Why does LED band gap decrease as temperature increases?

[Kara386]

I've tried to summarise the explanation my professor gave. Is it correct or have I misunderstood? It's a highly simplified view of things anyway, but here goes:

Taking the simplest 1D case, there are two possibiities for an electron in the lattice: it may be scattered and move back the way it came, or continue through unaffected. This sets up a standing wave, with the wavefunction having a component representing movement to the left (scattered) and one representing movement to the right (unaffected electron). Lattice spacing rises with temperature, and as such the wavelength of this standing wave will increase, resulting in a decreased bandgap.

Any good? Does this kind of picture extrapolate easily to 3D?

 

[Henryk]

No, I don't think this explanation is correct.
Energy gap is related to binding between atoms in a solid.
Basically, if you bring two atoms close enough, the atomic electron states are no longer eigenstates of the Hamiltonian, instead, the electron states of the neighbouring atoms are split into two new levels of different energies: the lower is the bonding state, the upper is antibonding state. In a crystal, the bonding states will form the valence band and the antibonding states will form the conduction band.
The energy gap between them depends on how much the original electron states overlap.
As the solid expands with temperature, the overlap decreases giving you the deceased energy gap.

 

[DrDu]

No, I don't think this explanation is correct.
Energy gap is related to binding between atoms in a solid.
Basically, if you bring two atoms close enough, the atomic electron states are no longer eigenstates of the Hamiltonian, instead, the electron states of the neighbouring atoms are split into two new levels of different energies: the lower is the bonding state, the upper is antibonding state. In a crystal, the bonding states will form the valence band and the antibonding states will form the conduction band.
The energy gap between them depends on how much the original electron states overlap.
As the solid expands with temperature, the overlap decreases giving you the deceased energy gap.

I don't think this picture is at variance with the picture scetched by kara386. You ar discussing it in terms of a tight binding approximation while kara386 uses a nearly free electron approximation. Both models agree in that the frequency shift is related to the thermal expansion of the lattice.

 

[ZapperZ]

I, on the other hand, don't understand why a simple Fermi broadening with increasing temperature is not used to explain the decreasing band gap.

There is a certain criteria to use a rigid-band approximation. If the lattice spacing varies that significantly as stated in the OP, then the band structure will change, and it is not just the band gap that will be different.

Zz.