Reduced buckling in one dimension versus two dimensions of a compressively strained film on a compliant substrate

Compliant substrates are useful for manipulating the strain state of thin films. However the compliant layer may permit undesirable roughening (buckling) of a compressively strained film. In this work, we quantitatively compare two-dimensional and one-dimensional buckling in thin silicon-germanium films under biaxial and uniaxial compressive stresses, respectively. For the same strain level, films with one-dimensional stress and thus one-dimensional buckling exhibit slower buckling and lower final steady state buckling amplitude, which makes them technologically advantageous compared to biaxially strained films, which exhibit two-dimensional buckling. The results are explained through modeling.