What is electric current?

It's something else I've never understood: what is electricity, anyway? I was always told it had something to do with loosely affiliated electrons moving around, but it's not quite like totally free electrons scooting along a pipe. As I understand it, electrons very rarely behave in ways that are analogous to the ballistic movement of large particles, and when they do it's generally in a vacuum (as in a cathode ray tube--the "rays" are projectile electrons), not in a solid material like the copper in an electrical wire.

To start with, we look at electrons in their most characteristic state, all staid and settled down in orbit around a positively charged atomic nucleus. I guess there are, on average, about the same number of electrons in the world as protons, and most of them have found a nice girl and moved to the suburbs with a 9-to-5 job. Electrons in a fully completed atomic shell or "band" don't produce an electric current; if they're "moving" in some sense, it's not the same sense as a movement along an identifiable path that we call an electric "current."

The outer shell of electrons around an atom is called the "valence band," and is associated with the kind of chemical reactions that we learned about in school: +2-valence atoms like to pair up with -2-valence atoms, and so on, until together they've achieved a stable, full valence band that conducts no current. But if a bit of energy shoots into a full valence band and juices up a particular electron enough to bounce it out so that it's still nearby, but not quite nailed down any more, we call its new hovering location a "conduction band." It's out there cruising around trying out new musical acts, starting up new tech ventures, and looking for girls, and it's capable of conducting electricity if circumstances are such as to line it up with a lot of other similarly bored, disaffected electrons.

The difficulty in bridging the gap between a stodgy suburban valence band and an exciting urban conduction band is called the "band gap" for that particular material. In good conductors like metals, the two bands may overlap, so there is no identifiable band gap; in that case a high percentage of electrons may wander around like ronin. In good insulators, the band gap is hopelessly huge; hardly anyone escapes the gray flannel suit. In certain very small or very pure samples of materials, however, there is a nice, clear band gap, fairly small but of slightly variable size, which can be affected by clever things we do to it. "Tuning" the band-gap produces little nano- or quantum-objects with various useful properties. Quantum dots, for instance, drink in all flavors of light, then spit out a single color consistently, depending on how hard the dot is squeezed into a smaller and smaller space, and therefore how big the band-gap is and what wave-length of light will be "fit" in it. More traditionally, a transistor has a characteristic band gap that controls what kind of current is needed to overcome its electrical "gate."