter 2. When atoms come together to form a solid, their valence electrons interact with each other and with nuclei due to Coulomb forces. In addition, two specific quantum mechanical effects happen. First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion . The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same energy. As a result of these effects, the valence electrons of atoms form wide electron energy bands when they form a solid. The bands are separated by gaps , where electrons cannot exist.

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6 MSE 2090: Introduction to Materials Science Chapter 18, Electrical Conductivity Energy Band Structures and Conductivity The highest filled state at 0 K Fermi Energy (E F ) The two highest energy bands are: ¾ Valence band the highest band where the electrons are present at 0 K ¾ Conduction band - a partially filled or empty energy band where the electrons can increase their energies by going to higher energy levels within the band when an electric field is applied Energy conduction band valence band unfilled bands filled bands band gap
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