Well done, it is possible (though not advised)  for people to use a single line or tangent for determining the point traceable to x axis (wavelength or eV). It is common practice and is advisable that you rather use two lines or tangents. This is essentially for accuracy purpose. Typically, you should have a line from the y-axis (absorbance or in your case kubelka munk function axis) and have another line coming from the top to x-axis (wavelength or as you have done - electron volt axis). Using the appropriate equations or formulae which i assume and can see you are aware of, you should be able to determine your optical band gap. Do check any of my references or that of Tahir et al, they can really be of help.  

Generally, the absorption coefficient (alpha) is related to photon energy (h*neo) by the known equation as:

       α = β/(hυ) (hυ - Eg)n         Or          (αhυ)1/n =β(hυ - Eg)                 

where β is a constant called the band tailing parameter, Eg is the energy of the optical band gap and n is the power factor of the transition mode, which is dependent upon the nature of the material, whether it is crystalline or amorphous. According to Tauc's relation:

The plotting of  (αhυ)^(1/2) versus the photon energy (hυ) gives a straight line in a certain region. The extrapolation of this straight line will intercept the (hυ)-axis to give the value of the indirect optical energy gap (Eg).

For more details Please go to:

https://www.researchgate.net/publication/281495242_Influence_of_composition_on_optical_and_dispersion_parameters_of_thermally_evaporated_non-crystalline_Cd50_S50-xSex_thin_films?focusedCommentId=58bfc21f82999cd4be0cb478

https://www.researchgate.net/publication/283338024_Effect_of_Se_addition_on_optical_and_electrical_properties_of_chalcogenide_CdSSe_thin_films?ev=prf_high

I hope they help you.

Good luck 

Article Influence of composition on optical and dispersion parameter...

Article Effect of Se addition on optical and electrical properties o...

Thank you Mr. David and Dr. Ahmed for the explanation. 

 Dear Dr. Cyril Robinson Azariah J you are always welcome.

I agree with my previous collegues; however with respect to the attached plot the answer is that the criteria it is not the tangent to the curve. You must take the linear part of the curve (between 4 and 4.5 eV), fit these points to a straight line and extrapolate this line until it intersects the base line (background). The intersection value (in eV) is the direct band gap according to Tauc's model.

Best regards

Pedro

Dear colleague Cyril Robinson Azariah J,

Have a nice time and good day.

I attached your figure after showing how to calculate optical band gap from the tauc plot, and theoretically in details simply how to process the optical properties through the following paragraph. please check. 

Due to the format of the Equations, it is included in the attached file so check the Eq. No. the see it in the attached file.

How to determine the direct or indirect band gap materials?

Optically you can follow the following sequence:

you can measure the reflectance, R at normal incidence with an aluminum reference mirror and also measure the transmittance, T. The absolute values of  transmittance, T and reflectance R of the substrates after correcting the  are given by [[**]A. A. Sagade,  R. Sharma, Sensors and Actuators B: Chemical, 133 (2008) 135-143 [**] M. Dongol, M. M. El-Nahass, A. El-Denglawey, A.F. Elhady, A.A. Abuelwafa. Current Applied. Physics 12 (2012) 1178.]

……………………………...... (1)

Ift and Iq are the intensities of the light passing through the film-quartz system and the reference quartz, respectively, and Rq is the reflectance of quartz. In addition, if the intensity of light reflected from the sample mirror reaching the detector is Ifr and that reflected from the reflectance reference mirror is Im, then

…………………… (2)

Ifr is the intensity of light reflected from the sample reaching the detector and Rm is the mirror reflectance.

T and R spectra were performed on thin film samples with single face. Extinction coefficient, k and refractive index, n were calculated using T, R and thickness d taking into account the experimental error of   the film thickness. T and R.

How to calculate  Absorption and extinction coefficient?

T, R and d are used to calculate the absorption coefficient, α

according to [[**]A. El-Denglawey, M. Dongol, M.M  El-Nahass, J. Lumin 130 (2010) 801.]:

………………………….…….…… (3)

α is given by:

 …………………………………… (4)

The calculated α is included within high absorption region (α ≥ 104 (cm)-1).  

Extinction coefficient, k of TiO2 film is calculated by using:

  ……………………………………….…. (5)

How to calculate  Optical gap?

            An absorption edge of semiconductors corresponds to the threshold of charge transition between the highest nearly filled band and the lowest nearly empty band. According to inter-band absorption theory, the film’s optical gap can be calculated according to [[**]J. Tauc (Ed.). Amorphous and Liquid Semiconductors, Plenum, New York, 1976].

 …………………………. (6)

 A is a parameter of transition probability, it measures the disorder of material 

A = 4πσmin / nc∆E, Where  σmin is the minimum metallic conductivity, n is the refractive index, c is the light-velocity, and  ∆E = ∆Ec - ∆Ev   represents the  band tailing

[[**]M. M. El-Nahass, M. H. Ali, A. El-Denglawey Trans. Nonferrous Met. Soc.      

       China 22(2012) 3003−3011].  

is the optical gap of the material, hυ is the incident photon energy and r is the transition coefficient. The reported values of r are 2 for the measurement of indirect optical gap and 1/2 for direct optical band gap.

To determine the value of r plot the relation

ln ahn  = ln B+ r ln(hn- Egopt) and find the value of r from the solpe of the line for Ex.

May you have both direct 

and indirect band gap

Due to phonon energy that assisting the indirect transition could be written as:

Ephonon  is the  phonon energy assisting the indirect transition.

The indirect optical gap, is evaluated by extrapolating the straight line part of (αhν)1/2 curves with energy axes (hυ) i.e (αhυ)1/2 = 0  according to eq:

……………………………. (7)

Direct optical gap,  is evaluated by extrapolating the straight line part of (αhν)2 curves with energy axes (hυ) i.e (αhυ)2 = 0  according to eq:

……………………………. (8)

Both direct, and indirect, optical gaps of TiO2 films may be found.

How to calculate refractive index and dielectric constant?

Both R, and k at different λ were used to calculate refractive index, n according to:

[[**] T. S. Moss. Optical Process in semiconductor. Butter Worths, London, 1959.]

     ………………………….… (9)

The dispersion of refractive index of TiO2 films is analyzed by the concept of the single oscillator and can be expressed by the Wemple–DiDomenico (WDD) relationship[ [**][S. H. Wemple, M. DiDomenico. Phys. Rev. B 3 (1971) 1338-1351] as: 

          ……………….(10)

 Eo is the single-oscillator energy and Ed is the dispersion energy which is a measure of the intensity of the inter-band optical transition, it does not depend significantly on the band gap. The oscillator parameters can be determined  by fitting a straight line to the experimental points according to [[**][A. El-Denglawey. J. Non-Cryst. Solids 357 (2011) 1757-1763.].

The relation between the lattice dielectric constant εL, and the refractive index, n as

[[**] A. El-Denglawey. J. Non-Cryst. Solids 357 (2011) 1757-1763.]:

 ………………………………….(11)

where εL is the lattice dielectric constant, N/m* is the ratio of the carrier concentration to the effective mass, c is the speed of light, and e is the electronic charge, εo is the permittivity of free space. The linearity of the plots of n2 versus λ2, verifying of Eq. (11). The value of εL is determined from the extrapolation of these plots to λ2 = 0 and N/m* from the slope of the graph.

Good luck

A. El-Denglawey

Firstly you should take transmittance, absorbance absorbance or reflectance readings and then calculate the absorption coefficient (α) by using following equations (i) For Reflectance α=1/t ln[(1-R)2/T] (ii) For Absorbance, α=2.303A/t (iii) For Transmittance, α= -ln(T)/t Where T is the transmittance, t is the thickness, A is the absorbance and R is the reflectance. After getting α you can follow the following equation to calculate the band gap of the semiconductor samples as: αhν=A(hν-E)n,

where A is a constant, ‘h’ is the photon energy and ‘Eg’ is the optical band gap of the semiconductor and ‘n’ is index related to the density of states for the energy band. It is assumed, n = ½ for direct allowed and n = 2 indirect allowed transitions, respectively. The band gap was determined from (αhν)2vs hν curve by drawing an extrapolation of the data point to the photon energy axis where (αhν) 2 =0 or, (αhν) 1/2 =0, gives the optical band gap Eg.

There seem to be a widely-spread general error in literature and discussion fora, this thread being one among them, mistaking α(hν), alpha as a function of photon energy, as product of α and hν, i.e., αhν, (See

Jacques I. Pankove, Optical Processes in Semiconductors, Chapter 3), I raise my case here for further discussions.

@Alireza Bargahi

It is incorrect to write A+T+R=1 if A is the absorbance. Absorbance is defined as A=-logT. Without reflection, R=0, T=I/Io=exp(-αt), hence A=αt*log(e), where the absorption coefficient α=4πκ/λo; for complex refractive index N, N=n+iκ, λo is wavelength of incident light in vacuum. For a slab of thickness t with only one reflection from surface, and another at the bottom surface, indeedT=(1-R)²exp(-αt), sometimes a good approximation, but if multiple reflections are significant, the sum of higher terms has to be calculated. There is no popular-science description for absorption, but when forced, it may be 1-T-R for whatever T and R measured. This absorption is the nonradiative part, possibly lost as heat or creation of phonons in fancy terms.

Let me reiterate the general error about use of αhν as the product of α and hν while it should have been α only. In literature, the quantity is so wirtten and used because of the misinterpretion of as α(hν) while in fact it represents α as a function of hν, not the αhν used to assist the extraction of band gap from T(hν) plot by seeking the intercept of a tangent. Most cases of so doing are not justified because the curves are not linear and as you keep magnifying the curve, or zooming out in reverse, the shapes all look similarly nonlinear, though their intercepts vary greatly and are untrustworthy. There should be a clear straight line, according to the equations derived and the way the curves plotted.

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)n = A(hν-Eg) you can get Eg by drawing a tangent. Take value of n, 2 and 1/2 according to the type of your material.

The optical band gap of semiconductor can be estimated from the intercept of the extrapolated linear fit for the plotted experimental data of (αhν) n versus incident photon energy (hν) near the absorption edge.

by take correction factor for each linear curve

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...

Agree with Ahmed Saeed Hassanien .

I have added a chapter of my research work in that extensive details of my band gap narrowed material optical study is given.

which is

"Non-Classical Crystal Growth Recipe" using nanocrystalline ceria: a detailed review .

Page No-16: how to distinguish Tauc and Urbach Region

Page No-23: bandgap narrowed ceria (having two linear region like your data)

Page No-25: Photoluminescence spectroscopy (Validating Two band gap observation)

which will help.

Regards

Santanu

Łukasz Jarosiński

Hello, how do you obtain the absorption plotted in fig 2 of your "Optical Material" paper?

You can easily draw Tauc Plot Online on this link -

https://www.instanano.com/2020/05/draw-tauc-plot-from-uv-vis-absorbance.html

You can check this article; J. Am. Ceram. Soc., 1–5 (2013) DOI: 10.1111/jace.

Every one has shared its own point but no one is explaning why we chose fix point to draw tangent at the absorption curve?

As per Dr. Ahmed answer plot the values of (αhυ)^2 vs hυ for direct band gap & for indirect band gap (αhυ)^1/2 vs hυ. And the choose straight line vertically downward to X-axis that value is your band gap.

I think you should take the linear region.

Watch this, this one will help

https://www.youtube.com/watch?v=P6Ioh6OunoU&t=392s

plot the values of (αhυ)^2 vs hυ for direct band gap & for indirect band gap (αhυ)^1/2 vs hυ. And the choose straight line vertically downward to X-axis that value is your band gap.

Equation 3.2 in Pankove's book α(hυ)=A*( hυ - Eg)1/2 actually reads as "alpha as a function of hυ", not "alpha times hυ", so the linear extrapolation should be done according to α2=A*( hυ - Eg). Even so, the linearity is often questionable and hence difficult to be used reliably to determine Eg. For a really direct bandgap material, photoluminescence, albeit not necessarily a panacea, would be better suited for this purpose. As for forbidden direct bandgaps, α(hυ)=A'( hυ - Eg)3/2, where A' indeed is inversely proportional to hυ, hence (αhυ)2/3=A"( hυ - Eg) would be correct with hυ multiplied to α.

Ahmed Saeed Hassanien I curious to know the general name of the term: (αhυ)1/n. Likewise term: hv stated as photon energy.

(αhυ)1/2 =β(hυ - Eg)

Dear Cyril

I see that your plot is over a very large photon energy range ~ (1.5 - 6.5) eV. Your range of interest is more limited ~ (4 - 4.5) eV. Using this whole plot make the estimation of your direct band gap quite rough. In order to examine the region of linearity more sensitively you should draw the data around this photon energy range only. Moreover, it is better to use standard linear least square fitting in the linear region of interest to avoid any personal bias in the estimation. If your straight line equation is in the form (y) = ao + a1(x) then the value of the band gap is the absolute value of the ratio ao/a1.

We agree with the text proposed by Abdulah Al Numan but with our hematite nanoparticles, we observed that it was easier to define the mathematical range to be use for making the calculations on (E*alpha) power 1/2 than on (E*alpha) power 2 curves because their first points were not perturbated by any other peak.

The correct values were then transfered on the (E*alpha) power 1/2 plot to obtain the cleaner Eg value

Cyril Robinson Azariah J. C.

Tauc used an equation in 1968 to calculate the absorption edges (bandgaps) of amorphous Ge and Si from their absorption data.

(αhν)γ=A(hν-Eg)

In this equation, α is the absorption coefficient, h is Planck’s constant, υ is the frequency of the incident photon, A is a proportionality constant (which is determined by the index of refraction, electron, and hole effective masses; however, it is usually taken as 1 for amorphous materials), and Eg is the bandgap energy. The important term is the exponent γ, which denotes the nature of the electronic transition, that is, when γ=2 it is a direct allowed transition, and when it is equal to 1/2, it is an indirect allowed transition. For γ=2/3 it is a direct forbidden transition, and for γ=1/3 an indirect forbidden transition. Typically, the allowed transitions dominate the basic absorption processes, giving either direct or indirect transitions.

Thus, the basic procedure for a Tauc analysis is to acquire optical absorbance data for a sample in question that spans a range of energies from below the bandgap transition to above it.

Plotting the (αhν)γ versus (hν) is a matter of testing γ=2 or γ=1/2 to compare which provides the better fit and thus identifies the correct transition type.

I have provided the Template file (Origin file) in the video description. Thanks

https://youtu.be/LLESVSsZmlg

Dear all,

This particular manuscript should help you out with the estimation of the band gap of semiconductors.

Article How To Correctly Determine the Band Gap Energy of Modified S...

https://www.youtube.com/watch?v=abI-XMwLM48

The following link is useful for this question

http://www.analyzetest.com/index.php/2021/04/04/determination-of-band-gap-using-uv-vis-spectra/

The following link is useful:

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

You should use, for example, Origin software and use the statistical tools to find the tangent (or linear slope), with confidence bands, the respective x-axis intercept, and most importantly, the statistical error:

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