Dear Colleagues!

I agree with your opinion. However on the other side for such very specialized questions there may be very little activist on the research gate who can answer it.

In every time and every where you will find people who are always ready to extend their hands to the others. They are not many but they exist.

There is the optical band gap and the electrical bandgap.

The electrical bandgap has been found to decrease with doping increase. This phenomenon is observed in bipolar devices where it is found there is an upper bound to the emitter injection efficiency by increasing the doping. Investigations showed the cause of this effect is the bandgap narrowing due to heavy doping.

This leads to an effective increase in the intrinsic concentration.

This phenomenon is a well known. It is explained and measured.

Not only that, it is so that when one increases the carrier concentration either electrons or holes or both the energy gap decreases.

In addition, for doping increase the ionization energy decreases in heavily doped semiconductors.

For more information please follow the papers in the links:

Article A New and Simple Model for Plasma and Doping induced Band Ga...

Best wishes

* The Moss-Burstein effect is an apparent increase of the measured bandgap of heavily doped semiconductors where impurity concentrations (Ni) are >> than the effective density of states (Nc or NV) of allowed (conduction and or valence) bands:

Eg measured = Eg nominal + delta E

where:

Eg nominal is the nominal energy bandgap of a material (very lightly doped) which remains unchanged, and

delta E is the Moss-Burstein shift i.e. Ef-Ec or Ef-Ev where Ec or Ev are the bottom of conduction band and the top of valence band, respectively.

Here the processes are associated with thermal excitation of carriers and hence the energy bandgaps are thermal energy bandgaps.

* How about the optical energy bandgap?

It is also affected by heavy doping but in another way:

In heavily doped semiconductors, there is another phenomenon which affects the optical bandgap: it is the Urbach tail effect characterized by an Urbach Energy Eu which tells us about the broadening of the optical bandgap which approximately (to make it simple) reads as follows:

Eg opt measured = Eg opt nominal - Eu

Instead of a sharp optical absorption edge which starts at E=hw=Eg= Eg opt nominal, in heavily doped semiconductors, the absorption starts at energies well below this absorption edge because of Urbach effect.

Here the Urbach effect is due to heavy doping induced disorder and nonhomogeneous impurity distribution which induce optical absorption edge broadening.

Now is it possible to have a Moss-Burstein effect >> than Urbach tail effect ?

Yes, in materials where Ni>>Nc can be easily fulfilled i.e.where carrier effective masses are rather small because Nc (or Nv) depends critically on m*e (or m*v).

Best regards,

Professor A. Kadri

Thank you so much Prof. Kadri. Your answer helped me a lot.

Unfortunately, few people in this scientific community share their scientific knowledge with others and contribute to the advancement of science, without any expectations. I'm glad to talk to another of these people. This morality of yours is praiseworthy for me.

Best regards,

You are most welcome Dr Milad Fallah,

I know there are too much people on RG who do not want to share their knowledge (if we suppose they do have some).

They want just to take as much as possible from RG and never give anything back nor help anyone.

At the same time, they spend all the day long to answer crazy futile questions as ''what do you think about covid 19?'' in order to increase their RG score and become finally ''clever'' with RG>>100.

We all know that the world is imperfect.

It is really imperfect.

Best regards

Prof. A. Kadri

Dear Prof. Kadri,

Thank you again for your answer and the important issue you mentioned. I completely agree with you. Perhaps that is why it is unreasonable to expect the emergence of a new Bohr, a new Tesla, or other people whose names will go down in history forever. I wish the scientists of the world would realize that by helping the circulation of information, not just in the form of publishing articles that are available in several ways, they can solve a challenge before they engage in it. We are lagging behind time and nature because few people are willing to share their experiences with others. However, in a world where the money is spent on war, porn, drugs, cinema, or soccer players, rather than the development of science and education to the next generation, and most scientists are just watching it, such aspiration seems far unattainable.

Respectfully,

Dear Colleagues!

I agree with your opinion. However on the other side for such very specialized questions there may be very little activist on the research gate who can answer it.

In every time and every where you will find people who are always ready to extend their hands to the others. They are not many but they exist.

There is the optical band gap and the electrical bandgap.

The electrical bandgap has been found to decrease with doping increase. This phenomenon is observed in bipolar devices where it is found there is an upper bound to the emitter injection efficiency by increasing the doping. Investigations showed the cause of this effect is the bandgap narrowing due to heavy doping.

This leads to an effective increase in the intrinsic concentration.

This phenomenon is a well known. It is explained and measured.

Not only that, it is so that when one increases the carrier concentration either electrons or holes or both the energy gap decreases.

In addition, for doping increase the ionization energy decreases in heavily doped semiconductors.

For more information please follow the papers in the links:

Article A New and Simple Model for Plasma and Doping induced Band Ga...

Best wishes

Milad Fallah,

welcome again!

What I brought previously is not a direct answer of your question.

Conceptually physical effects can not be prevented form occurrence but they may be counteracted. In the sense if the doping increase decreases the bandgap, then one can exploit an other effect to counteract this effect as stressing the semicondcutor.

This what is utilized in the strained base SiGe base where the doping with germanium decreases the bandgap of silicon in the base. This will compensate the bandgap narrowing of the heavily doped emitter and reincrease the emitter injection efficiency of the transistor.

If by staining you increase the lattice consatnt of the material you can increase the bandgap. In this way you can restore the value of the bandgap.

Best wishes

Dear Prof. Abdelhalim abdelnaby Zekry ,

Thank you very much for your answer and for introducing the paper. Your answers have always been helpful to me. Talking to Professor Abderrahmane Kadri and you gave me a definite answer, and I thank you both very much for this. According to all discussions, I realized that I should look into the issue with a focus on carrier density and effective mass. In this regard, fortunately, I found and read some articles that had addressed this issue in certain fields. They have dealt with similar cases, so I will put them at the end of this message for the use of other friends who may have this question. Now, it is attractive to me that I can engineer the band-gap in such a way that the effect of one of the important influences on it (Burstein-Moss effect) is weakened or strengthened.

I found that band-gap narrowing caused by the correlated motion of charged carriers and by their scattering against ionized impurities can compete with the Burstein-Moss effect. It seems that there is a critical value for carrier concentration to onset the band-gap narrowing as compared to the band-gap widening resulted from the Burstein-Moss effect. On the other hand, in some cases, due to, for example, the greater radius of the dopant, stresses will apply on the atomic network that this stress results in an interstitial position that prevents to contribute to the free carrier concentration. In fact, band-gap shrinkage can be related to a downward shift of the CB edge and an upward shift of the VB edge that is associated with the competition between many-body interactions such as electron-electron interaction (EEIs) or electron-impurity interaction (EIIs) and the Burstein–Moss effect.

Furthermore, the entrance of donor impurities transfers more electrons, and these extra charge carriers cause to produce a charge distribution in the shape of non-parabolic. This modified shape of the conduction band has a vital role in the shift of optical transitions.

Also, The Burstein-Moss widening is a sensitive function of effective mass, and the widening decreases with increasing effective mass because the effective mass value based on the parabolic band will replace by one based on the non-parabolic band structure in a critical carrier concentration. This results in carrier concentration-dependent effective mass.

Respectfully,

1. New Insights on the Burstein-Moss Shift and Band Gap Narrowing in Indium-

Doped Zinc Oxide Thin Films

2. An Understanding of the Band Gap Shrinkage in Sn-Doped ZnO for Dye-Sensitized Solar Cells

3. Acceptor-modulated optical enhancements and band-gap narrowing in ZnO thin films

4. BAND-GAP NARROWING IN TIN-DOPED INDIUM OXIDE FILMS

Dear Milad Fellah

You are most welcome.

Best regards

Prof. A. Kadri

Dear Milad,

I have written an old paper about the energy gap shrinkage in semiconductors.

Hope it will be useful to you.

Please follow the link:Article A new theory for band gap shrinkage

I would like to extend the energy gap based in the energy gap shrinkage.

So, if you have any literature about the variation of the dielectric consatnt on the microscopic scale in the semicondcutor materials.

Best wishes

Dear Prof. Abderrahmane Kadri ,

Thanks a lot.

Sincerely,

Dear Prof. Abdelhalim abdelnaby Zekry ,

Thank you very much for introducing your article. The subject of your article was the basis of my question.

Sincerely,

Dakhel, A. A. "Effect of thallium doping on the electrical and optical properties of CdO thin films." physica status solidi (a) 205, no. 11 (2008): 2704-2710.