Sub-Monolayer Accuracy in Determining the Number of Atoms per Unit Area in Ultrathin Films Using X-ray Fluorescence

Abstract

We present that the composition and thickness of thin films determine their physical properties, making the ability to measure the number of atoms of different elements in films both technologically and scientifically important. For thin films, below a certain thickness, the X-ray fluorescence intensity of an element is proportional to the number of atoms. Converting this intensity to the number of atoms per unit area is challenging due to experimental geometries and other correction factors. Hence, the ratio of intensities is more commonly used to determine the composition in terms of element ratios using standards or a model. Here, the number of atoms per unit area was determined using X-ray structure information for over 20 different crystallographically aligned samples with integral unit cell thicknesses. The proportionality constant between intensity and the number of atoms per unit area was determined from linear fits of the background subtracted X-ray fluorescence intensity plotted versus the calculated number of atoms per unit area for each element. The results demonstrate that X-ray fluorescence is very sensitive, capable of measuring changes in the number of atoms of less than 1% of a monolayer for some elements in a variety of sample matrices. Finally, using the calibrated values, an 8 unit cell thick MoSe<sub>2</sub> was grown and characterized, demonstrating the usefulness of the ablity to quantify the number of atoms per unit area in a film.