Band gap in metals

[Moreno]

Some sources claim there is a substantial band gap between valence and conduction bands in monovalent metals. It might be associated with half-filled zone. Is it true or not? If it's true then why they are still metals and not a semiconductors?

 

 

Fig.2.2.10 Possible energy band diagrams containing one filled or partially filled band and one empty or partially empty band. Shown are a) a half filled band, b) two overlapping bands, c) an almost full band separated by a small bandgap from an almost empty band and d) a full band separated by a large bandgap from an empty band.

https://ecee.colorado.edu/~bart/book/eband3.htm

 

http://www.schoolphysics.co.uk/age16-19/Electronics/Semiconductors/text/Semiconductors_/index.html

 

In the monovalent metals the electronic band structure is strongly affected by the size of the band gap E _s-E _p at the Brillouin zone faces, a large gap implying a large distortion of the Fermi surface. Here E _s and E _p are the energies of the purely s-like and p-like states on the zone faces.

 

http://whitenoise.kinja.com/graphene-miracle-material-1575961841

Edited May 27, 2017 by Moreno

[studiot]

 

Some sources claim there is a substantial band gap between valence and conduction bands in monovalent metals. It might be associated with half-filled zone. Is it true or not? If it's true then why they are still metals and not a semiconductors?

 

1)

Yes this is true of monovalent metals.

 

The monovalent metals enjoy a single electron in the outer s orbital in the free atom.

Thus the orbital is half full.

 

When N such atoms combine to form a metallic solid these combine to form the conduction band each original s orbital contributes 2 spaces to the band.

So the band has "N spaces and N electrons.

 

So it too is half full.

 

The next (empty band) is formed from the empty outer p orbitals. This has a definitely higher energy than the s conduction band.

 

So there is a definite gap between the upper half full band and the next empty band.

 

2)

So why does the resulting monovalent metal sold conduct?

Well the conduction band is half full.

This is ideal to accept an electron moving in from somewhere else.

If fact the maximum number of moving electrons that can flow is N.

N are moving in and N are moving out of a given zone.

To achieve this you need N filled and N vacant spaces.

 

 

An insulator has full band and cannot accept further electrons.

 

It is possible to develop this simplified explanation to cover pretty well all cases and consider the roles played by the various gaps, overlaps and abutments between bands.

[Moreno]

^ Does it mean free electrons and holes never recombine in monovalent metals? Under which conditions recombination can happen?

Edited May 27, 2017 by Moreno

[studiot]

^ Does it mean free electrons and holes never recombine in monovalent metals? Under which conditions recombination can happen?

 

Holes are formed when an electron is promoted into a higher level band, leaving behind a hole.

 

The electrons we are discussing are already in the band.

 

So there are no holes.

[Moreno]

 

Holes are formed when an electron is promoted into a higher level band, leaving behind a hole.

 

The electrons we are discussing are already in the band.

 

So there are no holes.

 

So, in this case monovalent metals suppose to show 0 hole conductivity and their Hall coefficient should be extremely

negative. But Hall coefficient of copper, for example is just (-0.5) in comparison to that of Bismuth (+5000).

 

Is there some examples of metals or metal alloys in which there is plenty of free electrons and holes, but they never recombine each other?

[studiot]

None of the classical or semi classical theories of metals and semiconductors (Drude, Free electron, Simple band) can explain the so called 'anomalous' Hall effect coefficients.

 

You need the full 3D quantum mehcanics combined with crystallogrphic lattice theory to get anywhere near it.

[Moreno]

 

1)

Yes this is true of monovalent metals.

 

The monovalent metals enjoy a single electron in the outer s orbital in the free atom.

Thus the orbital is half full.

 

When N such atoms combine to form a metallic solid these combine to form the conduction band each original s orbital contributes 2 spaces to the band.

So the band has "N spaces and N electrons.

 

So it too is half full.

 

The next (empty band) is formed from the empty outer p orbitals. This has a definitely higher energy than the s conduction band.

 

So there is a definite gap between the upper half full band and the next empty band.

 

2)

So why does the resulting monovalent metal sold conduct?

Well the conduction band is half full.

This is ideal to accept an electron moving in from somewhere else.

If fact the maximum number of moving electrons that can flow is N.

N are moving in and N are moving out of a given zone.

To achieve this you need N filled and N vacant spaces.

 

 

An insulator has full band and cannot accept further electrons.

 

It is possible to develop this simplified explanation to cover pretty well all cases and consider the roles played by the various gaps, overlaps and abutments between bands.

So, valence band in monovalent metals is completely empty and therefore it can't conduct even a single hole?

[Moreno]

Under which conditions a materials may have multiple conduction bands separated by band gap? For example:

Quote

Using combined experimental and computational studies, we show instead that a secondary conduction band with 12 conducting carrier pockets (which converges with the primary band at high temperatures) is responsible for the extraordinary thermoelectric performance of n-type CoSb₃ skutterudites.

http://www.nature.com/articles/nmat4430

Possibly this effect can be observed in some metals as well.

[Bender]

On 27-5-2017 at 11:07 PM, Moreno said:

So, valence band in monovalent metals is completely empty and therefore it can't conduct even a single hole?

It can't conduct a hole, because there are no holes to conduct. Even when an electron is knocked out of the valence band to leave a gap, it will be filled by one of the electrons in the conduction band before much gap mobility can happen.  

[Moreno]

On ‎1‎/‎29‎/‎2018 at 1:00 PM, Bender said:

It can't conduct a hole, because there are no holes to conduct. Even when an electron is knocked out of the valence band to leave a gap, it will be filled by one of the electrons in the conduction band before much gap mobility can happen.  

So, their valence band is completely full and their conduction band is half-full? It comes in sharp contrast with conductivity in semiconductors. And why II group metals are hole conductors? Their valence band is full as well?

[Moreno]

What is known about metals or materials which have two or more conduction bands? For example, is it true that lead has two conduction bands? Can a material can have to or more conduction bands separated by a band gap?

[Moreno]

Do exist some chemical elements (for example metals) in which a few atomic orbitals would be half full and there would be no energy overlap between them? Subsequently in solid state they suppose to form a few bands such as s-band, p-band or other bands which would be a half full and there would be no overlap?