Interplay of Quantum Size Effect and Surface Electron Scattering in Conductivity of Thin Films
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We constructed the most general theory of the classical and quantum static electron transport for 3D films with randomly rough boundaries. The electron-surface interaction was included via approximation with mildly sloping asperities, when the rms height ξ of boundary defects is less than their mean length L. Then we analyzed influence of spatial quantization and electron-surface scattering on the film conductivity ⟨σ⟩ and their interference. Joint action of those factors leads to peculiarities (sharp dips) of ⟨σ⟩ versus the sample thickness d appearing at points where a new conducting electron channel opens. The dips have fundamental quantum origin and are caused by size quantization of electron-surface scattering rate. When studying ⟨σ⟩ versus the bulk mean free path l of electrons, we revealed that, as bulk collisions vanish (l → ∞), the quantum conductivity approaches finite residual value associated with electron-surface interaction. The residual conductivity was first shown to possess either quantum or exclusively classical origin depending on d, l, and the electron wavelength. On the basis of the investigations provided, the relation between quantum and classical effects in the film conductivity was clarified. The theoretical results were successfully tested against recent experimental data concerning the conductivity of ultrathin films.
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