Chalcogenide phase change materials (PCMs), such as Ge-Sb-Te alloys, have outstanding properties, which has led to their successful use for a long time in optical memories (DVDs) and, more recently, in Phase Change Random Access Memories. The latter are the most promising candidate to replace the current FLASH memories. The main feature of PCMs are fast and reversible phase transformations between crystalline and amorphous states with very different transport and optical properties. Controlling their crystallization, however, is a challenge. In the present work, a new picture of the prototypical GeTe and Ge2Sb2Te5 thin film crystallization is provided from optical reflectivity, resistivity and Scanning Transmission Electron Microscopy studies of 100 nm thick films. The crystallization temperature Tx significantly varies as a function of surface oxidation. Whereas Ge2Sb2Te5 has been, and is still, the subject of many publications, the present results reveal that its crystallization mechanism was not fully understood. Heterogeneous crystallization of Ge2Sb2Te5 at the upper film surface, reported so far, results from a surface alteration. Adequately protected Ge2Sb2Te5 and GeTe crystallize through nucleation inside the amorphous phase. Preventing surface alteration due to oxidation as demonstrated in the present study, through suitable capping layer deposition methods, yields a spectacular increase in Tx above the values that have been reported in the literature. The present study demonstrates that interface engineering allows one to select the crystallization mechanism, and hence control the stability of the amorphous phase in PCMs.