# Refractive index of titanium dioxide films as a function of wavelength for 400 C ° annealed films

I used UV-Vis/NIR spectrophotometer to extract the measurements of refractive index %R corresponding with wavelengths in the range of 190-1100 nm of TiO2 thin film deposited on FTO glass substrate. The TiO2 material is known for its high refractive index and strong absorption in UV-Vis light region according to its phase, XRD shows that my samples was Anatase phase.
I aim to find the optical properties of this thin film including absorbance, band gap, refraction. For refractive index data, I used Jasco V-770 UV-Vis/NIR spectrophotometer (I stick the thin films inside this device and make sure that it cover the source of light) then using OriginLab I plot the attach graph. My questions are:

• Is it possible to determine the refractive index of this thin film from the graph? maybe the highest peak?
• I know that there’s no refractive index in thousands, so why the graph show that y-axes (refractive index) expands from -2900 to 2900? Can anyone explain what that’s mean?

The thickness of TiO2 film is 1.7μm-2.3μm roughly, but I’m not sure, because I used Swanepoel method to estimate it (based on the obtained refractive index measurments and obtained transmittance).

Swanepoel equation: d=(λ_1 λ_2)/(2(λ_1 n_2-λ_2 n_1)) where, n_1 and n_2 are the refractive index at two adjacent interference fringes (maxima or minima) of thin film transmission, at wavelengths λ_1 and λ_2

Here is the data extracting from UV-Vis spectrophotometer: https://docs.google.com/spreadsheets/d/e/2PACX-1vScyJ0NIye6Bpx6o6rqmIVkaaJvc77Cax7EzN2sI4dEw4lKRC5yokxfdoEVdhtyiD-lcGxjN_9mVxck/pubhtml

• This is impossible to debug in its current form. Please include the whole methodology (what is your spectrophotometer measuring and how, how do you prepare your sample, how do you calibrate your measurement, how do you ensure that you measure your sample, which calculations are involved to achieve those values etc.). We have no clue what you did or what your instrument did. Nov 9, 2023 at 12:23
• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Nov 9, 2023 at 12:26
• Hello @JoséAndrade, I used commercial TiO2 powder and dissolved it in ethanol and water, then deposited it on glass substrates using the traditional spray method and dried it after each coating to remove the liquids. Finally, the thin film of TiO2 was annealed at 400 C for an hour. I aim to find the optical properties of this thin film including absorbance, band gap, refraction. My question is how do you explain my obtained data from UV-Vis spectrophotometer of refractive index measurements corresponding with wavelengths in the range 190-1100 nm. Please read my questions above. Thank you
– Mona
Nov 9, 2023 at 13:09
• @JoséAndrade After that we will study the effect of femtosecond laser texturing on this thin film but my currently problem is that I cannot defined the approximate refractive index value of TiO2 thin film. so I want one to advise me if this graph looks right or not for n vs λ. because it's new aspect for me...
– Mona
Nov 9, 2023 at 13:16
• I read your question, but I still do not know what your spectrophotometer did (model would help), how did you load your sample into the spectrophotometer and how did you calibrate everything. How did you make sure that you only target your film? Are there any calculations involved? How do you deal with sample thickness in your measurement? By sample preparation I meant for this measurement in particular, not how you created the sample. How thick is your film roughly? Add all these information in the question, not in the comments Nov 9, 2023 at 13:29

I am not sure which spectrophotometer you are using, but the data looks reasonable from my perspective.

I am not sure why you would get directly a measurement of the refractive index from the spectrophotometer, as the determination of the refractive index for thin films is a bit of an involved process (I did it a few months ago for my PhD project). Some spectrophotometers have more advanced options to determine the refractive index, but typically you get interesting results when a) the sample is measured close to the Brewster's angle (dependent on the substrate) and b) additionally measuring ellipsometric properties of the film.

What you are seeing there is a strong absorption peak at ~689nm, these are easily explained by Kramers-Kronig relations of the refractive index and the extinction coefficient of the sample:

If you were able to measure the extinction coefficient (also by means of transmittance and reflectance) you would see a sharp peak at the resonance of 689nm, which means that you have a strong absorption of your material in that wavelength.

As I mentioned before, I am note sure what you are measuring there (I suppose the reference value $$n_0$$ is somewhat related?) but if you are measuring transmittance and reflectance, you may also need to do ellipsometry to retrieve the optical constants (ref. index and extinction coefficient). There is also a more pedestrian way by measuring the peaks of constructive and destructive interference only from transmittance and reflectance, but in my personal experience that was more difficiult to regress from the raw measurement data.

Ellipsometry should be your friend for this specific measurement.

EDIT: I saw your edit post-mortem so I will quickly comment:

Swanepoel equation: d=(λ_1 λ_2)/(2(λ_1 n_2-λ_2 n_1)) where, n_1 and n_2 are the refractive index at two adjacent interference fringes (maxima or minima) of thin film transmission, at wavelengths λ_1 and λ_2

Unless you have a really thick film (~1-5µm) the maxima and minima will be too far apart and the regression will give you very large error bars (as the distance between maxima and minima will be dependent on the film thickness).

EDIT 2: After a comment from @Jose Andrade, I have to add some additional information:

• Considering the thickness of the film, it may be possible to do a regression with the Swanepoel equation based on the interference patterns, but it is not the most precise method to retrieve the refractive index.
• The absorption peak is atypical for the material you are claiming to use.
• From the webpage of the Jasco photospectrometer it is not possible to know what kind of data analysis you did, as the refractive index, so I am not sure if you area measuring what you think you are measuring. You can also add screenshots of what exactly you did.
• My problem with the measurement is that an absorption at that wavelength does not correspond to any of the used materials: TiO2, ethanol, water. I would imagine substrate being BK7 or FS. So, something is weird.... Nov 10, 2023 at 11:17
• I agree and after a quick search I confirm that the absorption peak is not necessarily from the materials the OP claims. BK-7 I would not expect either, for visible wavelengths it is mostly transparent. I would assume that it is some contamination or a specific dye causing the absorption peak. Additionally I looked at OPs data and they claim a refractive index of 6-7. I also looked into the spectrophotometer they claim to use and it is not possible to directly measure the refractive index out-of-the box, so the data may not be representing the refractive index. Nov 10, 2023 at 13:09