A novel method to predict nanofilm morphology on arbitrary-topographical substrate

As physical properties of nanofilms are strongly influenced by their adhered substrates and presented morphologies, it is of vital importance to determine their attaching morphologies on substrates. However, the complex topography of substrate in the practical applications hinders the prediction of attached nanofilm morphology. Previous theoretical methods fail to analyze the complex topography, and molecular dynamics (MD) simulations are limited to small time and size scales. In order to predict the morphology of a nanofilm with an arbitrary size on a substrate with an arbitrary topography, a novel universal method is proposed by combining the mechanical analysis, discrete cosine transform, and multi-resolution analysis together, named multi-resolution discrete cosine transform (MRDCT) method. In this method, the attaching analysis for a complex-topographical substrate is transformed level by level into a sequence of simple mechanical analyses for a 2D-cosine-topographical substrate, of which a semi-analytical model is derived in advance based on the principle of minimum potential energy. Taking the advantages of the pre-derived mechanical model and the multi-level analysis, the MRDCT method has an extremely high efficiency, only about 10⁻⁴ of time cost of MD simulations, and moreover, it is not limited by the size scale of nanofilms. The results from both MD simulations and experiments highlight the competency of this method for various complex-topographical substrates. Furthermore, a general conformation criterion in terms of the substrate roughness is derived analytically based on the MRDCT method to assess whether the substrate can be fully conformed by the nanofilm. The proposed MRDCT method can not only be used in the mechanical analysis of film/substrate systems but also provide a new paradigm to solve other complex mechanical problems.