Fermi Level Concept: Probability & Forbidden Gap

In summary, the Fermi level in pure semiconductors lies in the center of the forbidden energy gap, but it still has a probability of being filled due to the Fermi-Dirac distribution and the density of states. This is because the problem of finding the bound states of many electrons can be separated into two parts: the free electron gas and the influence of the lattice on the occupation of the free states.
  • #1
Ahmad Kishki
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I was wondering if the fermi level lies in the centre of the forbidden energy gap on pure semiconductors, then how does it (by definition) have a probability 1/2 of being filled? Shouldnt the fact that the fermi level lies in the forbidden, forbid the fermi level from having any probability of electrons?

I understand that its wrong to make sweeping remarks in the realm of quantum physics about probability being zero, but i can't find a mental picture for what's happening. Thanks :)
 
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  • #2
In order to get the complete probability density, you have to mulitply the Fermi-Dirac distribution by the density of states which is zero in the forbidden region.

The mental picture would be that we are able to separate the complicated problem of finding the bound states of many electrons in the crystal lattice potential into two parts: a free electron gas where the electrons have an effective mass (this is described by the Fermi-Dirac distribution) and the influence of the lattice on the occupation of the free states (this is described by the density of states).
 
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  • #3
kith said:
In order to get the complete probability density, you have to mulitply the Fermi-Dirac distribution by the density of states which is zero in the forbidden region.

The mental picture would be that we are able to separate the complicated problem of finding the bound states of many electrons in the crystal lattice potential into two parts: a free electron gas where the electrons have an effective mass (this is described by the Fermi-Dirac distribution) and the influence of the lattice on the occupation of the free states (this is described by the density of states).

Wow thanks :)
 
  • #4
You are welcome :-)
 

1. What is the Fermi level concept?

The Fermi level concept is a fundamental concept in solid state physics that describes the energy level at which electrons have a 50% probability of being filled in a system at thermal equilibrium. It is also known as the Fermi energy or the chemical potential.

2. How is the Fermi level related to probability?

The Fermi level is directly related to the probability of finding an electron at a specific energy level. At thermal equilibrium, the Fermi level represents the energy at which there is a 50% probability of finding an electron. As the temperature changes, the probability distribution of electrons around the Fermi level also changes.

3. What is the significance of the forbidden gap in the Fermi level concept?

The forbidden gap, also known as the band gap, is the energy range in a material where no electron states are allowed. It plays a crucial role in determining the electrical and optical properties of a material. In the Fermi level concept, the forbidden gap represents the energy difference between the highest filled electron state and the lowest empty electron state.

4. How does the Fermi level concept apply to semiconductors?

In semiconductors, the Fermi level is located within the forbidden gap. The position of the Fermi level within the forbidden gap determines the conductivity of the material. At absolute zero temperature, the Fermi level is at the top of the valence band for pure semiconductors, and at the bottom of the conduction band for heavily doped semiconductors.

5. Can the Fermi level be manipulated in a material?

Yes, the Fermi level can be manipulated by changing the temperature or by introducing impurities into the material. For example, doping a semiconductor with impurities can shift the position of the Fermi level and change the conductivity of the material. This is the basis for many electronic devices, such as transistors and diodes.

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