Understand Semiconductor Elec. States at 0K and Room Temp

In summary, the Fermi level in semiconductors is the energy level where half of the states are (or would be) occupied and it can increase with temperature. However, at room temperature, the highest energy state of the valence band is below the Fermi level. This can be explained by the fact that heating a material can reduce the band gap and potentially shift the valence band edge up, but it does not necessarily mean that the Fermi level is also elevated. The Fermi level is a parameter of the Fermi-Dirac distribution function, which applies to electron gas systems and can change with temperature. However, for non-gas systems, the measured chemical potential cannot be viewed as the Fermi level and the
  • #1
sandakelum
2
0
In a semiconductor @ 0k highest energy state lie on fermilevel(all electrons @ valence band). but @ room temperature highest energy state of covelence band lie below the fermilevel. how can i understand this? pls help me.
 
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  • #2
The fermi level can increase with temperature. More energy -> the energy level where half of the states are (or would be) occupied is higher.
Where is the problem?
 
  • #3
sandakelum said:
In a semiconductor @ 0k highest energy state lie on fermilevel(all electrons @ valence band). but @ room temperature highest energy state of covelence band lie below the fermilevel. how can i understand this? pls help me.

What is your definition of Fermi level for semiconductors?
Note that according to the common use, the "Fermi level" in semiconductors is in the band gap. This is because what is called Fermi level in semiconductors is actually the chemical potential.
Even if you stick with the definition used for metals, Fermi level is the maximum energy level occupied at zero K. So it does not change with temperature, by definition.
The chemical potential is what changes with temperature.
 
  • #4
The central task of basic semiconductor physics is to establish formulas for the position of the Fermi level EF relative to the energy levels EC and E
[...]
and causes the Fermi level EF to shift
Found here

Looks like the regular Fermi level.

Do you mean the Fermi energy? That is at T=0.
 
  • #5
If fermi level is changing with temperature its ok. my quaestion was when temperature up energies of covalence band also up. so if highest energy electrons @ covalance band occupy near to fermilevel @ 0 K (fermi level is the upper ,argin of the fermi sea) when temperature up
higest covelence electrone energy must exceeds fermi energy.(some of them may have enough to go to conduction band).
 
  • #6
IF I understand correctly you believe that:
The fact that some of the valence band electrons managed to reach the conduction band edge at non-zero Temperature and hence exceeding the Fermi Level , means that the valence band edge now has to be considered shifted up as well exceeding the Fermi level.
This is not the case. The energy of the "free" electrons do not define where the edge of the valence band resides on the energy scale.
Having said that, I have a couple of comments on the ongoing discussion.
1) Heating the material generally leads to reducing the band gap , thus the valence band edge may indeed go up a bit (but not exceeding the Fermi Level).
2) Heating the material does not necessarily implies elevating the chemical potential of electrons (Fermi level). It may be the case that self doping effects can lead to lowering the Fermi level by heating up the system.
 
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  • #7
nasu said:
What is your definition of Fermi level for semiconductors?
Note that according to the common use, the "Fermi level" in semiconductors is in the band gap. This is because what is called Fermi level in semiconductors is actually the chemical potential.
Even if you stick with the definition used for metals, Fermi level is the maximum energy level occupied at zero K. So it does not change with temperature, by definition.
The chemical potential is what changes with temperature.

As I read it somewhere, Fermi level is a (the sole) parameter of Fermi-Dirac distribution function, which should apply to electron gas only(?), and FL does change with temperature. (And as I remember it, at FL the occupancy rate of state is 0.5.)

For an electron system that cannot be treated as gas, the measured chemical potential could not be viewed as Fermi level, and thus Fermi-Dirac distribution function could not apply.
 

1. What is a semiconductor?

A semiconductor is a type of 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 are the electronic states of a semiconductor at 0K and room temperature?

At 0K (absolute zero), a semiconductor is in its lowest energy state and all of the electrons are in the valence band. At room temperature, some electrons have enough thermal energy to jump from the valence band to the conduction band, creating both holes (positively charged) and free electrons (negatively charged).

3. How does the band gap of a semiconductor affect its electronic states?

The band gap is the energy difference between the valence and conduction bands in a semiconductor. A larger band gap means that more energy is required for electrons to jump from the valence band to the conduction band, resulting in fewer free electrons and holes at room temperature.

4. What is the significance of understanding semiconductor electronic states at 0K and room temperature?

Understanding the electronic states of a semiconductor at different temperatures is important for designing and optimizing electronic devices. At 0K, a semiconductor behaves differently than at room temperature, and this knowledge can be used to improve device performance.

5. How do impurities affect the electronic states of a semiconductor?

Impurities, or dopants, can be added to a semiconductor to change its electronic properties. For example, adding a pentavalent dopant, such as phosphorus, creates extra free electrons in the conduction band, making the semiconductor more conductive. Alternatively, adding a trivalent dopant, such as boron, creates extra holes in the valence band, making the semiconductor less conductive.

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