Calculating Bandgaps Experimentally

[Christian0412]

I've been doing a bit of reading on bandgaps of semiconductors and alloys of semiconductors. I was curious to know is the bandgap of a material, say Silicon, determined or calculated experimentally? How do scientists usually determine this in the lab?

 

[TeethWhitener]

You can usually determine the band gap of a material using spectroscopy. The electrons in the material can't absorb photons that have less energy than the band gap, since there aren't any energy levels in the band gap for the electrons to be absorbed into. This will be reflected in the absorption spectrum of the material. At photon energies less than the band gap, the material will be transparent, but once you reach the band gap, the material will begin to absorb light. The onset of this absorption edge is typically taken as the band gap.

Note: this is the basic idea, but it overlooks a lot of physics. How much light is absorbed will give you information about whether the band gap is direct (an electron can be excited directly with photons) or indirect (an electron has to couple with a lattice vibration, called a phonon, in order to absorb a photon). It also overlooks the possible presence of excitonic states (where an electron and hole form a bound particle with lower energy than the band gap). There's also an extremely powerful technique known as angle-resolved photoemission spectroscopy (ARPES) that allows direct mapping of the band structure of a material and is sort of the state of the art in semiconductor physics.

 

[ZapperZ]

You don't really get a band gap easily from ARPES, since it only tells you how far a band is below the Fermi energy in a particular k-direction. The band gap that one normally gets is a momentum-averaged gap over the entire BZ. Furthermore, ARPES doesn't probe the empty states, so one doesn't really get a value of the full gap.

Optical spectroscopy is certainly a common technique for such measurement. But the measurement that I think gives a very clear value of such a gap is tunneling spectroscopy, which has been used in semiconductors, superconductors, etc. The first derivative of the I-V curve corresponds to the density of states, and the band gap falls right onto your lap.

Zz.

 

[t!m]

One can do inverse photoemission to probe the empty (conduction band) states, although the measurement is much harder than conventional (occupied) photoemission. Also if I'm not mistaken, tunneling spectroscopy requires a few additional assumptions to hold true, to be interpreted in terms of the single particle density of states. For example, if the necessary applied voltage is too large to be treated perturbatively, then this is essentially a measurement of the non-equilibrium spectral function, which is not simply the DOS.

 

[ZapperZ]

One can do inverse photoemission to probe the empty (conduction band) states, although the measurement is much harder than conventional (occupied) photoemission. Also if I'm not mistaken, tunneling spectroscopy requires a few additional assumptions to hold true, to be interpreted in terms of the single particle density of states. For example, if the necessary applied voltage is too large to be treated perturbatively, then this is essentially a measurement of the non-equilibrium spectral function, which is not simply the DOS.

But how big is the band gap for one to apply THAT big of a bias voltage for it to be in a non-equilibrium state?!

The biggest assumption in tunneling spectroscopy is that you actually get the tunneling density of states, since the tunneling matrix elements are implicit in the data. In most cases, the matrix element has a weak effect that it can be ignored, especially in a 3D material.

Zz.

 

[t!m]

Indeed, I had in mind large-gap insulators. But perhaps even for gaps on the order of eVs, you can still use a relatively small bias?

One other technicality is that many of these techniques (PES and presumably STM) are surface sensitive, and the band gap near the surface isn't necessarily the band gap in the bulk, but there are ways to approximately correct for this.

 

[ZapperZ]

Indeed, I had in mind large-gap insulators. But perhaps even for gaps on the order of eVs, you can still use a relatively small bias?

One other technicality is that many of these techniques (PES and presumably STM) are surface sensitive, and the band gap near the surface isn't necessarily the band gap in the bulk, but there are ways to approximately correct for this.

But how big of a gap? 50 eV?

Tunneling technique has been applied to the study of insulator and semiconductors, especially in extracting band gap values. At what range do you think the tunneling model would no longer apply?

Besides, STM, one can also do either point contact, or even planar junction. May of these things are fabricated in situ without exposure to air, and thus, form almost pristine tunnel junction. Such techniques often probes the bulk properties, not surfaces.

Zz.