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Friday, December 28, 2012

How to Think About Band Theory

In chemistry, we learn about the three main types of materials in terms of their electrical properties: conductors (typically metals like copper or gold), non-conductors (most materials with covalent bonds), and semiconductors (something like silicon).  But how and why are there different behaviors - all atoms are made of the same pieces, so why the variety of materials?

The answer can begin to be found with a relatively simple model called band theory.  This uses the concept of fixed energy levels that you first learn about studying the Bohr model of an atom in chemistry.  Bound electrons of atoms can only have specific, fixed energies.  But this picture gets muddied when you start thinking about real materials with lots of atoms - all these atoms interact with each other because they are all made from electric charges.  These interactions cause the energy levels of individual atoms to shift slightly, where some increase in energy and others decrease.  Collectively, the energy levels blur and form more of a continuous energy band.  Specifically, two bands form, one where the bound electrons exist (valence band) and one where they have enough energy to move freely through the material (conduction band).  To be a conductor requires many free electrons in the conduction band.

Non-conductors have a large gap between the valence and conduction bands; semiconductors have small gaps between the two bands, and conductors have an overlapping between the two bands, meaning all sorts of electrons are free to move through the material.  Some call this the 'sea of electrons' in a conducting material.  Check out the model!  Also, feel free to play with a PhET simulation where you can have 1 - 10 atoms (or wells) near each other, and see how the energy levels change to begin forming bands.

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