Elastic properties of self-supported circular thin copper films calculated from equilibrium thermal vibration.

Thermomechanical vibration of ultrathin, self-supported copper films due to thermal fluctuations is studied via the molecular dynamics simulation at room temperature. The elastodynamic theory with pre-stress is adopted to extract the physical properties of the films by comparing with the molecular dynamics data. The edge-clamped circular films consist of several atomic layers of fcc copper with the [100] direction normal to the film surface. From the time-history trajectories of atoms and their Fourier frequency spectrums, it was found that the fundamental resonant frequency non-monotonically varies with the film thickness due to the existence of residual stress in the film. Multiple resonant modes are adopted for modulus calculation and residual stress determination. The value of Young's modulus increases with increasing thickness of the film and the residual stress decreases with increasing thickness. Thicker films exhibit less residual stress, indicating the equilibrium distance between copper atoms changes with the film thickness.