We report a systematic increase of the superconducting transition temperature T c with a biaxial tensile strain in MgB 2 films to well beyond the bulk value. The tensile strain increases with the MgB 2 film thickness, caused primarily by the coalescence of initially nucleated discrete islands (the Volmer-Weber growth mode.) The T c increase was observed in epitaxial films on SiC and sapphire substrates, although the T c values were different for the two substrates due to different lattice

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... ters and thermal expansion coefficients. We identified, by first-principles calculations, the underlying mechanism for the T c increase to be the softening of the bond-stretching E 2g phonon mode, and we confirmed this conclusion by Raman scattering measurements. The result suggests that the E 2g phonon softening is a possible avenue to achieve even higher T c in MgB 2 -related material systems.