We present evidence for the cooling of normal metal phonons by electron tunneling in a Superconductor - Normal metal - Superconductor tunnel junction. The normal metal electron temperature is extracted by comparing the device current-voltage characteristics to the theoretical prediction. We use a quantitative model for the phonon cooling that includes the electron-phonon coupling in the normal metal and the Kapitza resistance between the substrate and the metal. It gives an excellent fit to the data and enables us to extract an effective phonon temperature in the normal metal.
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