Far-field extraction of the dielectric function of exfoliated flakes near phonon resonances

The lateral dimensions of flakes of emerging low-dimensional materials that are mechanically exfoliated do not typically exceed some tens of micrometers. This prohibits the experimental extraction of their complex dielectric function (ϵ(ω)) at mid-infrared (IR) frequencies with conventional angle-resolved spectroscopic ellipsometry due to the large size of an IR beam that exceeds a flake’s size. To circumvent this challenge, previous approaches relied on mapping the dispersion of surface phonon polaritons using near-field scanning probes. These, however, involve expensive instrumentation, are sensitive to external conditions, require significant numerical fitting and become cumbersome in the presence of optical anisotropies and strong spatial dispersion. We introduce a simple empirical method to extract the in-plane components of the dielectric tensor of small-sized flakes using conventional Fourier Transform Infrared (FTIR) micro-spectrometry. By detecting minima in reflectance spectra near a phonon resonance, we obtain ϵ per frequency without fitting to any a priori known model. To recover ϵ(ω) over an extended spectral range, we apply this method to multiple flakes of various thicknesses, which are often available onto the same substrate upon exfoliation.