Spectroscopic thickness and quality metrics for PtSe$_2$ layers produced by top-down and bottom-up techniques

Thin films of noble-metal-based transition metal dichalcogenides, such as PtSe$_2$, have attracted increasing attention due to their interesting layer-number dependent properties and application potential. While it is difficult to cleave bulk crystals down to mono- and few-layers, a range of growth techniques have been established producing material of varying quality and layer number. However, to date, no reliable high-throughput characterization to assess layer number exists. Here, we use top-down liquid phase exfoliation (LPE) coupled with centrifugation to produce widely basal plane defect-free PtSe$_2$ nanosheets of varying sizes and thicknesses. Quantification of the lateral dimensions by statistical atomic force microscopy allows us to quantitatively link information contained in optical spectra to the dimensions. For LPE nanosheets we establish metrics for lateral size and layer number based on extinction spectroscopy. Further, we compare the Raman spectroscopic response of LPE nanosheets with micromechanically exfoliated PtSe$_2$, as well as thin films produced by a range of bottom up techniques. We demonstrate that the Eg1 peak position and the intensity ratio of the Eg1/ A1g1 peaks can serve as robust metric for layer number across all sample types and will be of importance in future benchmarking of PtSe$_2$ films.