Energy of donor or acceptor levels in semiconductors

In summary: No, you may be able to get the desired result by doping a base with the appropriate dopants.No, you may be able to get the desired result by doping a base with the appropriate dopants.
  • #1
Helena Wells
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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?
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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?
 
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  • #2
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.
 
  • #3
phyzguy said:
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?
 
  • #4
Helena Wells said:
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?
 
  • #5
phyzguy said:
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?
 
  • #6
Helena Wells said:
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)
 
  • #7
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.
 
  • #8
hutchphd said:
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)
 
  • #9
hutchphd said:
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
 
  • #10
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.
 
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  • #11
Isnt there available any stuff in the internet?
 
  • #12
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.
 
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  • #13
Actuall Bohr model gives a good approximation for the energy of dopant states, just wacth after 34:00 minute of this video:

 
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Related to Energy of donor or acceptor levels in semiconductors

1. What is the energy of donor or acceptor levels in semiconductors?

The energy of donor or acceptor levels in semiconductors refers to the energy levels of impurities that are intentionally introduced into the semiconductor material to alter its electrical properties. These levels are typically located near the conduction or valence band of the semiconductor and can either donate or accept electrons, leading to the formation of either n-type or p-type semiconductors.

2. How do donor and acceptor levels affect the conductivity of semiconductors?

The presence of donor or acceptor levels in semiconductors can greatly impact their conductivity. Donor levels, which have extra electrons, increase the number of free electrons in the material, making it more conductive. On the other hand, acceptor levels, which are missing electrons, create "holes" in the material, making it easier for electrons to move, also increasing conductivity.

3. What factors determine the energy levels of donor and acceptor impurities?

The energy levels of donor and acceptor impurities in semiconductors are determined by the atomic structure of the impurity, as well as the type of semiconductor material it is introduced into. The size and charge of the impurity atom also play a role in determining its energy level.

4. How do the energy levels of donor and acceptor impurities affect the band gap of a semiconductor?

The presence of donor or acceptor impurities in a semiconductor can alter its band gap, which is the energy difference between the valence and conduction bands. The introduction of donor impurities can decrease the band gap, making the material more conductive, while acceptor impurities can increase the band gap, making the material less conductive.

5. What is the significance of the energy levels of donor and acceptor impurities in semiconductors?

The energy levels of donor and acceptor impurities play a crucial role in the functioning of many electronic devices, including transistors and diodes. By controlling the type and concentration of impurities, the electrical properties of semiconductors can be precisely engineered, allowing for the creation of complex electronic circuits and devices.

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