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

Electron Energy Levels


By: Dan Mepham

Here’s where it starts to get complicated. We mentioned before that silicon ‘prefers’ to make four bonds in order to reach its lowest energy state. Of course, being an inanimate material, silicon has no will of any sort, rather it simply follows one of the basic laws of the universe; that any object, outside the influence of external forces, will naturally gravitate toward its lowest energy state. For example, if you hold a ball up and let it go, it will eventually return to the state in which it has the least possible energy; at rest, on the floor.

The question then begs, why does four bonds constitute the lowest possible energy state for silicon? Why not three bonds? Or none?

Let us now consider a lone atom. Proposed almost one hundred years ago by Niels Bohr, and reinforced by modern Quantum Mechanics, is the idea that electrons can exist only at specific energy levels. That is, an electron in orbit of our atom cannot orbit in any place it wishes, it is confined to certain allowed levels or ‘spots’. Think of them as steps – you can be on one step or the next, but never in between. In general, the further from the nucleus, the more energy the electrons have. Using this model, the valence, or outer electrons, possess more energy than the inner electrons. Since the silicon atom as a whole will naturally tend toward the lowest possible energy state, it makes sense that the first place to start to ‘cut’ energy would be from the energetic valence electrons.

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Fig. 4 - The various electron orbits or energy levels for a silicon atom. An electron can exist in any of these orbits, but not outside their confines.

A law of Quantum Mechanics says that two electrons can never exist at precisely the same spot at precisely the same time, which makes a lot of sense, if you think about it. So when we bring together two atoms that, individually, have electrons in the same energy level, the energy levels tend to separate very minimally so as to obey this law of quantum mechanics, known as the Pauli Exclusion Principle.

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Fig. 5 - When far apart, the energy levels for electrons in silicon are identical. When we bring them together, since the electrons cannot be in the same orbit, the two energy levels effectively 'push' eachother apart just a bit.

If we bring together millions or billions of atoms, as in a piece of Silicon, each new level must be very slightly different from the others, and the result is that these billions of levels come together to form a band – a small region containing so many possible levels that an electron can exist virtually anywhere within the region.

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Fig. 6 - When we combine millions upon millions of atoms, so many energy levels, pushed apart just a bit, exist in the same region, that they eventually simply blend into a solid band, in which an electron can exist anywhere.



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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