Thermionic emission and diffusion theory

[CKwT]

What is the main physical difference behind these two theories?

1) I understand that the thermionic emission theory is applied in metal-semiconductor contacts and heterostructures where the energy band off-sets are large. Whereas the diffusion theory is applied in a simple homojunction, of which the gradient of the quasi-fermi levels are continious.

2) On the other hand, I understand that the diffusion current and the thermionic emission current work in series, where the slowest process limits the current.

There seems to be contradictions between statement 1 and 2. What have I misunderstood?

 

[jsgruszynski]

What is the main physical difference behind these two theories?

1) I understand that the thermionic emission theory is applied in metal-semiconductor contacts and heterostructures where the energy band off-sets are large. Whereas the diffusion theory is applied in a simple homojunction, of which the gradient of the quasi-fermi levels are continious.

2) On the other hand, I understand that the diffusion current and the thermionic emission current work in series, where the slowest process limits the current.

There seems to be contradictions between statement 1 and 2. What have I misunderstood?

Thermionic emission crosses the barrier created by band gap difference through ballistic transport (due to raising the Fermi distribution tail over the barrier height) or tunneling or both, where both are fast in terms of mobility. Traditional vacuum tube thermionic emission is primarily ballistic transport across the cathode/vacuum barrier formed by the discontinuity of the metal interface to vacuum. The cathode is heated to raise the Fermi tail explicitly with heat rather than hot carriers. If you are getting ballistic or tunnel transport across an entire heterojunction layer that is forming the barrier, this is very fast.

Diffusion transport involves multiple collisions where transport is simply akin to that of a bulk semiconductor and PN junction between one or another heterojunction layer, so it's slow in terms of net mobility because it's minority carrier diffusion transport, recombination and majority carrier diffusion transport. In the limit as heterojunctions approach identity, you approach bulk diffusive transport. The dimensions of the layers are greater than the mean free path length for it to be diffusive.

You can get a superposition of several transport regimes depending on materials and physical dimensions.

I'm not sure how the two statements are problematic but maybe the mechanisms explain things. In series, the transit time of the slowest layer transport process certainly will dominate the total transit time of the entire heterojunction structure.