Introduction to semiconductors  (Page 3/2)

If we only had to worry about simple conductors, life would not be very complicated, but on the other hand we wouldn't be ableto make computers, CD players, cell phones, i-Pods and a lot of other things which we have found to be useful. We will now move on,and talk about another class of conductors called semiconductors.

In order to understand semiconductors and in fact to get a more accurate picture of how metals, or normal conductors actuallywork, we really have to resort to quantum mechanics. Electrons in a solid are very tiny objects, and it turns out that whenthings get small enough, they no longer exactly following the classical "Newtonian" laws of physics that we are all familiarwith from everyday experience. It is not the purpose of this course to teach quantum mechanics, so what we are going todo instead is describe the results which come from looking at the behavior of electrons in a solid from a quantum mechanicalpoint of view.

Solids (at least the ones we will be talking about, and especially semiconductors) are crystalline materials, whichmeans that they have their atoms arranged in a ordered fashion. We can take silicon (the most important semiconductor)as an example. Silicon is a group 14(IV) element, which means it has four electrons in its outer or valence shell. Siliconcrystallizes in a structure called the diamond crystal lattice, shown in [link] . Each silicon atom has four covalent bonds, arranged in atetrahedral formation about the atom center.

In two dimensions, we can schematically represent a piece of single-crystal silicon as shown in [link] . Each silicon atom shares its four valence electrons with valenceelectrons from four nearest neighbors, filling the shell to 8 electrons, and forming a stable, periodic structure. Once theatoms have been arranged like this, the outer valence electrons are no longer strongly bound to the host atom. The outer shellsof all of the atoms blend together and form what is called a band. The electrons are now free to move aboutwithin this band, and this can lead to electrical conductivity as we discussed earlier.

This is not the complete story however, for it turns out that due to quantum mechanical effects, there is not just one bandwhich holds electrons, but several of them. What will follow is a very qualitative picture of how the electrons are distributedwhen they are in a periodic solid, and there are necessarily some details which we will be forced to gloss over. On theother hand this will give you a pretty good picture of what is going on, and may enable you to have some understanding of how asemiconductor really works. Electrons are not only distributed throughout the solid crystal spatially, but they also have a distribution in energyas well. The potential energy function within the solid is periodic in nature. This potential function comes from thepositively charged atomic nuclei which are arranged in the crystal in a regular array. A detailed analysisof how electron wave functions, the mathematical abstraction which one must use to describe how small quantummechanical objects behave when they are in a periodic potential, gives rise to an energy distribution somewhat like that shown in [link] .