band gaps

Ravian

what is the practical use of the concept of band gap other than classification between material? can free carrier absorption be manipulated by changing band gaps?

ZapperZ

This is a very puzzling question. That's like asking "what is the practical use of the gaps between the rungs of a ladder". The gaps aren't simply a concept. It is there because there are no available states or band of states due to the electronic and physical structure of the material. Therefore, this is a part of the electronic band structure and a consequence of the nature of the material.

Secondly, "free carrier" does not have a band gap, so there's nothing to be manipulated here.

Zz.

Ravian

so the band gap for a particular material is a constant value e.g. 6.1eV for AlN or it can vary. Does not a band structure show many band gaps between different states of electrons? if electrons live in certain orbitals or shells of specific energy then how a band gap is formed i mean how can we determine that band gap lies between what orbitals.

ZapperZ

You are confusing band gaps in solids with atomic energy levels. These two are NOT the same!

Zz.

graphene

In an isolated atom, the electrons occupy states with discrete energy levels. But, when atoms come close, these discrete energy states become bands. (a band has a certain range of energies). These bands are now the 'energy states' of the electrons.

Each orbital changes into a band.
If you know basic quantum mech, you could read about the tight-binding model.

Yes, for a given temperature.

alxm

In a solid, the discrete energy levels/orbitals become continuous bands. Basically, if you take an atom and it binds to another atom, its levels split into multiple molecular orbitals. (e.g. a hydrogen atom's 1s orbital splits into [tex]\sigma[/tex] and [tex]\sigma^*[/tex] molecular orbitals when it binds to another hydrogen)

Add more atoms and you get more splitting, and for a solid (which is essentially an infinitely large molecule) you have continous bands. So the band gap between the valence and conduction bands are in this sense the direct equivalent of the HOMO-LUMO gap in a single atom or molecule, which is a well known concept in chemistry/chemical physics.

(And the tight binding model which Graphene mentions is essentially the same as [modern] valence bond theory in chemistry)

So I disagree with ZapperZ - atomic/molecular orbitals and electronic bands are fundamentally the same thing.

Ravian

excellent. so can you recommend some source which shows visualization of this overlapping. i surfed but get schematic diagrams of valence and conduction bands. thanks for your help.

stevenb

I don't have references on this handy, and it has been 20 years since I looked at this topic, so I don't want to quote too much from memory. However, I recommend you look at III-V and quartenary semiconductor systems. For example InGaAsP system. Typically, component ratios are varied to control both band gap and lattice constant to design electro-optic components like photodiodes and modulators.

http://www.tf.uni-kiel.de/matwis/ama...ne/r5_1_4.html

Ravian

so to sum up i can say when atoms interact to make a solid, their atomic orbitals mix to form two bands of orbitals namely valence band and conduction bands with an energy gap between them where no electronic states exist. Further, these electronic states are quantized and electronic transitions take place in accordance with pauli’s exclusion principle that is no two electrons of the same spin can occupy same state.
i guess my statement is correct?

alxm

Roughly. But whether or not you have a band gap or not depends on the material. A conductor, such as a metal, has no band gap. The unoccupied orbitals have the same energy as the occupied ones.

No, once they form a band they're no longer quantized, there's a continuum of states in the band, much as a free electron has a continuum of available states. So electrons in a conductor behave largely as if they were free electrons. They still do obey the Pauli principle though.

shime7250

what do mean 0 HOMO-LUMO gap