Why do the energy levels in electronic band structures start at negative values?

In summary, the energy axis in graphs of electronic band structures starts at 0 eV and increases, indicating positive energies for electrons. This is in contrast to the energy axis in other representations, such as the Fermi-Dirac distribution, where negative energies are possible. This is due to the relative nature of energy and can vary depending on the context and model being used. It is important to understand the context and not rely solely on memorization. Recommended books for further understanding include "Solid State Electronic Devices" by Streetman and "Semiconductor Physics and Devices" by Neamen.
  • #1
RaduAndrei
114
1
In the graphs that I see around the internet I see that the energy axis starts at 0 eV and it goes up. So the electrons have positive energies.

But in the electronic band structure, the electrons have negative energies. And if they go to infinity, then their energy becomes 0.

So, what is happening?
 
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  • #2
RaduAndrei said:
In the graphs that I see around the internet I see that the energy axis starts at 0 eV and it goes up. So the electrons have positive energies.

But in the electronic band structure, the electrons have negative energies. And if they go to infinity, then their energy becomes 0.

So, what is happening?

Energy is relative! Maybe the positive energy is the "binding energy" representation, meaning that is the energy needed to liberate the electrons. There can be other possibilities. Without you showing the sources, we can only guess.

Note that you have encountered something like this already in basic kinematics problems in intro physics. I can designate potential energy to be zero on the ground and having it positive going up, or I can designate some high up points as having zero potential energy and anything below it as having negative potential energy.

The most important lesson here is to look at the CONTEXT. Understand what is being presented, rather than memorizing what it should be like.

Zz.
 
  • #3
It would be better to read about it in a book, so you get the full context of the graphs.

In introductory solid state usually the first time you see the F-D distribution is when applied to the free electron gas model. This is like a classical ideal gas but following the quantum statistics rather than classical Boltzmann statistics. So, like in ideal gas, in this model the argument of the FD function is just KE and so always positive.
 
  • #4
Could you recommend a good book? I am looking for a book that introduces the structure of the atom in a quantum way. And preferably free and on the internet.
 
  • #5
Hi RaduAndrei,

The two books which I like for the introduction of Fermi-Dirac statistics in relation to semiconductor devices are "Solid State Electronic Devices" by Streetman and "Semiconductor Physics and Devices" by Neamen.
 
  • #6
Very nice books. Thanks.
 

What is the Fermi-Dirac Distribution?

The Fermi-Dirac Distribution is a statistical distribution that describes the probability of finding particles with half-integer spin values in a system at thermal equilibrium.

What is the significance of the Fermi-Dirac Distribution?

The Fermi-Dirac Distribution is an important concept in quantum mechanics and statistical physics, as it helps to explain the behavior and properties of particles with half-integer spin values, such as electrons.

How is the Fermi-Dirac Distribution different from the Boltzmann Distribution?

The Fermi-Dirac Distribution is specific to particles with half-integer spin values, while the Boltzmann Distribution applies to all particles regardless of their spin. Additionally, the Fermi-Dirac Distribution takes into account the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state, while the Boltzmann Distribution does not.

What is the Fermi energy in relation to the Fermi-Dirac Distribution?

The Fermi energy is the highest energy level that a particle with a given spin can occupy in a system at thermal equilibrium. It is determined by the Fermi-Dirac Distribution and is a key factor in understanding the electronic properties of materials.

How is the Fermi-Dirac Distribution used in practical applications?

The Fermi-Dirac Distribution is used in a variety of fields, such as solid state physics, semiconductor devices, and nuclear physics, to understand the behavior and properties of particles with half-integer spin values in different systems. It is also used in the development of advanced technologies, such as transistors and solar cells.

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