I started working on using the envelope (Swanepoel 1983) method to obtain the optical constants, I was able to calculate the refractive index n and the thickness, but there are some problems such as:
1- Calculating the absorption coefficient and hence the energy gap
2- Calculating the envelope curves passing throw the maxima (TM) and minima (Tm) for whole wavelength range
Can any one help me?
Note: the first figure I have obtained from my program but I need the second figure.
Hi, you do not need Swanepoel's method to calculate absorption coefficient and optical band gap. If you already know the thickness (d) of the film and have the transmittance (T) and reflectance (R) spectra you can use the approximate equation alfa=(1/d)ln((1-R)/T) to calculate alfa. Then you can use Tauc plot for determination of Eg. See for example our paper in the attachement
thank you Dr. Tsvetanka
i do not know the thickness of the film and I only have the transmittance (T) data,so i should use this method also I am working on developing my own program using Matlab to calculate the optical constants (n,k) and the absorption coefficient .
Dear Dr. Saad
I think that there is problem with the envelope curves Ti and Tm. According to the Swanepoel’s paper (J. Phys. E: Sci. Instrum. 16 (1983) 1214), the both envelope curves are collapsed in single curve in strong absorption region. In your case all curves (TM, Tm, Ti) are collapsed in the region of the shortest wavelength interference maxima replaced ~ 550 nm. If you use this data you would find smaller energy gap than real gap. The problem is because the points for Tm and Ti for this interference maximum are not on the exact position. Usually the absorption changes the position of this extreme. Really the reflectance spectrum gives the true position of interfernce extreme. About the calculation from R you can see in [35] Kushev D B, Zheleva N N, Demakopoulou Y and Siapkas D 1986 Infrared Phys. 26 385. I think that if you find the cross points of Ti and Tm with transmittance spectrum you will find correct description of TM and Tm in strong absorption region. This is the simple way.
Dr.Tsvetanka ,In your paper you mentioned that the refractive index n and thickness d of the films
were calculated simultaneously by minimization of an objective function, can you provide me more information about this.
For the absorption coefficient. In the spectral range of the interference extremes if you know the film’s thickness you can use the value of transmiatance for the interference maxima (T(Max)/) in the ratio x = T(Max)/Tsub = exp(-alpha*d) (Tsub is transmittance of clean substrate) to find absorption coefficient (alpha).
In strong absorption region 1).where TM and Tm collapse in single curve you have to use formula for T0 (equation 22 in J. Phys. E: Sci. Instrum. 16 (1983)1214). For initial estimate for the refractive index you can use extrapolation of your data applying Cauchy or Sellmeier’s equations, or 2. ) you can use the equation x = T(film)/Tsub = exp(-alpha*d) (where T film is the transmittance of thin film and Tsub is transmittance of clean substrate).
Hi, we use dispersion models for describing n and k. In the weak absorption range you can use exponential decay for k and Wemple-DiDomenico model for n. I use lsqnonlin matlab function for calculation. If you send me your T spectra I can run my programs to see what I will get.
Unfortunately we have never published the calculation procedure using transmittance. Recently we published similar calculation procedure for much thinner films. We use R spectra for calculation of n, k and d. You can take a look
thank you Dr.Rossen for your explanation ,I will follow your explanation in my work
The absorption calculated from trans and refl spectra is not accurate in large wavelength (>300 nm for some transparent materials). At DUV region, the absorption coefficient could be estimated by the equation provides above by Dr. Tsvetanka Babeva.
For the envelop curves, I think some commercial thin film software such as McLeod could solve the problem.
Hi Mostafa.
In brief, you do not to have to work with maxima and minima at the absroption region but with the envelope-extremes, i.e. the contacting points of the enevelope with the mesaured curve. For these points there is analytical solution even in the absorbing region but Swanepoel's method fails there.
In any case you need to measure better only reflectance or best if you measure also transmittance to separate absorption contribution (complex javascript:part of refractive index) from other parameters (n, Dn, d,...). If you have transmittance and reflectance you can use gamma function as defined in the attached work.
I want to find the optical film thickness from T spectra using envepole method? can you give me detailed infomration and papers in this regards
The thickness of a thin film can be calculated using the reflectance or transmittance data. The Manifacier equation is, generally, used to calculate the thickness of the film:
d = M λ1λ2 / (2[n (λ1)* λ2 −n(λ2)*λ1 ])
Where M is the number of oscillations between two extremes of the reflectance (M = 1 between two consecutive maxima or minima), λ1, n (λ1) and λ2, n(λ2) are the corresponding wavelengths and indices of refraction at the reflectance extremes
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