High resolution spot profile analysis low energy electron diffraction (SPA-LEED) and variable temperature scanning tunneling microscopy (STM) have been used to observe the growth of Pb on the Pb/Si(111)-alpha root 3x root 3 phase, which is driven by quantum size effects (QSE). A change in the rotation of the Pb grown islands with respect to the Si substrate has been observed with increasing coverage theta. At lower coverage, separated two-step islands are grown and are aligned with the [1 (1) over bar0] axis of the substrate. With increasing coverage above 1.5 ML, of the islands coalesce and form a bilayer, with additional islands grown on top. The preferred Pb island orientation changes to 5.6 degrees with respect to the [1 (1) over bar0] direction. These changes at the metal/semiconductor buried interface are obtained both with SPA LEED and STM as changes to the period of the Moire pattern. The method of analysis of the corrugation period and rotation angle of the Moire pattern measured with diffraction and STM can be applied to obtain the structure of buried metal/substrate interfaces in other epitaxial systems.