If you have studied the movement of either thermal or electrical energy through solids, you may be interested in how the energy bands are related to conduction and insulation.
The electric current that flows through a solid consists of electrons with energies associated with the conduction band. Solids that conduct heat or electric current (called conductors) will have many electrons with energies in the conduction band. Solids that do not readily conduct heat or electric current (called insulators) will have few electrons in the conduction band. Thus, the electrons in insulators are found mostly in the valence band. Solids that are good conductors will have many electrons in the valence band because these materials have enough electrons to fill all available energies in the valence band and many left over in the conduction band.
In addition to the difference in the number of electrons found in their respective conduction bands, conductors and insulators also differ in the size of their respective energy gaps. For conductors, the two bands either overlap or are so close together that electrons with energies in the valence band can easily acquire enough energy to have energies associated with the conduction band. Insulators, on the other hand, have energy gaps that are so large that thermal or light energy is not sufficient for electrons to move to the conduction band from the valence band.
The solids that make up LEDs are called semiconductors. As the name implies, a semiconductor is a solid whose physical properties place it somewhere between conductors and insulators. In semiconductors the energy gap is small enough that when sufficient energy (i.e. thermal, electrical, or light) is supplied, electrons gain enough energy to become the conduction band electrons.
The electrons in the conduction band carry the energy. Materials that have electrons in this band can transmit easily both thermal and electrical energy. The good electrical conductors are also good thermal conductors.