# If increasing applying energy to an atom excites electrons, why does electrical conductivity decrease as temperature increases?

Applying energy to an atom makes the electrons jump up to higher energy levels. This is known as excitation. Electrons on higher energy levels are easier to remove from an atom than those on lower energy levels. Since applying energy to an atom raises the electrons, the electrons become easier to remove.

It is intuitive to think that looser electrons means greater electrical conductance, since the electrons can move more easily between atoms and therefore allow electrical conductivity.

Yet, superconductors are usually kept at near 0 Kelvin, and thermal resistors increase resistance on an increase of temperature. Also, molten metals conduct less than those that are solid.

What is the flaw (if any) in this logic?

• Electrons in conductors don't need to be raised to the conduction band by thermal excitation, they are already there at any temperature. What causes electrons to lose energy while they are moving in an electric field is the interaction with lattice vibrations (phonons). The number of excited phonons grows with temperature, so the electrons are being scattered more strongly at higher temperatures. Superconductors require a very different explanation, though, since their conduction is not facilitated by electrons but by quasi-particles made from electron pairs and phonons. – CuriousOne Feb 3 '16 at 7:11
• @CuriousOne Shouldn't your awnser be poster as an awnser rather than as a comment ? – Dimitri Feb 3 '16 at 15:24

As a general rule adding thermal energy doesn't cause electronic transitions. That's because typical electronic transition energies are a few electron volts or around 100kT at room temperature.

In a metal the electrons aren't in discrete energy levels but instead reside in a continuous band of energy levels called the conduction band. While thermal energy can excite electrons within this band it makes little difference to the electron mobility as electrons in the conduction band are already highly mobile.

Electrical resistance arises because electrons scatter off the crystal lattice formed by the atoms making up the metal. The kinetic energy ends up transferred to the lattice where is appears as vibrations of the lattice i.e. heat. If the lattice is already vibrating, i.e. already hot, then it in effect presents a bigger target and the scattering increases and this is why conductivity of metals falls with temperature. If you heat the metal you increase the amplitude of the lattice vibrations and the electrons are scattered more strongly by the vibrating lattice.

However something like the effect you describe is seen in semiconductors. In many semiconductors the energy difference between the energy bands and gap states is comparable with $kT$. If you heat a semiconductor you can excite electrons and that does increase the conductivity. Just as in a metal the electrons are scattered by the lattice, and this scattering increases with temperature, however at moderate temperatures the excitation of the electrons wins and the resistance goes down.

For example look at this graph of the the conductivity-temperature curve for the metal tungsten and the semiconductor silicon:

This shows how the conductivity of the metal falls with temperature while the conductivity of the silicon rises.

• Thanks for this nice answer. I'm impressed by the variation of the conductivity of the silicon, in log scale in your plot. I wonder whether your explanation (occupation of the conduction band due to temperature) works for so large variation. Any idea ? Thanks anyway. – FraSchelle Feb 4 '16 at 10:01
• @FraSchelle: have you tried Googling for semiconductor conductivity temperature or even searching this site ... – John Rennie Feb 4 '16 at 10:18
• Thanks again ! Indeed, dopant follow Maxwell's distribution at first approximation, sorry for the mistake. – FraSchelle Feb 4 '16 at 13:22
• I'm confused, if you heat the metal do you increase the amplitude of the lattice vibrations? I thought it would increase the frequency of these vibrations. Or is it both?? When things are cold, the lattice barely moves, it becomes still while hot things move around a lot right? So what's the relationship between the frequency of lattice vibrations and temperature? – Aditya May 26 at 3:37
• @Aditya that's a big topic and probably best posted as a new question – John Rennie May 26 at 4:04