Exploring the limits of sensitivity for strain gauges of graphene and hexagonal boron nitride decorated with metallic nanoislands

The purpose of this work is to clarify the mechanism of piezoresistance in a class of ultra-sensitive strain gauges based on metallic films on 2D substrates ("2D/M" films). The metals used are gold or palladium deposited as ultrathin films (≤16 nm). These films transition from a regime of subcontiguous growth to a percolated morphology with increasing nominal thickness. The 2D substrates are either single-layer graphene or hexagonal boron nitride (hBN). By using either a conductor (graphene) or an insulator (hBN), it is possible to de-couple the relative contributions of the metal and the 2D substrate from the overall piezoresistance of the composite structure. Here, we use a combination of measurements including electron microscopy, automated image analysis, temperature-dependent conductivity, and measurements of gauge factor of the films as they are bent over a 1 μm step edge (0.0001% or 1 ppm). Our observations are enumerated as follows: (1) of the four permutations of metal and 2D substrate, all combinations except hBN/Au are able to resolve 1 ppm strain (considered extraordinary for strain gauges) at some threshold thickness of metal; (2) for non-contiguous (i.e., unpercolated) films of metal on hBN, changes in resistance for these small step strains cannot be detected; (3) for percolated films on hBN, changes in resistance upon strain can be resolved only for palladium and not for gold; (4) graphene does not exhibit detectable changes in resistance when subjected to step strains of either 1 or 10 ppm, but does so upon the deposition of any amount of gold or palladium, even for nominal thicknesses below the threshold for percolation. Our observations reveal unexpected complexity in the properties of these simple composite materials, and ways in which these materials might be combined to exhibit even greater sensitivity.