9.2 SEMICONDUCTOR BASICS

Semiconductor physics as a whole is beyond the scope of this book, but some fundamental aspects of semiconductors are crucial to the understanding of semiconductor lasers. This section will cover those aspects and semiconductor materials, before we get into the details of light emission and lasers.

9.2.1 Valence and Conduction Bands

Semiconductors get their name because they conduct electricity better than an insulator but not as well as a conductor. This arises from the nature of the bonds between atoms and their electrons in the solid. In an insulator like glass, the outer electrons are tightly bound to atoms, often in covalent bonds between pairs of atoms. In conductors like copper, the outer electrons are only loosely bound to atoms, so they can flow freely though the material if a voltage is applied across it. A semiconductor falls in between the two.

The difference can be explained by considering electrons to be in one of two levels: a valence band in which they are bound to atoms, and a conduction band in which they are free to move around in the solid. The valence band is at a higher energy level than the conduction band, but in a conductor the top of the valence band overlaps with the bottom of the conduction band, as shown in Figure 9-1. This reflects the low-energy bonding of electrons to met-

al atoms, which allows electrons to move and carry current easily in conductors. In a semiconductor, there is a small band gap between the lower valence band and the higher-energy conduction band, and a few valence electrons have enough energy to escape to the conduction band. In an insulator, the band gap is large, so a valence electron needs so much energy to escape that essentially no electrons are free to conduct current through the solid.

The number of electrons N in the valence and conduction bands depends on the bandgap energy ΔE and the temperature T:

where k is the Boltzmann constant. This is the same formula used to describe the relative proportions of atoms and molecules in a pair of different energy levels.

If you plug in numbers, it turns out that very few electrons are in the conduction band at room temperature. In 100% pure silicon, where the band gap is 1.1 electron volts, only 3 10 ¹⁹ of the electrons are in the conduction band at room temperature. That is enough to carry a feeble current, but it gives pure silicon a high electrical resistance.