In npn transistor, why doesn't some base current flow in conduction band?

Question

1. Free electrons in emitter are in conduction band.
2. Free holes in base are in valence band.
3. Since base is thin, most electrons pass the base while staying in the conduction band and enter the collector.

Since the life time of free electron in base region is quite large due to thin doping, is it possible for some free electrons in base region to reach the base terminal staying in the conduction band? That is can some base current happen entirely in conduction band avoiding the recombination?

In other words: Why must every electron that enters the base terminal be from the valence band? Why can't the base terminal attract few conduction band electrons like the collector?

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EDIT: Intuitively it feels like the electrons that entered the base from emitter have 3 options:

1. Go directly into the collector
2. Recombine - fall into valence band and go out the base lead to the base supply
3. Go directly out the base lead to the base supply

Answer 1

That's the whole point of P-type doping — the dopant atoms "sop up" any free (conduction band) electrons in the base region, because the overall system energy is lower if their outer shells are filled.

Ignoring the injected electrons for the moment, the only way for charge to move through a P-type semiconductor is for valence electrons to jump from one atom to the next, which looks like "holes" (the absence of an electron) flowing in the opposite direction.

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Response to edit:

Theoretically, they do have three choices. But the relative probabilities of the three choices make the third option essentially impossible.

The diagram may be misleading. In a real transistor, the distance across the base region (between the emitter and collector) is many orders of magnitude smaller than the distance between there and the external base connection. The probability of recombination rises exponentially with distance.