6.5 Criterion for Stress Generation by Nelson and Oriani
163
Fig. 6.5 Evolution of the cell voltage V and of the curvature κ of the cantilever electrode during
anodic oxidation of a sputter-deposited Ti thin film at a constant current density of 4 mA cm −2 in
1.0 M H 2 SO 4 solution, exhibiting three distinct stages (I), (II), and (III) [20]. Reproduced from [20]
with permission from The Electrochemical Society
in Sect. 2.3 of Chap. 2, stress variations can be measured from the changes in κ.
Three distinct stages (I), (II), and (III) can be observed from the changes in V and κ.
At the first stage (I) in Fig. 6.5, κ changes rapidly toward compressive direction at
the very beginning of anodic oxidation, accompanying the initial jump of cell voltage,
followed by the slight changes of κ toward compressive direction in the cell voltage
region (up to 7 V) where the cell voltage rises at a constant rate. The stress·thickness
product (σ f · d f ) calculated from κ at 5 V is −4.3 J m
−2 . The separate experiment
of the current interruption from 5 V to an open-circuit potential showed the change of
(σ f · d f ) from −4.3 to 0.06 J m
−2 [20]. The detailed analysis [20] of the curvature
data at this stage indicated that the average stress of the film at 5 V is −290 ±
50 MPa which consists of a reversible, field-induced, compressive electrostriction
stress of −370 ± 50 MPa and of an irreversible, growth-induced, tensile stress of 79
± 20 MPa. The sign of the tensile stress for the irreversible film growth is consistent
with the results obtained by an anodic potential scanning or cyclic voltammetry, but
it is opposite to the results obtained by a potentiostatic anodic oxidation for 1 h in
pH 8.4 borate solution [19] or by scanning repeatedly the cell voltage from 1 to 9 V
in 1.0 M H 2 SO 4 solution [29].
163
Fig. 6.5 Evolution of the cell voltage V and of the curvature κ of the cantilever electrode during
anodic oxidation of a sputter-deposited Ti thin film at a constant current density of 4 mA cm −2 in
1.0 M H 2 SO 4 solution, exhibiting three distinct stages (I), (II), and (III) [20]. Reproduced from [20]
with permission from The Electrochemical Society
in Sect. 2.3 of Chap. 2, stress variations can be measured from the changes in κ.
Three distinct stages (I), (II), and (III) can be observed from the changes in V and κ.
At the first stage (I) in Fig. 6.5, κ changes rapidly toward compressive direction at
the very beginning of anodic oxidation, accompanying the initial jump of cell voltage,
followed by the slight changes of κ toward compressive direction in the cell voltage
region (up to 7 V) where the cell voltage rises at a constant rate. The stress·thickness
product (σ f · d f ) calculated from κ at 5 V is −4.3 J m
−2 . The separate experiment
of the current interruption from 5 V to an open-circuit potential showed the change of
(σ f · d f ) from −4.3 to 0.06 J m
−2 [20]. The detailed analysis [20] of the curvature
data at this stage indicated that the average stress of the film at 5 V is −290 ±
50 MPa which consists of a reversible, field-induced, compressive electrostriction
stress of −370 ± 50 MPa and of an irreversible, growth-induced, tensile stress of 79
± 20 MPa. The sign of the tensile stress for the irreversible film growth is consistent
with the results obtained by an anodic potential scanning or cyclic voltammetry, but
it is opposite to the results obtained by a potentiostatic anodic oxidation for 1 h in
pH 8.4 borate solution [19] or by scanning repeatedly the cell voltage from 1 to 9 V
in 1.0 M H 2 SO 4 solution [29].