Semiconductors and their electronic bands [closed]

Question

While studying colors of sulfides and searching for the reason why they are black I came across this question:

https://chemistry.stackexchange.com/questions/138309/the-color-of-the-most-sulfides-of-p-and-d-block-elements#:~:text=The%20colours%20tend%20to%20be,of%20the%20transitions%20is%20small.

In it, the top commenter explained the fact that those sulfides are black with the valence band model, because their band gap is so small, they can absorb every visible wavelength of light.

I thought the valence band model only applied to metals, whose atomic orbitals mix with every other atomic orbital in the solid and therefore have an infinite amount of close lying orbitals, thus forming a band. How are ionic solids then able to do the same, when they are composed of different ions? Or does the theory work for all kinds of condensed matter.

Answer 1

As indicated in some comments, all solids, and for that matter all condensed matter, has a band structure. If atoms are packed densely enough, the orbital overlaps that produce "molecular" orbitals become interconnected throughout the volume of the material, and you have bands of energy levels that are filled with closely spaced orbitals. It is true that having discrete molecules, or an ionic structure where the anions tend to hold all the valence electrons, can limit the delocalization of electrons and thus produce narrow bands with wide gaps between them. But the band structure is still there. In the case of water, understanding the band structure, even of a molecular material in the liquid state, is essential to understanding electrochemical reactions commonly carried out in that medium (seehere).

The impact of band structure on color is illustrated in black and white, literally, when we compare magnesium silicide ($\ce{Mg2Si}$) with sodium sulfide ($\ce{Na2S}$). Both have eight valence electrons per formula unit and an antifluorite structure, yet their colors are as shown below. Can you tell which is which (without clicking the attributions) in the pictures below?

Compound A

Compound B

Sodium sulfide, with a large difference in energy between the atomic valence orbitals of the two elements, has its valence electrons largely localized onto the more electronegative sulfur atoms, as in a classically ionic compound; with little delocalization the bands are narrow and the gaps so wide that sodium sulfide can barely absorb visible light. In fact the yellow color seen here actually comes from polysulfides, whose sulfur-sulfur bonding broadens the sulfur-based band and narrows the bandgap somewhat. Pure sodium (mono)sulfide is white.

Not so with magnesium silicide, whose much smaller difference in energy levels between magnesium and silicon atoms facilitates a great amount of electron delocalization and a narrow bandgap. The bandgap of magnesium silicide, like other black semiconductors, is so narrow that it actually falls into the IR range; such materials,including magnesium silicide itself, are candidates for thermoelectric applications.

Answer 2

Metals have a "sea" of electrons at the lowest level, i.e., even at room temperature or close to absolute zero. A potential of even 1 µV will cause a flow of charge in Cu. Metallic conductivity decreases with increasing temperature due to vibration disturbing the regularity of the structure. At operating temperature, a tungsten filament might have ten times its cold resistance.

Semiconductors' electrons need a "boost" to move up and out. In Si diodes, for example, at room temperature, it might take 0.7 V to overcome the barrier between p- and n-type (doped) Si. However, conductivity of semiconductors increases with increasing temperature, as electrons are knocked loose.

It also depends on allotrope, too. For example, in a diamond lattice, undoped C is a nonconductor at room temperature (though doped, it is a semiconductor), but in planar graphite, it's a conductor.

BTW, there are many colored sulfides (and oxides). Cinnabar ($\ce{HgS}$) was used to make vermilion, a bright orange-red. Covellite ($\ce{CuS}$) is blue. Orpiment ($\ce{As2S3}$) is yellow.