Energy Band Diagrams (Solid State)

In summary, the Shockley equation explains the inverse relationship between energy and voltage in terms of a band diagram, and can be used to analyze MOS-Capacitors.
  • #1
roeb
107
1
My professor has said several times that if you increase the potential (electrostatic) you will get a lower energy in terms of a band diagram.

In particular, I have been working with MOS-Capacitors and this seems to be the case.
For example for an n-type semiconductor. If you apply a positive charge to the metal, the fermi energy level will increase on the metal side, because the voltage potential is decreasing.

My problem is that I have been unable to find an equation that expresses this inverse relationship. Does anyone know of anything that would show me why energy and voltage are inversely related in terms of this? Perhaps I am screwing my thinking up because E = Vq is what I remember from E&M.

Thanks
roeb
 
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  • #2
elThe equation you are looking for is the Shockley equation, which deals with the relationship between energy and voltage in terms of a band diagram. It states that the energy level (E) is inversely proportional to the applied potential (V). The equation is as follows: E = E_0 - kTln(1+exp(-eV/kT))Where E_0 is the intrinsic Fermi level, k is Boltzmann's constant, T is temperature, e is the charge on an electron, and V is the applied voltage. This equation shows that as the applied voltage increases, the energy level decreases. This is because the exponential term decreases with increasing voltage, resulting in a lower energy level.
 

Q: What is an energy band diagram?

An energy band diagram is a graphical representation of the energy states of electrons in a solid material. It shows the allowed energy levels or bands that electrons can occupy, as well as the energy gap between these bands.

Q: How are energy band diagrams used in solid state physics?

Energy band diagrams are used to understand the electronic properties of solid materials, such as their conductivity, optical properties, and magnetic behavior. They also help to explain the behavior of semiconductors, insulators, and conductors.

Q: What factors affect the shape of an energy band diagram?

The shape of an energy band diagram is affected by the composition and arrangement of atoms in a material, as well as external factors such as temperature and applied electric fields. The type of material (metal, semiconductor, or insulator) also plays a role in determining the shape of the energy bands.

Q: How does band gap affect the properties of a material?

The band gap, which is the energy difference between the top of the valence band and the bottom of the conduction band, determines the electrical and optical properties of a material. Materials with a smaller band gap, such as metals, are good conductors, while those with a larger band gap, such as insulators, are poor conductors.

Q: Can energy band diagrams be used to predict the behavior of materials?

Yes, energy band diagrams can be used to predict the behavior of materials by showing the energy states available for electrons to occupy. This information can be used to understand and predict the material's electrical conductivity, optical properties, and response to external stimuli such as electric fields or light.

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