Simulating Bulge Test of Wrinkled Diamond Membranes

Nanomembranes (NMs) are very thin (≤ 500 nm) and have very high aspect ratios of thickness to lateral dimension (≥ 10⁴). This makes them extremely flexible due to the linear decrease of bending strain with thickness. At the extreme thinness, materials fold much easier. When nanocrystalline diamond (NCD) thin films are grown on substrates, which have a higher thermal expansion coefficient than diamond, unavoidably, compressive stress is generated. When a NCD NM is released from such substrate a pattern of wrinkles evolves. The out-of-plane deformation is associated with the onset of an elastic instability, where the total energy is best minimized by the film bending rather than straining in-plane. Membranes are used to determine the mechanical properties of thin film materials by performing the bulge test experiment. The bulge test technique and existing models associated with it are well-known and widly used. However, the existing analytical models cannot accurately predict the behaviour of membranes that are wrinkled due to compressive in-plane stress. The formation of wrinkles affects the membrane’s response to the load, and thus, one cannot disregard their presence and use the existing models.<br/>In this work, we present finite element simulations of compressive stress relaxation in a diamond NM as it is released from a supporting substrate. After the relaxation, the bulge test experiment simulation is performed on wrinkled diamond NM of various thickness (50 to 500 nm) and dimensions (0.1 to 10 mm). The results are compared with available experimental data. To study the impact of elastic constants on the bulge test, the calculations were made with different Young's moduli (150 – 1200 GPa) and Poisson's ratios (0.00 – 0.21). The compressive stress within the membranes was varied in the range from −10 kPa up to −5 GPa, and the bulging pressure was varied from 0 to 50 mbar. The simulation results indicate that the sensitivity of the membrane to the load increases with increasing size of a membrane or decreasing the in-plane stress, Young’s modulus, Poisson’s ratio or membrane thickness. The same behaviour is observed experimentally. We demonstrate that the bulge test is not valid for Young’s modulus determination on large membranes if they are buckled and wrinkled due to compressive stress. The Young’s modulus is underestimated, the higher the stress, the larger the discrepancy. Finally, we derive an empirical equation that relates the wrinkled membrane response to the load as a function of elastic constants, membrane dimensions and compressive stress.