Doped semiconductors

Doped semiconductors are semiconductors, which contain impurities, foreign atoms incorporated into the crystal structure of the semiconductor. Either these impurities can be unintentional, due to lack of control during the growth of the semiconductor, or they can be added on purpose to provide free carriers in the semiconductor.

The generation of free carriers requires not only that impurities are present, but also that the impurities give off electrons to the conduction band in which case they are called donors. If they give off holes to the valence band, they are called acceptors (since they actually accept an electron from the filled valence band). The ionization of shallow donors and acceptors are illustrated by Figure 2.6.5. Indicated are the donor and acceptor energies, Ed and Ea. The donor energy level is filled prior to ionization. Ionization causes the donor to be emptied, yielding an electron in the conduction band and a positively charged donor ion. The acceptor energy is empty prior to ionization. Ionization of the acceptor corresponds to the empty acceptor level being filled by an electron from the filled valence band. This is equivalent to a hole given off by the acceptor atom to the valence band.

Figure 2.6.5: Ionization of a) a shallow donor and b) a shallow acceptor

A semiconductor doped with impurities, which are ionized (meaning that the impurity atoms either have donated or accepted an electron), will therefore contain free carriers. Shallow impurities are impurities, which require little energy - typically around the thermal energy, kT, or less - to ionize. Deep impurities require energies much larger than the thermal energy to ionize so that only a fraction of the impurities present in the semiconductor contribute to free carriers. Deep impurities, which are more than five times the thermal energy away from either band edge, are very unlikely to ionize. Such impurities can be effective recombination centers, in which electrons and holes are captured and annihilate each other. Such deep impurities are also called traps.

Ionized donors provide free electrons in a semiconductor, which is then called n-type, while ionized acceptors provide free holes in a semiconductor, which we refer to as being a p-type semiconductor.

Ionization energy model
The energy required to remove an electron from a donor atom can be approximated using a hydrogen-like model. After all, the donor atom consists of a positively charged ion and an electron just like the proton and electron of the hydrogen atom. The difference however is that the average distance, r, between the electron and the donor ion is much larger since the electron occupies one of the outer orbitals. This is illustrated by Figure 2.6.6.