Summary: From the silicon's crystal structure to discuss how to make doped semiconductors and the mechanics.

To see how we can make silicon a useful electronic material, we will have to go back to its crystal structure. Suppose somehow (and we will talk about how this is done later) we could substitute a few atoms of phosphorus for some of the silicon atoms.

Again, if this were the end of the story, we still would not have any calculators, stereos or "Agent of Doom" video games (Or at least they would be very big and cumbersome and unreliable, because they would have to work using vacuum tubes!). We now have to focus on the few "empty" spots in the lower, almost full band (Called the valence band.) We will take another view of this band, from a somewhat different perspective. I must confess at this point that what I am giving you is even further from the way things really work, then the "cups at different energies" picture we have been using so far. The problem is, that in order to do things right, we have to get involved in momentum phase-space, a lot more quantum mechanics, and generally a bunch of math and concepts we don't really need in order to have some idea of how semiconductor devices work. What follow below is really intended as a motivation, so that you will have some feeling that what we state as results, is actually reasonable.

Consider Figure 3. Here we show all of the electrons in the valence, or almost full band, and for simplicity show one missing electron. Let's apply an electric field, as shown by the arrow in the figure. The field will try to move the (negatively charged) electrons to the left, but since the band is almost completely full, the only one that can move is the one right next to the empty spot, or hole as it is called.

A short time after we apply the electric
field we have the situation shown in Figure 4,
and a little while after that we have Figure 5.
We can interpret this motion in two ways. One is that we have a
net flow of negative charge to the left, or if we consider the
effect of the aggregate of all the electrons in the band (which
we have to do because of quantum mechanical considerations
beyond the scope of this book) we could picture what is going on
as a single positive charge, moving to the right. This is shown
in Figure 6. Note that in either view we
have the same net effect in the way the total
*net* charge is transported through the
sample. In the mostly negative charge picture, we have a net
flow of negative charge to the left. In the single positive
charge picture, we have a net flow of positive charge to the
right. Both give the same sign for the current!

If an electron deficient material such as boron is present, then
the material is called p-type silicon, and the hole
concentration is just

If both donors and acceptors are in the material, then which
ever one has the higher concentration wins out. (This is called
compensation.) If there are more donors than
acceptors then the material is n-type and

One other fact which you might find useful is that, again,
because of quantum mechanics, it turns out that the
*product* of the electron and hole
concentration in a material must remain a constant. In silicon
at room temperature:

The picture of "cups" of different allowed energy
levels is useful for gaining a pictorial understanding of what
is going on in a semiconductor, but becomes somewhat awkward
when you want to start looking at devices which are made up of
both n and p type silicon. Thus, we will introduce one more way
of describing what is going on in our material. The picture
shown in Figure 9 is called a band diagram. A
band diagram is just a representation of the energy
as a function of position with a semiconductor device. In a
band diagram, positive energy for electrons is upward, while for
holes, positive energy is downwards. That is, if an electron moves *upward*, its potential energy *increases* just as a with a normal mass in a gravitational field. Also, just as a mass will "fall down" if given a chance, an electron will move down a slope shown in a band diagram. On the other hand, holes gain energy by moving *downward* and so they have a tendancy to "float" upward if given the chance - much like a bubble in a liquid.
The line labeled

Comments:"Accessible versions of this collection are available at Bookshare. DAISY and BRF provided."