Ultra-thin oxide films are of interest in energy conversion technologies such as low temperature solid oxide fuel cells and permeation membranes. Understanding their thermo-mechanical stability is an important problem. Edge clamped, self-supported thin film membranes show hierarchical wrinkles; with the largest wavelengths in the center, while smaller ones arise near the clamped boundary; correspondingly the largest strains, with tensile stress comparable to the residual stress, are in the vicinity of the clamped boundary. Our results can be understood by simple scaling arguments and are valid for membranes in the post-buckling regime far from threshold. We confirm the validity of our analysis by quantitative experimental comparison to self-supported, square micro-machined yttria-stabilized zirconia membranes of edge length 160 mu m fabricated by lithography. The modeling and experiments combined provide a foundation for designing failure resistant self-supported membranes of interest to energy conversion. We show this by utilizing such membranes to fabricate thin film solid oxide fuel cells and demonstrate power generation utilizing natural gas as fuel at similar to 400 degrees C. (c) 2012 Elsevier BM. All rights reserved.