A model of electron gas scattering at surface inhomogeneities was developed and applied to describe a surface roughness influence on the electrical resistivity of thin metallic films. The model is developed to be simple enough for fast calculations without detailed investigation of surface topology. The film’s shape is assumed to be described by the average thickness, the surface rms, and the correlation length. The scattering mechanism corresponds to electrical potential changes caused by inhomogeneities. It was found that the electrical resistivity of thin films increases with the increase of the roughness of surface for films of any thickness, whereas the law of this effect depends on film’s thickness. Basing on the developed model, formulas for the electrical resistivity as a function of the roughness rms and the correlation length in cases of thick enough, thin, and extremely thin films have been obtained and discussed with comparison to other models already in literature and experimental data.

中文翻译：

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快速计算具有粗糙表面的金属薄膜电阻率的理论模型

建立了在表面不均匀处电子气散射的模型，并将其用于描述表面粗糙度对金属薄膜电阻率的影响。该模型开发得足够简单，可以快速进行计算，而无需详细研究表面拓扑。假定膜的形状由平均厚度，表面均方根值和相关长度来描述。散射机制对应于由不均匀性引起的电势变化。已经发现，对于任何厚度的膜，薄膜的电阻率都随着表面粗糙度的增加而增加，而这种作用的规律取决于膜的厚度。根据开发的模型，