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 mm 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 w400
C.