Dynamic Stress Analysis at Solid Electrodes
Authors: Stafford Gery R. , Bertocci Ugo 
Published: February 2020

Wafer curvature and cantilever bending techniques have been used by the electrochemical community to examine stress development during electrochemical processing. Surface stress changes as low as 10−3 N/m can typically be resolved from cantilever electrodes immersed in solution and under potential control. Such resolution makes this measurement useful for examining virtually all aspects of electrochemistry; i.e., electrocapillarity, adsorption processes, underpotential deposition, electrodeposition, battery reactions, and metal hydride formation. Often these processes occur either simultaneously or in rapid succession and we are often limited to measuring the influence of the dominant process in the time-scale of the experiment. Electrochemical impedance spectroscopy (EIS) is a technique in which one measures the impedance of an electrochemical system over a range of frequencies, revealing information about the reaction mechanisms: different reaction steps will dominate at frequencies dictated by their relaxation times. Whereas traditional EIS determines the transfer function of the current in response to potential modulation, Dynamic Stress Analysis (DSA) examines the transfer function of the stress (as measured from cantilever curvature) to the same potential modulation. This will provide us with the time constants for the stress response that might enable us to directly link the stress to specific electrochemical phenomena.
We first use DSA to examine the electrocapillarity (surface stress vs. charge density) behavior of (111)-textured Au and Pt cantilever electrodes in 0.1 M HClO4 electrolyte. Our measurements confirm that a direct relationship between the surface stress and the charge density exists over a wide range of frequencies and potentials. We define a general stress-charge coefficient
ς
=
jωYsZ

e
that can be obtained from experimental values of the electrochemical impedance (
Ze

) and the stress admittance (
Ys

), where
j
and
ω
have their usual meaning. For both Au and Pt in the double layer region, the surface stress was found to be 180° out of phase with respect to the charge density, yielding
ς
 of -2.0 V and -0.7 V, respectively. These values are in agreement with first-principles calculations that appear in the literature.1, 2 In the hydrogen adsorption region,

stress and charge are in phase (
ς

is positive; i.e., negative charge induces compressive stress). This compressive stress response for H adsorption is contrary to charge distribution models for adsorbate-induced surface stress but supports first-principles calculations for hydrogen adsorption onto Pt (111).3, 4

We also apply DSA to electrodeposition, making use of separate stress-charge coefficients for electrocapillarity and metal deposition. Since these stress-generating mechanisms have dramatically different frequency dependency, Cu deposition is a nice demonstration that highlights the attributes of DSA; i.e., using frequency to separate the various stress contributions.
1. J.-M. Albina, C. Elsasser, J. Weissmüller, P. Gumbsch and Y. Umeno, Phys. Rev. B
85, 125118 (2012).
2. Y. Umeno, C. Elsässer, B. Meyer, P. Gumbsch, M. Nothacker, J. Weissmüller and F. Evers, EPL
78, 13001 (2007).
3. P. J. Feibelman, Phys. Rev. B
56, 2175 (1997).
4. H. Ibach, J. Vac. Sci. Technol.
A12, 2240 (1994).