![]() The detailed analysis of the experimental results indicates that accurate E gap values can be obtained by fitting a sigmoid (Boltzmann) function to their corresponding optical absorption spectra. Stimulated by these aspects, this work investigated the semiconductors silicon, germanium, and gallium-arsenide in the crystalline (bulk and powder) and amorphous (film) forms. Within this context, optically-based methods were of special importance since, amongst others, they presented details about the electronic states and energy bandgap E gap of semiconductors which, ultimately, decided about their application in devices. Such a progress comprised the development of materials and models that, allied to the knowledge provided by spectroscopic techniques, resulted in the (nowadays) omnipresent electronic gadgets. Calculate the number of layers in the selected region by dividing its optical contrast by the expected monolayer contrast.Along the last two centuries, the story of semiconductor materials ranged from a mix of disbelief and frustration to one of the most successful technological achievements ever seen.Repeat the measurements for regions with different thickness to estimate the optical contrast expected for monolayer from the minimal difference between adjacent thicknesses.Calculate the optical contrast as C = (I sample – I substrate)/ (I sample + I substrate).Use mouse to drag the selection onto the substrate, keeping the minimum distance between the measurement points, and repeat the measurements. ![]() Press M to perform intensity measurements. Use circular selection tool to select an area of your flake.Open the acquired imaged in ImageJ by using the file menu or by dragging and dropping the file onto ImageJ window.Save the image as a high-quality file (tiff or jpeg with at least 90% quality).Acquire an image of the flake, making sure that it is properly focused and exposed.It can be done using different software, but one of the most convenient choices is ImageJ, a free and power software for microscope image processing. Optical contrast is calculated by measuring the intensity of three colour channel (red, green, and blue) in the digital colour image. Moreover, this difference (around 0.11 for the samples shown above) is equal to the optical contrast of a monolayer region – this allows you to estimate the expected value for a single layer region even before you find one. ![]() Even though the contrast values for each thickness show random fluctuations caused by variation of acquisition parameters and non-uniform illumination, the difference between adjacent thicknesses is sufficiently high to accurately estimate the number of layers in each region. Figure above shows another example of a WSe 2 flake deposited onto PDMS substrate, as well as optical contrast values extracted from mono- and few-layer regions of eight different samples. For more quantitative measurement, optical contrast can be calculated using an image processing software. An experience user working with a familiar microscope, substrate, and material can identify monolayers with almost 100% accuracy. Optical contrast measurements are most commonly used in a qualitative way during flake search to identify monolayers based on their translucent appearance and low optical contrast. ![]()
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