Resistive-nanoindentation on gold: Experiments and modeling of the electrical contact resistance

Abstract

This paper reports the experimental, analytical and numerical study of resistive-nanoindentation tests performed on gold samples (bulk and thin film). First the relevant contributions to electrical contact resistance are discussed and analytically described. A brief comparison of tests performed on gold and on natively-oxidized metals highlights the high reproducibility and the voltage-independence of experiments on gold (thanks to its oxide-free surface). Then the evolution of contact resistance during nanoindentation is fully explained in terms of electronic transport regimes: starting from tunneling, electronic transport is then driven by ballistic conduction before ending with pure diffusive conduction. The corresponding analytical expressions, as well as their validity domains, are determined and compared with experimental data, showing excellent agreement. From there, focus is made on the diffusive regime.Resistive-nanoindentation outputs are fully described by analytical and finite-element modeling. The developed numerical framework allows a better understanding of the main parameters: it first assesses the technique capabilities (validity domains, sensitivity to tip defect, sensitivity to rheology, effect of an oxide layer,…), but it also validates the different assumptions made on current line distribution. Finally it is shown that a simple calibration procedure allows a well-resolved monitoring of contact area during resistive-nanoindentation performed on samples with complex rheologies (ductile thin film on elastic substrate).Comparison to analytical and numerical approaches highlights the strength of resistivenanoindentation for continuous area monitoring.

Understanding Nanoscale Plasticity by Quantitative In Situ Conductive Nanoindentation

“…Reproduced with permission. [217] Copyright 2019, AIP Publishing LLC. Equation ( 39) is valid only for Γ values between 0.0483 and 0.134, i.e., in the applied load range 1.2-5.2 N. Using Equation (39), the H (¼ P A c ) was calculated (see Figure 9d).…”

“… for the BDD tip, and is the rounded apex height of the tip. In a recent article by Volpi et al, the A and B constant were determined (245, 2.52 × 10 5 , respectively) [ 217 ] using R contact versus Because of the h c term involved in the equation, it is possible to monitor A c by increasing h continuously (because the calibration step relates R contact and h c ). In general, in the case of soft thin films on stiff substrates, the contact area is determined using the Fredholm integral [ 220–222 ] (or finite element model (FEM) studies) coupled with a postmortem AFM scan of the residual indent at a given h .…”

“…Very recently, Volpi and colleagues [ 217 ] reported the results of experimental, analytical, and numerical studies of contact resistance on (100) Au bulk and polycrystalline films using custom‐made resistive nanoindentation using a BDD tip (0.2–2 Ω cm) to understand the evolution of contact resistance at different regimes, the effect of surface oxidation (on Cu and Al), surface rheology effects, etc. As we have already discussed in the previous section, the total resistance includes the sum of the resistance of the setup, sample, tip, and interface.…”

“…Before the surface is detected by the indenter tip (i.e., before the tip–sample contact, 2–3 nm above the surface), the flow of electrons can take place from the tip to the sample (because a V is given to the sample) through tunneling phenomena. The corresponding tunneling resistance can be obtained bywhere is the quasi‐static penetration depth, is constant (1 × 10 14 in Volpi et al [ 217 ] experiment), , where is the barrier height for the electrons to cross and is the RMS tip oscillation (0.65 nm). The tunneling barrier height can be estimated by subtracting the applied bias and negative electron affinity of diamond (0.5 eV) [ 219 ] to the bandgap of diamond (5.5 eV).…”

Development of a multifunctional nanoindenter integrated in-situ Scanning Electron Microscope - application to the monitoring of piezoresponse and electro-mechanical failures

“…Beyond the instrumental development, a challenging step of this electro-mechanical coupling remains the quantitative processing of raw data [26,30,34,35]. As already stated, the real-time imaging of nanoindentation tests has been widely reported, but only few attempts have been 5 made to combine electrical measurements and real-time observations in-situ SEM: for the electro-mechanical characterization of graphene in a dedicated device (nanoindenter was then used for mechanical actuation only) [36], for post-mortem observations of indentation imprints [37] or for the local characterization of multi-phased alloys [38].…”