Complex Refractive Index Determination via Microspectroscopy Through Magnifying Optics: Challenges and Opportunities

Abstract

For the design and optimization of optoelectronic devices, accurate knowledge of the complex refractive indices of the constituent materials is essential. Herein, we present a fast and non-destructive approach for the extraction of the refractive indices from reflectance and transmittance spectra of samples with lateral dimensions down to the micrometer scale. Microspectroscopy, based on the combination of a standard optical microscope and a spectrometer, enables the assessment of the optical response of multilayer stacks using high-magnification optics with correspondingly large numerical apertures. Employing a numerical formalism explicitly accounting for the influence of the numerical aperture, allows for precise retrieval of the refractive index without resorting to dispersion models. We demonstrate the applicability of the proposed method for large-area, homogeneous, optically incoherent samples such as transparent glasses and absorbing 4H-SiC, for a SixNy thin film on glass substrate, and for mechanically exfoliated flakes of highly oriented pyrolytic graphite and MoO3, as representatives of uniaxial and biaxial optical anisotropy. While the results prove excellent agreement with values reported in literature, the case of graphite highlights the limitation for probing the out-of-plane refractive indices due to reduced sensitivity. Finally, we discuss possible extensions towards retrieving the full anisotropic tensor of the refractive index, establishing the proposed approach as a methodologically sound alternative to spectroscopic ellipsometry.