Conductivity & Atomic Packing Factor

Main Question or Discussion Point

First question, is atomic packing factor as described in wiki the same as fill factor?

If so, how does it relate to the conductivity? Does conductivity increase will the increase in atomic packing factor or fill factor?

I don't understand the relationship between conductivity and fill factor. Especially as it relates to semiconductors.

If anyone can help me understand then it would be great or provide some reading material.
 

Answers and Replies

alxm
Science Advisor
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I'm not sure what 'fill factor' is, but it does sound like it's related to the atomic packing factor.

The atomic packing factor is really mostly a geometric concept. It doesn't have a terrible lot of uses, because the 'radius' of atoms is not constant. Basically when you talk about the radius of atoms in a crystal, you're defining the radius to be half the atom-atom distance. There's no physical reason to assume that it'll be the same in another crystal or compound. It usually isn't. Atoms aren't tiny hard spheres.

Basically, atoms pack the way they do into crystals depending on their electronic structure. How many valence electrons, and in which orbitals. The electronic structure also determines their conductance. It's not as simple as whether atoms are close together or not.

For a substance to conduct, it depends on the electrons forming the bonds between the atoms. Their energy level is called the 'valence band'. The next (empty) level in energy above that is called the 'conduction band'. If the energy range of the two bands overlap, then it acts as a conductor. To put this in another (more chemistry-ish) way, if the atoms can bind to each-other in more than one way (at the same energy level), then it conducts.
 
I'm not sure what 'fill factor' is, but it does sound like it's related to the atomic packing factor.
Yeah I think it is related to atomic packing factor from what I was reading. Atomic packing factor does relate to Electronic Structure, no?

The electronic structure also determines their conductance.

For a substance to conduct, it depends on the electrons forming the bonds between the atoms. Their energy level is called the 'valence band'. The next (empty) level in energy above that is called the 'conduction band'. If the energy range of the two bands overlap, then it acts as a conductor. To put this in another (more chemistry-ish) way, if the atoms can bind to each-other in more than one way (at the same energy level), then it conducts.
Your starting to get me to understand. Lets take body centered cubic and face centered cubic. One has more of an atomic packing factor than the other and therefore has more electrons forming bonds, correct? Since there are more electrons forming bonds there should be an increase in conductivity, correct? If not could you please help me to understand.

Also, probably the same question but, does the increase in atomic packing factor and/or electronic structure make the bandgap much smaller? I'm asking because you said that if the two bands overlap then you get a good conductor (paraphrasing). Therefore it would take less energy to move an electron from one band to the other, correct?

Thank you so much for the reply.
 

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