Abstract
Scanning probe microscopy is a fundamental technique for the analysis of surfaces. In the present work, the interface statistics of surfaces scanned with a probe tip is analyzed for both in silico and experimental systems that, in principle, do not belong to the prominent Kardar–Parisi–Zhang universality class. We observe that some features such as height, local roughness and extremal height distributions of scanned surfaces quantitatively agree with the KPZ class with good accuracy. The underlying mechanism behind this artifactual KPZ class is the finite size of the probe tip, which does not permit a full resolution of neither deep valleys nor sloping borders of plateaus. The net result is a scanned profile laterally thicker and higher than the original one implying an excess growth, a major characteristic of the KPZ universality class. Our results are of relevance whenever either the normal or lateral characteristic lengths of the surface are comparable with those of the probe tip. Thus our finds can be relevant, for example, in experiments where sufficiently long growth times cannot be achieved or in mounded surfaces with high aspect ratio.
Highlights
Universality beyond scale invariance and critical exponents is well established in both equilibrium [1, 2] and nonequilibrium [3] critical systems
Motivated by the experimental observations of KPZ distributions and the well known smoothing effect inherent to the scanning probe microscopy (SPM) technique [34], we investigated the role played by a probe tip in the statistics of surfaces
Profiles were acquired using atomic force microscopic (AFM) under both contact and tap modes and using scanning electron microscopy (SEM), the last one rendering surfaces rid of tip effects
Summary
Universality beyond scale invariance and critical exponents is well established in both equilibrium [1, 2] and nonequilibrium [3] critical systems. Despite of the lack of rigorous results in d = 2 + 1, a meticulous analysis of several models [16,17,18], accepted as belonging to the KPZ class, and the numerical integration of the KPZ equation itself [16] strongly indicate that the ansatz given by Eq (2) holds for the threedimensional case with the corresponding growth exponent β = 0.241 and a new universal stochastic quantity χ with mean χ −0.83, variance χ2 c 0.237, skewness S =. We observe that the scaled KPZ distributions can be found in the scanned surfaces when the original ones do not belong to the KPZ class.
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