Band Structure of a solid is not related to the size/doping?

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Discussion Overview

The discussion revolves around the relationship between the band structure of a solid and its size or doping levels. Participants explore how these factors influence the density of states, Fermi level, and the overall band structure in both macroscopic and nanoparticle contexts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant asserts that a specific block of solid has a unique band structure and Fermi level, suggesting that size and doping do not affect the valence bands of silicon blocks.
  • Another participant counters that the density of states increases proportionally with volume, implying that size does have an impact on band structure.
  • A follow-up response questions whether the height and width of a band remain unchanged regardless of the number of electrons or impurities present.
  • Some participants mention that effects related to particle number decrease with increasing size and are considered negligible for macroscopic bodies, suggesting that corrections are only significant for nanoparticles.
  • There is a query about the influence of doping on the potential well and whether it causes any notable differences in band structure.

Areas of Agreement / Disagreement

Participants express disagreement regarding the influence of size and doping on band structure, with some asserting that these factors do not matter while others argue that they do. The discussion remains unresolved with multiple competing views presented.

Contextual Notes

Participants highlight that the effects of particle number and doping may vary significantly between macroscopic solids and nanoparticles, indicating a potential dependency on scale that is not fully resolved in the discussion.

ugenetic
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Look at the diagram below, after all that doping, 2 blocks of Si have the same band structure?
00906x01.png


My understanding of band structure and fermi level is that: Given a block of solid (Please note, not a TYPE of solid, but this PARTICULAR block of solid) it will have its own unique band structure and Fermi level as well. Because band structure and fermi level is the result of trillions of electrons interact with each other (obeying exclusion principle and other quantum mechanics rules) in this PARTICULAR block of solid with its particular arrangement of positive ions, lattice, imperfections, shape, mass.

The above diagram tells me that, doesn't matter if you have a block 2 billion of Si atoms or a block of 1 Billion of Si atoms or whatever kind of impurity , Valance bands will be EXACTLY the same for those 2 blocks of Si.
 
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That is not true, the density of states making up the band increases proportionally with volume.
 
DrDu said:
That is not true, the density of states making up the band increases proportionally with volume.
Thank you, that's such a relief for me here. The density of state will change, however, the height and width of a band (top edge to bottom edge) will remain the same? doesn't matter if we have 1 thousand or 1 trillion electrons? doesn't matter if the impurity's nucleus have altered the potential well/landscape/box?
upload_2015-4-1_7-45-10.png
 
These effects decrease like 1/N with increasing particle number and are therefore considered unimportant for macroscopic bodies. Only when studying nano-particles composed of only some hundred atoms, it is worth to think about corrections.
 
DrDu said:
These effects decrease like 1/N with increasing particle number and are therefore considered unimportant for macroscopic bodies. Only when studying nano-particles composed of only some hundred atoms, it is worth to think about corrections.
Thanks, so number of total electrons doesn't matter. Then what about the potential well/box change? doping atom's nucleus and electron cloud should cause... some difference right?
 

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