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Thermally induced film wrinkling is a fabrication and reliability challenge for thin-film stacks consisting of a compliant film capped by a stiffer film. The current understanding of film wrinkling is largely restricted to thin-film stacks on blanket substrates. An understanding of wrinkling in thin-film stacks on patterned substrates is of greater practical relevance to the microelectronic industry. Toward this goal, a numerical technique based on a spectral method is employed to simulate wrinkling in a stiff-film/compliant-film system on a rigid patterned substrate. A coupling term in the Fourier space is introduced to capture the interaction between wrinkling amplitudes above patterned regions and surrounding regions. This coupling in wrinkling amplitudes suppresses wrinkling above patterned regions. Wrinkling amplitudes for a thin-film stack on a patterned substrate are shown to be dependent on the size of the patterns and their relative spacing.
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