You know what? Time to go on the offensive, rather than just react on defense. While the technical details of this stuff can get very complicated, the actual base principles are not that difficult to understand. Let's just head this off at the pass. This is how semiconductors work in general, and how solar cells work in particular, and in very particular how our understanding of them is rooted in a lot of other science, from physics to chemistry to quantum mechanics.
Silicon is what chemistry calls a "group 4" element (technically, these days it is called group 14, but it was group IV when I learned it, and semiconductor jockeys still call these materials group 4 for reasons that will become evident in a bit). It includes elements like carbon, germanium, and lead. These elements all share certain similarities when it comes to chemical properties because all of them have the same configuration of their outer electrons. Every atom has a nucleus with some protons and neutrons at the center and electrons orbiting around it. The electrons form shells with some closer and some farther away, like satellites orbiting the Earth. However, quantum mechanics limits which orbits electrons can be in: they can't just arbitrarily orbit the electron. These quantum mechanics-restricted orbits are called "orbitals" or "shells" and we can calculate what they are for every atom.
The group IV elements all have four electrons in their outermost electron shells, and those shells all have the same basic shape and properties, except for their size (distance from the nucleus). Because how two atoms interact is mostly a function of those outer electrons - because those are the ones that can bump into each other and interact - that's why they tend to be similar chemically. Similar, but not identical.
This outer shell of electrons can theoretically hold up to eight electrons: four pairs. There's actually a quantum mechanical reason for this. There is a principle called the Pauli exclusion principle which states that no two fermions can have exactly the same quantum state. It is sort of the quantum mechanical equivalent to the "two things can't occupy the same space at the same time" rule. Electrons are fermions, and when an electron is in an orbital of an atom all of its quantum numbers are defined except for one: spin. Electrons can have one of two spins, which classically can be thought of as "clockwise" and "counterclockwise" although in quantum mechanical terms it isn't really (we usually call them "spin up" and "spin down"). So if no two electrons can have the same quantum numbers, once an electron enters an orbital shell only one more electron can do so: an electron with opposite spin. After that, you can't put any more electrons in there because then you'd have two electrons trying to "occupy" the same quantum state.
The silicon atom would like to fill up that outer orbital - to be more precise, full orbitals have a lower energy state. Things tend to want to fall into low energy states because once there, it takes extra energy to kick them back out of it. So these silicon atoms would love to grab four more electrons and fill them. But in a crystal of silicon it can't do that, because it is surrounded by other silicon atoms that all want to do the same thing, just as hard. However, in a crystal of pure silicon something interesting happens. Two neighboring silicon atoms each have one unpaired electron in an orbit facing the other, and each wants to steal the other's electron to fill its orbital. What happens is the two electrons pair up because that's the lowest energy state for *them*, and then start orbiting *both* silicon atoms. Heisenberg uncertainty allows them to basically "smear" themselves out throughout both orbits, and while each silicon atom is not happy to have to share, they both find it is better than not having anything at all. In physical terms, the energy state of a pair of electrons orbiting both is lower than each silicon atom having only one electron in that orbit. It is a lower energy state, so the electrons "fall" into that state, forming what chemistry calls a "covalent bond."
These bonds are pretty strong. That's what gives silicon crystals their strength: they are actually very strong. Silica glass' strength comes from that silicon bond, and the fact that with the ability to make four such bonds in all directions you end up with an extremely strong structure. But because they are that strong, pure silicon is extremely non-conductive. If you think about it, if electric current is about moving electrons, and all the electrons are tied up in these strong covalent bonds, none of them will move when you apply a voltage, unless the voltage is really really high. Basically, pure silicon is an insulator.
But what if I mess up that happy structure? Suppose I were to remove one silicon atom and replace it with something like phosphorus. Phosphorus has five electrons in its outer shells, not four. When you stick phosphorus in there, the silicon still tries to pair up with phosphorus and make four covalent bonds, but then there's one electron left over. That electron *cannot* occupy the orbital it was in originally because Pauli exclusion kicks it out. Basically, its four friends get room mates for the four bedrooms, and now it has to sleep on the couch. That means it gets kicked farther away from the phosphorus nucleus, and the bottom line is that it is now much less strongly connected to that phosphorus. And moreover, if it moves in any direction it will run into silicon atoms that also have full orbitals. No room at the inn, and it can't find a home. Although this leaves the phosphorus atom electrically charged (it has one less negative charged electron) that atom is surrounded by trillions of electrons that dilute that charge. The electron doesn't "see" it very well, and is free to roam around. Now, if you apply a voltage, that electron can move with the voltage and provide a current. I've just magically turned silicon from an insulator into a conductor. That's what semiconductors basically are: materials we can adjust the conductivity of by changing their structure.
Had I stuck a boron atom in there instead, boron has three electrons in its outer shell instead of five. What happens then? Well, silicon still tries to make four covalent bonds but it can only make three. Boron then runs out of electrons to pair up. One of the silicon atoms ends up with a hanging electron unable to form a covalent bond. Here's the tricky part. What happens if I apply a voltage now? Well, I said that in pure silicon nothing happens because all those electrons are held in place by strong bonds, and the voltage can't move them so no current. You might think the same thing happens. Ah, but the situation is different: we have a hanging electron trying to pull an electron from one of its neighbors because it is just hanging there. It cannot, because it is basically pulling with the same force its neighbors are using to hold its electrons. That tug of war is a draw, so that silicon atom gets stuck with an unpaired electron.
Imagine a row of chairs each with someone sitting in it. Now imagine each person is holding a ball in each of their hands, except for one guy in the middle. He has one ball in his left hand and nothing in his right hand. He wants to have a ball in his right hand so he tries to take the ball away from the guy sitting to his right. He can't because they are equally strong: he tries to pull the ball away, the other guy tugs back, and the net result is that nothing happens. Now imagine that there are strings tied to each ball, and we can tug on them. It we start tugging on those strings and pulling all of the balls to the left, what happens is that the guy who was trying to yank the ball to the left from the guy on the right now wins: we helped him steal that ball. Now the guy to the right has only one ball, so *he* tries to steal one from the guy to *his* right. And because we are helping him by pulling to the left, he also wins. Notice that the *balls* move to the left, but it kind of looks like the "empty hand" is moving to the right.
That's what happens to silicon with that boron atom in there. Under voltage the electrons start moving in the direction of the force, while the "hole" moves in the opposite direction. If we think of the "hole" as a positively charged thing in a sea of negatively charged things, then it is as if a positively charged current is moving in the opposite direction that (negatively charged) electrons would move. It isn't: it is a bit of an illusion. But the descriptions both describe the same situation: negative charge flows in one direction, while the absence of negative charge (positive charge) flows in the opposite direction.
And that's how we make silicon semiconductors. We take silicon, which is an insulator, and we dope it with other atoms. This creates either a set of loosely bound electrons which can move much more easily, or a set of loosely bound "holes" which can move much more easily, and this allows us to control silicon's conductivity. We can engineer silicon to do what we want it to do electrically. And based on the laws of chemistry and physics, we can calculate exactly how silicon's behavior will change depending on what we do to it. These calculations work, which tells us that our understanding of how the pieces work is probably correct. Almost certainly correct, given the fact that in effect all of the billions of transistors mankind has created over the years test and retest those calculations by functioning as designed trillions of times a day.
How do we get from here to solar cells? One bite sized step at a time. Next time we should get from how semiconductors work to what happens when we start sticking them together. To me, that is one of the most interesting things in all of physics, and the modern world is essentially built upon what happens in that specific situation.
