What actually are electron holes?

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    Electron Holes
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SUMMARY

Electron holes represent the absence of electrons in a crystal lattice, effectively acting as positive charge carriers. Their movement occurs as adjacent electrons fill these vacancies, resulting in a directional flow opposite to that of the electrons. The Hall Effect demonstrates that in certain metals, such as zinc, the Hall Voltage can be positive, indicating that holes, which behave as particles with positive mass due to their association with electrons of negative effective mass, are responsible for this phenomenon. This relationship is crucial for understanding solid-state physics and the behavior of charge carriers in materials.

PREREQUISITES
  • Understanding of solid-state physics concepts
  • Familiarity with the Hall Effect and Hall Voltage
  • Knowledge of electron band theory and effective mass
  • Basic principles of crystal lattice structures
NEXT STEPS
  • Study the Hall Effect in various materials, focusing on zinc and its properties
  • Explore electron band theory and its implications for effective mass
  • Read "Solid State Physics" by Ashcroft and Mermin for in-depth understanding
  • Investigate the role of Bragg scattering in electron momentum and behavior
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Students and professionals in solid-state physics, materials scientists, and anyone interested in the behavior of charge carriers in semiconductor materials.

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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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