L3- Energy levels and band gaps

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6 Terms

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Fermi level (Ef)

The energy of the highest filled state in the energy band at 0K

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Fermi function f(E)

The probability that an energy level, E, is occupied by an electron. 0< f(E) <1

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Relationship between f(E) and T

f(E) = 1/[1+exp((E-Ef)/kT)]

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Why are metals good electrical conductors?

Thermal energy is sufficient to promote electrons above the Fermi level to unoccupied energy levels.

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<p>Insulator case e.g. diamond</p>

Insulator case e.g. diamond

  • Ef falls in centre of band gap

  • for solid, promotion of electron from valence band to conduction band needs E>Eg

  • f(E) = 1 throughout valence band + 0 throughout conduction band

  • Inability of thermal energy to promote e-s → conduction band ⇒ diamond = poor conductor

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<p>Semiconductor case e.g. Silicon </p>

Semiconductor case e.g. Silicon

  • Si has smaller band gap than diamond

  • ⇒ thermal energy promotes small but sig no .e-s from valence band → conduction band

  • Each e- promotion creates e- hole pairs.

  • Holes = produced in valence band (Equal no. e-s in cond band)

  • +ve and -ve charge carriers present in mod numbers so okay conductivity