Why conductors bonds in such way that leaves the valence band not full

[abotiz]

Hi,

Iam trying to understand the differences between metals, semiconductors and insulators. Regarding the conductivity properties. Iam new to this area so please correct me if I am wrong.

I may be simplifying things now;

1) If I put a voltage over a solid, I only measure a current if there are empty energy states for the electrons to occupy with their available energy (thermal or whatever).

2) The reason why metals conduct electricity so good is because there are empty (higher) energy states. And the reason for that, is because when these atoms bind into a solid, they bond in such way that the electron configuration leaves some available states in the sub shells, e.g. s- or p-sub shells are not full.

3) Semiconductors and insulators bond in such way that all states are full. However, the differences between semi and insulators is the band gap, and Iam not really sure what determines this, the magnitude of the bandgap. Maybe something with cosinus function, K values and Schrödinger equation?

If I am right in this (2), why (or what makes them not to) does metal not bond in covalent bonds in such way that all states are full, like in insulators.

Thank you very much for your time!

 

[rigetFrog]

You're making a valiant effort to fuse a number of separate phenomena (electronic structure Fermi energy/level, their bonding together with electrical conductivity) within a unified coherent model. While this is a correct approach that maybe solvable with advanced computational techniques that are beyond me, I believe the introductory models split these up into separate phenomena (see textbook by ashscroft and mermin, and kittel)

1) electronic structure / band theory

2) electrical conductivity

There are many ways to get from 1 -> 2. (e.g. Drude model using 1 for collision time, semi-classical, Boltzmann diffusion, and phonon scattering)

I'll try and directly address some of your questions

if a band is empty, there are no electrons to carry current when voltage is applied.

if a band is full the electron is stuck cause it has no where to move to (see mott type insulators for a surprising application of this which will confuse you more).

yes the difference between insulators and semiconductors is the size of the band gap. I believe the threshold is around ~2eV, but don't quote me. Yes, it is arbitrary. Ab init calculations of the band gap is one of the unsolved problems in solid state, at least according to Wikipedia last I checked.

your (2) is correct

Your final question. The filling depends on the number of electrons available. Atomic transition metals have roughly half filled 3d states, so their condensed counterpart have the possibility to be half filled.

Atomic Si, Ge, can completely fill their spd shells, so their condensed counter part can be completely filled.

 

[DrDu]

If I am right in this (2), why (or what makes them not to) does metal not bond in covalent bonds in such way that all states are full, like in insulators.

Metals differ from non-metals in their electronegativity being low (the boundary being somewhere near 2.5).
That means that in non-metals, bonds are covalent, i.e. there is very little ionic character. On the other hand, in metals ionic structures are of large importance, e.g. something like $\rm Na^+ Na^-\leftrightarrow Na^- Na^+$ in addition to covalent contributions. As Coulombic interactions are not directed, a metal can have bonding interactions with much more neighbours than a non-metal.

 

[HeavyMetal]

2) The reason why metals conduct electricity so good is because there are empty (higher) energy states. And the reason for that, is because when these atoms bind into a solid[...]

3) Semiconductors and insulators bond in such way that all states are full. However, the differences between semi and insulators is the band gap, and Iam not really sure what determines this, the magnitude of the bandgap.

The reason metals conduct electricity so well is because of the accessibility of their higher energy states. The band gap is defined as the energy required to liberate a bound valence electron into a delocalized, unbound "fluid." On average, metals are easier to oxidize than non-metals. In other words, they are more willing to allow for one of their electrons to become unbound. As electrons are promoted into the conduction band, they access this sort of pseudo-oxidation state. The sea is made up of charge carriers, so the oxidation state is still considered 0. However, these conduction electrons are no longer bound.

To answer your other question, band gap can be determined with UV/Vis spectroscopy. This would be a good page if you want to read more: http://science.unitn.it/~semicon/members/pavesi/CaseStudy_uv81.pdf

yes the difference between insulators and semiconductors is the size of the band gap. I believe the threshold is around ~2eV, but don't quote me. Yes, it is arbitrary.

I've heard that a good line to draw it at is 3eV. Although, it is arbitrary, like you said . I guess it depends on the material's behavior during its usage. I would assume that temperature dependence plays into it.