What is Energy Band Theory of Crystals

Energy band theory of Crystals is a quantum physics approach to describe the behavior of the electronic orbits of an atom in a closely packed crystal lattice. We know that in an isolated gaseous atom, these orbits consist of discreet and sharply defined energy levels, as is stated by the well known and accepted Bohr’s atomic model. Now what happens when these isolated atoms are closely packed in a crystal lattice? The answer to that is important because most of the metals and semiconductors that form the building blocks of our technological age exist in crystalline forms and that answer is provided by the Energy band theory of Crystals.

When atoms are closely packed in a lattice structure, the outer orbit electrons of neighboring atoms comes in to a state of interaction with each other and these electrons behave like they belong to the crystal as a whole. Now according to Pauli’s exclusion principle, no two electrons can occupy the same quantum state. The various outer discrete energy states associated with each of the atoms can’t exist without contradicting this principle, as the electrons in them are now to behave like they belong to one entity. So these discrete energy states cease to exist and intermingle with each other to form bands which are spread out on the energy scale between a minimum and a maximum value. The inner most orbits continue to exist as discreet energy states because the electrons in them remain shielded to prevent any interaction with the neighboring atoms. The upper most band containing electrons is known as the Valence band while the lower most band that is empty is known as the Conduction band. For an electron to participate in the conduction process, it must possess enough energy to jump from the valence band to the conduction band. This can be visualized as an electron breaking free from the covalent bond of a lattice structure after absorbing some energy. Only electrons in the Conduction band can form an electrical current on the application of an electrical field. The conductivity of a material, thus very much depends on the energy gap between the valence and the conduction band. This is almost negligible in case of metals, moderate in case of semi conductors and very high in case of insulators. The band theory can be extended to describe many other electronic and electrical effects associated with crystalline solids such as doping, effect of temperature on resistivity etc.

Thus we can’t use the approach of discreet and sharply defined energy levels when it comes to analyzing the crystal lattice structures in the sphere of electronics. It is the energy band theory which helps us in understanding the various electrical properties and phenomenon associated with these materials.

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