It is well known that in general conductivity of metals increases with decreasing temperature. Although there are less electrons that are thermally excited above the Fermi energy to contribute to conduction, the decrease in thermal vibrations that scatters conducting electrons has a larger effect, thus conductivity increases.

Similarly, electrical conductivity of semiconductors increases with increased temperature because there is more thermal energy to excite a greater number of electrons from the valence band to the conduction band. However, as more electrons populate the conduction band the influence of thermal scattering becomes dominant and conductivity begins to decrease like in a metal.

If electrons need to be excited above the Fermi energy in order to contribute to conduction, would a metal at 0 K become an insulator since there is no thermal energy to excite electrons?

Let me know if I am thinking about this correctly. Thanks

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