Atomic Force Microscopy Nanomechanics of Hard Nanometer-Thick Films on Soft Substrates: Insights into Stretchable Conductors

Abstract

The nanomechanical properties of ultrathin and nanostructured films of rigid electronic materials on soft substrates are of crucial relevance to realize materials and devices for stretchable electronics. Of particular interest are bending deformations in buckled nanometer-thick films or patterned networks of rigid materials as they can be exploited to compensate for the missing tensile elasticity. Here, we perform atomic force microscopy indentation experiments and electrical measurements to characterize the nanomechanics of ultrathin gold films on a polydimethylsiloxane (PDMS) elastomer. The measured force-indentation data can be analyzed in terms of a simple analytical model describing a bending plate on a semi-infinite soft substrate. The resulting method enables us to quantify the local Young's modulus of elasticity of the nanometer-thick film. Systematic variation of the gold layer thickness reveals the presence of a diffuse interface between the metal film and the elastomer substrate that does not contribute to the bending stiffness. The effect is associated with gold clusters that penetrate the silicone and are not directly connected to the ultrathin film. Only above a critical layer thickness, percolation of the metallic thin film happens, causing a linear increase in bending stiffness and electrical conductivity.

Figure 1

Nanomechanical and electrical characterization of thin gold films on the elastomeric substrate. (a) Scheme of the AFM experimental setup. (b) Force–indentation curves on thin metal films of thickness 38 nm (Au, red) and 57 nm (Ti/Au, blue), compared to the pure PDMS substrate (black). (c) Height and stiffness map (128 × 128 pixel) of Au deposited on PDMS. (d) Force–indentation and conductive AFM curves of PDMS/Ti/Au (40 nm thickness) with different force limits.

Figure 2

Indentation models for hard films on soft substrates: (a) Scheme showing the main parameters. On the right, the main equations of the model in the case of indentation of a uniform layer bonded to an elastic half-space are reported. (b) Calculated force–indentation curves according to the analytical solution (blue) and its linearized version (red). The two curves start to diverge significantly at indentations exceeding 10 μm. The inset shows the calculated indentation curves in the experimental range of indentation. The black data correspond to the result of the FE numerical simulations.

Figure 3

Experimental validation of the indentation model: (a) Force–indentation curves acquired with three different AFM tips on both pure PDMS (warm colors) and PDMS/Ti/Au (blue colors). (b) Stiffness dependence on the thin film thickness. Note that the experimental data shown in Figure 3b correspond to the average of the stiffness of the loading and unloading curves. This avoids possible systematical errors due to thermal drift during the AFM acquisition. (c) Comparison between the experimental indentation curves and the model predictions for PDMS/Ti/Au samples of different thicknesses (h = 21 nm, h = 38 nm, and h = 53 nm).

Figure 4

Relationship between gold layer thickness and electrical properties: (a-c) Noncontact mode AFM images acquired on (a) pure PDMS and PDMS/Au with gold film thickness (b) below and (c) above the threshold value h₀^mec. (d) Force–indentation curves of PDMS/Au with gold film thickness above and below the threshold value h₀^mec. (e) Sheet resistance of samples with different film thicknesses. (f) Qualitative representation of the effective thickness interpretation.