What actually are electron holes?

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    Electron Holes
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Discussion Overview

The discussion revolves around the concept of electron holes in solid-state physics, particularly in relation to their behavior as charge carriers and their implications in phenomena like the Hall Effect. Participants explore the nature of holes, their movement, and the effects of effective mass in the context of electron dynamics within a crystal lattice.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes electron holes as the absence of electrons in a crystal and explains their movement as a result of adjacent electrons filling these vacancies.
  • Another participant introduces the concept of effective mass, noting that electrons near the top of a band can exhibit negative mass, which influences their movement in the presence of a magnetic field.
  • A later reply suggests that the Hall voltage being positive in certain metals indicates that the effective negative mass of electrons leads to a positive charge carrier behavior for holes.
  • One participant emphasizes the need to clarify that holes are not simply the absence of electrons but specifically the absence of electrons with negative effective mass.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of holes and their role in charge transport, particularly in relation to the Hall Effect. There is no consensus on the implications of effective mass and its relation to the behavior of holes.

Contextual Notes

The discussion includes assumptions about the behavior of electrons and holes in a crystal lattice, the definition of effective mass, and the interpretation of Hall voltage, which may not be fully resolved or universally accepted among participants.

Who May Find This Useful

This discussion may be of interest to students and professionals in solid-state physics, materials science, and electrical engineering, particularly those exploring charge transport mechanisms in semiconductors and metals.

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What actually are electron holes?

I have come to read that electron holes are nothing but the blank space that is left behind when an electron is missing in a crystal where it ought to have been present. I have also learned that the movement of holes are due to adjacent electrons jumping into the holes (hence creating a hole in its former position). So a hole movement in one direction is created by electron movement in another direction.

But what bothers me is the Hall Effect. Hall Voltage in some metals like Zn are positive which is only possible if the charge carriers are positive.
Saying that holes are a kind of positive charge carrier doesn't answer the riddle because the holes movement are actually the electron movement in the other direction! so the magnetic force acts on these electron and hence negative Hall voltage should have been established?!.

Whats the point I am missing here?
 
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The "effective mass" of an electron is given by the curvature of the band. Hence electrons near the top of a band have a negative mass and also the velocity is anti-parallel to the driving force. So you are right, the electrons really move in the other direction than what you would expect if they were free. The hole picture fits in here nicely. A missing electron of negative mass will behave like a particle with positive mass. The reason for the negative effective mass is that an increase in the crystal momentum of the electrons will lead to an increased Bragg scattering of the electrons. Near the top of the band, this increase in the backscattered wave outweights the increase in crystal momentum.
 


So, you mean that, when measuring Hall voltage, the magnetic force causes the electron drift towards negative direction due to its effective negative mass so that the hall voltage is +ve. Thank you, I understand that.
But, shouldn't it be emphasized that holes are not merely absent of electrons but absent of electrons with negative effective mass?
 


Yes, and I think any good book on solid state theory does that (try e.g. Ashcroft/ Mermin).
 

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