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ME 119, Department of Mechanical Engineering University of California at Berkeley

Z. M. Posner & N. R. Injo

December 3, 2022

A novel method for fully constraining parts in three dimensions has been designed and analyzed. The concept centers around a locking hinge with low assembly force and high breaking force, which makes fluidic assembly a promising prospect. This design can be adapted to variable angles, automated assembly, and maintains high angular accuracy of ±3.9° . Potential uses include a new type of anemometer, angled mirrors, and many devices using a typical hinge [2]. Before attempting to produce the fully constrained hinge, it is important to understand all the design choices and design constraints.

The surface micromachining process operates by the repeated deposition of thin film materials on a wafer substrate and the selective etching away by use of lithography. As a result, surface micromachining offers high planar resolution, but low vertical resolution. Therefore, it is an ideal process for planar applications, but not practical for three-dimensional structures. To enable high vertical resolution, a process for which structures are fabricated using surface micromachining and then rotated 90° out of plane by an integrated micro-hinge is presented below. In order to constrain the structure vertically, a self-locking feature is incorporated in the hinge design.

The locking hinge is designed for the PolyMUMPS fabrication process which in general, consists of an initial nitride layer, three polysilicon layers, and two sacrificial oxide layers. The process starts with a n-type (100) silicon wafer doped with phosphorous (Figure 1a). A low stress nitride layer is deposited followed with polysilicon (Poly 0) by low-pressure chemical vapor deposition (LPCVD). Photoresist is lithographically patterned for plasma etching to remove the unwanted polysilicon. This etch defines the opening in the base for the lift plate to rotate about. A sacrificial oxide layer (Oxide 1) is deposited by LPCVD. Another polysilicon layer (Poly 1) is deposited, patterned, and etched away. Poly 1 defines the ’lift plate’ which will rotate out of plane once the structure is released.

Hole perforations are also patterned and etched away from the lift plate, providing drain holes for complete release. Next, a second sacrificial oxide layer (Oxide 2) is deposited by LPCVD. The wafer is re-coated with photoresist (Figure 1b), and the first and second oxides are 1 pattern etched away to form a Poly 2-to-Poly 0 anchor. The third polysilicon layer (Poly 2) is deposited by LPCVD, patterned, and etched away. This polysilicon defines the ’staple’ geometry which holds the Poly 1 captive to the substrate. This etch also defines the cantilever beam element which is critical to the assembly into the constrained position. Lastly, the structures are released by immersing the wafer in 49% HF (Figure 1c) which cause the sacrificial oxides to etch away.

The constrained hinge has several components that are important to understand if attempting to build an identical or similar version. By sharing the design intent of the specific features, individuals attempting to replicate a constrained hinge are able to correctly modify the design to suite their needs. Furthermore, this aids in catching design issues prior to manufacturing.

First and foremost, the constrained hinge is designed to be produced with the PolyMUMPS fabrication process [1], so layer thicknesses were chosen accordingly. The design was done working backwards with durability as the main goal. In order to achieve maximum durability, it is evident that the lift plate (as seen in Figure 2) should be on the thickest possible Poly layer. The thickest layer using the MUMPS process is the 2.0 micron layer (Poly 1). This leaves Poly 2 to serve as the staple geometry and Poly 0 to serve as the base. After this, the only layers left are Nitride and Poly 0. One or both of them could serve as an effective base layer. Using the MUMPS process, the Nitride layer is not etched. The Nitride is included, but only the Poly0 is etched with a hole. In processes that allow Nitride to be etched, creating a similar etched groove should be considered for higher load bearing capability.

The staple and lift plate act similar to a drop cam and follower [3]: as the lift plate rotates, the staple beam element rises until the lift plate clears the beam, causing it to suddenly drop down to its original position. To ensure the staple returns without plastic deformation, the stress felt in the staple must be less than the yield strength of polysilicon: 1.2 GPa [4]. To analyze the stress state of the beam using a first principles approach, the staple can be thought of as a cantilever beam fixed at one end and a point load applied at the free end from the lift plate 4. The relation between the max beam deflection and the force applied is defined by Equation 1a, where E is the elastic modulus of polysilicon (150 GPa [4]) and I is the area moment of inertia of the beam section. While the force applied by the lift plate is unknown, the max deflection can be approximated as the Poly 2 thickness of 2.0 microns. The maximum normal stress is felt near the fixed support at a point furthest from the neutral axis, which in this case is the top and bottom of the beam. This can be rewritten in terms of the applied force (Equation 1b) and therefore the max deflection (Equation 1c). From these variables, δ, E, and h (thickness of the Poly 2) are constants. The only design parameter is the length of the beam, L, which has an inverse-square relationship to σ.

Thus, a plot of stress in the beam vs beam length with a limit set at the yield stress of polysilicon (1.2 GPa [4]) was used to inform the the beam design (Figure 5). A beam length of 26 microns was chosen which meets a factor of safety of 1.5. Considering that the beam is loadcycled once only during assembly, failure from fatigue is not a concern.

The constrained hinge has the potential to hold plates at non-normal angles. By modifying the hole positions in the staple and base, it is relatively easy to modify the desired angle. For the constrained hinge, there is a limit with angular adjustment. The closer the lift plate gets to horizontal, the wider the holes in the staple and base need to be. At a certain point, the holes need to be infinitely long. Another issue with low-angle lift plates is a large decrease in angular accuracy. As angle approaches horizontal, the cross section contained in the staple needs to increase in order to have one end protruding through the hole in the staple and the other securely in the base hole. However, an increase in cross section means that the arm is now applying a larger torque to the staple spring. Additionally, the lift plate now applies a bending force rather than a compressive force to the beam. These two issues are more evident when comparing the two lift plate angles in Figure 6a and Figure 6b.

Both of these sources of angular inaccuracy are non-trivial to analyze and could be aided by FEA and the consideration of load cases. These are not in the scope of the project, but are indeed possibilities for further research.

From the the stress analysis, the max force required to deflect the beam was determined to be 410 µN. This force can be used to estimate the lift force required to assemble the lift plate. Considering the free body diagram in Figure 7, it is apparent that the lifting force is amplified by the long lever arm of the lift plate, providing a mechanical advantage of 100:7. As a result, the lifting force is much lower at 30 µN. This can be further reduced by designing the lift plate with a longer lever arm.

The torque the lift plate is able to withstand once assembled is limited by the expected failure 3 mode in the structure. As the lift plate is perturbed, a reaction force is generated at the beam which acts to compress it (Figure 8a). Due to the staple’s long and thin nature, creating geometric instability, the staple is susceptible to buckling failure. The critical buckling load can be calculated for a fixed-free cantilever beam (Figure 8b) based on the length of the beam, modulus, and area moment of inertia. The critical load to buckle the beam is 5851 µN. To consider the torque the lift plate is able to withstand before buckling the beam, a moment balance is performed. The critical torque is 0.043 µNm, which is equivalent to 430 µN applied 100 µm from the point of rotation. This is fourteen times larger than the force required to assemble the lift plate.

There are numerous feasible assembly methods, given the low assembly force of 30 µN. A manual approach using a probe to raise the lift plate can be performed. The DI rinse used in the release process can be exploited to generate hydrodynamic forces large enough to raise and lock the structure [2]. The use of fluidic assembly allows for the process to be automated at scale. This idea can be extended to focused air streams

A variety of micromachined devices can take advantage of a 90° locking hinge, namely: a hotwire anemometer, micro-probe, tissue-growth dynamometer, and parallel-plate gripper [2]. The angled locking hinge has some unique applications as well. The structure can support a mirror at a set angle for optics based MEMS such as a Vertical Scanning Micromirror [5]. The angled lift plate can also be used as a ramp to redirect fluids or generate drag force (e.g. an air brake). The cantilever beam and mechanical advantage of the lift plate can be leveraged in devices. One could devise a force gauge to measure the critical buckling load or a beam deflectometer which can be used to measure wind speed hitting the lift plate.

An important aspect of constrained hinges is the ability to maintain a constant angle and position. However, all mechanical systems have a certain amount of error and quantifying it is critical. It is easy to analyze the 90° hinge, and a diagram is presented below to clarify the math terms that follow.

This novel fully constrained hinge has the potential to simplify MEMS hardware in the third dimension. A lot of design time and engineering analysis has gone into this microstructure platform. To continue this forward, the next steps would be CFD analysis and FEA, followed by fabrication and test of a physical prototype. The hinge angle and tolerance are both adjustable, which give the designer the power to adjust for ease of assembly or angular tolerance, among other things.

From Figure 9, we can conclude that the misalignment is 

±Θ

where

For the vertically constrained design, dimensions can be taken from the PolyMUMPS Design Handbook [1] to populate the following material thicknesses:

however,

are taken from the cad design. The result is an angular misalignment of

±3.9°

This result only applies to a hinge that constrains to a 90 degree angle. The angular error increases as the constrained angle decreases, which requires further investigation.

We would like to thank Professor Liwei Lin for his teaching and guidance. His in class questions always remind us that engineering is about understanding, and designers must have a strong grasp on reality. It seems simple, but engineering is about human vs natural laws, and there are no hidden tricks, only ignorant designers.