48
2 Methods for Investigating Electro-Chemo-Mechanical …
gauge cement via a thin polyimide film (7.5 µm) for electric isolation. The working
electrode is encapsulated into a Teflon holder. The electrochemical cell is composed
of a Teflon cylinder into which the working electrode assembly is clamped from one
end.
This working electrode assembly has been employed for differential surface
stress measurements of a polycrystalline Au foil electrode in 1 M NaClO 4 solutions
containing 10
−4 –10
−2 M KI [17]. The surface stress maximum of the Au electrode
in 1 M NaClO 4 solution without KI appeared at E max = 0.13 and 0.02 V (SHE) in the
anodic and cathodic potential scans (20 mV s
−1 ), respectively. On the other hand, the
mean value of E max shifted toward negative direction by 0.64 V due to an addition of
3 × 10
−3 M KI in the solution, indicating a strong contact adsorption of iodide ions.
However, Seo et al. in this paper [17] as well as other their papers [9, 10, 14–16]
neglected the term of
∂q
∂ε
as compared to the surface charge density q and regarded as
E max = E pzc . Afterward, Seo et al. [18, 19] investigated the relationship between
∂g
∂E
and q by using a cantilever bending method (see Sect. 2.3 of this chapter) and found
a significant deviation of
∂g
∂E
from q at potentials more positive than E pzc .
2.3 Cantilever Bending Method for Measurement
of Changes in Surface Stress
2.3.1 Relationship between Surface Stress and Curvature
of Cantilever
Surface stress g can be calculated from a cantilever bending (bending beam, wafer
curvature, etc.) using elasticity theory. Figure 2.8 shows schematically the bending
of a rectangular substrate (the both edges are not clamped) with a thickness of d s
when a thin film with a thickness of d f is uniformly deposited on the top side of the
substrate. In the case where the internal compressive stress (σ f < 0) is developed
within the film, the substrate is convexly bended as shown in Fig. 2.8a. Similarly,
in the case where the internal tensile stress (σ f > 0) is developed within the film,
the substrate is concavely bended as shown in Fig. 2.8b. By convention, the sign of
curvature κ or curvature radius R is minus for convex bending (compressive stress)
and plus for concave bending (tensile stress) in accordance with the sign of stress.
In the mechanical equilibrium of the bending, the compressive forces or tensile
forces developed within the film are balanced by the tensile or compressive forces
in the substrate; i.e., the net force F vanishes and simultaneously the net bending
moment M also vanishes on the film-substrate cross section. Therefore, the following
relationships hold [1]:
F = ∫ σ dA = 0,
(2.10)
2 Methods for Investigating Electro-Chemo-Mechanical …
gauge cement via a thin polyimide film (7.5 µm) for electric isolation. The working
electrode is encapsulated into a Teflon holder. The electrochemical cell is composed
of a Teflon cylinder into which the working electrode assembly is clamped from one
end.
This working electrode assembly has been employed for differential surface
stress measurements of a polycrystalline Au foil electrode in 1 M NaClO 4 solutions
containing 10
−4 –10
−2 M KI [17]. The surface stress maximum of the Au electrode
in 1 M NaClO 4 solution without KI appeared at E max = 0.13 and 0.02 V (SHE) in the
anodic and cathodic potential scans (20 mV s
−1 ), respectively. On the other hand, the
mean value of E max shifted toward negative direction by 0.64 V due to an addition of
3 × 10
−3 M KI in the solution, indicating a strong contact adsorption of iodide ions.
However, Seo et al. in this paper [17] as well as other their papers [9, 10, 14–16]
neglected the term of
∂q
∂ε
as compared to the surface charge density q and regarded as
E max = E pzc . Afterward, Seo et al. [18, 19] investigated the relationship between
∂g
∂E
and q by using a cantilever bending method (see Sect. 2.3 of this chapter) and found
a significant deviation of
∂g
∂E
from q at potentials more positive than E pzc .
2.3 Cantilever Bending Method for Measurement
of Changes in Surface Stress
2.3.1 Relationship between Surface Stress and Curvature
of Cantilever
Surface stress g can be calculated from a cantilever bending (bending beam, wafer
curvature, etc.) using elasticity theory. Figure 2.8 shows schematically the bending
of a rectangular substrate (the both edges are not clamped) with a thickness of d s
when a thin film with a thickness of d f is uniformly deposited on the top side of the
substrate. In the case where the internal compressive stress (σ f < 0) is developed
within the film, the substrate is convexly bended as shown in Fig. 2.8a. Similarly,
in the case where the internal tensile stress (σ f > 0) is developed within the film,
the substrate is concavely bended as shown in Fig. 2.8b. By convention, the sign of
curvature κ or curvature radius R is minus for convex bending (compressive stress)
and plus for concave bending (tensile stress) in accordance with the sign of stress.
In the mechanical equilibrium of the bending, the compressive forces or tensile
forces developed within the film are balanced by the tensile or compressive forces
in the substrate; i.e., the net force F vanishes and simultaneously the net bending
moment M also vanishes on the film-substrate cross section. Therefore, the following
relationships hold [1]:
F = ∫ σ dA = 0,
(2.10)