# Electropolishing--A Practical Method for Accessing Voids in Metal Films for Analyses
## 3 Electropolishing Setup
The third regime corresponds to voltages of above 2.5 V, at which oxygen bubbles [34; 46; 50] are formed at the anode's surface disturbing the viscous layer. Bubbles that are trapped on the surface potentially result in the formation of severe etch pits [37; 47; 59]. An experimental series is presented, where the optimal working point in the current-voltage curve (Figure 2) with respect to surface smoothing has been determined. Within this series pristine (thermo-mechanically non-stressed) poly-heater samples have been electropolished for 360 s at different voltages in the range from 0.0 V to 4.5 V and afterwards their surface roughness has been characterized by confocal laser scanning microscopy (utilizing a Sensofar S neox). Corresponding line profiles (with a projected length \(L_{0}\) = 175 \(\upmu\)m and a spacing between data points \(\Delta x\approx\) 0.129 \(\upmu\)m) are depicted in Figure 3a and the profile of the non-electropolished sample is discussed first. In a simplified approach the profile can be interpreted as being composed of a larger-range corrugation that is undulated by short-range roughness features. These short-range features are comprised of micro peaks and micro valleys that can be attributed to grain boundary grooves, as the grains of the investigated Cu are characterized by an equivalent circular diameter of (2.7 \(\pm\) 0.6) \(\upmu\)m [60; 61]. The line profiles of the electropolished samples in Figure 3a qualitatively corroborate the general surface smoothing observations of electropolishing in the different voltage regimes. In particular, one can see that for voltages exceeding 1.0 V micro features are smoothed very effectively. For a quantitative evaluation, the two roughness parameters \(R_{\text{q}}\) and the less known tortuosity [62], also referred to as relative line length [63], have been determined from thirteen independent line profiles and are presented as error bar plots in Figure 3b,c. The tortuosity has been calculated according to  
\[tortuosity=\frac{L-L_{0}}{L_{0}}, \tag{1}\]  
where \(L_{0}\) = 175 \(\upmu\)m is the before-mentioned projected length of the profile (see Figure 3a) and \(L\) is the line integral of the profile. For both \(R_{\text{q}}\) and tortuosity (Figure 3b,c) it can be seen that electropolishing at voltages of 0.0 V and 0.5 V clearly does not contribute to surface smoothing. By means of the \(R_{\text{q}}\) parameter, one can argue that very good polishing  
Figure 2: Current-voltage curve of the sample-setup configuration used within this work. Optimal electropolishing results in terms of surface smoothing are achieved in the polishing regime, characterized by a constant current density. results can be obtained for voltages between 1.0 V and 2.0 V and that for higher voltages the smoothing becomes less effective. The particular effect of micro levelling [64] grain boundary grooves is very well explained by means of the tortuosity. A highly significant difference between the etched samples (0.0 V and 0.5 V) and the polished samples (>0.5 V) is observed. Especially for the samples polished in the oxygen evolution regime (\(\geq\)2.5 V), it can be seen that micro levelling is still very effective (Figure 3a,c) and that the slight increase in tortuosity in this regime (inset image in Figure 3c) is attributed to pitting. In agreement with the \(R_{\text{q}}\) evaluations, a global minimum of the tortuosity at 2.0 V can be found, denoting the optimal electropolishing voltage. The two thermo-mechanically cycled poly-heaters have been electropolished at these optimized parameters (2.0 V for 360 s), resulting in a material removal of \(\approx\)5 um, quantified by confocal microscopy. By this means degradation voids in the interior of their Cu metallization have been accessed at a depth corresponding to the material removal, as shown in the cross-sectional schematic illustration in Figure 4a. Subsequent imaging in top view therefore allows quantification of the accessed voids along the lateral direction of the metallization.