Mueller matrix metrology for measuring the critical dimensions of nanostructures

Many diverse applications rely on lithography at the nanoscale, including semiconductor devices, biological probes, solar energy harvesting, spectroscopy and smart materials. The critical dimensions of the resulting nanostructures require characterization to very high precision, but currently employed techniques, such as atomic force microscopy and scanning electron microscopy, have disadvantages. They only test a limited area, exhibit a lack of speed and integrability, and may even degrade the sample.

Here, Mueller matrix metrology was investigated as a tool for analyzing the critical dimensions of nanostructures. Mueller matrix ellipsometry is a technique that measures a sample’s complete Mueller matrix describing its response to excitation by polarized light in either reflection or transmission configurations. The researchers demonstrate that the data collected on depolarization in the measured Mueller matrices can be exploited to reveal deviations from the desired sample shape to within 1 to 2 nanometers.

The study was motivated by the need to characterize structures in the nanometer range with a high lateral resolution over a large scale. Additionally, small deviations from the mean values over a large area should ideally be analyzed in a single measurement, which remains a challenging feat for most scanning microscope techniques.

The researchers fabricated six samples of gold nanostructures — either ordered square or random arrays of non-overlapping nanodiscs — on a fused-silica substrate. They combined Mueller matrix ellipsometry with the appropriate matrix decompositions as a method to analyze the critical dimensions in a fast, scalable, and nondestructive way. The technique was able to characterize the arrays with high precision by observing very small deviations in their diameter and statistical deviations from a perfect circular base.

Source: “Mueller matrix metrology: Depolarization reveals size distribution,” by Ievgen Voloshenko, Bruno Gompf, Audrey Berrier, Martin Dressel, Gabriel Schnoering, Marcus Rommel, and Jürgen Weis, Applied Physics Letters (2019). The article can be accessed at http://doi.org/10.1063/1.5094409 .