Physics of conduction in solids
Electrical insulation is the absence of electrical conduction. Electronic band theory (a branch of physics) says that a charge flows if states are available into which electrons can be excited. This allows electrons to gain energy and thereby move through a conductor such as a metal. If no such states are available, the material is an insulator.
Most (though not all, see Mott insulator) insulators have a large band gap. This occurs because the "valence" band containing the highest energy electrons is full, and a large energy gap separates this band from the next band above it. There is always some voltage (called the breakdown voltage) that gives electrons enough energy to be excited into this band. Once this voltage is exceeded the material ceases being an insulator, and charge begins to pass through it. However, it is usually accompanied by physical or chemical changes that permanently degrade the material's insulating properties.
Materials that lack electron conduction are insulators if they lack other mobile charges as well. For example, if a liquid or gas contains ions, then the ions can be made to flow as an electric current, and the material is a conductor. Electrolytes and plasmas contain ions and act as conductors whether or not electron flow is involved.
When subjected to a high enough voltage, insulators suffer from the phenomenon of electrical breakdown. When the electric field applied across an insulating substance exceeds in any location the threshold breakdown field for that substance, the insulator suddenly becomes a conductor, causing a large increase in current, an electric arc through the substance. Electrical breakdown occurs when the electric field in the material is strong enough to accelerate free charge carriers (electrons and ions, which are always present at low concentrations) to a high enough velocity to knock electrons from atoms when they strike them, ionizing the atoms. These freed electrons and ions are in turn accelerated and strike other atoms, creating more charge carriers, in a chain reaction. Rapidly the insulator becomes filled with mobile charge carriers, and its resistance drops to a low level. In a solid, the breakdown voltage is proportional to the band gap energy. When corona discharge occurs, the air in a region around a high-voltage conductor can break down and ionise without a catastrophic increase in current. However, if the region of air breakdown extends to another conductor at a different voltage it creates a conductive path between them, and a large current flows through the air, creating an electric arc. Even a vacuum can suffer a sort of breakdown, but in this case the breakdown or vacuum arc involves charges ejected from the surface of metal electrodes rather than produced by the vacuum itself.
In addition, all insulators become conductors at very high temperatures as the thermal energy of the valence electrons is sufficient to put them in the conduction band.
In certain capacitors, shorts between electrodes formed due to dielectric breakdown can disappear when the applied electric field is reduced.