On the dependence of surface undulation on film thickness

• Surface undulation of a thin film is energetically favourable.
• There is a critical wavelength determined by the minimum strain energy density.
• The critical wavelength is thickness-dependent.
• Surface undulation does not bring about noticeable residual stress relaxation.

This paper investigates the dependence of surface undulation on a film thickness considerably greater than the critical value of a thin film system. It considers that surface tension and residual stress are the main cause of surface undulation. The study found that there is a critical undulation wavelength that minimizes the free energy of a thin film system, that this critical wavelength depends on the film thickness, and the effect of undulation amplitude is insignificant. The research also found that the surface undulation has a negligible influence on the residual stresses in the thin film system.