1 - Erich Schmid Institute

A.6 Discussion of Possible Sources of Error
to take a closer look on the stresses in the thin film during the annealing process and the
actual cantilever experiment.
The film was annealed at 600 ◦ C to obtain a nearly stress-free state. On cooling to room
temperature, the thermal stress in the Ni film according to the coefficients of thermal
expansion (αSi = 2.6 × 10 −6 K −1 and αNi = 16 × 10 −6 K −1 ) 12, 13 should be 1330MP a,
which is significantly greater than the experimentally determined mean stress. Those high
stresses are reduced by plastic relaxation in the thin film, which leads to the determined
stress distribution.
However, during the fabrication of the cantilever and the subsequent gradual reduction
in the film thickness, the stress distribution in the thin film changes and additional plastic
deformation could be the result.
A closer look at the stress distribution of the relaxed cantilever shows that the maximum
stress of 620 ± 87MP a appears during the reduction of the Ni film thickness
when the majority of the thin film is removed (Fig.A.14). The minimum stress of about
−300±20MP a is found for a film thickness of about 650nm. Although the maximum and
minimum stresses that appear in the Ni film during the experiment are not negligible,
they are lower than the maximum stress in the initial system (792 ± 103MP a). Furthermore,
the calculated and the measured deflections of the second cantilever experiment,
in which the cantilever thickness is reduced bottom-up, would not correlate if notable
plastic relaxation occurred. This leads to the conclusion that a significant change in the
stress field due to plastic deformation does not take place during the experiments.
Figure A.14: Minimum and maximum stresses σf,min and σf,max (black lines) in the Ni film of the
relaxed cantilever, which occur during the top-down removal of the sublayers, as a function
of the cantilever thickness. The grey lines represent the upper and lower bound for the
minimum and maximum stresses calculated from the determined stress distribution in the
initial system plus/minus the standard deviation. The stresses in sublayer 1 (sl 1) are
not evaluated, because it is regarded as a composite material with one biaxial Young’s
modulus.
Finally, it should be noted that in critical cases, the choice of an adequate cantilever
thickness can be used to reduce the stresses in the thin film and avoid plastic relaxation.
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