Energy of donor or acceptor levels in semiconductors

[Helena Wells]

TL;DR Summary

Which are the factors which set the donor or the acceptor level in a semiconductor?

How can we calculate the energy of a hole or an electron in p and n type semiconductors?

Which are the contributions from different sources we must take into account? I know it is the dopant and base but if we change one of them how that changes it ? Maybe the interatomic distance has something to do with it?

 

[phyzguy]

It's not the interatomic distance, it's the number of valence electrons. Silicon has 4 valence electrons, so they are all used up bonding to the neighboring Si atoms. So pure Si has basically no free electrons, except for the very few that are thermally excited. Phosphorous has 5 valence electons, so when you replace a Si atom with a P atom, there is one extra electron that is not bonded, and so is free to move about the lattice. Boron has 3 valence electrons, so when you replace a Si atom with a B atom there is one electron missing, which acts as a "hole" or positive charged carrier that is free to move about the lattice.

 

[Helena Wells]

It's not the interatomic distance, it's the number of valence electrons. Silicon has 4 valence electrons, so they are all used up bonding to the neighboring Si atoms. So pure Si has basically no free electrons, except for the very few that are thermally excited. Phosphorous has 5 valence electons, so when you replace a Si atom with a P atom, there is one extra electron that is not bonded, and so is free to move about the lattice. Boron has 3 valence electrons, so when you replace a Si atom with a B atom there is one electron missing, which acts as a "hole" or positive charged carrier that is free to move about the lattice.

Yeah I know that.How can we calculate the energy of the hole or the energy of the electron?

 

[phyzguy]

Yeah I know that.How can we calculate the energy of the hole or the energy of the electron?

The energy with respect to what? Do you mean where the donor and acceptor energy levels are relative to the conduction and valence bands? What exactly are you trying to calculate?

 

[Helena Wells]

The energy with respect to what? Do you mean where the donor and acceptor energy levels are relative to the conduction and valence bands? What exactly are you trying to calculate?

No I know where the donor and acceptor energy levels are relative to the conduction and the valence band.What I try to do is this:Put a semiconductor for base and dope it with N-type or P-type dopants.Which is the energy level of the hole or of the electron depending on which element I pick for dopant?Which is the energy of the hole and the electron depending on the base and the dopants?

 

[hutchphd]

Which is the energy of the hole and the electron depending on the base and the dopants?

The issue you are worrying about is not very important: small compared to the band gap of the substrate and small compared to thermal energies.
Try this:
https://en.wikipedia.org/wiki/Doping_(semiconductor)

 

[hutchphd]

I think the dopants are chosen partially for metallurgical reasons (how easy is it to infuse them into the substrate and do they stay put etc) and cost. The real wizards of "tuning" are the folks who make LEDs and it took a forty years of cleverness to get the panoply of sources we have today. Most of this is beyond my direct knowledge and there are many many many books. I simply don't know enough to give you a complete answer, but you should search it out. I know it took a very long time to make a good blue LED (and then a UV one), and Nichia in Japan did some lovely stuff.

 

[Helena Wells]

The issue you are worrying about is not very important: small compared to the band gap of the substrate and small compared to thermal energies.
Try this:
https://en.wikipedia.org/wiki/Doping_(semiconductor)

Ok but what if we want to dope some bases with the appropriate dopants (not all dopants do for all bases)

 

[Helena Wells]

I think the dopants are chosen partially for metallurgical reasons (how easy is it to infuse them into the substrate and do they stay put etc) and cost. The real wizards of "tuning" are the folks who make LEDs and it took a forty years of cleverness to get the panoply of sources we have today. Most of this is beyond my direct knowledge and there are many many many books. I simply don't know enough to give you a complete answer, but you should search it out. I know it took a very long time to make a good blue LED (and then a UV one), and Nichia in Japan did some lovely stuff.

so by doping a base with random dopants we may even have the donor or the acceptor inside the valence band of the base

 

[hutchphd]

I think there are reasons you want them marginally inside the gap but I will leave you to a good solid state textbook. Good luck.

 

[Helena Wells]

Isnt there available any stuff in the internet?

 

[Useful nucleus]

If I understand this thread correctly, you seek a method to predict the levels of a dopant in a host.
This is exactly what computational materials scientists/physicists do. The gold standard in this field is using density functional theory simulations to predict the energy levels of a dopan in a semiconductor.
This is a very vast and well-established field. See for example Fig. 2 in this paper that shows the density of states of ZnO (semiconductor) doped with Lithium
https://d1wqtxts1xzle7.cloudfront.net/45595590/Ferromagnetism_in_Dilute_Magnetic_Semico20160513-9274-ixj6en.pdf?1463136126=&response-content-disposition=inline%3B+filename%3DFerromagnetism_in_Dilute_Magnetic_Semico.pdf&Expires=1614027465&Signature=T0GgM0Ppv51duxX7--RcPohkXd2ddnzRxLNZtgwVQr1-dd0O79TzlQEpQ~-MqzTxGnIme0OYNBDL6iGEuvb1WPv7JreAZXgGgS8EwquIZA5EA2vvNyKytd9gSyhs6Zt~wqTBaSCccMNce8xVF4aENS7a4vLPvKQXLQGcvYIHEr7oTmwxsiwR3zcwlftT4kPLFJfEuPtguugmjvbmcKS33sOrBtKqDXYYlez6cekcpPCagJHXjTket~-KGfa1E3ZtbxmuysjI8TZqSYvJKV2BiQ6rFknOyUj3x0VvNUkB1vIMXWG6bnvNq7kZnjWINpwqepd~~NzpLyNZDzg8Iq5CHQ__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA

If you want to get into this field, you will need to study some materials science, solid state physics, and thermodynamics.

 

[hacivat]

Actuall Bohr model gives a good approximation for the energy of dopant states, just wacth after 34:00 minute of this video: