Dear colleague Raghad Zein,

Have a nice time and good day.

peace be up on you [al-salamo Alicom wa rahmato Allah wa barakatoh].

There are two answers; short and in details. Herein fined the short answer:

It was suggested that [1-3] to find the value of r the relation between (αhν)1/r and incident energy (αhν) for all values of r should be figured. The value of r which release a straight line represent the value of r and the electronic transition type.

The values of r are 2, 3, 1/2 and 3/2. The values 2 and 3 are corresponding to allowed and forbidden indirect electronic transition respectively. The other values; 1/2 and 3/2 are corresponding to the allowed and forbidden direct electronic transition [4]. please see equations 6,7,8 through the attach file

 [1] Y. Li, L. Xu, X. Li, X. Shena, A. Wang, Appl. Sur. Sci. 256 (2010)  

      4543.

[2] G. Saffarini, J.M. Saiter, H. Schmitt, Opt. Mater. 29 (2007) 1143.

[3] R.P. Tripathi1, M.S. Akhtar, M.A. Alvi, S.A. Khan,  J Mater Sci: Mater Electron. (2016) DOI 10.1007/s10854-016-4828-3

[4] M. M. El-Nahass, M. H. Ali, A. El-Denglawey Trans. Nonferrous

Met. Soc.China 22(2012) 3003.

 I hope this is useful and help you

Yours

A. El-Denglawey

Dear colleague Raghad Zein,

Have a nice time and good day.

peace be up on you [al-salamo Alicom wa rahmato Allah wa barakatoh].

Herein fined all what you need about optical properties from A to Z. in details including the direct and indirect transition akso the references are included.

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.

First you measure transmittance, T reflectance, R and/or absrobance.

If your spectrometer is not calibrated so you need to  calibrate your measured parameters otherwise go to step 2. Herein fined how to calculate the optical gap and constants of the film also the references are mentioned and all you need to overcame the all problems of optical properties [five items]. Due to the format of Equations it is attached in a separate file, just you know the equation number please check it through the attach file.

1- How to calculate the correction of T and R?

The reflectance was measured at normal incidence with an aluminum reference mirror. 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.]

Equation No.……………………………...... (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

Equation No.…………………… (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.

2- 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.]:

Equation No.………………………….…….…… (3)

α is given by:

Equation No. …………………………………… (4)

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

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

Equation No. ……………………………………….…. (5)

3- 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].

Equation No.…………………………. (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.

4- To determine the value of r plot the relation.

In case you know the value of Eg from the literature you can use:  ln (αhυ) = ln B+ r ln(hυ- Egopt) and find the value of r from the slope of the line for Ex.

 May you have both direct  and indirect band gap

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:

Equation No.……………………………. (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:

Equation No.……………………………. (8)

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

OR

to find the value of r the relation between (αhν)^1/r and incident energy (hν) for all values of r should be figured. The value of r which release a straight line represent the value of r and the electronic transition type.

5- 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.]

Equation No.     ………………………….… (9)

The dispersion of refractive index of the 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: 

Equation No.          ……………….(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].

Plotting  vs (hν)2 allows to determine the oscillator parameters by fitting a straight line to the experimental points. By extrapolating the linear part of WDD optical dispersion relationship towards the infrared spectral region (hν = 0), static refractive index n(0), could be defined by the infinite wavelength dielectric constant ε∞ or n(0)2,

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.]:

Equation No. ………………………………….(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.

Please notice that there is a direct calculation of ( hu) by this relation using wave length only.

E= hu =1240/wavelength (nm). 

I wish that is useful and help you.

Don't hesitate to ask about any thing concerning optical, electrical and structural properties.

Good luck

Yours

A. El-Denglawey

Dear colleague Raghad Zein,

Have a nice time and good day.

peace be up on you [al-salamo Alicom wa rahmato Allah wa barakatoh].

you can fined more information at research gate by searching on "direct and indirect band gap" on the attached link.

I wish this is useful and help you.

Yours

A. El-Denglawey

https://www.researchgate.net/search.Search.html?type=question&query=direct%20and%20indirect%20band%20gap&tabViewId=57404ae75b4952070a6cc980&previous=researcher

Dear our sister Raghad Zein

السلام عليكم ورحمة الله وبركاته

You can simply know the type of semiconductor if it is direct or indirect via the absorption coefficient from Tauc relationship, which is given by this equation:

:                                                          αhν = A (hν - Eg )n

where α is absorption coefficient and (hν) is the photon energy (hν=1240/Lambda).

If any one plot a graph between (αhν)1/n  versus (hν), he can get a straight line. This line intersects the X-axis at (αhν)1/n = 0 . The values of Eg have been estimated from this intercept.  The value of n is dependent on the electronic transition type. Where:

n=1/2 verified the direct allowed transition, 

n= 2 for indirect allowed transition, 

n=3  for direct forbidden transition and 

n=3/2 indirect forbidden transition.

You should try to select the suitable n according to your samples and their preparations. It is worthy to mention that the selected value of n here is determined according to the obtained straight line (the tallest line which passes by the largest number of points). 

The appended papers may help you; they are examples of direct and indirect allowed transitions.

Good luck

Your,

Ahmed Saeed Hassanien

https://www.researchgate.net/publication/283338024_Effect_of_Se_addition_on_optical_and_electrical_properties_of_chalcogenide_CdSSe_thin_films

https://www.researchgate.net/publication/281495242_Influence_of_composition_on_optical_and_dispersion_parameters_of_thermally_evaporated_non-crystalline_Cd50_S50-xSex_thin_films

How to calculate optical band gap from UV spectra? - ResearchGate. Available from: https://www.researchgate.net/post/How_to_calculate_optical_band_gap_from_UV_spectra/3 [accessed May 21, 2016].

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

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

Dear Raghad Zein 

Allah willing, You will do it successfully

Don't hesitate to connect me.

Thanks 

dears prof.A. Eldenglawey and prof.Ahmad Saeed Hassanien

thank you for yours answers

I prepared ZnS thin films using CBD ,during the study of optical properties i plot (ahv)^1/r vs (hv) for r=1/2 and r=2 which due to allowed direct and allowed indirect gap respectively, and i found straight line in both cases.

May i have two types of band gap?

thanks

Dear Raghad Zein

What is the crystal structure of your samples?

If they are crystalline and according to tuac argument, then the probable transition is direct. But if the sample are amorphous the probable transition is indirect.

On the other side if the sample are partially crystalline the two probabilities may be found.

It worthy to mentioned that the crystalline ZnS  has a direct energy band.

Good luck