| MadSci Network: Physics |
Helloooo....Megan! The bandgap energy and the bond dissociation energy are closely related in silicon. In pure silicon, the bonding electrons are in the valence band. When they receive the additional energy (ca. 1.1eV) necessary to kick them up into the conduction band, they no longer act to hold the lattice together but are "free" to roam the crystal. Work function is not directly related to the bandgap, but more a consequence of how easy/hard it is to ionize the atoms (e.g. materials such as sodium that are fairly easily ionized tend to have low work functions) and pull the electron away from the bulk crystal (i.e. separating it from the positive image charge left behind). Pure silicon has a workfunction of about 4.7eV. This value is readily modified by doping the silicon; n-type being lower workfunction than p-type. What is true always is that the workfunction is the energy difference between the Fermi level of the material (be it silicon or anything else) and the vacuum level (i.e. the electron's energy after being pulled away from the crystal to infinity), and this makes sense because the Fermi energy is essentially the chemical potential of electrons in the material. More generally, you can't say that the bandgap and bond dissociation energies are always so neatly related. Metals have no bandgap, and thus the bond dissociation energy (formation of metallic bonding does have an energy delta associated with it) can't be related to something that doesn't exist. Moreover, there are two major types of metals. In some (e.g. sodium), a band is half-filled, making it easy to promote electrons in it to higher energy levels (the energy levels are very closely "packed" within the one band). In other metals (e.g. magnesium), there are valence and conduction bands but they overlap, leading again to easy promotion of electrons to higher energy states. This is a complicated subject, and the short paragraphs above can be considered only the barest of introductions to it. You will have to read books to get an in-depth understanding. Start with "The Structure and Properties of Materials, vol. IV" by Rose, Shepard, and Wulff (this is an old book now, and may be hard to find), and/or "The Solid State" by Rosenberg. For a more complex and thorough treatment with all the ugly mathematics, you should read the appropriate chapters in Kittel.
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