Semiconductors. Movement of Charge Carriers

Junction Diode. Transistor and Applications

Energy Bands in Solids

As we see later, the allowed energy levels in a single atom are discrete (separate) and spaced widely apart. In the solid state, however, as in a crystal, large numbers of atoms are packed closely together, and the electrons are influenced strongly by the assembly of nuclei. The allowable energy levels then broaden into bands of energy, Fig. 39.1 (i). The bands contain allowable energy levels very close to each other, as at P. There may also be forbidden bands of energy, as at Q, which electrons cannot occupy. The lowest available energy band is called the valence band. The next available energy band is called the conduction band.

In an insulator, the valence band energy levels are completely filled by electrons. The conduction band is empty and the two bands are separated by a wide energy gap much greater than k Т in magnitude where k is the Boltzmann constant (p. 223), called the 'forbidden' band, Fig. 39.1 (ii). The electrons in the valence band have thermal energy of the order k Т but at room temperature they cannot gain sufficient energy from an applied p.d. to move to higher unoccupied energy levels. So the material is an insulator.

Semiconductors are a class of materials with a narrow forbidden band between the valence and conduction bands; the energy gap is of the order kT. At О К, all the energy levels in the valence band are occupied and the material is then an insulator. At normal temperatures, however, the thermal energy of some valence electrons, of the order kT, is sufficient for them to reach the conduction band, where they may become conduction electrons. The gap left in the valence band of energies by the movement of an electron is called a hole. Fig. 39.1 (ii). In semiconductor theory, both holes and conduction electrons play an active part, as we soon see.

In metals, however, the valence and conduction bands can overlap, as shown diagrammatically in Fig. 39.2. The electrons in the overlapping region of energy are conduction electrons. Since there is a large number of conduction electrons, metals are good conductors.

Semiconductors. Movement of Charge Carriers

Semiconductors are a class of solids with electrical resistivity between that of a conductor and an insulator. For example, the resistivity of a conductor is of the order 10^-8 Ohm m, that of an insulator is 10⁴ Ohm m and higher, and that of a semiconductor is 10^-1 Ohm m. Silicon and germanium are examples of semi­conductor elements widely used in the electronics industry.

Silicon and germanium atoms are tetravalent. They have four electrons in their outermost shell, called valence electrons. One valence electron is shared with each of four surrounding atoms in a tetrah^dral arrangement, forming 'covalent bonds' which maintain the crystalline solid structure (p. 133). Figure 39.3 (i) is a two-dimensional representation of the structure.

At О К, all the valence electrons are firmly bound to the nucleus of their

particular atoms. At room temperature, however, the thermal energy of a vale electron may become greater than the energy binding to its nucleus. The covalent bond is then broken. The electron leaves the atom, X say, and becomes a free electron. This leaves X with a vacancy or hole, Fig. 39.3 (ii). Since X now has a net positive charge, an electron in a neighbouring atom may then be attracted. Thus the hole appears to move to Y.

The hole movement through a semiconductor is random. But if a battery is connected, the valence electrons are urged to move in one direction and to fill the holes. The holes then drift in the direction of the field. Thus the holes move as if they were carriers with a positive charge +e, where e is the numerical value of the charge on an electron, Fig. 39.3 (iii). The current in the semi-conductor is also carried by the free electrons present. These are equal in number to the holes in a pure semiconductor and drift in the opposite direction since they are negative charges. The mobility of an electron, its average velocity per unit electric field intensity, is usually much greater than that of a hole.

In electrolytes (p. 676), the current is also carried by moving negative and positive charges but the carriers here are ions. It should be noted that, in a pure semiconductor, there are equal numbers of electrons and holes, the charge carriers. Electron-hole pairs are said to be produced by the movement of an electron from bound state in an atom to a higher energy level, where it becomes a free electron.

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