Bistable Micro Caps Fabricated by Sheet Metal Forming

Abstract

Traditional fabrication techniques are not suitable for the manufacturing of three-dimensional micro-scale structures. In this work, we report on a modified self molding punch-less sheet forming technique allowing fabrication of initially curved, non-planar, shallow micro shells. These structures, when appropriately configured, may exhibit the coexistence of two equilibria under the same loading. A ≈ 400 nm thick layer of Al, or ≈ 2.5 µm of Cu was deposited on top of a Si wafer. Next, circular openings of the radii varying between ≈ 100 µm and up to ≈ 700 µm were created in the Si substrate by means of the deep reactive ion etching (DRIE), with the metallic layer serving as the etch stop. Finally, the circular free-standing metallic sheet was pressed by a soft uniform foam layer serving as a stamp and pushing the metal foil into the opening in the wafer. Induced plastic deformation resulted in a residual strain shaping an initially planar metal sheet into a shallow cap with the midpoint elevations up to ≈ 50 µm. Metallic as well as metal-polymer bimorph caps, of the thickness varying between ≈ 400 nm and up to ≈ 2.5 µm and of the desired curvature, were successfully fabricated by the suggested process. Snap-through and snap-back of the fabricated devices under mechanical and electrostatic actuation was demonstrated experimentally.

Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

“…In contrast to the previously considered devices of this type, the plate analyzed here is bell-shaped in its initial, stress-free, configuration and is also sufficiently curved as to be bistable. The choice of the initial geometry of the structure and its dimensions is motivated by, and is consistent with, the actually fabricated devices previously reported by us [41]. We show that in the bell-shaped plates, the vibrational modes may differ significantly from those of the initially flat or slightly curved imperfect plates, or of the shallow spherical caps.…”

“…In all the calculations, plates with a radius of 700 µm, thickness of 400 nm, and initial elevation-to-thickness ratio varying from 0 to 30, were considered. This specific geometry was adopted since plates of the same dimensions were previously fabricated using the mold-less stamping technique and their bistable behavior was demonstrated theoretically and in the experiment [41].…”

“…The thickness d of the plate is assumed to be small compared to the plate radius R. The initial shape of the plate is described by the function ŵ0 (r) = ĥ0 z 0 (r), where ĥ0 is the elevation of the plate central point above its clamped edge and z 0 (r, θ) is a non-dimensional function such that max (z 0 (r)) = 1. Since the device is assumed to be fabricated by the self-molding stamping approach [41], the plate is assumed to be bell-shaped and stress-free in the initial as-fabricated configuration. The plate is actuated by a transverse-distributed electrostatic force (electrostatic pressure) generated by a gap-closing flat electrode spanning the entire plate area and located at a distance ĝ0 from the plate outer boundary.…”

“…The bistability of the pressurized graphene membrane was investigated in studies [39,40]. The bistable behavior of electrostatically actuated initially curved circular plates was recently investigated theoretically [6] and later demonstrated experimentally [41]. The theoretical analysis, in the framework of the Föppl von Kármán plate theory, was based on a reduced-order model built using the Galerkin method.…”

Research Status and Development Trend of MEMS Switches: A Review

“…Although it is difficult to fabricate curved bistable microplates in the MEMS process, it is still a promising research direction. For instance, Asher et al [104] presented a self-molding forming technique for extruding non-planar thin-walled microstructures with a soft foam stamp. The bistable microcap was fabricated and its bistability was verified for the first time.…”