Suppose we mix into melted germanium (Z = 32) a small amount of arsenic.(Z = 33), the next element after germanium in the periodic table. This deliberate addition of impurity elements is called doping. Arsenic is in Group V; it has five valence electrons. When one of these electrons is removed, the remaining electron structure is essentially identical to that of germanium. The only difference is that it is smaller; the arsenic nucleus has a charge of +33e rather than +32e, and it pulls the electrons in alittle more. An arsenic atom can comfortably take the place of a germanium atom as a substitutional impurity. Four of its five valence electrons form the necessary nearest-neighbor covalent bonds. The fifth valence electron is very loosely bound (Fig. 44-25a); it doesn’t participate in the covalent bonds, and it is screened from the nuclear charge of +33e by the 32 elec A donor (n-type) impurity atom has a fifth valence electron that does not participate in the covalent bonding and is very loosely bound. In fact, if its probability density were drawn to scale, the maximum would be well off this page. (b) Energy-band diagram for an n-type semiconductor at a low temperature. The donor levels lie just below the conduction band. One donor electron has been excited into the conduction band. The Fermi level is between the donor levels and the bottom of the conduction band; as the temperature increases, it will move closer to the center of the energy gap.
Example 44-10 shows that at ordinary temperatures and with a band gap of 1.0 eV, y a very small fraction (of the order of IO~ of the states at the bottom of the contion band in a pure semiconductor contain electrons to participate in intrinsic nductivity. Thus we expect the conductivity of such a semiconductor to be about 109 smaller than that of good metallic conductors, and measurements bear out this prediction. However, a concentration of donors as small as one part in 108 can increase the
conductivity so drastically that conduction due to impurities becomes by far the dominant mechanism. In this case the conductivity is due almost entirely to negative charge (electron) motion. We call the material an n-type semiconductor, with n-type impurities . Adding atoms of an element in Group ill (B, AI, Ga, In, Tl), with only three valence electrons, has an analogous effect. An example is gallium (Z = 31); as a substitution impurity in germanium, the gallium atom would like to form four covalent bonds, but it has only three outer electrons. It can, however, steal an electron from a neighboring germanium atom to complete the required four covalent bonds (Fig. 44-26a). The resulting atom has the same electron configuration as Ge but is somewhat larger because gallium’s nuclear charge is smaller, +31e instead of +32e.
44-26 (a) An acceptor (p-type) impurity atom has only three valence electrons. It can borrow an electron from a neighboring atom to complete four covalent bonds. The resulting hole is then free to move about the crystal. (b) Energy-band diagram for a p-type semiconductor at a low temperature. The acceptor levels lie just above the valence band. One level has accepted an electron from the valence band, leaving a hole behind. The Fermi level is between the top of the valence band and the acceptor levels; as the temperature increases, it will move closer to the center of the energy gap.
This theft leaves the neighboring atom with a hole, or missing electron. The hole acts as a positive charge that can move through the crystal just as with intrinsic conductivity. The stolen electron is bound to the gallium atom in a level called an acceptor level about 0.01 eV above the top of the valence band (Fig. 44-26b). The gallium atom, called an acceptor, thus accepts an electron to complete its desire for four covalent bonds. This extra electron gives the previously neutral gallium atom a net charge of -e. The resulting gallium ion is not free to move. In a semiconductor that is doped with acceptors, we consider the conductivity to be almost entirely due to positive charge (hole) motion. We call the material ap-type semiconductor, with p-type impurities. Some semiconductors are doped with both n- and p-type impurities. Such materials are called compensated semiconductors.
CAUTION ~ Saying that a material is a p-type semiconductor does not mean that the material has a positive charge; ordinarily, it would be neutral. Rather, it means that its majority carriers of current are positive holes (and therefore its minority carriers are negative electrons). The same idea holds for an n-type semiconductor; ordinarily, it will not have a negative charge, but its majority carriers are negative electrons. ~ We can verify the assertion that the current in n and p semiconductors really is carried by electrons and holes, respectively, by using the Hall effect (optional Section 28-10). The sign of the Hall emf is opposite in the two cases. Hall-effect devices constructed from semiconductor materials are used in probes to measure magnetic fields and the currents that cause those fields.