1 - Erich Schmid Institute

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A A Direct Method of Determining Complex Depth Profiles of Residual Stresses
A.6 Discussion of Possible Sources of Error
A.6.1 Systematic and Statistical Errors
Systematic errors that can be caused by insufficient calibration of the SEM and statistical
errors that are caused by inaccurate measurements or inappropriate choice of Young’s
moduli influence the accuracy of the result. In the present example, the systematic errors
are neglected because the SEM was calibrated well and therefore, the statistical errors
are dominant. For the calculation of errors of the stress distribution in the straightened
cantilever and the initial system, the following values for the standard deviations ∆X of
the input parameters X are assumed: ∆t [1−8] = 15nm for the thickness of the individual
sublayers; ∆t [0] = 150nm for the thickness of the substrate; ∆δ [0−8] = 10nm for the
measured deflections; ∆lA = 200nm and ∆lB = 300nm for the lengths of sections A and
B; ∆E [0] = 18GP a for the Young’s modulus of the Si substrate; ∆E [1] = 30GP a for the
Young’s modulus of sublayer 1; and ∆E [2−8] = 40GP a for the Young’s modulus of the
Ni sublayers 2 - 8.
Here, the authors are considering only the errors for this special experiment. A more
general analysis of the errors will be presented in a forthcoming paper. Generally, it must
be pointed out that the statistical errors can be reduced by dividing the thin film into
fewer sublayers, which improves the ratio tsublayer
at the expense of a reduction in the
∆tsublayer
resolution of the stress profile. In other words, a decreasing spatial resolution leads to
an increase in accuracy.
For the system presented, a mean sublayer thickness of about 120nm is a good compromise
between resolution and accuracy.
A.6.2 Remarks to Ion Damage
Ion damage cannot be avoided when working with a focused ion beam workstation. Damage
caused by implanted Ga ions is difficult to quantify, but it has a certain influence
on the mechanical properties and the residual stress field in the affected volume. Investigations
have shown that the ion implantation depth generally depends on the ions and
materials involved, the acceleration voltage, the incident angle, and the ion current. 10
Stopping and range of ions in matter (SRIM) 11 simulations were performed to estimate
the implantation depth of the Ga ions. For an acceleration voltage of 30kV and ion
incidence almost parallel to the surface, the simulations show maximum Ga penetration
depths of about 20nm in Ni and 30nm in Si, which is small compared to the thickness
of the individual sublayers. Additionally, it must be taken into account that ion damage
occurs at the top as well as the bottom of the cantilever, and ion-induced compressive
stresses may partially cancel each other out. The damage can be neglected, especially
when similar materials are involved at the top and the bottom of the cantilever.
A.6.3 Remarks to Plastic Relaxation of the Ni Film During the Experiment
The calculation procedure assumes linear elastic behavior of the system. In case of plastic
relaxation during the experiment, the developed calculation procedure usually leads to
an underestimation of the residual stresses in the initial system. Therefore, it is essential
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