# Investigation of the Influence of Sublayer Thickness on Pairing of Metallic MEMS Shutter Blades
## 4 Experimental Results and Discussion
### 3D Self-Assembled Paired Shutter Blades (Yin-Yang shapes)  
The 3D self-assembly pairing is a highly complex, nonlinear, and dynamic process. The process occurs between two neighbouring shutters (A and B) involving the respective blades. The shutter blades' initial curling state and movement during the drying process  
Figure 6: The measured radius of curvature (RoC) of the curled shutter blades as a function of the thickness of the top Al layer (\(d_{\text{A2}}\)). The highlighted region refers to the thicknesses values that show pairings. Figure 7: Quantitative representation of the individual degree of curling as a function of different \(d_{\text{A2}}\) values. The curling states with highlighted fading background are those ones revealing pairing in the subsequent figures. determine the details of the pairing. Based on the evaluations of the experiments (paired and unpaired cases), a relatively large technological processing window for pairing (3D self-assembly of shutter blades) has been identified when the top Al layer thickness \(d_{\text{Al2}}\) ranges between 70 nm and 88 nm (see highlighted green region in Figure 6). Two significant results from the paired shutter analysis are observed: the geometrical changes in shutters A and B (forming a Yin-Yang shape) compared to the circular geometry of the unpaired shutters and the different pairing scenarios of the shutter blades. The RoCs of the unpaired shutters are identical. During the drying process, the shutters are deflected by surface tension forces, enabling the pairing, but these forces are not present after drying. Therefore, the RoCs of shutters A and B are not different before pairing (green curve in Figure 5a). After pairing, shutter A and shutter B form a Yin-Yang shape. Now, the curvatures of the two shutters, A and B, differ. The curvature contours of shutter A are shown in orange, and those of shutter B are shown in blue (Figure 5b). The geometry of the paired shutter blades (Yin-Yang shape) is expected to be more elliptical instead of circular compared to that of the unpaired shutters since both of the shutters pull at each other under the influence of Casimir forces as they are at a very close distance to one another. Therefore, the changes in the geometry have been evaluated by fitting ellipses to shutter B. Since shutter A is suffers from stiction to the substrate, deflecting its elliptical geometry, the evaluation focuses on shutter B. However, the stiction duration of shutter A to the substrate has been evaluated. The major axis is always oriented horizontally, i.e., parallel to the substrate, and the minor axis is perpendicular to it (Figure 5b). The eccentricity \(\varepsilon\) of shutter B is introduced to quantify the geometrical change and as a qualitative measure for the stiffness of the investigated paired shutters. Equation (1) [31] was used to calculate the eccentricity utilising the measured major axis \(2p\) and the minor axis \(2q\) of the fitted ellipses. \[\varepsilon=\frac{\sqrt{p^{2}-q^{2}}}{p} \tag{1}\]  
\(p\) and \(q\) are the major semiaxis and minor semiaxis, respectively. When \(p=q\), then \(\varepsilon=0\), and the ellipse becomes a circle (refer to text and Figure S3 in the Supplementary Material for a representation of the ellipse equation, the figure of a standard ellipse, the definition of all of the involved parameters, as well as several figures illustrating a selection of different cases of eccentricity). The results are plotted in Figure 8, showing the eccentricity as a function of \(d_{\text{Al2}}\). The plot reveals that the smaller \(d_{\text{Al2}}\) is, the more circular shutter B's geometry is, which also agrees with the results of the unpaired shutter blades, since increasing intrinsic stress (in the hybrid metal stack) results in a decreasing RoC, as well as qualitatively stiffer shutter blades. The error bars represent the conducted statistical variance in the investigated Yin-Yang geometries.