In solid-state physics, band theory accounts for the structure and properties of solid materials. Band theory proposes that the available energy states for electrons in solids are not discrete, as in the case of free atoms, but are merged into continuous, or wide, bands. This model is very successful for understanding the difference between conductors, insulators, and semiconductors.
The continuous energy bands are referred to as energy bands, and they are visualized as consisting of overlapping molecular orbitals. For example, sodium has a total of 11 electrons distributed as follows by increasing order of orbital energy: two electrons each in the 1s and 2s orbitals, six electrons in the 2p orbitals, and one electron in the 3s orbital. The next orbital (3p) with 3 suborbitals is empty. To make a sodium crystalline solid, sodium atoms are packed together in a configuration, in which the atoms are equally spaced, and space between the atoms is minimized. Although the interactions between one Na atom and an adjacent Na atom are weak, each sodium atom in the metallic solid is associated with many neighboring atoms. The bonding interactions sum to form a bonded metallic solid.
When the 3s orbital of one sodium atom overlaps the 3s orbital of its immediate neighbor in a crystal lattice, two molecular orbitals are formed: a bonding orbital of lower energy and an antibonding orbital of higher energy. When a third atom overlaps the first two, a third molecular orbital is formed, a nonbonding orbital encased by the lower energy bonding orbital and the higher energy antibonding orbital of the other two sodium atoms. Similarly, when N atoms come together in a single line, N molecular orbitals are formed with N distinct energy levels. These N molecular orbitals are very closely spaced in energy and form an essentially continuous band covering a range of discrete energies. The wide 3s band contains the freely moving valence electrons and is referred to as the valence band. The 3p band, empty of electrons, is called the conducting band. The extent of the gap between the valence and conducting bands of various materials determines their electrical conducting properties. If the gap is small, electrons will be able to jump from the valence to the conducting band and will be good conductors; if the gap is too large, electrons will remain in the valence band and the material will be a good insulator. The best conductors are metals, because in these materials, the valence and conduction bands overlap. Semiconductors have a small gap between their valence and conduction bands so that thermal or other excitations can bridge the gap by allowing electrons to jump to the conducting band. Because the gap in semiconductors is small, the presence of a small percentage of a doping material can also significantly increase conductivity.
Most solid substances are insulators, which means that in most solid substances, a large, forbidding gap exists between the energy of the valence electrons and the energy at which the electrons can move freely through the conduction band. A good example is provided by glass. Glass is an insulating material, but the fact that it is transparent to visible light allows its color to be changed. Visible light photons do not have enough energy to bridge the band gap of the glassy material and promote the electrons up to the conduction band. The addition of a very small percentage of impurity atoms to the glass can provide specific available energy levels to absorb certain colors of visible light, but the band gap is too large to transform glass into a good conductor by doping.
On the other hand, a semiconductor's conductivity can be significantly altered by doping. A semiconductor's band gap is small, and, in addition to the energy level of its valence and conduction bands, it is also characterized by a flexible Fermi level. This level, located between the valence and conduction bands, represents the maximum energy level that can be occupied by an electron at absolute zero. The Fermi level can be shifted by the addition of impurity atoms, which can drastically modify the conducting properties of semiconductors. For example, the application of band theory to n-type semiconductors shows that the addition of impurities shifts the Fermi level near the top of the band gap so that electrons can easily jump into the conduction band. In p-type semiconductors, the Fermi level is shifted close to the valence band, which results in extra holes in the band gap allowing excitation of valence band electrons, leaving mobile holes in the valence band.
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