Semiconductors

Abstract

The theory of the chemical bonding in crystalline solids such as pure metals and alloys, insulators and semiconductor materials may be well understood by an expansion of the linear combination of atomic orbitals (LCAO). In this theory the atomic orbitals (AO) of two atoms can be combined together in order to form bonding and antibonding molecular orbitals (MO) symbolized by σ and σ* respectively. In the case of three neighboring atoms, it creates a string of atoms with bonding that connects all three. Hence there appear a bonding orbital, an antibonding orbital, and a new orbital called a nonbonding orbital. Essentially a nonbonding orbital is an orbital that neither increases nor decreases the net bonding energy in the molecule. The important feature here is that three atomic orbitals must produce three molecular orbitals. Hence, the total number of orbitals must remain constant. If we apply this concept by considering combinations of four atoms, it will give four molecular orbitals, two bonding and two antibonding. Notice that the two bonding and two antibonding orbitals have not exactly the same energy. The lower bonding orbital is slightly more bonding than the other and symmetrically one antibonding orbital is slightly more antibonding than the other. As a general rule, if we consider a large number of atoms, N, where N could have an order of magnitude similar to that of Avogadro’s number, it will lead to the combination of a large number of bonding and antibonding orbitals. These orbitals will be so close together in energy that they begin to overlap creating a definite band of bonding (i.e. highest occupied (HO) energy band or valence band) and a band of antibonding orbitals (i.e., lowest unoccupied (LU) or conduction band), the empty energy region between the valence and conduction bands is called the energy band gap. These definitions arise because electrons that enter the antibonding band are free to move about the crystal under an electric field strength (i.e., electrical conduction). It is this existence of valence and conduction bands that explains the electrical and optical properties of crystalline solids. The Fermi level with its energy EF is a level at which the probability of an electron occupying it is 1/2. The Fermi level is the highest occupied state at absolute zero (i.e., −273.15 °C).