Introduction: Thin Film Interference Demonstration With a Spectrometer

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Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, increasing reflection at some wavelengths and decreasing it at others. When white light is incident on a thin film, this effect produces colorful reflections.

Thin-film interference explains the multiple colors seen in light reflected from soap bubbles and oil films on water. It is also the mechanism behind the action of antireflection coatings used on glasses and camera lenses. If the thickness of the film is much larger than the coherence length of the incident light, then the interference pattern will be washed out due to the linewidth of the light source.

The reflection from a thin film is typically not individual wavelengths as produced by a diffraction grating or prism, but rather are a mixture of various wavelengths. Therefore, the colors observed are rarely those of the rainbow, but rather browns, golds, turquoises, teals, bright blues, purples, and magentas. Studying the light reflected or transmitted by a thin film can reveal information about the thickness of the film or the effective refractive index of the film medium. Thin films have many commercial applications including anti-reflection coatings, mirrors, and optical filters. (Wikipedia)

As shown in the figure, a thin film is generally a transparent layer of thickness d, and refractive index n2, on a substrate. In this demonstration, the substrate is a silicon wafer, and the thin film is a silicon nitride layer (Si3N4) with a refractive index close to 1.8 (see for example https://refractiveindex.info/?shelf=main&book=Si3N4&page=Vogt-1.91 ).

Consider light incident on a thin film and reflected by both the upper and lower boundaries. The optical path difference (OPD) of the reflected light must be calculated in order to determine the condition for interference. Referring to the ray diagram above, the OPD between the two waves is the following:

Using Snell's law, 

Interference will be constructive if the optical path difference is equal to an integer multiple of the wavelength of light, .

This condition may change after considering possible phase shifts that occur upon reflection. (Wikipedia)

The Interference Condition for Thin Films can be found at: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/interf.html

Silicon wafers with different coatings can be purchased online, from retailers or companies such as University Wafer.

For full calculation of the reflectance spectrum, the transfer matrix method is typically used ( https://en.wikipedia.org/wiki/Transfer-matrix_method_(optics) ). In this method, matrices containing complex transmission and reflection coefficients at each interface is cascaded to calculate the full transmission or reflection as a complex amplitude.

The detailed description of the method and an Octave/Matlab library of functions for such calculations can be found at an online academic website that also contains a free PDF book ( https://www.ece.rutgers.edu/~orfanidi/ewa/ ). However, an easier path to calculating the reflectance or transmittance of a multilayer optical structure is to go to the reflectance calculator found at https://www.filmetrics.com/reflectance-calculator . Here, a number of thin film layers can be added on a substrate and the reflection spectrum can be calculated at an arbitrary angle of incidence and polarization.

Color charts are valuable tools for people working in microfabrication, and gives an idea about the film thickness through a visual inspection. The color of a silicon wafer will change depending on the coating material refractive index and its thickness. Reflectometers are typically used to rapidly measure film thickness based on thin film interference.

In this demonstration, we use a scrap silicon wafer with silicon nitride coated regions to measure the reflectance. We then use the online reflectance calculator to estimate the thickness of the silicon nitride layer.

Supplies

Helping Hands

White light source (e.g. Maglite Xenon bulb)

3V Power source (e.g. Arduino Uno 3.3V output pin)

Cables to power the white light bulb

A fiber optic spectrometer (e.g. Spectryx Blue)

A steel plate or a mirror (to be used as a reflectance reference surface)

Step 1: Put Together the Refletance Measurement Setup

Plug in the white light bulb to the Arduino 3.3V and GND pins using jumper cables.

Position the light source and fiber on the two crocodiles of the helping hands. Make them face towards the table. Place the silicon wafer or mirror. Connect the spectrometer to the computer and run the GUI. Observe the light signal and adjust fiber orientation until a satisfactory reflection signal is captured.

Step 2: Get a Reference Measurement

Place the steel mirror (or other type of blank mirror) under the light source and observe spectrum. Use this spectrum as reference.

Step 3: Measure Silicon Nitride Coated Wafer

Switch GUI software to Relative mode (Transmission/Reflection) , and position the silicon wafer under the setup. Measure the reflectance.

Save the reflectance.

Constructive and destructive interference fringes can be seen in the reflectance spectrum if the film is thick enough.


Step 4: Model Using a Reflectance Calculator

Go to online reflectance calculator website: https://www.filmetrics.com/reflectance-calculator

Select silicon nitride as the film material. Enter a starting thickness. Set the wavelength range to 350-850 nm. Set the angle of incidence to 10 deg (or 0 deg, shouldn't matter much).

Select silicon as the bottom substrate material.

Plot the reflectance. In the first example, a trial value of 500 nm is entered, however, the positions of the fringes were not as observed. So by trial and error, the value is estimated to be closer to 850 nm.

The online calculator allows downloading the plots, so using Octave, the data from the spectrometer is plotted along with 850, 860 and 870 nm Si3N4 thickness as shown here. It is observed that 860 nm fits best, and in principle the accuracy can be below 10 nm, since deviations result in distinguishable spectra.

For near normal incidence, polarization does not matter so much, but the experiment can be repeated at different angles of incidence by adjusting the positions of the light source and fiber. This is a good quantitative demonstration of a fundamental optical effect. It is a great starting point for those who are interested in thin film optics.