Question About Indirect vs. Direct Bandgap Semiconductors

[question2004]

I have one question to trouble you.

Why some semiconductors have a direct bandgap, while some have an indirect bandgap? Is there any very crude "thumb rule" of predicting/justifying it? Thanks a lot

[don rigby]

bandgap= ?
are you talking about ttl vs mos?

[OldTee]

Bandgap in semiconductor is the energy gap between the conduction and valence band. Whether a semiconductor's bandgap is direct or indirect can be determined from the E-k diagram, which is obtained by solving Bloch equation using comprehensive numerical technique. I don't think there's a rule of thumb that allow us to specify the bandgap characteristic from cold. But to date most of the technologically exploited III-V semiconductor compound are direct bandgap (GaAs, InP etc), while group IV are indirect (eg Si, Ge).

[Dielectra]

hi!

A question.....why the big difference? Lets say Si and Ge where both have the same structure, the only difference is the 18 extra electrones, but Si have an indirect bandgap and Ge a direct. What in the theory makes the band structure direct or indirect bandgap? Is it that the Bolch waves of the valence electrones "see" different amount of electrons and therefore feel a different potensial or the small difference in cell parameter or something completely different?

Dielectra (.......exame soon :uhh: )

[ZapperZ]

hi!

A question.....why the big difference? Lets say Si and Ge where both have the same structure, the only difference is the 18 extra electrones, but Si have an indirect bandgap and Ge a direct. What in the theory makes the band structure direct or indirect bandgap? Is it that the Bolch waves of the valence electrones "see" different amount of electrons and therefore feel a different potensial or the small difference in cell parameter or something completely different?

Dielectra (.......exame soon :uhh: )

There isn't anything obvious, or "rule of thumb" to know which will give you wish. The only way that I know is via direct band structure calculation and/or experimental observation. There is nothing obvious simply by looking at either the atomic structure, or the crystal structure. The crystal structure especially can severely influence the band structure, but again, there is nothing direct that I know of that can point one way or the other.

Zz.

[Gokul43201]

I suspect that the big difference between the behaviors of Si and Ge comes from the differing crystal structures (in addition to other possibilities). Si has a diamond structure, while Ge has a cubic close packed structure...that by itself provides more than a plausibility argument for the different dispersions.

[Dielectra]

ok....

I read some more.....and do you think it can be a result of the tight binding model? And then because of overlap of atomic orbitals? Then for Si we get s(+)-p(+)-p(-)-s(-) because of a high Vss potensial and a smaller Vxx, and the valence electrons and for Ge is s(+)-p(+)-s(-)-p(-). Can we then get an easier exitation of electrons from p(+) to s(-) in Ge than p(+) to S(-) in Si? Can that be the case?

[ZapperZ]

ok....

I read some more.....and do you think it can be a result of the tight binding model? And then because of overlap of atomic orbitals?

Unfortunately, your question now doesn't make a lot of sense. It is BECAUSE of the overlap of atomic orbitals that you have to consider the tight-binding model. They are not different things.

Then for Si we get s(+)-p(+)-p(-)-s(-) because of a high Vss potensial and a smaller Vxx, and the valence electrons and for Ge is s(+)-p(+)-s(-)-p(-). Can we then get an easier exitation of electrons from p(+) to s(-) in Ge than p(+) to S(-) in Si? Can that be the case?

It isn't this easy. Tight-binding model can include nearest neighbor, next nearest neighbor, next next nearest neighbor, etc. It depends on how much there is an overlap, and the crystal structure. That is why you have the so called hopping integral.

Zz.

[SilWeb]

Direct semiconductors have minimum conduction band and maximum valence band at k=0 in E-k diagram. That’s allows direct carrier recombination.
In indirect semiconductors (Si) electron got some energy in minimum conduction band and mediator needed for transferring energy (phonons usually) in recombination process.
So it’s big difference in carrier lifetime.
If you asked HOW it happens – the answer is – such E-k diagram.
If you asked WHY it happens – nobody knows I guess… ))))