Oscillating Cracks in Glassy Films on Silicon Substrates

An experimental study of cracks that develop during the annealing of hydrogen-rich amorphous silica films deposited on crystalline silicon substrates shows an interesting duality of behaviour. Cracks in films deposited on cubic (001) silicon surfaces tend to form in two principal directions, cube-edge directions such as [100] or diagonal directions [110] and, while the [100] cracks are straight, those at 45° in [110] directions have an exactly regular oscillating structure. Sections through the wafers show that the oscillating cracks have a complex three-dimensional structure that extends through the glassy film and into the underlying silicon substrate. While a complete theoretical treatment of the behaviour would be extremely complicated, a simple theory shows that an oscillating crack has a minimum energy per unit length for a particular wavelength and amplitude which depends upon the physical parameters of both film and substrate. When the energy at this minimum is compared with that of a straight crack, it is found that for certain parameter ranges it can be less than for a straight crack, so that the oscillating geometry is preferred. Because the elastic strain energy and surface energy of the crystalline substrate are anisotropic and the behaviour depends sensitively upon these parameters, it is not surprising that cracks in some directions are preferentially straight while those in other directions are oscillatory.