In terms of electron energy band structure, discuss reasons for the difference in electrical conductivity between metals, semiconductors, and insulators.

Electrical conductivity is a measure of how well a material can allow the flow of electric current. In essence, it tells us how easily electrons can move through a material when an electric field is applied. This relies heavily on the availability of free charge carriers—usually electrons.

Materials with high electrical conductivity, like metals, have an abundance of free electrons that can move with minimal resistance. Consequently, they are excellent conductors of electricity. On the other hand, materials with poor conductivity, known as insulators, have very few available charge carriers, making them ineffective at conducting current under normal conditions. Semiconductors fall in between these two extremes, with their conductivity varying under different conditions such as temperature changes or impurity additions (doping).

Understanding the electron energy band structure is critical in explaining these variations in conductivity, as it dictates the ease with which electrons can move from one energy level to another and thereby conduct electricity.

Semiconductors possess a unique place in the electron energy band structure because they have a small, but crucial, band gap. At low temperatures, this band gap keeps them acting like insulators—few electrons have the energy to leap across the gap to contribute to conductivity. As the temperature increases, more electrons acquire enough energy to jump across the band gap into the conduction band, which allows them to participate in electrical conduction.

Their conductivity can also be manipulated by adding impurities in a process called doping. Depending on the type of impurity added, semiconductors can be made to have an abundance of negative charge carriers (n-type) or positive ones (p-type). This control over electrical properties is what makes semiconductors the foundation of modern electronic devices like transistors and solar cells.

In insulators, electrical conductivity is exceptionally low due to the large band gap in their electron energy band structure. This gap is so great that it's highly unlikely for electrons to gain enough energy to cross over from the valence band to the conduction band. Consequently, insulators are often used to protect us from the unintended flow of electric current—they are excellent materials for casing wires and creating barriers around conductive parts.

Insulating materials include ceramics, glass, and plastics, all of which are integral to a wide array of devices, offering safety and stability. The distinctive property of having a large band gap ensures that under normal conditions, insulators do not contribute to electrical conduction.

Metals are recognized for their excellent electrical conductivity, which can be attributed to the overlapping of their valence and conduction bands. This overlap means that there is no band gap that electrons must overcome in order to conduct electricity. As a result, even at room temperature, there's a sea of free electrons in metals available to flow and thus carry an electric current.

This property not only makes metals perfect for wiring and electrical circuits but also explains their effectiveness as thermal conductors, as the same free electrons can transfer energy in the form of heat. Commonly used conductive metals include copper, aluminum, and silver, each chosen for their specific properties relating to resistance, cost, and the environment in which they will be used.

The band gap is a fundamental concept in understanding the electronic properties of materials. It refers to the energy difference between the valence band, filled with electrons, and the conduction band, where electrons can move freely and contribute to conduction. The size of this gap determines how a material behaves in response to electrical stimuli.

Large band gaps result in insulating behavior, as electrons don't have enough energy to make the jump to the conduction band under ordinary circumstances. Small or nonexistent band gaps, like those found in semiconductors and metals, respectively, allow for various degrees of conductivity. This concept is critical not only for engineers designing electronic components but also for advancements in photovoltaics and other technologies aiming to exploit the unique behaviors of electrons in different materials.