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(This page is under development, and might be completed Winter 2002).
In some materials it is possible for a gap, the "band gap," to occur at some point within a band. This has important consequences for color where there happen to be exactly four valence electrons per atom available for entry into the band. As shown at the left in Fig. 20, the result is that the lower-energy band, the "valence band," is exactly filled to capacity, and the upper band, the "conduction band," is exactly empty. The magnitude of the energy spacing between the two bands is the "band gap" or "energy gap," usually designated Eg. Consider now the absorption of light as represented by the vertical arrows A, B, and C in Fig. 20. Since there are no electron energy levels in the band gap between the valence and conduction bands, the lowest-energy light that can be absorbed corresponds to arrow A, involving the excitation of an electron at the top of the valence band up to a level at the bottom of the conduction band, corresponding to the band-gap energy Eg. Light of any higher energy can also be absorbed as indicated by the arrows B and C.
If the substance represented by this figure has a large band gap, such as the 5.4 eV of diamond or the similar value of corundum, then no light in the visible spectrum can be absorbed and these substances are indeed colorless when pure. Such "large-band-gap semiconductors" are excellent insulators and are more usually treated as covalently bonded materials.
Color of some band-gap semiconductors
Substance
name
name
gap
(eV)
Consider now a "medium-band-gap semiconductor," a material with a somewhat smaller band gap, such as the compound cadmium sulfide CdS; this is also the pigment cadmium yellow and the mineral greenockite (more examples in table at right). Here the 2.6 eV band-gap energy permits absorption of violet and some blue but none of the other colors, leading to a yellow color, as can be deduced from the color scale at the right of Fig. 20. A somewhat smaller band gap that permits absorption of violet, blue, and green produces an orange color; a yet-smaller band gap as in the pigment vermillion (the mineral cinnabar HgS) with a band gap of 2.0 eV results in all energies but the red being absorbed and thus leads to a red color. All light is absorbed when the band-gap energy is less than the 1.77 eV (700nm) limit of the visible spectrum and these "narrow-band- gap semiconductors" are black, as in the last three materials of Table 11.
PLATE IX. Mixed crystals of yellow cadmium sulfide CdS and black cadmium selenide CdSe, showing the intermediate-band-gap colors as in Fig. 20.
An illustration of this change in the band-gap size is shown by mixed crystals of yellow cadmium sulfide CdS, (E, = 2.6 eV), and black cadmium selenide CdSe (Eg = 1 .6 eV), which have the same structure and form a solid-solution series. Plate IX illustrates the yellow-orange-red-black sequence of these mixed crystals as the band-gap energy decreases, following the sequence of Fig. 20. Mixed crystals such as Cd4SSe3 form the painter's pigment cadmium orange and are also used to color glass and plastic. Mercuric sulfide HgS exists in two different crystalline forms. Cinnabar (the pigment vermillion) with Eg = 2.0 eV is a deep red but can transform on exposure to light in an improperly formulated paint to the black metacinnabar with Eg = 1.6 eV in as little as five years; this has happened in a number of old paintings.
FIG. 20. The absorption of light in a band-gap material (left), and the variation of color with the size of the band gap (right); see also Plate IX.
