Non-equilibrium conduction electrons

[BeauGeste]

Here's the issue I'm trying to wade through:

1. If you excite electrons from valence band to conduction band (with a laser say), you are out of thermodynamic equilibrium. In some recombination time, the system will go back to equilibrium. All well in good.

2. Now let us consider a very long recombination time. What are the non-equilibrium electrons in the conduction band doing? Do they relax to the band minima? Are they distributed according to the Fermi function? What is the chemical potential doing? Is it possible to even define a chemical potential here?

Any help with these questions would be appreciated.

Thanks.

 

[ZapperZ]

Here's the issue I'm trying to wade through:

1. If you excite electrons from valence band to conduction band (with a laser say), you are out of thermodynamic equilibrium. In some recombination time, the system will go back to equilibrium. All well in good.

2. Now let us consider a very long recombination time. What are the non-equilibrium electrons in the conduction band doing? Do they relax to the band minima? Are they distributed according to the Fermi function? What is the chemical potential doing? Is it possible to even define a chemical potential here?

Any help with these questions would be appreciated.

Thanks.

Er.. something with a "long recombination time" would be a semiconductor at room temperature with the band gap small enough to sustain a population of charge career in the conduction band. Isn't this the same thing? If it is, then don't we know a lot already about the behavior of the electrons in the conduction band?

Zz.

 

[Modey3]

BeauGeste,

Do they relax to the band minima?

Sure. As long as the band minimum isn't populated then these electrons will relax to the band minimum through electron-phonon interaction. The conduction electron will emit a photon when it relaxes back to the valence band.

Are they distributed according to the Fermi function?

Absolutely not! The Fermi-Dirac distribution function applies only to electrons that are thermally excited.

What is the chemical potential doing? Is it possible to even define a chemical potential here?

The chemical potential doesn't change. It is strictly a function of temperature and not on the level of electron-photon excitement.

Best Regards

modey3

 

[Manchot]

I'm afraid that I have to disagree with Modey, because it's all a matter of timescale. In most semiconductors, the interband lifetime is relatively long, on the order of microseconds. However, intraband scattering processes are usually short, having lifetimes on the order of 100 fs or even less. These intraband processes will thermalize the distribution within the band rather quickly, and so you're actually right: they'll reach a quasi-equilibrium distributed according to the Fermi function. In semiconductor lasers, we call this a quasi-Fermi level.

 

[Modey3]

I stand corrected. For very long recombination times that makes sense and as you said the Fermi distribution can only apply for small time scales between the excitement and recombination of electrons.

modey3