Material Science and EngineeringCHE F243

Karthik Chethan V.BITS Pilani, Hyderabad Campus

2015

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Electrical properties

• Electrical conduction:How many moveable electrons are there in a material (carrier density)?How easily do they move (mobility) ?• Conduction in ionic and polymeric materials• Dielectric behavior

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Stimulus and response

• 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, Ω, V/A].• R depends on the intrinsic resistivity ρ of the material

[Ω- m] and on the geometry (length l and area A through which the current passes): R = ρl/A

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• In most materials (e.g. metals), the current is carried by electrons (electronic conduction). In ionic crystals, the charge carriers are ions (ionic conduction).

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• The electrical conductivity (the ability of a substance to conduct an electric current) is the inverse of the resistivity:

σ = 1/ρ• Since the electric field intensity (per unit

length) in the material is E = V/l, Ohm's law can be rewritten in terms of the current density

J = I/A as: J = σ E, J is the current flux

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Energy Bands

• In an isolated atom (gaseous state) electrons occupy well defined energy states.

• When atoms come together to form a solid, their valence electrons interact with each other (e – e) and with nuclei (e-atom) due to Coulomb forces in addition to atom-atom interactions.

• Two specific quantum mechanical effects happen. First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume perturbs their energy, this is called energy perturbation (some increase and some decrease).

• 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 (relatively smaller or larger), where electrons cannot exist.

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Charge Mobility

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Semi-conductors

• Conductivity intermediate between metals and insulators (glass, wool etc.).

• Conduction in semiconductors can be altered by light, electrical field, temperature or impurities.

• Examples: Si, Ge, GaP, GaAs etc.

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Semi-conductivity

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Summary

Number and Mobility of charges (electrons and ions)Conduction pathObjective is to reach the electrodes and dissipate at electrodes

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Polarize and accumulate at the electrode or reorient inside the material, but bound

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