Electrical Conductivity in Semiconductors

Electrical conduction in semiconductors can be visualized by using either a localized bonding model or a model based on band theory.

The Local Bonding Model

Let us first consider a localized bonding model. In such a model, a physical picture is obtained by focusing on the bonds that bind the silicon atoms together. If the temperature is very low, all of the valence electrons are localized in two-electron Si - Si bonds. Since these bonds are relatively strong, the electrons are held fairly tightly, and are not at all mobile. However, if the temperature is increased so that absorption of thermal energy occurs, a few super-energetic electrons are created. Some of these vibrate so vigorously that they are ejected from localized bonds into the surrounding crystal. This process leaves behind a number of one-electron bonds, one of which is indicated in Figure 1 by a dashed line. The most powerful formalism that has been developed to treat electrical conduction in semiconductors is to view the missing electrons in these one-electron bonds as positively charged particles called "holes" (designated in Figure 1 as h+).

The electrical conductivity is then determined by both the free electrons ejected from localized bonds, and by the holes created by this process. To see why this is so, consider what happens when a voltage is applied to the semiconductor. The relatively mobile "free electrons" acquire additional energy and migrate toward the positive terminal. At the same time, the holes (or one-electron bonds" migrate toward the negative terminal. The mechanism by which this later process occurs is explained below.

Consider a "normal" two-electron bond situated immediately adjacent to a hole. When an electric field is applied to the crystal, the electrons in this bond are accelerated towards the positive terminal. Occasionally one of them acquires sufficient energy to "jump" into the vacant hole. When this occurs, the original one-electron bond is restored to two-electron status. However, a new one-electron bond (or hole) is created from the original "normal bond". As this process is repeated, the original hole migrates, one bond at a time, toward the negative terminal. It is this migration towards the negative terminal that encourages us to think of the hole as being positively charged.

Both of the processes described above are illustrated in Figure 2. The migration of holes is also depicted in the cartoon shown in Figure 3.

Here, the chairs represent one-electron bonds, and the students represent the additional electrons that "migrate" to complete unsatisfied one-electron bonds.

Band Theory

Now let us consider how the conduction of electric charge can be visualized by using band theory.

At very low temperatures, the valence band is fully occupied, and the conduction band is completely empty. Under these conditions, no current flows and the semiconductor acts as if it were an insulator. However, as the temperature is increased, some thermal energy is acquired, and a few electrons are promoted from the valence band to the conduction band. This process is illustrated in Figure 4, which shows four negatively charged electrons entering the conduction band. In doing this, they leave four vacancies or "holes" in the valence band. Since the conduction band orbitals in the semiconductor are relatively delocalized, charge can be easily transported though the crystal by the small number of electrons promoted to this band. Moreover, the holes can move from one orbital to another in the valence band, also contributing to the overall conductivity.

At room temperature, very little thermal energy is available, and only a few electrons can be promoted to the conduction band of any semiconductor having a band gap greater than about 0.1eV. In fact, in pure silicon (band gap =1.1eV = 105 kJ/mol), only 1 electron in 1012 occupies an orbital in the conduction band when equilibrium is established at 300 K. This explains why semiconductors are much poorer conductors than are metals. However, as the temperature is raised, the number of electrons promoted to the conduction band increases, as does the conductivity.