I am working on semiconductor thin films. When I recorded transmittance spectra of thin films deposited at different thicknesses, for some films i got interference patterns and for some films i didn't get interference patterns in the spectra. What is the reason?
You are probably matching the interference condition for some thin films.
When you send a light beam to a surface it partially reflects in the first surface and part goes throuhg the film and reflects in the second surface and goes out as the first reflected beam, but with a phase shift, both beams interfere and cause the interference. That is true for reflection, and you are measuring transmittance... the explanation is also valid for that case: The incoming beam hit the first surface of the thin film, part is reflected and part goes into the film and this part is splited again when it arrives to the back surface of the thin film, a fraction is reflected and send to towards the surface, and another part is transmitted. Now the beam reflected in the back side of the film arrives to the first surface of the film and again is divided, part goes out the film and part is reflected back to the rear surface of the film, and once more it is splitted, part is reflected and part is transmitted... this transmitted beam interferes with the first transmitted beam, if they are out of phase they interfere and you see the interference pattern in your spectra. Sometimes you see it, sometimes not, it depends on the thickness and refractive index of your thin film material.
Please, have a look to the following links:
https://en.wikipedia.org/wiki/Thin-film_interference
https://oceanoptics.com/wp-content/uploads/App-Note-Transmission-Measurements-of-Polymer-Thin-Films.pdf
I hope it helps.
As the refractive index of most inorganic oxides/nitrides is between 1.38 (MgF2) - SiO2 (1.45) and 2.8 (Si3N4), as soon as you get a continuous film (say > 7 nm), you will see interference patterns.
The condition for interference in thin film is thickness of the thin film is grater than the half wavelength
t>(Lambda/2)
We recorded spectra from 200 nm to 3000 nm .Which Lambda should i consider. Is it critical wavelength or other wavelength?
The two important parameters for thin film interference are film thickness and refractive index. Optimum film thickness are on the order of a QWOT (quarter wave optical thickness) which is equal to the physical thickness times the refractive index. If you have a thin film stack, larger differences in refractive index tend to enhance interference effects.
The simplest type of thin film coating is the AR (anti-reflection) coating. AR coatings reduce the reflectance compared to an uncoated substrate and thus increases transmittance. It is explained by the destructive interference between the wave front reflected from the surface of the coating and the wave front reflected from the surface of the substrate (more precisely the interface between the coating and the substrate). A complete model considers multiple reflections within the film.
Optimum refractive index of an AR coating (for a substrate operating in air) is equal to the square-root of the refractive index of the substrate. For glass with an index of 1.5 the optimum refractive index is sqrt(1.5) = 1.22. There are not many practical materials with an index that low. Historically, MgF2 with an index of 1.38 at 550 nm provided an acceptable coating. The optimum refractive index will be higher for a higher index substrates. If the refractive index matches that of the substrate, you will not see thin film interference effects at all.
The optimum thickness of an AR coating is equal to one QWOT - a quarter of the wavelength of the light being considered divided by the refractive index of the film. A MgF2 QWOT operating at 550 nm with a refractive index equal to 1.38 will have a physical thickness of 550/(4*1.38) = 100 nm. This type of single layer AR coating creates a broad peak in the transmittance spectra centered at 550 nm (and minimum reflectance at 550 nm).
Now imagine what happens near 550 nm as the single layer AR coating becomes thicker or thinner. As the film gets thicker, the central peak shifts to longer wavelengths. Increasing the thickness further results in the film thickness being multiples of a QWOT. Harmonics are generated and there will be more and more peaks in the transmittance spectra. As the film gets thinner, the central peak shifts to shorter wavelengths. Interference effect get weaker, until there is no film at all and you get the transmittance of the uncoated substrate. This is why an AR coating designed to operate in the UV range is not visible at longer wavelengths like the visible range -the film is too thin. Similarly, a thicker film designed to operate in the IR region results in coloration and multiple peaks in the visible part of the spectrum.
Thin film modeling programs like TFCalc or Essential Macleod can help you model the transmittance and reflectance spectra for your particular system. The website refractiveindex.info can help you identify the refractive index of several materials.
The minimum thickness is wavelength devided by 4n, where n is refractive index
You have to take into account the light diffusion in the bulk, which is very important for thin films with very small grains.
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