What happens when you try to add an electron to a semiconductor?

In summary, the conversation discussed the behavior of electrons in a semiconductor and their ability to join the conduction or valence bands. It was noted that new electrons can only be added to the conduction band through an electrical connection and potential difference. The question was raised about how an electron with energy εC could be added to the conduction band if μ<εC, and it was clarified that the electron actually joins the valence band, which may seem contradictory due to the exclusion principle. Ultimately, the question remained about where the electron comes from, as it can only occupy an empty quantum state.
  • #1
BucketOfFish
60
1
This is a question about the band gap. In a semiconductor, the chemical potential is in between the valence and conduction bands, so that the valence band is full and the conduction band is empty at T＝0. What happens if you try to add another electron to the system? It seems that it wouldn't have enough energy to join the conduction band, but all the states in the valence band are filled!

I realize that for a real semiconductor the valence band is filled completely, with not even a single electron left over, so this problem doesn't occur. In that case, what causes the valence band to end exactly at the energy level needed to accommodate all electrons?
 
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  • #2
New electrons can only be added to the conduction band ... consider: where did it come from?
There must be an electrical connection with some part of the semiconductor, and a potential difference.
 
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  • #3
Yes, I agree that it would only make sense for a new electron to join the conduction band, but perhaps I was not making my question clear. I actually meant to ask why an electron of energy εC could be added if mathematically μ<εC. It seems like with that amount of energy the electron would end up in limbo somewhere in the band gap.

EDIT: Wait, I misread. The electron joins the valence band? But all the states there ought to be filled, right? So by Pauli exclusion shouldn't electrons be forbidden from joining the valence band?
 
  • #4
Actually you read it right - I just wrote it wrong.
The electron can only occupy an empty quantum state.
So you need to answer the question: where does the electron come from?
 

FAQ: What happens when you try to add an electron to a semiconductor?

What happens when you try to add an electron to a semiconductor?

Adding an electron to a semiconductor can result in several different outcomes depending on the specific semiconductor material and other factors. Some of the most frequently asked questions about this process include:

What is the band gap of a semiconductor?

The band gap of a semiconductor refers to the energy difference between the highest energy level in the valence band (where electrons are bound to atoms) and the lowest energy level in the conduction band (where electrons can move freely). In other words, it is the minimum amount of energy required to move an electron from the valence band to the conduction band.

What happens to the band gap when an electron is added?

When an electron is added to a semiconductor, it can either occupy an empty energy state in the conduction band, or it can cause a shift in the energy levels of the valence and conduction bands. This shift can result in a decrease in the band gap, making it easier for electrons to move from the valence band to the conduction band.

How does adding an electron affect the conductivity of a semiconductor?

Adding an electron to a semiconductor can increase its conductivity by providing free electrons that can move through the material and carry an electric current. This is why semiconductors are often used in electronic devices such as transistors and computer chips.

Can adding too many electrons to a semiconductor cause damage?

Yes, adding too many electrons to a semiconductor can cause damage by altering the delicate balance of charge carriers in the material. This can lead to unwanted effects such as overheating or short circuits in electronic devices.

How does the addition of impurities affect the behavior of semiconductors?

The addition of impurities, also known as doping, can significantly alter the behavior of semiconductors. By adding small amounts of impurities, the conductivity and other properties of the material can be manipulated, making it more suitable for specific applications such as solar cells or light-emitting diodes.

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