Bands and the Conductivity Properties of the Elements

Recall from the introduction to the Experiment that substances conduct electricity if they contain mobile charged particles (i.e., ions or electrons). In a solid, electrons can become mobile if the electrons can be promoted to unfilled orbitals in the conduction band of the solid. How can we account for the electrical conductivity of metals? Think again about an individual Na atom, containing only one valence electron in the 3s orbital (recall Figure 3). This atom has a half-filled 3s orbital (because the 3s orbital can hold up to 2 electrons) and three unfilled 3p orbitals, as you will learn later in Chem 111. All of these are valence orbitals and combine with those from other atoms in the solid to form the band of "mixed" orbitals described above. However, the number of electrons contained in the valence band is much smaller than the number it is capable of containing. The reason the band is filled much less than its capacity is that each atom contributes only one electron to the band, but contributes four orbitals to the band; hence, the band is capable of holding up to eight electrons per atom. The filled and unfilled portions of the band are continuous (recall Figure 3); no band gap is present like in carbon and other nonmetal solids. Therefore, electrons can easily (i.e. with very little energy input) be promoted from filled orbitals in the band to unfilled orbitals in the band, and hence move throughout the metal solid. Therefore, metals conduct electricity because the partially-filled band of orbitals allows electrons to move easily throughout the sample.

What about nonmetals? We know that nonmetallic solids form two distinct bands. The lower-energy band, known as the valence band, contains all of the valence electrons (the band is filled with electrons), while the higher-energy band, the conduction band, contains no electrons (recall Figure 4). Electrons in the filled valence band cannot move to other orbitals within the band, because all of the orbitals are already filled. No motion of electrons occurs in the conduction band, because it is empty. Now, recall that these bands are separated by a large band gap. Therefore, a large amount of input energy is required to promote an electron from the filled lower-energy (valence) band to the unfilled higher-energy (conduction) band. Thus, without the high-energy input to promote an electron from the lower-energy band to the higher-energy band, there are no mobile charge carriers, and the nonmetallic solid cannot conduct electricity.

As you should observe in lab, semimetals such as silicon (Si) have intermediate properties between those of metals and nonmetals. The band gap in semimetals is small enough (recall Figure 5) that an electron can be promoted from the filled lower-energy band to the unfilled higher-energy band with a moderate input of energy (such as the thermal energy that dissipates in the solid when electrical current is passed through it). Then, the lower-energy (valence) band is no longer completely filled and the higher-energy (conduction) band is no longer completely empty; i.e., both bands are partially filled (Figure 7). In the valence band, electrons can move between orbitals (and thus throughout the solid) once some of the orbitals have become vacant. Promotion of electrons to the conduction band allows them to move easily between the band's many empty orbitals. Hence, semimetals can conduct electricity with a moderate input of energy.

Figure 7 In a semiconductor, the band gap is small enough that electrons can be moved from the orbitals in the valence band to the orbitals in the conduction band. This leaves both bands partially filled, so the material can conduct electricity.

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