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In terms of band theory, what is the difference (1)Between a conductor and an insulator (2)Between a conductor and a semi conductor ?

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Conductors

Conductors are characterized by overlapping valence and conduction bands (otherwise stated: Fermi level lies inside conduction band of conductors, and this band is partially filled with electrons). Valence electrons can freely transit to higher energy states in the conduction band, therefore applied voltage will cause their drift - electrical current.

Insulators

Insulators are characterized by Fermi level lying in between valence and conduction band. Valence band is therefore full and its electrons can't contribute to current. Conduction band is therefore empty and there are no electrons which can contribute to current at all.

Does this mean that an insulators can't conduct current at all? Well, no. It means that if you want to see current flow in insulator, you must transfer huge energy to electrons in order to transit them from valence band into conduction band (the energetic separation between these bands is called band gap).

Semi-conductors

Semi conductors have the same band structure as insulators, with Fermi level lying inside the band gap. The only difference is that the band gap of semiconductors is relatively small, which allows for low energy transitions of electrons from the valence band into the conduction bands. The energy for this transition may be gained from electrostatic energy, optical energy, heat energy etc...



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