Non-equilibrium conduction electrons

In summary, the electrons in a conduction band in a semiconductor laser will thermalize and reach a quasi-equilibrium distribution according to the Fermi function.
  • #1
BeauGeste
49
0
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.
 
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  • #2
BeauGeste said:
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.
 
  • #3
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
 
  • #4
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.
 
  • #5
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
 

1. What are non-equilibrium conduction electrons?

Non-equilibrium conduction electrons are a type of electrons that are found in materials, such as metals, which are able to conduct electricity. These electrons are not in a state of equilibrium, meaning they are not at rest and have a net flow of energy.

2. How do non-equilibrium conduction electrons contribute to electrical conductivity?

Non-equilibrium conduction electrons contribute to electrical conductivity by being able to move freely within the material, carrying an electric current. This is due to their high mobility and ability to respond quickly to an applied electric field.

3. What causes non-equilibrium conduction electrons?

Non-equilibrium conduction electrons are caused by the presence of impurities or defects in a material. These impurities or defects create energy levels within the material that allow electrons to move more easily, leading to a non-equilibrium state.

4. How do non-equilibrium conduction electrons affect the properties of materials?

Non-equilibrium conduction electrons can significantly affect the properties of materials. For example, they can increase the electrical conductivity and thermal conductivity of a material, as well as influence its optical and magnetic properties.

5. Can non-equilibrium conduction electrons be controlled?

Yes, non-equilibrium conduction electrons can be controlled through various methods such as applying an external electric field or changing the temperature of the material. This control allows for the manipulation of the material's properties and can be useful in applications such as energy harvesting and electronic devices.

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