Determination of refractive index and layer thickness of nm-thin films via ellipsometry

Recent technological advances have led to development of various fields that recurrently require the characterization of very thin layers. It is known that the properties of films: optical and mechanical strength, can be tuned by accurately controlling the film thickness. Several techniques such as surface plasmon resonance, quartz crystal microbalance and ellipsometry are available for this purposes. Ellipsometry is a measurement and data analysis optical technique based on classical optics. This technique is capable of measuring two film properties: refractive index and thickness, with high precision, simultaneously. Unfortunately, the technique only works if the film thickness is sufficiently large, say exceeding 15nm. Below this value, the film thickness and refractive index are coupled parameters and cannot be determined independently.

To this note, recent research undertaken by Dr. Peter Nestler and Professor Christiane Helm from University of Greifswald in Germany developed a novel technique that would unlock the held up potential of ellipsometry. “I always deemed this limitation an unsatisfying blemish in the otherwise highly elegant mathematics underlying ellipsometry” said Nestler. To be more specific, they exploited Drude’s approach to calculate the complex reflection coefficients from electromagnetic theory. They hoped that the latter approach would allow determine the first and second ellipsometric moments, which in this case represents the properties of the thin film and independent of incident angle. Their work is published in the research journal, Optics Express.

Briefly, the researchers started the experimental setup by undertaking the thin film approximation so as to reveal the thickness and index of refraction of a non-absorbing nm-thick layer via ellipsometry. Next, they plotted the real part of the ellipsometric ratio against the square of the imaginary part for a series of samples that could be as small as the uncoated substrate and one value of film thickness. They then calculated the slopes of the plotted graphs. Eventually, they characterized the nanometer-thick silicon oxide films, observed the growth of a polyelectrolyte multilayer, and quantified a parameter map obtained by imaging ellipsometry.

The authors observed that the slope of the straight line depended on refractive index, but not on film thickness. The two researchers also noted that by knowing the refractive index of the film, one could calculate the film thickness which was seen to depend on the distance between specific points in the plotted graph. Furthermore, by characterizing the nanometer-thick silicon oxide films and observing the growth of a polyelectrolyte multilayer, the researchers were able to demonstrate the potential for diverse application that their new approach could be employed for.

Nestler and Helm study has successfully presented a novel alternative technique to compute the thickness and refractive index from an ellipsometric ratio. The researchers here employed Drude’s definition to carry out a series of expansion to the second order. It has been seen that the developed slope yields the refractive index while the interval between the points gives the thickness of the film. Altogether, this novel approach enables one to determine both thickness and refractive index parameters independently, even for very thin films which could not be described unambiguously up to now.