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

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Discussion Overview

The discussion revolves around the concept of energy levels in electronic band structures, particularly why these levels are represented as starting from negative values in certain contexts. Participants explore the implications of energy being relative and the importance of context in understanding these representations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that while energy levels in electronic band structures can appear negative, this is a matter of representation, as energy is relative.
  • One participant suggests that the negative energy could represent binding energy, indicating the energy required to liberate electrons.
  • Another participant emphasizes the importance of context when interpreting energy levels, comparing it to potential energy in classical physics where zero can be defined at different points.
  • A participant mentions that introductory solid state physics often first introduces the Fermi-Dirac distribution in the context of the free electron gas model, which typically involves positive kinetic energy.
  • There is a request for book recommendations that cover the quantum structure of the atom, indicating a desire for further reading on the topic.

Areas of Agreement / Disagreement

Participants express varying interpretations of the representation of energy levels, indicating that multiple competing views remain. The discussion does not reach a consensus on the reasons behind the negative energy levels in electronic band structures.

Contextual Notes

Participants highlight the need for context in understanding energy representations, suggesting that definitions and assumptions may vary based on the specific framework being discussed.

Who May Find This Useful

Readers interested in solid state physics, quantum mechanics, or the interpretation of electronic band structures may find this discussion relevant.

RaduAndrei
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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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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.
 
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.
 
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.
 
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.
 
Very nice books. Thanks.
 

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