Some semiconductor physics

Band structure and Doping

The principles of semiconductor physics are best illustrated using the example of silicon, a group 4 elemental semiconductor. The silicon crystal forms the so-called diamond lattice where each atom has four nearest neighbours at the vertices of a tetrahedron. The four-fold tetrahedral co-ordination is the result of the bonding arrangement which uses the four outer (valence) electrons of each silicon atom . Each bond contains two electrons, and you can easily see that all the valence electrons are taken up by the bonds. Most other industrially important semiconductors crystallise in this or closely related lattices, and have a similar arrangement of the bonding orbitals.

This crystal structure has a profound effect on the electronic and optical properties of the semiconductor. According to the quantum theory, the energy of an electron in the crystal must fall within well-defined bands. The energies of valence orbitals which form bonds between the atoms represent just such a band of states, the valence band. The next higher band is the conduction band which is separated from the valence band by the energy gap, or bandgap. The width of the bandgap E_c - E_v is a very important characteristic of the semiconductor and is usually denoted by E_g. This table gives the bandgaps of the most important semiconductors for solar-cell applications.

A pure semiconductor (which is called intrinsic) contains just the right number of electrons to fill the valence band, and the conduction band is therefore empty. Electrons in the full valence band cannot move - just as, for example, marbles in a full box with a lid on top. For practical purposes, a pure semiconductor is therefore an insulator.

Semiconductors can only conduct electricity if carriers are introduced into the conduction band or removed from the valence band. One way of doing this is by alloying the semiconductor with an impurity. This process is called doping. As we shall see, doping makes it possible to exert a great deal of control over the electronic properties of a semiconductor, and lies in the heart of the manufacturing process of all semiconductor devices.

Suppose that some group 5 impurity atoms (for example, phosphorus) are added to the silicon melt from which the crystal is grown. Four of the five outer electrons are used to fill the valence band and the one extra electron from each impurity atom is therefore promoted to the conduction band. For this reason, these impurity atoms are called donors. The electrons in the conduction band are mobile, and the crystal becomes a conductor. Since the current is carried by negatively charged electrons, this type of semiconductor is called n type.

A similar situation occurs when silicon is doped with group 3 impurity atoms (for example, boron) which are called acceptors. Since four electrons per atoms are needed to fill the valence band completely, this doping creates electron deficiency in this band. The missing electrons - called holes - behave as positively charged particles which are mobile, and carry current. A semiconductor where the electric current is carried predominantly by holes is called p-type.

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© University of Southampton, 1997