Sparse Spectral Imaging for Thickness Mapping of 3R-MoS$_2$ on PDMS

Abstract

We present a non-destructive, spatially resolved thickness characterization method for rhombohedral (3R) molybdenum disulfide (MoS$_2$) on polydimethylsiloxane (PDMS) substrates. Unlike broadband spectroscopic approaches, the proposed method reduces the measurement to a small number of discrete intensity images, enabling direct thickness mapping with a conventional microscope architecture and commercially available bandpass filters. Our approach combines a systematic framework for selecting optimal discrete wavelength samples of the material's reflectance with a robust thickness retrieval algorithm based on a multivariate Gaussian probability model. By sampling the reflectance with just five strategically chosen near-infrared bandpass filters, we demonstrate thickness characterization up to 691 nm with a mean 95% confidence-interval width of 8.3 nm. The method is adaptable to other van der Waals materials and conventional optical thin-film systems. It therefore provides a foundation for scalable, real-time thickness characterization in, e.g., dry-transfer fabrication workflows, where thickness screening remains a critical bottleneck for the production of van der Waals heterostructure devices.