In this paper, phonon-mediated superconductivity has been investigated in MgB2 bulk structure and bilayer thin film by using first-principles calculations. The electronic band structure, total and partial density of states (DOS and PDOS), phonon dispersion, isotropic Eliashberg function α2F(ω), and electron–phonon coupling have been calculated within the framework of density functional theory (DFT). Our results indicate that holes at the top of boron σ bands mainly and holes in the boron π band partially contribute to formation of coupled holes in superconductivity state. The density of states at the Fermi energy level is increased for MgB2 bilayer with respect to its bulk structure. According to the phonon dispersion and Eliashberg function curves, coupling considerably occurs between holes at the top of the boron σ band by means of optical phonon mode for both structures. This phonon mode has the E2g symmetry at the Г point. We obtain electron–phonon coupling constants of 0.74 and 0.91 for bulk and bilayer structures, respectively. By using the Allen–Dynes formula, we estimate superconducting transition temperature TC of 40 K for bulk and 48 K for the thin film.

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