Compressive Stress in Diamond Nanomembranes

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.¹ 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 and wrinklons 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. These deformations strongly affect the electrical properties of B-doped NCD NMs.² Therefore, one cannot disregard the influence of wrinkles when dealing with any type of device that is based on NMs.<br/><br/>In this work, finite element simulations of compressive stress relaxation under gravity in a diamond NM as it is released from a supporting substrate are presented. As NCD consists of hard diamond grains and soft grain boundaries, the Young's modulus and Poisson's ratio are not expected to be the same as in bulk diamond.³ To study the impact of elastic constants on wrinkling, calculations were made with different Young's moduli (<i>E</i> = 300, 600, 900, and 1200 GPa) and Poisson's ratios (<i>ν</i> = 0, 0.07, 0.14, and 0.21). The initial compressive stress of the NM was varied in the range from 0 Pa up to - 6 GPa. When a NCD thin film, which is 150 nm thick and has a compressive stress of up to −10⁴ Pa, is released from the substrate as the NCD membrane, it relaxes without forming wrinkles. Symmetrical wrinkles form when the membrane relaxes from −10⁵ Pa and higher compression. At absolute stresses larger than - 1 GPa the asymmetric wrinkling is dominant. The Young’s modulus and Poisson’s ratio does not have notable impact on the relaxed membrane shape as stress does. However, the Young’s modulus has higher impact on the relaxed membrane area and out-of-plane deformation range than Poisson’s ratio. The higher the Young’s modulus (or Poisson’s ratio), the smaller the area (and out-of-plane deformation range) of the nanomembrane is obtained after the compressive stress relaxation. Finally, the obtained results on wrinkling phenomena are explain through the system’s energy minimization.<br/><br/>[1] J.A. Rogers, <i>et al.</i>, Nature <b>477</b>, 45 (2011).<br/>[2] S. Drijkoningen, <i>et al.</i>, Scientific Reports <b>6</b>, 35667 (2016).<br/>[3] C.A. Klein and G.F. Cardinale, Diamond and Related Materials <b>2</b>, 918 (1993).