Thank you very much Peter Kapusta. In order to use the equation (αhv)2 = A(hν-Eg)2, I need the value of α to plot the (αhv)2 on y-axis and hν on x-axis. hv can be obtained simply by using hv = 1240/λ(nm). So, then do I calculate α from intensity of the absorbance using the equation A = - log T, where T is the transmittance? Then I use T = e^-αl. It then becomes α = - ln T/l where l is the path length in the case of liquid cell or thickness in the case of thin films. Do I just insert l= 1 cm in the equation?

Even I have the same question as how to calculate the value of alpha.

how can I identify if the newly synthesized compound has a direct or indirect,..., transition?

Sorry about that. The real Tauc equation should just be (αhν)2 = A(hν –E). The power 2 is because ZnO has direct, allowed transition from CB to VB. I have performed a simple arithmetic.  α = 2.303 A/d where A is the absorbance and d is the path length for liquid cell or thickness for thin films. I don't really understand why are you saying the actual value α is irrelevant. It is indeed crucial to plot the Tauc relationship. and draw the tangent line afterwards. 

The A in the equation α = 2.303 A/d is not the same A in the Tauc equation (αhν)2 = A(hν-Eg). Or I can change the latter to C, hence it (αhν)2 = C(hν-Eg). In a nutshell, to construct the Tauc plot and extrapolate the tangent, we need this (2.303 Ahν/d)2 = C(hν-Eg). I think you misunderstood my question. The d, 2.303 can be absorbed in the equation since they are constant throughout the measured wavelengths. 

That is why I said the constants can be absorbed without affecting the intercept on the x-axis (Eg).

Dear Peter sir,

In some papers, I had seen the graph of square of Absorbance against Energy and the taking the linear fit to find band gap for direct band gap material. 

Can you comment on the same.

Thank you sir

Warm Regards

Suhail

Agree with Dr Peter's view. You can simply draw by excel/ origin. For your convince, I attached 2 papers./ see it. Hope it helps you.

http://www.sciencedirect.com/science/article/pii/S0927024807001948

Rohul Adnan, I tried replacing the alpha value with A. We get the same Eg value. It makes no difference. 

I have a question here that whether the tauc equation is a linear equation like y=mx+c.

Means in this case αhv = C(hν-Eg)n, What is C? 

Can we simply take the first derivative of the absorbance spectrum to get Eg ? 

@Dr. Peter

Thanks for your reply. In the equation  αhv = C(hν-Eg)n, we plot ahv v/s hv plot to get Eg but I am unable to co-relate, the maths with the plot. If we avoid C though to get Eg, from the Tauc equation, Eg= hv+(ahv)n so couldn't co-relate that how a liner extrapolation is satisfying this equation.

I get your point. Thanks

I'm very satisfied with response of Peter Kapusta.

However, the tauc plot relationship is not valid for ZnO semiconductor.

The absorbance of this semiconductor is influenced by the excitonic effect. As a consequence, the tauc plot doesn't permit a correct ZnO band-gap value.

Cordially

Thank you Dr. Peter! The above discussions helped me also a lot.

To do the calculation, What value is added in place of C in this equation?

αhv = C(hν-Eg)n 

Origin Pro software you may use for analysis (draw and extrapolate).

@Peter Kapusta

I see (and have) the problem at the subjectivity of choosing the linear region of Tauc's plot. Do you have any recommendation or advise about how to choose it properly? Thanks!

Thanks for the answer! I was only relying on the R².. @Peter 

My compound absorbs at two wavelength region. Could it be possible to get the Tauc's plot?

My compound absorbs at two wavelength region. Could it be possible to get the Tauc's plot?

My compound absorbs at two wavelength region. Could it be possible to get the Tauc's plot?

Yes it is possible. Preferably you should plot "Tauc plot" separately for both the regions. Because in your compound, two different bandgap material are present separately so it is absorbing two different wavelengths. 

In that case, I will get two band gaps. So which will be the real band gap for my material? Is it possible to have two band gaps for the same material?

The bandgap is a property which is associated with the elements, particle size and some other parameters of a material. For one material with a certain average particle size, the bandgap will be one only. In your case, I don't know what is the material? As I guess, it is a mixture of two or more elements and as you said that you got two absorption wavelengths so it is possible that those elements are present in the compound as unreacted or as individual so exhibiting the two different bands than one. 

pls see the file for tauc plot

how do we draw a tangent to get the band gap value? 

you may look for the curvature or edge in the graph ahv v/s hv and then draw a tangent to that which will intersect at x axis and that will be the approximate bandgap of the material.

Hi @AZAD KUMAR, I have seen your origin file, but I still can't figure out what are column D and L about , could you please explain me?

thanks!

For ZnO I believe the material follows a direct allowed mechanism. Therefore, you simply need to plot (aE)^2 and then fit a line to the steepest part of the absorption onset edge. You must be certain that you have the steepest part otherwise your "energy" will be too low. I typically use 2 -4 points about the inflection point, obtained by fitting the first derivative. After you get a line you need to extrapolate this to cross the x-axis (x=0). You effectively want the fit the edge to return the largest possible x intercept value that still looks approximately linear to the absorption edge. Many edges are simply not linear, so if you have some deviation this is fine as long as you fit the line with at least 3 points in it.

I would also like to share a more general method I developed using a computed absorption spectrum for LaFeO3. Please see my paper and supplemental info attached. This method is universal to all materials to the best of my knowledge. My method involves Tauc extrapolation along the steepest part of the transition onset edge in all cases.

The first step is to determine the correct Tauc model for experimental analysis. Depending of the study, do not assume your Tauc model is correct or should always be the same. Determining the proper model always involves Tauc fitting the theoretical absorption spectrum for the compound of interest, using all four Tauc Models.

Fitting the absorption edge is the same as above for theoretical data and experimental data. Take the first derivative of the Tauc plot { (aE)^2, (aE)^2/3, etc.} and then note the peak position. Now go back to the Tauc plot, then fit a linear region about the point that corresponds to the peak position in the first derivative (this is also known as the inflection point). This linear region should be as few points as possible, you want this line to be "tangent" to any "curvature" in this region, between 2 and 4 points are typical. After getting a line, extrapolate this line to extend across the x=0 line. The value where your line crosses x=0 is the estimated transition energy for that absorption edge.

Using this method, one of the Tauc models will yield an extrapolated line that intersects x=0 at the exact same energy that separates the valence band from the conduction band in the E vs k and DOS vs. E plots.

The model which returns the same energy as the theoretical band gap energy from the DOS vs E and E vs k is the correct model and should then be applied to your experimental data. For LafeO3 it was actually determined that the material follows a direct forbidden absorption mechanism despite the Indirect transition being 10meV lower energy. In LaFeO3 the direct forbidden transition is still strongly absorbing due to hybridization of Fe and O in the VB and CB.

It is well known that DFT underestimates Eg, but the dispersion and relative spacing should all be captured. Therefore, we can ignore the "shift" between the theory and experimental data and use the theory to guide our experimental model selection. For ZnO I am pretty sure you use a direct allowed transition but the process using the calculated absorption spectrum would verify this. Regardless, you always need to fit the steepest part of the absorption edge with whatever model you use. Don't get caught up in the Urbach region or worrying if it follows the absorption edge "enough". If you use my method correctly it will be nearly impossible to get a higher energy returned from the analysis and it may also look like your extrapolation line is steeper than the absorption edge. These visual discrepancies can certainly happen and should be noted during analysis.

Please feel free to reach out to me directly with any questions.

Mark

my compound is actually indirect band gap semiconductor, when we plot (αhν)0.5 Vs hv, the band gap energy is found to be around 1.0eV it is very low for my compound but when i plot (αhν)2 Vs hv it is giving more accurate band gap energy. Please share your ideas regarding my problem. Thank you.

Tauc equation (αhν)2 = A(hν-Eg)

i have a question is the dimension of this equation is correct???

Naorem Ramananda : Did you find the answer? I also encountered the same problem.

You can find the answer in my thesis. Chapter 5 shows the plots that I created using PSI Plot software. Excel doesn't have the ability to do this work, so you will need something more robust. My thesis is in my profile, but if you cannot access it, let me know.

Did you find the answer? I also encountered the same problem.

you can done by using origin pro. software (https://www.youtube.com/watch?v=MG981Wzoo90)

Article Sunlight active U3O8@ZnO nanocomposite superfast photocataly...

Hi Ragulan, U can use this XL sheet for drawing Tauc plot. Insert your UV values of X and Y axis on A and B then take the value from H and J that can give exact Tauc plot of your desired materials.

For this calculation you can use Origin software.

First you have to calculate absorption coefficient using

α = (2.303xA)/t

where A is absorbance  and t is thickness.

Then using the Tauc's equation (αhν)2 = A(hν-Eg) you can get Eg by drawing a tangent.

Dear Rohul with the help of Touc plot find the band of semiconductor quantum dots. i suggest you to visit this paper link for more detail

Article Controlled synthesis and optical properties of tunable CdSe ...

Thien Loc Still i am unable to solve the problem.

Dear Rohal

Please see these links:

https://en.wikipedia.org/wiki/Tauc_plot

https://www.youtube.com/watch?v=KIfaVTfHMZc

https://www.youtube.com/watch?v=vXxNrb8rmaE

Rohul Adnan

Hi, colleagues! We recently published a new method of spectrophotometric data analysis very similar to the Tauc method but with many advantages over it. In the Tauc method, the main problem is to determine the energy gap without knowing the nature of the optical transition (described with the parameter m). Our method does not require knowledge of the parameter m. The value of energy gap and parameter m can be obtained simultaneously thanks to one linear fit. Other advantages and description of how to use this method are described in the article. We encourage you to read the paper!

Article Inverse logarithmic derivative method for determining the en...

These videos on youtube make it clear:

https://www.youtube.com/watch?v=vXxNrb8rmaE

https://www.youtube.com/watch?v=tbyJjCMkDtc

Agree with Saeid Amjadian.