For a general case, the answer to the question is in the negative. Energy gap is measured by means of photo-emission spectroscopy, where one has an incoming beam of radiation of a certain energy and momentum and measures the energy and momentum (when one performs angle-resolved photo-emission spectroscopy) of ejected electrons. In the UV-Vis spectroscopy, on the other hand, where one measures merely the absorption, the exited electrons can form bound states with the holes they leave behind, that is they do not need to leave the system under investigation. The finial states in the UV-Vis experiments are therefore in general considerably different from the final states in photo-emission experiments. When in the former experiments the bound states are weakly bound (i.e. when excitonic effects are negligible), the two gaps are nearly identical.

For the angle-resolved photo-emission spectroscopy, I refer you to the following review article by Damascelli, Hussain and Shen:

http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.75.473

Thank you Behnam Sir. I agree, that the energy gap can be measured by means of photo-emission spectroscopy properly. If it would become possible, I would try the photo-emission spectroscopy. But here my point of concern is that I want to get the approximate bandgap value from UV-Vis spectra. Further for the nanostructures, whether I can consider absorption edge as nearly the band gap value??

Dear Bappaditya, as I wrote above the identifications of the two gaps is not valid in general. However, on general grounds one can say that the gap one obtains from the UV-Vis is an lower bound to the quasi-particle gap, the gap as determined from the behaviour of the single-particle Green function and measured with the aid of photoemission and inverse-photoemission spectroscopy. This follows from the fact that the UV-Vis measures the excitonic gap (the gap of neutral excitations, as determined from the behaviour of the density-density response function), and this gap is by the amount of the largest excitonic binding energy smaller than the quasi-particle gap. How smaller, one can estimate this by means of a theoretical calculation. Mott has done such calculation (true to his style, a back-of-envelope calculation), which if my memory is not failing is reproduced in the Solid State book by Ziman. Both Kittel and Ashcroft & Mermin present brief accounts of excitons (see pp. 626-628 of the latter book; I believe that the expressions on p. 628 are due to Mott).

To clarify some of the issue. Those thinking that a gap could reliably be determined from photoemission (photoelectron spectroscopy) alone, would be mislead. In B. Farid's second contribution he rightfully mentions the combination of photoelectron and inverse photoelectron spectroscopy. (Its angular resolved variant, ARPES, usually is not of so much relevance for nanoparticles, though).

This is (in principle) true in cases where the independent electron picture applies. B. Farid has mentioned excitons (electron hole interaction) to be a cause for the picture to break down in optical (interband) spectroscopy at the band edge. Coulomb correlations would be the one on the side of the electron spectroscopies.

the reason behind this is that all these spectroscopies measure final (excited) states which belong to different Hilberst spaces altogether: if the ground state has N electrons, then the optically excited states has the same number, a photoemission final state one electron less (N-1), an inverse photoemission final state one more (N+1). Generally speaking, we can't take for granted that these things are related.

In very small particles, it is possible to obtain photoelectron spectra in gas phase experiments, starting from anions. A HOMO-LUMO-gap in the electronic structure of the neutral particle, is then visible in the spectra as the energy distance between the HOMO-peak and the (HOMO-1)-peak (of the anion). This is yet another version to the story, quite closely related to the optical gap but has peculiarities of its own.

Dear Bappaditya Pal, that was getting a little off your point...

Absorption edges do have different power law dependences when they're direct or indirect. The choice of exponent in a Tauc plot depends therefore on the material considered.

One point with excitons is that these may gain spectral weight in nanoscale particles (compared to the bulk) and might even change a power law behavior into one exhibiting a peak at the edge. It would not be wise then to try interpreting the rising edge of the peak in terms of a Tauc plot discussion.

In many nanoscale materials a dependence of the band gap is observed as a function of particle size - owing to the spatial confinement of the low energy band edge states to within the particle. Then, if you do not have a narrow particle size distribution, the edge may appear broadened due to a distribution of gap energies. An extrapolation of such data such as in a Tauc plot again would easily be an invalid exercise, since the observed spectrum would be that of an inhomogeneous specimen.

You see that there are quite a few things to consider. A general answer seems difficult to me at best. You do need to consider known properties about the material(s) you're about to study. The less is known, the stronger is the need for good specimen characterization with complementary techniques.

Dear Fauth Sir,

Thanks for the discussion and the points as you explained. I understand that exact Eg measurements need to take care of lot effects like photoelectron and inverse photoelectron spectroscopy. As the 2nd script of yours is more relevant to my experimental data I would like to talk about that. My sample is ZnO a direct gap material, so I have done the Tauc plot accordingly. But the problem is that its not giving satisfactory result. As you mentioned that particle size distribution might be the reason that I am not getting a Sharpe edge to calculate the band gap. Though the photoluminescence measurement is giving good results. For my sample particle size distribution is as: for Undoped ZnO, 5% and 7% Co doped ZnO sizes are of 300nm, 80nm, 80nm respectively. 7% doped sample is rod shaped in length wise(600-800 nm). My query is that for this particular case what best conclusion can be made from UV-Vis absorption measurement?? I have attached a figure for Uv-Vis and PL measurement.

I am probably not the most competent person to discuss this in detail. Let me first ask you some questions:

1) have you done a literature search on absorbance data on pure ZnO in form of

(i) thin films (dependence on thickness)

(ii) spherical particles (dependence on diameter)

(iii) ellipsoidal particles (dependence on minor and major axis dimensions)

to see what the experimental trend is there, when trying to do a Tauc plot analysis?

Not all of these datasets might exist, but in order to get a reference (if you don't have your own) that would be an essential starter.

2) I guess that panels b), c) and d) display photoluminescence data? What is the excitation energy?

3) What exactly justifies your statement that the PL data look good? (I need your help here, I don't have or know enough about criteria to judge upon this) In what sense do they look good? What information do you derive from them?

The next kind of questions I have would address the arrangement of the absorbance measurement: What do the samples look like, what is the experimental setup and geometry, how are measured intensities converted to a numerical value for absorbance? Do the formulae that are being applied appropriately represent the conditions under which the experiments are being taken?

I ask these questions because it is not always evident that "absorbance" evaluations are adequately being done, especially if these numbers are automatically generated by the measurement apparatus. (Such internal calculations always have some theoretical concept they are being based on. These may or may not apply in your specific case. A particular and typical example of a potential source of error would be the inappropriate handling/treatment of radiation scattered off the beam (instead of being absorbed)).

It looks like you definitely have strong excitonic effects, which is typical for high bandgap materials like ZnO. In addition, your optical absorption bandgap will be affected by size affects and a Burstien-Moss shift (due to doping - if the dopants are shallow enough). For a look at an excitonic lineshape, you could look an old article of mine (Phys Rev B 56, page 4037) which is also available at http://web.pdx.edu/~jfreeouf/Freeouf%20Publications/Holden_PhysRev_Model_p4037_1.pdf

Here you can find good explanation and band gap calculator,

http://www.instanano.com/characterization/theoretical/uv-vis-spectroscopy-band-gap-calculation/