A unified model for determining fracture strain of metal films on flexible substrates

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Failure strain determination of polymer-supported thin films is a key for the design of the flexible devices.A theoretical model R/R0=(L/L0)2 (R,L are the electrical resistance and the length of the stretched film,respectively.R0,L0 are the corresponding initial values.) has been widely used to determine the fracture strain of thin films on flexible substrates.However,this equation loses its function in some special cases.Here,a simple and universal theoretical model was proposed to determine the fracture strain of metal thin films on flexible substrates in more generally situations.With this model,we investigated the thickness-dependent failure strains of Cu-5 at.% Al films with thickness of 10 nm,200 nm,1000 nm,and Ti films with thickness of 50 nm,100 nm,300 nm.This model was also employed to study the published data available.The results showed that the new model provided a fairly good prediction of the failure strains of different films.
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