In this study, the amorphous-phase roughening transition thickness has been determined as a function of process variables in plasma-enhanced chemical vapor deposition (PECVD) of hydrogenated amorphous silicon-germanium alloys (a-Si1-xGex:H). Among the process parameters varied include the H2-dilution gas flow ratio, the alloying flow ratio, the electrode configuration (anode vs. cathode), and the He-dilution ratio. One clear feature of this study is a maximum in the amorphous roughening transition thickness (and hence surface stability) at a H2-dilution ratio just below the transition from amorphous to mixed-phase (amorphous+ microcrystalline) (a+μc) growth. A second feature for high Ge content films is a significant increase in the roughening transition thickness for cathode PECVD (with a self-bias of ∼ -20 V) relative to anode PECVD. Additional features of interest involve suppression of the transition to (a+μc) for (i) alloying with Ge, (ii) biasing the substrate cathodic, and (iii) diluting the gas with He. The close correlation of high surface stability with enhanced short-range order and overall electronic performance has led to a simple model for the transition in terms of a competition between roughening due to the atomic size and smoothening due to precursor surface diffusion. It is proposed that diffusing precursors are immobilized by surface defects (or by other diffusing precursors), and the pre-existing (or resulting) defects are ultimately incorporated in the bulk.