We study amorphous silicon-germanium (a-SiGe:H) as intrinsic absorber material for thin-film silicon-based triple and quadruple junction solar cells. First, we present the development of a-SiGe:H single junction devices, in particular the Ge-content grading in the absorber layer, the influence of the Ge-content on electrical properties and (infra)red-response, and the influence of using different types of players. We subsequently show the incorporation of optimized single-junction devices in triple junction cells and discuss the interplay between Ge-content and intermediate reflector thickness. For triple junction devices with amorphous silicon (a-Si:H) top cells, a-SiGe:H middle cells and microcrystalline silicion (mu c-Si:H) bottom cells, we obtained an initial efficiency of 13.6% and an efficiency of 11.3% after light-soaking. We also present a quadruple junction device with an a-Si:H top cell, a low Ge-content a-SiGe:H second cell, and mu c-Si:H third and bottom cells. In this device configuration, we obtained an open-circuit voltage as high as 2.57 V. The performance of these cells was limited by not yet optimized current matching, leading nevertheless to an initial efficiency of 10.1%. A brief roadmap towards quadruple-junction devices with stabilized efficiencies of 14% is also outlined. (C) 2014 Elsevier B.V. All rights reserved.