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  Semiconductor Physics, Part 1 
  Jan 21, 2003, 08:30am EST 
 

Band Formation, Things Get Complicated


By: Dan Mepham

We’ll now pause for a moment to summarize what we’ve learned thus far. We know that electrons in individual atoms can exist only at exact specified energy levels. But the Pauli Exclusion Principle says that two electrons cannot exist in the same space at the same time, so when we bring together billions of atoms, the electrons move their orbits ever-so-slightly, so that each one is different. When we combine all these orbits, each different by a miniscule amount, the result is the formation of a ‘band’ of energy levels, in which an electron can exist virtually anywhere.

Taking it a step further, and without unnecessary explanation, when we combine billions of atoms in a piece of silicon, we observe the formation of two discrete bands. One is closer to the nuclei of the atoms (therefore electrons in this band have less energy), and is known as the Valence Band. The second is farther from the nuclei (thus electrons residing in it have more energy), and we call it the Conduction Band. Separating the two is a space in which no electrons can exist, called the Bandgap.

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Fig. 7 - The energy bands formed by a silicon sample. Energy increases along the y-axis in this diagram, so the electron in the Conduction Band has more energy than those below it in the Valence Band.

So, as the diagram shows, electrons can exist either in the Valence or Conduction band of the material, but not in between. Think of electrons in the Valance Band as being electrons trapped in bonds; that is to say, they are not free to participate in conduction. As one might infer from the name, and finally answering our earlier question, electrons in the Conduction Band are those which have broken out of their bonds, and are free, floating about the material, and able to participate in the conduction of current.

Logically, the more electrons that manage to jump up into the Conduction Band, the more conductive the material will be. For the sake of interest, we can use the bands to explain our earlier classification: Insulators are materials with very large bandgaps. Bandgaps so large, in fact, that it is all but impossible for electrons to jump up. Since the gap is simply too large for electrons to traverse, Insulators have no electrons in their Conduction Bands, and therefore cannot conduct electricity. Conductors such as metals, in contrast, have no bandgap. That is, their Valence and Conduction Bands overlap, thus all valence electrons are in the Conduction Band at all times, making them very good conductors.

Semiconductors lie somewhere in between, and are defined as materials with a small bandgap. The loose, but widely accepted formal definition of a semiconductor is a material with a bandgap on the order of 1.5 to 4 eV (Electron-Volts) in size.**

**Since the “bands” are in fact energy levels, the separation between them is measured in units of energy. The appropriate unit for this case is the Electron-Volt. For example, if the top of the Valence Band were at 3 eV, and the bandgap was 2 eV in width, then the bottom of the Conduction Band would be at 5 eV. All electrons in the Conduction Band would have 5 or more eV of energy, while all those in the Valence band would have 3 eV or less.



1. Introduction
2. Before the 'How', Ask Yourself 'Why?'
3. Crystal Structure, Forming the Bonds
4. Electron Energy Levels
5. Band Formation, Things Get Complicated
6. Electron Excitation, Making the Leap
7. Summary

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