Hello,

Tip deflection not only depends on the thin film residual stress (after deposition), length and thickness, but also the shape (stress/strain distribution) of the cantilever.

I would suggest, you must try to simulate it in any one of the software before fabrication-

1. Coventorware

2. COMSOL

3. Intellisuite

Based on the simulation results, you can guess the order of non-linearity in the tip deflection.

Best Regards.

As per  "Kumar, A.; Heidari-Bafroui, H.; Charbaji, A.; Rahmani, N.; Anagnostopoulos, C.; Faghri, M. Numerical and Experimental Modeling of Paper -Based Actuators. Chem. Proc. 2021,5,15. https://doi.org/10.3390/CSAC2021-10468"

Deflection of MEMS cantilever is proportional to L^2, and the relation is give by:

wp=C*x^2

where,

wp: is deflection of cantilever

x: is length coordinate

and C is give by:

C=Q/(2*λ)

Increasing value of fluid loading parameter Q*, results in higher maximum deflection of PBC. Fluid loading parameter is considered as the mass of fluid acting transversely on PBC, the phenomenon of imbibition of fluid from capillary is carried out until the paper attain its saturation, at this point the PBC will corresponds to maximum deflection. Different paper capilarte different amount of fluid based on their physical properties. Higher value of Q* signifies high fluid carrying capacity of paper.

Internal stress parameter λ* is another significant factor that needs to be addressed for the analysis of parametric mode. Generally, internal stress results in stress emerging in the structure of loading. In the case of paper, it is comfortable to adapt these resultant stresses in PBC due to the phenomenon of hygro-expansion and bending (rotation). In case of large deflection, these components cancel out others. . Contrary to parameter Q*, increasing value of parameter λ* will result in lower maximum deflection of PBC.