Decoupling substrate thickness and refractive index measurement in THz time-domain spectroscopy


Terahertz time-domain spectroscopy (THz–TDS) is an attractive choice for characterizing electrical properties of materials owing to its contactless, non-destructive nature. For efficient application, either the thickness or refractive index of the material being studied must be known precisely. The specimen is typically placed on top of a substrate, such as quartz or high-resistivity silicon, after which their characteristics are determined by studying the light-matter interactions at the substrate-sample interface. Since THz–TDS measures the electric field in the time domain, any uncertainty in the value of the substrate thickness or refractive index can cause errors to cascade into sample property calculations related to the detected phase. Therefore, in practice, one of these values has to be assumed, or their product must be numerically optimized to converge on suitable values. Whatsoever the approach, errors are inherent and may mask some real features or properties of the material being measured. This is one of the stumbling blocks for implementing THz spectroscopy in industrial applications.

Farah Vandrevala (PhD student in Electrical Engineering) and Professor Erik Einarsson (jointly appointed by the Department of Electrical Engineering and the Department of Materials Design and Innovation) at the University at Buffalo found a way to mitigate this problem. They utilized THz–TDS in reflection geometry to accurately and independently determine both thickness and refractive index by illuminating the step-edge of a substrate atop a metal stage, thereby minimizing error in both values. Their work has been published in the research journal Optics Express.

In order to achieve their goal, the researchers focused a THz beam with a spot size of approximately 3 mm on the top surface of a substrate. They then positioned the substrate such that the step-edge was illuminated. A ten-degree incidence angle ensured there were three reflected signals: one from the top of the substrate, one from the underlying metal stage, and a third that was delayed due to travel inside the substrate.

The research pair explain that the time delay between the first two reflections corresponds only to the substrate thickness. “We were quite delighted to learn that the math involved in finding the substrate thickness was nothing more than simple trigonometry. The simplicity of our method is what makes our solution so elegant,” said Vandrevala. As a consequence of independently determining the thickness, the researchers were then able to calculate the optical properties of the substrate with high confidence.

The Vandrevala–Einarsson study presents a fractional-reflection measurement, taken using THz–TDS at the step-edge of a substrate, that allows the thickness and refractive index measurements to be decoupled. Their novel approach has been seen to be advantageous in that all the necessary information is obtained in a single time-domain measurement. In addition, this new technique can be easily applied to a wide range of substrates and still yield precise results regardless of how transparent or opaque the substrate is. Altogether, this technique can come in handy when the effects of the supporting substrate must be carefully accounted for, such as applications involving the study of coatings, thin-films, two-dimensional materials, or biological samples.

Decoupling substrate thickness and refractive index measurement in THz time-domain spectroscopy. Advances in Engineering


About the author

Farah Vandrevala received her Bachelors in Electronics and Telecommunications from University of Mumbai, and Masters in Electrical Engineering from University of Texas at Arlington (UTA) in 2010 and 2013, respectively. From 2011 to 2013 she worked as a student associate modeling and characterizing semiconductor devices in the Analog Integrated Circuits Research group at UTA to find failure precursors in the near-threshold region. Since 2014, her research work at the Applied Nanoscale Materials Lab (ANaMaL) in University at Buffalo, New York, has been focused on materials characterization using Terahertz Time-Domain Spectroscopy (THz-TDS).

Her research pursuits include studying optical properties of 2D materials for plasmonic applications, finding innovative ways to measure diverse materials, including biological cells, and exploring varied methods of extracting information from those measurements. She is currently in the final year of her doctoral studies.

About the author

Dr. Erik Einarsson is an assistant professor in the Department of Electrical Engineering and the Department of Materials Design and Innovation at the University at Buffalo in Buffalo, NY. He received a BS in physics from New Mexico Tech and an MS in physics from Portland State University before moving to Japan to complete his studies. After obtaining a PhD in mechanical engineering from the University of Tokyo for his work on single-walled carbon nanotubes, he remained in Tokyo as a postdoctoral fellow and a project assistant professor.

In 2013 he moved to Buffalo where he leads the [Applied Nanoscale Materials Lab], where research efforts are focused on THz spectroscopy and low-dimensional materials.



Farah Vandrevala and Erik Einarsson. Decoupling substrate thickness and refractive index measurement in THz time-domain spectroscopy. . Vol. 26, No. 2 | 22 Jan 2018 | Optics Express 1697

Go To Optics Express

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