Fast fourier transform and multi-Gaussian fitting of XRR data to determine the thickness of ALD grown thin films within the initial growth regime

Abstract

While a linear growth behavior is one of the fingerprints of textbook atomic layer deposition processes, the growth often deviates from that behavior in the initial regime, i.e. the first few cycles of a process. To properly understand the growth behavior in the initial regime is particularly important for applications that rely on the exact thickness of very thin films. The determination of the thicknesses of the initial regime, however, often requires special equipment and techniques that are not always available. We propose a thickness determination method that is based on X-ray reflectivity (XRR) measurements on double layer structures, i.e. substrate/base layer/top layer. XRR is a standard thin film characterization method. Utilizing the inherent properties of fast Fourier transformation in combination with a multi-Gaussian fitting routine permits the determination of thicknesses down to $t \approx 2$ nm. We evaluate the boundaries of our model, which are given by the separation and full width at half maximum of the individual Gaussians. Finally, we compare our results from two layer stacks with data from X-ray fluorescence spectroscopy, which is a standard method for measuring ultra thin films.