As mentioned previously, my mental model of semiconductors and the like is a fireman's water brigade, were either the majority of the line has buckets or empty hands.
It helps if, instead of a line, you think of a LOT them standing in a two-D array (like in the yard of the burning building, or a section of a parade that's stopped to do a little demo). It's really three-D, but we'll want to use up/down for something else in a bit...
For metallic electron conduction everybody has TWO buckets, one for each hand, and when a guy by the fire throws a buck of water on it (bucket and all) on the fire, a guy farther back immediately tosses him a bucket, the guy behind him essentially instantly throws HIM a bucket, andso on. Hands are effectively never empty.
For semiconductors, imagine two layers of these guys, the second standing on the firsts' shoulders or on a scaffold right above them, and about enough buckets for each of the guys on the ground to have two and the guys on the scaffold to have none. (There's actually many layers of scaffold, but the rest are so far up that it's hard to get a bucket to them, so they mostly just stand around.)
Usually nothing useful is happening. Everybody on the bottom layer has both hands full of buckets, and it's hard to hand a bucket up to the guys on the top.
- Electron-hole pair creation: Somebody comes up with the energy to heave a bucket up to the guys on the upper layer, leaving a guy with one hand empty in the lower layer. (Maybe somebody (a photon, for instance) comes along with a lacrosse stick and whacks a bucket up to a guy in the top row - dying or becoming exhausted and much weaker from the effort.) Now you've got one guy with a free hand in the lower layer (a hole) and one bucket on the top layer (a free electron).
- Electron conduction in a semiconductor is that bucket on the upper layer. The guys there can hand it around easily, or toss it along a diagonal until it would hit a guy - who catches it. They're all standing on accurately-spaced platforms so the bucket can go quite a way before somebody has to catch it. Suppose there's a slope to the yard, with the fire at the bottom. Then, if tossed too far, the bucket might pick up substantial speed and knock the guy who catches it out of place (electromigration), or fall down to the lower layer and knock another bucket out of somebody's hand and bounce, ending up with TWO buckets on the upper layer and an empty hand below (avalanche electron-hole creation).
- Hole conduction is when you've got an empty hand on the bottom layer: Now it's easy for a guy with two buckets to hand a bucket to a guy with only one, exchanging a bucket for an empty hand. But now the guy whose hand had been empty has two buckets and nobody in the downhill/toward-fire direction to hand a bucket to, while the guy who handed it off has an empty hand and can grab a bucket from somebody farther uphill / closer to the water source - or beside him, or diagonally. So "empty-handedness" (a hole) can move around as a persistent entity while the individual buckets gradually work their way in the general direction of the fire, only making a bit of progress "when a hole comes by". Though the water makes progress toward the fire, the action is all where the holes are making progress away from the fire.
- Electron-hole annihilation: Somebody has a bucket on the upper layer when a guy below him has an empty hand. So he drops the bucket. CLANG! Ouch! Now there's no "free bucket" on the upper layer, no free hand on the lower layer, and the energy of their separation went somewhere else (knocking the guy sideways so he bumps into his neighbor and generally making the guys vibrate, "creating a guy with a lacrosse stick who runs off to whack at buckets", etc.)
- P-type doping: A guy in the bottom layer had a sore hand and only brought one bucket to the fire, thus having a free hand from the start. He can take a bucket when a neighbor pushes it at him (the hole moves away). But he'd like to hand it off and have his sore hand free again (so holes tend to stick around at his site). It's lots easier to "make a free hole" by convincing him to hold a bucket in his sore hand than by tossing a bucket up to the guys on the scaffold, but does take a little effort.
- N-type doping: One of the guys on the upper level really likes to hold a bucket, so he brought one with him. The guy next to him can grab it from him, but if another comes along he'll try to hold on to it a bit until somebody shames him into letting go again or wrestles it from him. It's lots easier to get him to let you use his bucket for a while than to pull one up from the guys on the ground, but it does take a little effort.
- Tunneling through a potential barrier: There's a ridge across the field. It's hard to hand buckets up to the guys on the ridge, so they don't flow across it very well (unless someone at the side of the field is pushing the buckets really hard...) Occasionally the guys on one side of the ridge hand a bucket through the legs of the guys standing on the ridge to the guys on the other side.
And so on. B-)
I'm keenly interested in finding more material to read up on the observed Hall effect measurements. Thanks again for your contribution to the discussion.
The wikipedia article on the hall effect has a section on the hall effect in semiconductors, but both it and the reference it uses start from treating the hole as a charge carrier with a fixed charge and a mobility different from a free electron, and just computes formulai from there.
If the hall effect on hole currents were fallout from the hall effect on the individual electron bucket-transfers, rather than the hole acting like a positive charge carrier in its own right, you'd think it would go the other way