A couple questions about energy bands and Fermi energy

In summary, the Fermi energies of two materials in contact must be equal at thermal equilibrium, which is the physical reason for this equation. In a p-dope semiconductor, the Fermi energy is smaller due to the addition of dopants, making it easier for electrons to become mobile charge carriers. The workfunction difference between the metal and semiconductor creates a built-in potential difference in a MOS system, causing the energy bands of silicon to bend. The oxide Fermi level and workfunction also play a role in the bending of energy bands.
  • #1
eliotsbowe
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Hello, I'm studying digital integrated circuits and I'm new to solid state physics. I've studied PN junctions, drift and diffusion currents, now I'm trying to see these subjects in terms of energy bands and I'd really appreciate it you could explain to me a couple concepts.

When two materials contact each other, at thermal equilibrium their Fermi energies must equate. I'm ok with this if I see a band diagram and I understand that if this wasn't true a pn junction would not exhibit any built-in voltage. But what's the physical reason for this equation?

In a p-dope semiconductor, the Fermi energy is smaller than its intrinsic value; that is, it gets closer to the upper bound of the valence band.
I think of it like this: in a p-dope region it's easier, for an electron that leaves its atom (for example, a silicon atom), to get catched by a positive ion (for example, a boron atom) than to "jump" out of the valence band and become a mobile charge carrier. Is my interpretation correct?My last question is about energy bands in a MOS system with a p-dope semiconductor.
The book I'm studying says:
"Because of the work-function difference between the metal and the semiconductor, a voltage drop occurs across the MOS system. Part of this built-in voltage drop occurs across the insulating oxide layer. The rest of the voltage drop (potential difference) occurs at the silicon surface next to the silicon-oxide interface, forcing the energy bands of silicon to bend in this region."

Here's the band diagram: http://s21.postimage.org/ue37uaaqf/Immagine_9.png

The metal and semiconductor Fermi levels match, but the oxide Fermi level doesn't show up; plus, the oxide work-function isn't even mentioned. Don't these two parameters have any influence on the bending of energy bands? Thanks in advance.
 
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  • #2
The physical reason for the equation of Fermi energies is that at thermal equilibrium, the probability of electrons in the conduction band of one material and holes in the valence band of the other material must be equal. In other words, the number of electrons and holes must be the same in each material. This means that the chemical potentials (Fermi energies) must also be equal. Your interpretation of the p-dope semiconductor is correct. The addition of dopants creates extra positive charges, which attracts electrons from the valence band and makes it easier for them to become mobile charge carriers. This reduces the Fermi energy and brings it closer to the upper bound of the valence band. Regarding your last question, yes the oxide Fermi level and oxide workfunction do have an influence on the bending of energy bands. The workfunction difference between the metal and the semiconductor causes the Fermi levels of both materials to be unequal. This creates a built-in potential difference across the MOS system, which forces the energy bands of silicon to bend in this region. The oxide Fermi level affects the amount of bending, since it determines the potential of the oxide layer.
 

1. What are energy bands?

Energy bands refer to the allowed energy levels that electrons can occupy within a solid material. These energy levels are determined by the electronic structure of the material and can vary depending on factors such as the number of electrons and the arrangement of atoms.

2. How are energy bands related to the Fermi energy?

The Fermi energy, also known as the Fermi level, is the highest energy level occupied by an electron at absolute zero temperature. This energy level falls within the valence band, which is the highest energy band occupied by electrons in a solid. The energy bands above the valence band are called conduction bands, and the energy level at the top of the valence band is known as the Fermi energy.

3. What is the significance of the Fermi energy?

The Fermi energy plays a crucial role in determining the electrical and thermal properties of a material. It serves as a reference point for the energy levels of electrons and dictates their behavior, such as their ability to conduct electricity and transfer heat.

4. How does temperature affect energy bands and the Fermi energy?

As temperature increases, electrons gain more thermal energy and are able to occupy higher energy levels. This can cause the Fermi energy to shift upwards, leading to a broader distribution of electrons in the energy bands. This effect can also result in increased conductivity and thermal conductivity in the material.

5. Can energy bands and the Fermi energy be manipulated?

Yes, energy bands and the Fermi energy can be altered through various methods such as doping, which involves introducing impurities into the material to change its electronic properties. Additionally, external factors such as electric and magnetic fields can also affect the energy bands and the Fermi energy.

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