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Superconducting tunnel junctions (STJ), with a buffer layer between the silicon substrate and junction, are being developed for use as high-resolution X-ray detectors. Aluminum-oxide (Al/sub 2/O/sub 3/) is employed as the buffer layer in order to suppress the phonon mediated background from the Si substrate. The extent of phonon insulation was studied by measuring the X-ray spectra of STJs as a function of buffer layer thickness. The phonon insulation ability of Al/sub 2/O/sub 3/ was compared to that of magnesium-oxide. The Al/sub 2/O/sub 3/ layer should be a good phonon insulator, with the ability to suppress phonons with a single buffer layer.