X-Ray Reflectometry Determination of Structural Information from Atomic Layer Deposition Nanometer-Scale Hafnium Oxide T
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X-Ray Reflectometry Determination of Structural Information from Atomic Layer Deposition Nanometer-Scale Hafnium Oxide Thin Films D. Windover1, D. L. Gil2, J. P. Cline1, A Henins1, N. Armstrong3, P. Y. Hung4, S. C. Song4, R. Jammy4, and A. Diebold5 1 Ceramics Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899 2 Coruscavi Software, Washington, DC, 20037 3 Department of Physics and Advanced Materials, UTS, Sydney, Australia 4 SEMATECH, Austin, TX, 78741 5 College of Nanoscale Science and Engineering, University at Albany, Albany, NY, 12203
ABSTRACT This work demonstrates the application of a Markov Chain Monte Carlo (MCMC) approach to modeling X-ray reflectometry (XRR) data taken from a sub 10 nm Hafnium oxide film. We present here a comparison of two structural models for a 6 nm HfxOy atomic layer deposition (ALD) film on Si. Using the MCMC method and two distinct structural models, we show evidence of a thin interface between the HfxOy and Si layers with a density much higher than native SiO2. Results from genetic algorithm XRR analysis and thickness measurements using cross-sectional transmission electron microscopy are included for comparison. We also demonstrate that our interpretation of HfxOy thickness differs between the two structural models (i.e., total film thicknesses may be partially additive within each model). INTRODUCTION X-ray reflectometry (XRR) analysis measures thickness of thin film layers with contrasting electron density using interference phenomena observed in grazing, specular X-ray reflections [1,2]. Model and data fitting is required to extract structure information from XRR. Modeling consists of smooth, constant-electron-density layers which have two modeling parameters: thickness, t, and complex index of refraction, n. Parratt developed a recursion relation relating t and n for an arbitrary number of layers allowing XRR analysis for complex structural models [3]. This recursion-based modeling approach (known as the Parratt method) was later expanded to include film roughness by introducing a perturbation-based roughness term, σ, [4]. The XRR characterization provides theoretical, first-principles determination of thickness information [5]. However, the XRR model-data refinement requires robust, computationally intensive methods to overcome complex parameter interdependencies. Genetic algorithms (GAs) have been applied to XRR analysis, due to the fast and robust nature of GA optimization approaches [6]. This paper demonstrates the effectiveness of a Markov Chain Monte Carlo (MCMC) sampling approach for XRR refinement. The MCMC provides quantitative information on parameter standard uncertainty and, ultimately, structural model validity [7].
This work uses XRR with MCMC refinement to examine the thickness of an atomic layer deposition (ALD) HfxOy thin film with nominal thickness of 6 nm [8]. The film was deposited on a Si wafer for 65 cycles with a per cycle deposition rate of 0.088 ± 0.006 nm [9]. Two structural models were used to refine XRR d
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