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

In summary, the conversation discusses the band structure and Fermi level of a particular block of solid, which is affected by the arrangement of positive ions, lattice, imperfections, shape, and mass. The diagram shown indicates that the valence bands will be the same for two blocks of Si, regardless of their size or impurities. However, the density of states making up the band may change with volume. It is also mentioned that the potential well or box may be altered by doping atoms, but this is only significant for nano-particles composed of a smaller number of atoms.
  • #1
ugenetic
50
3
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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  • #2
That is not true, the density of states making up the band increases proportionally with volume.
 
  • #3
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
 
  • #4
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.
 
  • #5
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?
 

1. How does the band structure of a solid affect its size?

The band structure of a solid is not directly related to its size. The band structure is determined by the arrangement of atoms and the energy levels of the electrons in the solid. Therefore, changing the size of the solid will not necessarily have an impact on its band structure. However, the size of a solid can indirectly affect its band structure through factors such as strain and confinement effects.

2. Does doping affect the band structure of a solid?

Yes, doping can affect the band structure of a solid. Doping refers to the intentional introduction of impurities into a solid material. These impurities can alter the arrangement of atoms and the energy levels of electrons, thereby changing the band structure. This can have significant effects on the electrical and optical properties of the solid.

3. How is the band structure of a solid determined?

The band structure of a solid is determined by various factors such as the crystal structure, the type of atoms present, and the arrangement of atoms in the solid. It can also be calculated using techniques such as density functional theory and quantum mechanics. Additionally, experimental techniques such as photoemission spectroscopy can provide information about the band structure of a solid.

4. Can the band structure of a solid be modified?

Yes, the band structure of a solid can be modified through various methods such as strain engineering, alloying, and doping. These methods can change the energy levels of electrons and alter the band structure, leading to changes in the properties of the solid. However, it is important to note that the band structure is a fundamental property of a solid and cannot be completely changed.

5. How does the band structure of a solid affect its properties?

The band structure of a solid plays a crucial role in determining its properties. For example, the band structure determines the electrical conductivity, optical properties, and thermal properties of a solid. A higher band gap means the solid is an insulator, while a lower band gap indicates a semiconductor. The band structure also affects the mobility of electrons and their ability to carry a charge, which is important for electronic devices.

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