Dear colleague Shantanu Saha,

Have a nice time and good day.

To decide if the semiconductor is still DBG or IBG Tauc plot should be plotted.

Please see the two attached files. the most fitted relation through the attached file represent the transition;direct or indirect.

If you want to calculate or process the optical calculations follow the next procedure:

How to process the calculation to get Tauc plot for direct and indirect transition and finally the optical relations please follow the next:

In case if you measure the mentioned parameters , T , R and/or A herein fined all what you need about optical properties from A to Z. in details including the direct and indirect transition  also  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 using any spectrometer. 

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 Shantanu,

Annealing after ion implantation is used for decades in order to remove the crystal defects. A lot of theses studies confirmed that almost perfect crystalline structure can be achieved.

Let us assume that your technology for annealing works well. Then a direct band-gap material is also present after annealing. In particular, ZnO and related alloys are characterized by a very deep conduction band minimum at the Gamma point of the Brillouin zone as well as by a strongly pronounced valence band maximum see dor example M.D. Neumann et al.,Applied Physics Letters 108 (2016) 221105).

Even when crystal defects would remain, no band mixing can occure causing a change to an indirect band gap. However, some of these defects may cause below band-gap absorption, but this has nothing to do with an indirect band gap.