Interband transition no photon

[Goodver]

Consider photoluminescence in GaAs.

I have been told that if excitation of electrons from the valence band happens with the light energy of wavelength of which is higher than the band gap energy, then electron gets excited to the conduction band, but not to the edge of the conduction band. And then by means of interband transitions it "falls" to the edge of the conduction band and then eventually to the valence band emitting photons with the energy equals the band gap.

Why photons are not emitted in case of interband transitions? I assume energy goes to phonons, then why transition without creating of phonon is not possible?

Thank you.

 

[Simon Bridge]

You mean : What is the mechanism behind these "interband transitions"?
How close are the energy levels inside a band?
Lets say a transition was electromagnetic, what would be the wavelength of the resulting photon for a transition between adjacent levels?

 

[Goodver]

I understand that in case of a macro crystal, energy levels in bands are infinitely close. So, transition between infinitely close energy level would correspond to a photon emission of 0 energy. But since in reality energy levels are NOT continuous, then in case of interband transition energy must go somewhere. And my question is why this energy does not convert to photons? Or photons are emitted, but since energy of them is ~0 they are not detected?

 

[Simon Bridge]

OK, since the energy gap is very small but non-zero, what is the likely wavelength?
Can you characterize the sort of photon that would be emmitted?

But you also need to consider if there are other mechanisms that could cause an electton to lose energy.

 

[Goodver]

Thanks for the responses Simon, my question is just are photons emitted in interband transition or not? Or since energy gaps between interband levels are ~0, while electron "drifts" to the edge of the conduction band, we have infinite number of photons with infinite wavelength emitted?

 

[Cthugha]

You got your terminology messed up.

I have been told that if excitation of electrons from the valence band happens with the light energy of wavelength of which is higher than the band gap energy, then electron gets excited to the conduction band, but not to the edge of the conduction band. And then by means of interband transitions it "falls" to the edge of the conduction band and then eventually to the valence band emitting photons with the energy equals the band gap.

The transition across the band gap is an interband transition. The transitions that occur while the electron relaxes to the conduction band edge are intraband transitions.

Why photons are not emitted in case of interband transitions? I assume energy goes to phonons, then why transition without creating of phonon is not possible?

I assume you mean intraband transitions and not interband transitions. In GaAs photons are meitted in interband transitions, but usually not in the relaxation processes towards the conduction band edge. In principle it might be possible, that these transitions involve the emission of a a photon. If so, one would naively assume spontaneous emission. Now the spontaneous emission rate for a known energy can be calculated simply using Fermi's golden rule. Have a look at the matrix elements: http://en.wikipedia.org/wiki/Spontaneous_emission

Have a look at the energy dependence of spontaneous emission in the dipole approximation and plug in some numbers and you should be able to find out, why optical transitions are not that important in this scenario.

 

[Goodver]

Thank you, this helped!

 

[Goodver]

However, I still have a question.

Yes I meant intraband transitions, thank you. If we consider intraband transitions as a spontaneous emission, rate of which can be expressed as a Fermi golden rule, then from Fermi golden rule, rate is proportional to the 3d power of angular frequency. As far as understand rate of spontaneous emission means how often spontaneous emission happens per unit of time. In this case, since energy gap between energy levels in the band is ~0, then rate of spontaneous emission ~0, meaning electrons should not relax to the lower energies, which is not the case.

Hence it still not clear to fully clear to me, which in case of the INTERband transition it is likely that photon is emitted, and in case of INTRAband very unlikely.

 

[Cthugha]

Yes I meant intraband transitions, thank you. If we consider intraband transitions as a spontaneous emission, rate of which can be expressed as a Fermi golden rule, then from Fermi golden rule, rate is proportional to the 3d power of angular frequency. As far as understand rate of spontaneous emission means how often spontaneous emission happens per unit of time. In this case, since energy gap between energy levels in the band is ~0, then rate of spontaneous emission ~0, meaning electrons should not relax to the lower energies, which is not the case..

You are almost correct. What Fermi's golden rule tells you is not that electrons should not relax towards the lower energies at the bottom of the conduction band within a reasonable time. Fermi's golden rule tells you,that electrons should not relax towards the lower energies at the bottom of the conduction band within a reasonable time just by spontaneous emission of photons. So there are other relaxation mechanism that are way more likely like those including phonons.

 

[Goodver]

And the last question (sorry for disturbing). It seems clear why emission of photon does not happen in case of intraband transition between adjacent energy levels in a band. But do I understand it correctly that transition within the band can occur not only between adjacent energy levels, but say from the level at the upper edge of the conduction band to the lower edge of the conduction band, and in this case energy gap between such levels is NOT ~0. Therefore Fermi Golden rule approach proving that spontaneous emission is unlikely due to low frequency of a photon does not work. Are photons emitted in case of such mentioned transition?

 

[DrDu]

An important point is the factorial increase of the density of states (DOS) of the phonons with energy. The DOS enters in Fermi's golden rule so that with increasing energy phonon transitions become much more intense than photon transitions.