Semiconductor and fermi energy

In summary, the participants are discussing the concept of the Fermi energy level in different energy states, including continuous energy states and discrete energy states. They also mention how the Fermi energy level is affected by temperature and how it can be determined in the case of a semiconductor with non-smooth energy states. They conclude that the Fermi level is the energy at which hypothetical states would be filled to 50%, and it can be determined by drawing a smooth curve and finding the point where the y-axis reaches 1/2. The concept of asymmetry in the energy states is also mentioned as a factor that affects the determination of the Fermi level.
  • #1
iScience
466
5
hey guys i just wanted to confirm something;

so, for systems of continuous energy states (or small separations of discrete energy states), we can plot a graph like this and call the fermi energy the middle point where Probability=1/2. like this

ULjgmtc.png


where, if T=0K, the transition from occupancy to no occupancy is sharp. as T increases the fermi level doesn't change, as the constituent particles say... the electrons, occupy higher energy states. but this is for a smooth ("smooth"...) distribution of energy states.

but for the case of a semiconductor, where the existent energy states are not so smooth going from the valence band to the conduction band, how do i know where the fermi energy level is?

pm2OL5r.png


the graph in this image/scenario I've plotted for a non-zero temperature case (as apparent by the nonzero occupancy in the C-band region).
Take a look at the red region; I'm almost sure that this region should have zero occupancy of electrons BUT, I'm reading an introductory paper on semiconductors and they are referring to the fermi level being right in the middle between the V-band and C-band for the case where there are no excess carriers (no excess electrons and no excess holes).
I don't understand how the fermi level can be in the middle when the fermi level is defined as (i thought..) the energy at which the probability of occupancy is 1/2. but the occupancy probability in the band gap is zero.. so how can it be there?

thanks
 
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  • #2
If there are no states available, the Fermi level is the energy where (hypothetical) states would be filled to 50%.

as T increases the fermi level doesn't change
In general it does change a bit, but that is unrelated to the main question.
 
  • #3
In general it does change a bit, but that is unrelated to the main question.

i thought the electrons at the edges entering the higher energy states corresponds to the curve just becoming smoother with the 50% point remaining the same. Could you give me a brief explanation of what is changing the fermi level?

If there are no states available, the Fermi level is the energy where (hypothetical) states would be filled to 50%.

so then am i just drawing a smooth hypothetical curve from the valence band energy edge to the conduction band energy edge and then calling the fermi level where the y-axis ([itex]\bar{n}[/itex]) hits 1/2?
 
  • #4
iScience said:
i thought the electrons at the edges entering the higher energy states corresponds to the curve just becoming smoother with the 50% point remaining the same. Could you give me a brief explanation of what is changing the fermi level?
The curve is not perfectly symmetric. This is obvious where you reach the lowest energy states (as there are no electrons below 0, but electrons can be above 2*Ef), but the asymmetry exists everywhere. For small temperatures this is a small effect.

so then am i just drawing a smooth hypothetical curve from the valence band energy edge to the conduction band energy edge and then calling the fermi level where the y-axis ([itex]\bar{n}[/itex]) hits 1/2?
Right.
 

1. What is a semiconductor?

A semiconductor is a material that has electrical conductivity between that of a conductor and an insulator. This means that it can conduct electricity, but not as well as a metal. Examples of semiconductors include silicon, germanium, and gallium arsenide.

2. What is fermi energy?

Fermi energy, also known as fermi level, is the highest energy state that an electron in a solid material can occupy at absolute zero temperature. It represents the energy at which the probability of finding an electron is 50%. At higher temperatures, electrons can occupy higher energy states above the fermi energy.

3. How is fermi energy related to semiconductors?

In semiconductors, fermi energy plays a crucial role in determining the electrical properties of the material. At the fermi energy, the valence band and the conduction band of the semiconductor are separated by a small energy gap. This energy gap allows for the controlled flow of electrons, making semiconductors useful for electronic devices.

4. What factors affect fermi energy in semiconductors?

Fermi energy in semiconductors is affected by temperature, impurity doping, and external electric fields. As temperature increases, the fermi energy also increases due to more electrons occupying higher energy states. Impurity doping, in which foreign atoms are intentionally introduced into the semiconductor, can shift the fermi energy level. External electric fields can also manipulate the fermi energy by altering the energy levels of the electrons in the semiconductor.

5. How is fermi energy measured in semiconductors?

Fermi energy in semiconductors is typically measured using a technique called Hall effect. This involves applying a magnetic field perpendicular to a semiconductor sample and measuring the voltage across the sample. From this, the carrier concentration and mobility can be determined, which can then be used to calculate the fermi energy level.

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