Well, I work with semiconductors, and we absolutely use D for degree of electron motion.
Now this is almost off the front page. Hopefully someone reads it and learns something, haha.
I'm going to make this shorter than last time since it's now late (lost by accident) - but here goes:
Silicon has 4 of its 8 outer band electron states filled, ([Ne]+3s2+3p2) which hybridize into 4 sp3 orbinals in a Si crystal. If you start with a single Si atom, it has discrete energy levels away from its nucleus (aka orbitals). If you bring another Si atom (which has exactly the same energy states) closer and closer, eventually these energy states interact and split (i.e. when the covalent bond is formed). The split produces one higher in energy, and one lower in energy. The lower one ends up with both of the electrons (one spin up, one down), and the upper is empty. The lower energy state is shared (covalent bond) between both atoms. Adding more silicon atoms in a similar fashion, similar splits are seen in the new energy levels, but the splitting amount gets smaller each time. When you add thousands (or, in a real crystal, 10^23 !) of atoms, you essentially have tons of very very closely spaced (in energy) levels that are filled in the lower energy position, and tons that are empty in the higher energy position. The lower "band" of states is called the valence band in semiconductor terminology, and the upper band called the conduction band. The "band" is just tons and tons of very similar energy states. At 0K in a crystal, the valence band is full, and the conduction band is empty.
Depending on the material and the way these energy bands look, there can exist a forbidden energy gap between the two bands (valence and conduction) where no energy states exist. If you input energy into the system (heat, light, etc), you can excite the electrons into the higher energy conduction band. When this happens, the electron is only very weakly bound to the atom that it came from, because the underlying valence electrons screen the positively charged nucleus. With only a small amount of additional thermal energy (plenty at room temperature) - the electron is free to float around freely in the conduction band between other atoms. It is thus not bound to one atom. This free electron will fall to the lowest available conduction band energy state - and this energy state is shared amongst the atoms. It does not belong to one atom. The state exists because there are so many atoms. Because it's shared, it is considered "non localized" - it is everywhere at once (to a limit) -- it is behaving as a wave. (you can read more by searching for wave-particle duality).
In an insulator (glass, rubber, etc) the gap between valence and conduction band is very large -- too large for there to be any electrons in the CB at room temperature. There are thus no "free" electrons to contribute to current. In a metal, there is zero gap, and any tiny bit of thermal energy can excite electrons into the conduction band and you end up with a sea of free electrons - giving excellent electrical current abilities. Semiconductors like Silicon are somewhat in the middle -- there is a gap, but it's not too large. Some electrons will be excited at room temperature. The number of excited electrons can be modified vastly (many orders of magnitude) by doping (adding atoms with more or less available electrons like P or B) or by turning an electric field on or off (how a transistor works).
Holy s***. I just spent an hour typing out a response to you, and I changed my slashdot editing options and it lost my response after saving!. I'll retype it later after my wife uses the computer.