How does the interatomic spacing of alloys differ from that of pure crystals?

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Discussion Overview

The discussion centers on the differences in interatomic spacing between alloys, specifically Silicon-Germanium (SiGe), and pure crystals. Participants explore how the arrangement of atoms in alloys affects bond lengths and lattice parameters, as well as implications for band diagrams in semiconductor physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that in pure crystals, interatomic distances are well defined, while in alloys, the spacing can vary based on whether the alloy is ordered or random.
  • It is proposed that ordered alloys have specific bond lengths (Si-Si, Ge-Ge, Si-Ge), whereas random alloys exhibit a spectrum of bond lengths.
  • Questions are raised about the dependence of interatomic distances on the lattice constant, which may vary with the composition of the alloy.
  • Participants discuss that for random alloys, the reported lattice parameter is an average, leading to a distribution of bond lengths across unit cells.
  • There is a suggestion that band diagrams for alloys differ based on doping levels, with dilute doping maintaining the host's band structure, while concentrated doping leads to the formation of new continuous bands that can significantly alter the band gap.
  • One participant posits that a P-type semiconductor can be viewed as an 'alloy', with the band diagram reflecting both the original semiconductor and the effects of doping.
  • It is stated that the band diagrams before and after doping are different, with new valence and conduction bands forming as a result of the alloying process.

Areas of Agreement / Disagreement

Participants express differing views on the nature of interatomic distances in alloys, whether they are ordered or random, and how this affects band structure. The discussion remains unresolved regarding the implications of these differences for band diagrams and the specific effects of doping concentrations.

Contextual Notes

Limitations include the dependence on definitions of order in alloys, the averaging of lattice parameters, and the complexity of band structure changes due to varying doping levels. These factors contribute to the uncertainty in the discussion.

Helena Wells
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In pure crystals the interatomic distance is well defined :in a carbon crystal lattice it is the distance between 2 carbons.

However if we have an alloy(Silicon-Germanium) how does the spacing between atom work?

If we have SiGe(50-50 alloy) how can we find the interatomic distance?
 
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Alloys can be ordered or random. IF the alloy is ordered , then their will be a set of well defined bond lengths (Si-Si, Ge-Ge, and Si-Ge). IF the alloy is random, then we will have a "spectrum" of bond lengths.
 
Useful nucleus said:
Alloys can be ordered or random. IF the alloy is ordered , then their will be a set of well defined bond lengths (Si-Si, Ge-Ge, and Si-Ge). IF the alloy is random, then we will have a "spectrum" of bond lengths.
Don't the interatomic distances depend on the lattice costant , which varies linearly with the composition of the 2?If it is as you say how can we draw a band diagram for an alloy?
 
For a random alloy, the lattice parameter reported is an average over all unit cells. Each unit cell can have a slightly different lattice parameter than other unit cells. Thus, we have an average lattice constant but a distrubition of bond lengths.

The band diagram is a different story. If you have a dilue limit doping (say less than 1%), then the band diagram is the same for the host (99%) modified by dopant (or impurity) levels. Once the doping moves into the conecetrated alloy regime, the levels merge to form a continuous band of their own modifying the host original band diagram. Because of the formation of the new continuous bands, the collective band gap of the alloy can change dramatically (e.g. closing the gap and changing from a semiconductor to metal).
 
Useful nucleus said:
For a random alloy, the lattice parameter reported is an average over all unit cells. Each unit cell can have a slightly different lattice parameter than other unit cells. Thus, we have an average lattice constant but a distrubition of bond lengths.

The band diagram is a different story. If you have a dilue limit doping (say less than 1%), then the band diagram is the same for the host (99%) modified by dopant (or impurity) levels. Once the doping moves into the conecetrated alloy regime, the levels merge to form a continuous band of their own modifying the host original band diagram. Because of the formation of the new continuous bands, the collective band gap of the alloy can change dramatically (e.g. closing the gap and changing from a semiconductor to metal).
Yeah i thought the same a P type semiconductor can be considered an 'alloy' and the band diagram of is just the band diagram of the semiconductor with the only addition being the acceptor level. About higher concentration(50-50) if I understand correctly are you saying we can have '2' valence bands and by 2 I mean the valence band before the 'doping' and a valence band formed due to the injected atoms and they form a single energy band?
 
You are right the band diagram before doping is different that the band diagram after doping. Together both elements will form new valence and conduction bands.
 

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