A stiff thin film on a heated compliant substrate may buckle when the system is cooled due to
the thermal expansion mismatch between the film and substrate. Highly ordered and
disordered herringbone patterns (wavy structures) then emerge as the system continues to
cool. We have established an analytic approach to study one-dimensional, checkerboard,
and ordered herringbone buckling patterns. The analytical approach gives the buckle wave
length and amplitude in terms of the thin film and substrate elastic properties, thin film …