Dear colleague Juliet Sheela K A

Have a nice time and good day.

The following text- PART-1- [supported by references] is teaching you easy how to calculate and study the optical properties through UV, Vis or IR regions (including refractive index-due to the formate of equations, it was included in a spearate file called optical equations) just read the steps and apply carefully:

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.]

……………………………...... (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.

In case ok knowing the value of Eg from the literature we can determine the value of r by 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.

 (see attached Fig.)

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.

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 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: 

          ……………….(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.]:

 ………………………………….(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

Dear colleague Juliet Sheela K A

Have a nice time and good day.

                                                            PART-2

The two  attached papers applied the aforementioned procedure may be useful and help you.

Yours

A. EL-Denglawey

Dear colleague Juliet Sheela K A

Have a nice time and good day.

                                                            PART-3

The attached link and picture may also help you.

Yours

A. EL-Denglawey

https://www.researchgate.net/search.Search.html?type=researcher&query=How+to+calculate+refractive+index+of+Zno+thin+film+from+UV+data

Dear Eldenglawey Sir,

I have tried applying WDD model to find optical constants of undoped ZnO thin films deposited by spin coating technique on glass substrates. But i am getting carrier concentration in the order of 10^20/cm^3.. which is too high... I would like to know wht may be the reason for this.