If the change in band gap is due to quantum confinement that size of the quantum sized particle can be correlated to the change in band gap by using formula for this effect as available in literature. Generally size of the particles should be < 10 nm for this effect to be responsible. However there can be other reasons for band gap change. Quantum confinement would give increase in gap with decrease in size.  

I think the absorption spectra of QDs are not enough to "estimate" the QD size. Actually, we need to perform k . p calculation in order to get numerical values of transition energy as a function of QD size (e.g., diameter). The calculated transition energy that matches the energy peak position in the absorption spectra tells us the estimated QD size. Please note that the QD size obtained by this method means an average size.

The things are not straight forward. You can get an idea of greater or lesser size of particles of QDs observing absorption spectra but can not get the idea of absolute size of the particles. You may try Scherrer formula in XRD pattern to get an idea about average particle size. I thing it might help.

XRD and TEM are probably the only reliable methods for determining particle sizes (where the Debye-Scherrer method relies on round or slightly elongated particles with standard size distribution around an average but has problems with  more complicated particle forms or bimodal distributions which can be easily measured by TEM).  

You could try to use Brus' equation and see if the results make any sense. I would also recommend to use XRD or TEM but don't know if it is possible because of your glass matrix.

The change in optical band gap due to quantum confinement effect is a generally observed in quantum dots. The radius of the quantum dots can be estimated by using observed band gap data in the formula attached to this note (also  available in literature). However, to confirm that the observed change in band gap is only due to the change in size of QD, you should follow the suggestions as given by Maetee Kunrugsa.

Energy gap for semiconductors increases with the decrease of particle size particularly for diameters below 10nm. For more information you can see the attached page from a PhD thesis and related published articles

Thanks to all for sharing your valuable opinion on my difficulty....Since I am working on glasses, calculation of size from Scherrer formula is difficult task due to noise of the glass matrix. But the band gap study gives perfect variation according to the growth of the QDs. 

Dear Prof P.K. Shukla,

Sir,you have suggested formula for the calculation of QDs size. But how to get the parameters  epslon(zero), epslon(r), effective mass of hole and electron ? Are they same for all semiconductors?

Hi Sudhirkumar

You can estimate the size of the QDs from the absorption peak but it is not accurate as from the TEM and HRTEM.

Attached very famous article published by W. William Yu et. al. (Chem. Mater. 2003, 15, 2854-2860). In this paper they stated a formula that you can use it to predict the QDs size from the absorption and PL peaks. Also, attached excel sheet using the same equation stated in this article for easier use. Hope this helps.

I think that, you should read this :

 W. Yu, L. Qu, W. Guo, X. Peng, Experimental determination of the extinction coefficient of CdTe, CdSe, and CdS nanocrystals, Chem. Mater. 125 (2003) 2854–2860. http://pubs.acs.org/doi/abs/10.1021/cm034081k (accessed June 19, 2014).

For cases if their nanoparticle be quantum dots.

I have a worksheet in execel, that can help yourself.

There is two formulate to calculate size of quantum dots CdTe e CdSe. You need put the follow variables :

Absorbance of the first peak absorption =?

Full width at the half-maximum of the PL spectrum (nm) ?

Wavelenght of first peak absorption (nm)?

So you have follows answer:

Diameter (nm) CdTe=?

Wavelenght (nm) for electrovolts=?

Extinction coefficient of semiconductor CdTe=?

Absorbance corrected (CdTe)=?

Concentration of CdTe [mol L-1]=?

Concentration of CdTe [μmol L-1]=?

Is it useful to you?

Thank you Yasser & Gustavo ....

You can calculate the size from XRD, very explanation is given here,

http://www.instanano.com/characterization/theoretical/xrd-size-calculation/

You can use Brus equation to relate the QD radius to the emission energy (not absorption).

Hi,

Can anyone please explain the unit of FWHM in the formula, D=hVf/Pi*(ΔE1/2) where, Vf is fermi velocity of electron of that particular material, h is plank constant and ΔE1/2 is FWHM of Absorption band. Bcoz, if we do the dimensional analysis then the unit of  ΔE1/2 comes out to be in units of Energy. So while calculating the particle size what value of FWHM to be inserted? nm or in units of energy? Please clarify

The unit of FWHM is eV