How electrical current works in intrinsic semi-conductors

Question

I understand that there are two types of currents going on when voltage source is applied in pure semi-conductor material - electron current and hole current. What I'm trying to do is imagine it.. So basically correct me if I'm wrong:

• Voltage gets applied in a pure silicon crystal. Free electrons in the conduction band go towards the positive side of the voltage source and holes go towards the negative side(because they are considered like a positive charge).

Okay so my real question is.. can free electrons in the conduction band occupy a hole in the valence band temporarily just to travel across and leave and enter conduction band again and i heard this theory that a free electron in the conduction band can bump out and replace a valence electron outside its energy level and massively increase its speed and i want to know if it's true. Oh and does the movement of electrons happen so fast that when electrons change holes it's barely noticeable?

Answer 1

For an electron to hop between bands, an energy exchange must have occurred. In which case, by definition, it's not a conduction electron anymore (or hole, as the case may be).

The exact mechanics of recombination, scattering, electron-phonon interaction, defects/impurities, etc., I suppose aren't too important on an overview level (it's also been long enough since I worked with them that I'm rather rusty on these topics(!)).

Note that valence band electrons are not mobile by themselves; they are a bound state. They can only move when a vacancy arises -- an emergent behavior, which itself acts like a particle, hence we call it a pseudoparticle: a hole.

The conduction band is unbound (well, in relevant respects), so such an electron can simply move until bumped with enough energy to stop, or recombination occurs. In fact, both are necessary: a completely filled valence band means recombination is prohibited, because electrons are fermions which cannot occupy identical states, and filled states means no vacancy. Thus recombination can only occur (electron-hole annihilation), and the energy is exchanged through whatever applicable means; which might be an electron-phonon interaction (i.e. directly into thermal heat energy; and vice-versa, which is where spontaneous ionization comes from at T > 0), or emission of a photon (direct bandgap semiconductors), etc.

Ionization and recombination is a somewhat rare event, for room-temperature silicon; the half-life is on the order of several microseconds, and at diffusion drift rates, carriers can travel several micrometers. This is also why the concentration is minuscule, of course (~10¹⁰ cm^-3; compare to atom density on the order of 10²³ cm^-3).

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I don't recall a mechanism for conduction electrons to gain "super speed". Note that any excess energy is subject to rapid loss, as there are numerous exchange methods (e.g. electron-phonon) to sap that energy back down to the minimum; high energy electrons are only a short-range phenomena.

Excess energy is possible, of course; it is a conduction band after all, where energy levels within the band are practically a continuous variable, until the upper band edge. But travel distance at energy, is limited by available energy loss mechanisms.

Answer 2

can free electrons in the conduction band occupy a hole in the valence band temporarily just to travel across and leave and enter conduction band again

Yes, but not transparently. When a free electron and a hole co-esist at the same atom, they recombine. They may later re-form into a hole and a free electron, but they are no more likely to do so than their neighboring atoms. Further, spontaneous generation of a free electron-hole pair in intrinsic silicon is occurs much less frequently than the spontaneous movement of a free electron or a hole. So it would very much seem like the hole and electron got "stuck" while "passing through" each other. Hence my comment that that the "passing through" would not be transparent.

does the movement of electrons happen so fast that when electrons change holes it's barely noticable?

That question is really subjective. Yes, from my timescale, the movement of an electron from a neutral atom to a hole, which constitutes the movement of a hole, happens so quickly that, to me it would be barely noticeable. But it does take some time, and that time is not zero. So in some contexts, that time is quite significant.