Determination of hBN thickness by optical contrast

Van der Waals materials are crystals that can be peeled into atomically thin layers. When a number of different layer types stack upon one another, different physical properties appear. A commonly studied van der Waals material is hexagonal boron nitride (hBN). Hexagonal boron nitride is highly stable and has a structure similar to that of graphite. Such atomic arrangement allows hBN to be extremely hard, have novel electrical properties, and excellent thermal conductivity. However, whenever hBN layers are stacked upon one another, the physical and optical properties of the crystal differ with thickness, and so with the number of hBN layers. By using Fresnel's equations, a plot function was coded in MATLAB that compared a range of wavelengths with a range of hBN thicknesses. The ranges were plotted against the values of the light contrast from the samples. The plot was tested experimentally by shining 6 different colored LEDs with different wavelengths, at normal incidence, onto a sample made up of an unknown number of hBN layers on a Silicon (Si) chip with a 300 nm thermally grown oxide layer. A microscope was used to capture images of the different samples. The images were transferred into a python program that measured the contrast of the grayscale images and returned the thickness of the samples. The results of the code were compared to the thickness measurements of the sample received by an atomic force microscope (AFM). Flake 1 was measured using the AFM for a thickness of 5 nm and the equations using the image contrasts calculated a thickness of 3 nm. Flake 2 was measured using the AFM for a thickness of 14 nm and the equations using the image contrasts calculated a thickness of 18 nm.