Mechanical systems with adapted linearity

Abstract

A mechanical system that has the following features: a bending transducer structure (12) configured to provide a bending response to an applied electrical signal (16) and / or to provide an electrical signal (16) responding to an applied external force (F) causing the bending, wherein a structural stiffness (52) of the bending transducer structure (12) provides a first nonlinear mechanical stiffness contribution with respect to the bending; an adaptation structure (18) which is mechanically coupled to the bending converter structure (12) by mechanical coupling in order to provide an adaptation deformation together with the bending, wherein a structural stiffness (52) of the adaptation structure (18) provides for a second nonlinear mechanical stiffness contribution with respect to the bending based on the mechanical coupling during deformation; wherein the adaptation structure (18) has a bending beam structure (84) which is coupled in parallel to a bending beam structure (26) of the bending converter structure (12) and which has a local stiffening between a first end and a second end of the bending beam structure (84) of the adaptation structure (18); and / or wherein at least one of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution is based on a mechanical contact between a first element and a second element of the mechanical system, wherein the mechanical contact provides a variable magnitude of mechanical forces acting on the bending converter structure (12) and / or the adaptation structure (18) upon an increase in a bending amplitude; and wherein the mechanical system is configured to provide the mechanical contact between the bending converter structure (12) and the adaptation structure (18), wherein the bending converter structure (12) and the adaptation structure (18) are arranged such that they increase a contact area between each other upon an increase in the bending of the bending converter structure (12), wherein the contact area between is formed from the following: • the adaptation structure (18) and the bending transducer structure (12); • a first element of the adaptation structure (18) connected to a first bending element (261) of the bending converter structure (12); and a second element of the adaptation structure (18) connected to a second bending element (262) of the bending converter structure (12).

Description

[0001] The present invention relates to mechanical systems comprising a bending transducer and an adaptation structure that contributes to the bending of the bending transducer, for example, to adapt its bending behavior. The present invention further relates to modulating the response of bending transducer systems based on the design of elementary cells.

[0002] A well-known concept for counteracting nonlinearity in the response of a transducer system employing nonlinear mechanical stiffening is known from the prior art and publications (1-5). However, most of these solutions are highly design-specific with limited applicability and performance levels. For example, bending transducer systems that rely on nonlinear stiffening through contact formation and evolution, such as electrostatically actuated zipper actuators, typically suffer from motion hysteresis due to contact formation and breakage [4, 6-9], instabilities due to electrostatic attraction (or pull-in) [4, 6-8], static friction problems, abrupt response changes [6, 8, 10], the need for design based on complex residual stress engineering [7], requirements for dedicated external structures [1, 2, 3, 5, 11], etc.

[0003] In most zipper configurations, a directed deflection or movement of a specific structural area is used instead of bending curvature of the entire cell / component geometry. Simultaneous modulation / linearization of different system responses (bending curvature, bending moment, available force, capacitance change, motion resolution, frequency response, etc.) with an actuation signal in such configurations is difficult (usually only one or more than two responses are modulated in a given design). Furthermore, electrostatic zipper actuators exhibit tightening instability, which makes controlling them challenging

[12] .

[0004] DE 10 2015 206 774 A1 relates to an MMS with an actively deformable element. Activation is achieved through a layered structure.

[0005] WO 2020 / 078541 A1 refers to a bending transducer, which is a sensor or actuator.

[0006] DE 602 08 930 T2 relates to a microactuator with a volume-changing layer.

[0007] US Patent 6,329,738 B1 relates to an electrostatically controllable actuator with a stationary electrode and an auxiliary element.

[0008] DE 10 2019 211 941 B3 relates to a microstructured element with a membrane and a fluid channel.

[0009] Therefore, there is a need for reliable and stable mechanical systems.

[0010] One object of the present invention is to provide reliable and stable mechanical systems. This object is achieved by the subject matter of the present invention.

[0011] One insight of the present invention is that the behavior of a bending converter structure can be adapted, i.e., with respect to an increase or decrease in linearity, by mechanically coupling the bending converter structure to an adaptation structure that causes deformation in conjunction with the bending of the bending converter structure. The deformation of the adaptation structure results in forces acting on the bending converter structure, thereby adapting its bending behavior. By using such an adaptation structure, the behavior of the bending structure can be tailored to a desired property.

[0012] According to one embodiment, a mechanical system comprises a bending transducer structure configured to provide a bend in response to an applied electrical signal and / or to provide an electrical signal in response to an applied external force causing the bend, wherein structural stiffness of the bending transducer structure provides a first nonlinear mechanical stiffness contribution to the bend. The mechanical system comprises an adaptation structure mechanically coupled to the bending transducer structure by means of a mechanical coupling to provide adaptation deformation along with the bend. Structural stiffness of the adaptation structure provides a second nonlinear mechanical stiffness contribution to the bend based on the mechanical coupling during deformation.The combination of the first and second nonlinear mechanical stiffness contributions enables precise design and a reliable and stable structure. The adaptation structure features a bending beam structure that is coupled in parallel to a bending beam structure of the bending converter structure and provides local stiffening between a first end and a second end of the bending beam structure of the adaptation structure.Alternatively or additionally, at least one of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution is based on mechanical contact between a first element and a second element of the mechanical system, wherein the mechanical contact provides a variable magnitude of mechanical forces acting on the bending converter structure and / or the adapting structure as the bending amplitude increases; and wherein the mechanical system is configured to provide the mechanical contact between the bending converter structure and the adapting structure, wherein the bending converter structure and the adapting structure are arranged to increase a contact area between each other as the bending of the bending converter structure increases, the contact area being formed from the following: • the adaptation structure and the bending transducer structure; • a first element of the adaptation structure connected to a first bending element of the bending converter structure; and a second element of the adaptation structure connected to a second bending element of the bending converter structure.

[0013] According to an embodiment of the present invention, a mechanical system comprises a bending transducer structure configured for nonlinear deformation based on bending in response to an applied electrical signal and / or for nonlinear provision of an electrical signal in response to an applied external force causing the bending. The mechanical system includes an adaptation structure mechanically coupled to the bending transducer structure, wherein the bending and deformation of the adaptation structure are causally correlated, the deformation adaptation structure providing a nonlinear force to the bending transducer structure, which reduces the magnitude of any nonlinearity in the overall response. Linearization can be achieved based on the mechanical implementation, but this is not necessary.Based on spring configurations, a desired increase in nonlinearity can be achieved in parts of the response regime. However, compared to systems without springs, this can also lead to a reduction in overall nonlinearity in the response. The bending transducer structure has at least two bending elements that are mechanically coupled in parallel, with a gap between the two bending elements.

[0014] Further embodiments relate to a method for producing and / or controlling a mechanical system.

[0015] Advantageous embodiments of the present invention are defined in the dependent claims.

[0016] Exemplary embodiments of the present invention are described in detail below with reference to the accompanying drawings, in which: Fig. Figure 1a shows a schematic side view of a bending transducer system having an adaptation structure outside an active area of ​​a bending transducer, configured to contact the active area of ​​the bending transducer, according to an embodiment; Fig. Figure 1b shows a schematic side view of a bending transducer system having an adaptation structure outside an active area of ​​a bending transducer configured to not contact the active area of ​​the bending transducer, according to an embodiment. Fig. Figure 1c shows a schematic side view of a bending transducer system that has an adaptation structure in a volume of an active area of ​​a bending transducer, configured to contact the active area of ​​the bending transducer, according to an embodiment; Fig. Figure 1d shows a schematic side view of a bending transducer system having an adaptation structure in a volume of an active area of ​​a bending transducer configured to non-contact the active area of ​​the bending transducer, according to an embodiment; Fig. Figure 2a shows a schematic top view of a mechanical system according to an embodiment, which has two bending elements as part of the bending converter structure, according to an embodiment; Fig. Figures 2b-e show different configurations of mechanical systems according to exemplary embodiments, a plurality of cells according to Fig. 2a in different configurations according to exemplary embodiments; Fig. 2f-g show different modifications of the mechanical system. Fig. 2a according to exemplary embodiments; Fig. Figures 3a-d show schematic views of mechanical systems according to exemplary embodiments, which have at least part of the adaptation structure as a layer on a bending element of the bending converter structure; Fig. Figures 3f-g show schematic views of mechanical systems according to exemplary embodiments, which have an adaptation structure that includes at least part of a tongue and groove structure; Fig. Figures 4a-b show schematic views of mechanical systems according to exemplary embodiments, which have different stiffnesses of different bending element sections of the bending converter structure; Fig. Figures 5a-b show schematic views of mechanical systems according to exemplary embodiments, which have bent bending elements of the bending structure; Fig. Figure 6a shows a schematic view of a double-dome configuration of a mechanical system according to an exemplary embodiment; Fig. Figures 6b-e show schematic diagrams of the bending behavior of the mechanical system. Fig. 6a; Fig. Figures 7a-d show schematic views of bending transducer systems according to exemplary embodiments in which the adaptation structure is arranged outside a volume of the active area of ​​the bending transducer; Fig. Figures 8a-b show schematic views of mechanical systems according to exemplary embodiments, which have an adaptation structure that includes a nonlinear spring; Fig. Figure 8c shows a schematic diagram of the bending behavior of the mechanical system. Fig. 8b; Fig. Figure 8d shows a schematic view of a mechanical system according to an embodiment having an adaptation structure comprising a multi-layered non-linear spring; Fig. Figures 8e-g show schematic views of mechanical systems according to exemplary embodiments in which the adaptation structure is arranged on two outer sides of the bending transducer structure; Fig. Figures 9a-c show schematic views of mechanical systems according to exemplary embodiments, which have at least two bending transducer structures; and Fig. Figures 10a-c show schematic views of mechanical systems according to exemplary embodiments implementing different actuation principles.

[0017] Identical or equivalent elements, or elements with the same or equivalent functionality, are designated with the same or equivalent reference symbols in the following description, even if they appear in different figures.

[0018] The following description presents a number of details to provide a more comprehensive explanation of embodiments of the present invention. However, it is apparent to those skilled in the art that embodiments of the present invention can be implemented without these specific details. In other cases, known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the present invention. Furthermore, features of the different embodiments described below can be combined unless specifically stated otherwise.

[0019] Mechanical systems are described below. Part of the disclosure set forth below relates to micromechanical systems (MMS), and in particular to microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). However, the present invention is not limited to micromachines.

[0020] Exemplary embodiments of the present invention relate to influencing the bending behavior of a bending transducer structure exhibiting nonlinear deflection behavior by means of another structure mechanically coupled to the transducer structure in order to adjust the bending behavior by introducing additional forces. Such an influence can be implemented for micromechanical systems, as well as for micromechanical systems or, more generally, for mechanical systems.

[0021] Some of the figures presented below relate to bending transducers configured to deflect planarly with respect to a stack of layers, as is particularly illustrated in the technical field of MEMS. However, the embodiments presented here are not limited to planar deflection. Based on a freely selectable configuration of clamping and / or deflection direction, any direction, e.g., planar or extraplanar, can be realized.

[0022] Typical dimensions (not necessarily the limits) of structures of different embodiments presented herein are: A. MEMS / NEMS area: 1. Insulator / dielectric layers: Width: 10 nm - 10 µm (height and length are usually the same as the bending cell dimensions) 2. Electrode dimensions: Width: 10 nm - 100 µm (height and length are usually the same as the bending cell dimensions) 3. Dimensions of air gaps: Width: 10 nm - 100 µm (height and length are usually the same as the bending cell dimensions) 4. Cell dimensions: Length: 10 nm - 10 mm; Width: 50 nm - 500 µm; Height: 10 nm-10 mm, length is usually the same as the bending cell dimensions; B. Macro level: all dimensions can range from a few mm to several cm. Voltage ranges: A. MEMS / NEMS: 0 - 500 V B: Macro-level designs: 0 - 10,000 V (normally until electrical breakdown of the insulator / air gap used is reached) Materials: A. Possible materials for MEMS / NEMS (those mentioned are mainly CMOS compatible, however this is not a necessary condition): 1. Electrodes: highly doped semiconductors (Si, GaAs, etc.), metals (aluminium (Al), tungsten (W), TiAl, etc.), conductive polymers / polymers coated with metal (in production based on additive manufacturing), plastic-based materials, piezoelectric ceramics, etc. 2. Dielectric: Al2O3, SiO2, Si3N4, polymers (in production based on additive manufacturing), etc. B. Possible materials for the macro level: 1. Electrodes: all metals / conductors (steel, Al, etc.) or conductive polymers / polymers coated with metal (in production based on additive manufacturing) 2. Dielectric: Al2O3, SiO2, Si3N4, polymers (when produced using additive manufacturing), ceramics, etc.

[0023] Possible production processes (but not the only ones): A. MEMS / NEMS: 1. Planar bending structures: standard batch micromachining processes for single crystalline wafers (e.g. SOI wafer DRIE, ALD, chemical wet etching via TMAH, etc.), high-resolution additive manufacturing with printing of conductive material / metal coating of polymers along with conformal deposition processes for dielectric material (e.g. ALD). 2. Extraplanar bending structures: Surface micromachining processes, crystalline silicon wafer bonding of two layers and structuring of the same by DRIE and anisotropic TMAH etching processes, high-resolution additive manufacturing with printing of conductive material / metal coating of polymers together with conformal deposition processes for dielectric material (e.g. ALD). B. Macroscale: 1. Additive manufacturing processes (with printing of conductive material / metal coating of polymers) 2. High-precision mechanical manufacturing processes such as injection molding, high-precision machining such as CNC, etc.

[0024] A bending transducer system can be understood as a mechanical system, or at least as part of one. Such systems, as described herein, may have an active region that includes or is defined by an electrostatic gap and potential-carrying electrodes, e.g., for NEDs, and / or potential-carrying electrodes for actuators, such as piezoelectric and thermal configurations. It is important to note that the adaptation structures described herein may still be part of the overall cell (i.e., the entire bending transducer structure) because, compared to cases where they are not present (although they are still inactive parts of a cell, as they may not have a potential difference with respect to an active region and contribute mainly as loads or mechanical feedback systems), they will always have a causal direct / indirect influence on the cell's response to bending.The adaptation structure can therefore be viewed as part of a cell, regardless of whether it is located inside or outside the active area.

[0025] The embodiments presented herein generally relate to a mechanical coupling of a bending transducer structure with an adaptation structure. These embodiments can differ from one another based on several criteria. One such criterion is whether the adaptation structure is incorporated into a volume of the bending transducer structure, for example, whether the adaptation structure is "inside" the volume of the bending transducer structure or not. Another criterion is whether the adaptation structure is designed to facilitate contact, e.g., a zipper (or zipping), with another structure, such as the bending transducer structure, or alternatively, whether a coupling surface changes or not. The latter allows for highly flexible adaptation of the mechanical system with regard to its behavior.Specifically, the linearity or non-linearity of the overall mechanical system can also be influenced based on whether or not it exhibits (a change in) contact formation.

[0026] Embodiments of the present invention relate to a bending transducer structure. The mechanical coupling of the adaptation structure can, at least in some embodiments, involve coupling the adaptation structure to two disjoint regions of the bending transducer structure, for example, to both ends thereof. In such a case, the adaptation structure can act as a kind of parallel connection with the bending transducer structure, instead of providing an additional support point or a connection to a substrate or the like.

[0027] The invention relates to bending transducer configurations that can operate as actuators, sensors, or both, and its application lies primarily, but not exclusively, in the field of microelectromechanical systems (MEMS). The invention relates to all bending actuation principles, such as electrostatic, piezoelectric, electrothermal, electroactive polymer actuators (e.g., dielectric elastomer actuators (DEAs)), etc., and commonly used sensing mechanisms, such as capacitive sensing, piezoresistive sensing, piezoelectric sensing, etc.

[0028] In numerous bending transducer systems, e.g., electrostatic bending transducers

[13] , responses such as bending curvature, bending moment, applied force, capacitance change, etc., exhibit a nonlinear relationship with the applied transducer signal and / or a load condition. This often leads to complex drive, readout, and / or control for such systems. The invention presents concepts for modulating the response of the bending system with the transducer signal and / or a load condition in order to eliminate or reduce the magnitude of the nonlinearity. This is achieved primarily by changing the mechanical stiffness (linear / nonlinear) of the elementary bending cells and / or the geometry of the electrodes with the applied transducer signal and / or the load condition. The presented configurations also inherently offer the possibility of a sensing mechanism with linearity or a reduced magnitude of nonlinearity.Thus, response modulation can be effectively used to simplify the required actuation, sensing, and / or control systems. Furthermore, the present invention can also be used for bending transducer systems that need to modulate the generated response by changing the bending cell stiffness and / or the electrode geometry to meet a specific application requirement, e.g., reducing the available actual force in a specific range of an applied transducer signal for electrothermal bending transducers, which are known for generating high forces for small voltage changes, for improved and controlled handling of sensitive biological samples.

[0029] One of the main advantages of the invention is that the required response modulation is derived directly from the configuration of the elementary cells of the bending transducer, thus providing a high degree of freedom in the design and performance of the bending transducer. Furthermore, the area / volume required to implement the system can be optimized more efficiently while achieving the required performance levels, particularly compared to configurations that use externally dedicated loading mechanisms to modulate a system response [1, 11].

[0030] Thus, the invention can be used to optimize all schemes / mechanisms of bending transducers, which requires modulation of a system response and / or linearization with respect to an applied transducer signal (actuation and / or readout signal) and / or a load condition. Furthermore, the fundamental concepts presented in the invention for obtaining response modulation at an elementary level are not limited to bending configurations but can also be extended to other transducer systems, particularly where the system response needs to be modulated based on a change in mechanical stiffness (linear / nonlinear) and / or deformation of electrodes, which arises from the design of the basic element cells.

[0031] Since the invention is applicable to the basic elementary level of the transducer, it can be used in numerous applications and devices, such as MEMS micropositioning systems, MEMS pumps, optical MEMS switches, MEMS capacitive diodes, MEMS energy collectors, etc.

[0032] The invention relates in particular to electrostatic bending actuators such as nanoscopic electrostatic drives (NEDs) described in patent WO 2012 / 095185 A1

[14] .

[0033] The different design configurations presented in this invention offer solutions to the problems described above. For the electrostatic configurations with contact-based operation in this invention, contact formation can be achieved with or without the use of a pull-in effect. For configurations without the use of a pull-in effect, the pull-in-based design challenges and associated nonlinearities can be avoided, and a slow and smooth transition into the response modulation / linearization region can be obtained. However, if an abrupt transition into the contact region for response modulation / linearization is required, and a rapid contact break is needed to reduce the probability of permanent static friction, a pull-in effect can also be used.In configurations based on a bending spring (with / without feedback to the cell electrodes), nonlinear stiffening in a bending cell can be achieved even without contact formation, thus eliminating problems with frictional adhesion, contact-based motion hysteresis, etc. Furthermore, the frequency response in such configurations exhibits no sudden disturbances due to contact formation.

[0034] The invention can be used to reduce nonlinearity and / or modulate the effect of motion hysteresis (particularly in configurations with mechanical feedback to cell electrodes) in DEAs and also piezo actuators. It can also be used to reduce the applied force and / or increase the motion resolution for bending systems based on electrothermal actuators (if required for certain applications).

[0035] WO 2020 078541 A1: In this document, specific bending cell configurations and control based on a controller with specialized drive signals were implemented to achieve linearity in electrostatic bending actuator cells (which typically exhibit a highly nonlinear response [13, 14]). Linearization is achieved using a specific cell geometry and operating it within a specific range of actuator response. A special configuration of drive signals with a very specific configuration of three or more electrodes is required (not necessarily required for the present invention). The usable range for linearization and response is more limited compared to the present invention.Furthermore, the forces achieved will be lower compared to contact-based configurations presented in this invention, and thus higher bending curvatures and deflections can be achieved in the present invention.

[0036] Patent US 7,679,261 B2: This document describes the use of a pivot configuration in conjunction with a zipper actuator to generate multiple degrees of motion. The system requires a specific configuration and does not ensure a reduction in the nonlinearity of the system response. The present invention employs a very different approach to counteract nonlinearity and does not require the specific configuration discussed therein.

[0037] US 2021 / 061648 A1: This document describes the use of electrodynamic levitation to counteract the attraction effect and nonlinearity of electrostatic transducers. However, the system requires a highly specialized design configuration (thus limiting design freedom) and a complex control scheme with very high drive voltages. The present invention uses a very different approach to counteract nonlinearity and does not require a complex drive scheme.

[0038] US 10,693,393 B2 and US 2019 / 036463 A1: These documents use a tri-electrode configuration with a specific drive scheme to counteract an attraction effect and exhibit reduced nonlinearity at reduced drive voltages. The present invention uses a very different approach to counteract nonlinearity and does not require such a drive scheme, while the reduced drive voltage conditions can still be met if necessary. The configurations presented in this invention also offer a greater degree of design flexibility.

[0039] The responses of the bending actuator, such as bending curvature, peak deflection, available actual force, bending moment, generated force, structural stiffness (localized or overall), frequency response (mechanical and / or electrical, e.g., structural hardening and / or softening with higher-frequency mechanical movements, change in the cutoff frequency of the electrical actuation signal due to capacitance changes, etc.), etc., can be modulated based on the geometric design and electrode configurations in the individual elements of the bending actuator (referred to as "bending cells") when an actuation signal is applied. Response modulation is primarily achieved through linear / nonlinear stiffening at the elementary cell level using causal bending of the electrodes based on contact formation and / or an internal bending system.

[0040] The configurations set forth in this invention can generally be divided into the following basic variants: 1. Structural stiffening (linear / nonlinear) with cell bending based on contact formation and its evolution in cell geometry: a. Contact formation and evolution between electrodes in the electrostatic gap based on a material of an electrical insulator / dielectric material (e.g. Al2O3, SiO2, etc.). b. Contact formation outside the electrostatic gap (electrical insulator not necessarily required). 2. Structural stiffening (linear / nonlinear) with cell bending based on a spring configuration in the cell geometry; a. Bending spring configurations in the cell geometry without a feedback loop to the deformation of the bending electrodes. b. Bending spring configurations in the cell geometry with direct / indirect feedback loop to the deformation of the bending electrodes.

[0041] It is always possible to combine the different basic variants to form different cell configurations depending on the requirements for the system response.

[0042] Contact formation and its evolution within the cell geometry under applied signal can occur within the electrostatic gap between the cell electrodes or outside of it. The position of the initial contact formation and the evolution of the contacts during actuation depends on the geometry and topography of the electrodes, the material properties of the electrodes, the insulating layer in the electrostatic gap, the maximum applicable voltage (insulator thickness required to withstand the voltage in the electrostatic gap), and other factors. Based on these various configurable factors, the response of the bending actuator to applied voltage can thus be designed and modulated according to requirements.

[0043] The internal bending system can be directly or indirectly connected to the geometry of the deforming electrodes to exert a direct or indirect influence on electrode deformation. This also allows for a feedback loop system to adjust electrode deformations based on mechanical deformations and forces generated within the cell geometry when a conversion signal is applied. For bending actuator cells using electrostatic / electroactive polymers (e.g., DEAs), the bending system can be used with a direct or indirect structural feedback loop to the electrodes. This feedback loop can influence not only the geometric shape of the electrodes but also the local or overall shape of the electrostatic gap during bending, and thus also the electrostatic forces generated within these gaps. This can be used to further extend the feedback loop.For piezoelectric bending actuator cells, the structural feedback loop to piezoelectric layers will influence their actual mechanical deformation and any stress in the layers, which will effectively also influence the actual forces generated in them when a voltage is applied.

[0044] One of the main advantages of the invention is that the response modulation can be obtained directly from the cell geometry itself, thus avoiding the use of external spring mechanisms [2, 3], external mechanisms for nonlinear loads, articulated end conditions [1], etc., and thus effectively reducing the overall system area, since the actuators can be readily stacked in series and parallel based on the cell geometry.

[0045] Furthermore, in the case of electrostatic bending actuator configurations based on contact formation, greater forces can be achieved than in conventional configurations that rely solely on air gaps without contact between electrodes (e.g., conventional NEDs [13, 14, 15]). Due to the use of contact based on a dielectric material between the electrodes, much greater electrostatic forces (∝ ε) can be generated. r , g 2 ) are generated because the gap (g) is drastically reduced compared to typical minimum values ​​of 1 / 3 of an air gap (to avoid attraction between electrodes of conventional NEDs), and a higher effective relative permittivity (ε) is achieved. r ) can be achieved in the electrostatic gap upon contact based on a material with a high dielectric constant.

[0046] In the configurations of the present invention, the dielectric material can be conformally deposited onto the electrodes or as detached layers between the electrodes (using special production methods), such that the pre-deflection upon release in the cells due to residual stress is negligible. This dielectric deposition-based approach can be used to reduce the effective electrostatic air gap between the electrodes, in contrast to production resolution limitations, i.e., where directly produced electrostatic air gaps cannot be reduced beyond a certain dimensional limit, such as planar NED cells based on DRIE etching, where a minimum trench width is limited by a certain aspect ratio with respect to depth.This further enables the maximum forces generated to be increased by achieving a narrower effective electrostatic air gap between electrodes than is possible due to production limitations, thereby reducing the system area and / or the voltage level required to achieve the necessary force and displacement levels. Another significant advantage is that actuation is also possible at voltages higher than the attraction voltage (lateral and / or vertical attraction) of the electrostatic bending actuators' electrodes, unlike conventional NEDs. This allows any losses in target functionality due to variations introduced by production, load conditions, etc., to be compensated for simply by adjusting the applied voltage.

[0047] Furthermore, the main advantages of the configurations presented based on contact formation (to achieve a change in flexural cell stiffness) in relation to conventional zipper actuators [1-8, 10-12] are as follows: 1. Contact formation within a single cell is used to achieve a bending deformation of the entire cell geometry, instead of a continuous zipper function of an actuator (which typically uses a stationary electrode and a zipper / bend electrode) for response modulation upon signal application. Thus, many cells, with multiple electrodes and air gaps, can be used in series and / or parallel to achieve required response parameters, such as deflection, force, etc., with a smaller effective contact area compared to conventional zipper actuators. This reduces the likelihood of frictional adhesion and motion hysteresis during zipper release, as the contact area can be significantly reduced while achieving similar or improved performance parameters. 2. Bending deformation based on limited contact points (or in some configurations even just a single contact point) can also be used instead of the continuous contact-based zipper function as in conventional zipper actuators. Apart from the first contact point, the other direct contact points are not required for the principle to function; in the outer corners of a bending cell, it is even possible to have no contact position at all, while modulation / linearization is achieved due to bending of the entire cell geometry. This further reduces the probability of frictional adhesion and motion hysteresis during the release of the zipper connection, thus significantly improving the reproducibility and reliability of the system's performance. 3. In contrast to conventional electrostatic zipper actuators, electrostatic attraction is not required for initial contact formation or its evolution. This allows for a smooth transition into a contact region without abrupt changes in the system response during a transition into a region of modulation / linearization with an applied signal, and also avoids attraction-related instabilities during contact formation. If a sudden transition is required, for example, to mark the change in a region of modulation / linearization or to sharply interrupt contact during a zipper release process to further reduce static friction probabilities, an attraction effect can also be used in the present configurations as needed.

[0048] For contact-based configurations, the potential problems arising from static friction between the electrodes could be reduced by increasing the roughness of the contact surfaces (e.g., sidewall corrugations from DRIE etching), structuring contact surfaces, and / or using an anti-static coating in between, e.g., conformal FDTS (perfluorodecyltrichlorosilane) single-layer coatings deposited by ALD (atomic layer deposition).

[0049] The dielectric charging of electrical insulation can be reduced and / or regulated in the present configurations due to a limited volume of dielectric material and appropriate interface usage, reduced areas for effective contact formation (especially for insulation contact-based configurations), floating electrodes (for charging and / or discharging dielectric areas for response regulation), etc. This further helps to increase system response reproducibility and reduce the probability of static friction due to dielectric charging between the contact surfaces.

[0050] Linearization / modulation of the bending cell response can also be read out using a detection signal, and due to the reduction of detected nonlinearity in the response, the required detection system can also be simplified. Detection can be based on inherent response changes such as a change in capacitance between the bending electrodes (e.g., capacitance change in the electrostatic gap can also be linearized or modulated to a lower order of linearity, along with the curvature of the cell during bending), structural deformation and / or stress in electrodes (which, for example, causes a resistance change based on piezoresistance (material such as crystalline silicon), or generates a voltage due to the piezoelectric effect), etc.

[0051] Fig. Figure 1a shows a schematic side view of a mechanical system 101, e.g., a bending transducer system, according to an exemplary embodiment. The mechanical system has a bending transducer structure configured to provide a bend, e.g., along a bending direction 14. The bending direction 14 is, according to a non-restrictive Cartesian coordinate system, along a z-direction, which, in the sense of a MEMS, may be planar or extraplanar. Without limiting the examples described herein, an x / y direction, with reference to a MEMS, may be referred to as a planar direction, while a direction along the z-coordinate may be referred to as an extraplanar bend or movement.

[0052] The bending transducer structure can be configured as an actuator to bend in response to an electrical signal 16. This can include, for example, electrostatic and / or electrodynamic actuators, as well as capacitive or piezoelectric actuators. However, the energy provided by the electrical signal 16 can also be converted into other types of energy, such as thermal energy, magnetic forces, or the like.

[0053] Alternatively or additionally, the bending transducer structure can effectively provide the electrical signal 16 in response to an applied force F, where the force F causes the bending. That is, the bending transducer structure can also function as a sensor. Both modes of operation can be implemented in an either / or manner, i.e., the bending transducer structure can be either a sensor or an actuator. However, a combined mode of operation is also possible, for example, if the bending transducer structure is operated sequentially as a sensor during a first period and used as an actuator during a separate second period.Another way of using both mechanisms, functioning as a sensor and functioning as an actuator, can be, for example, when the bending transducer structure is operated or controlled by providing the electrical signal 16, for example by using a control unit and / or an amplifier or the like, and by evaluating the electrical signal 16 (or another signal) with regard to a superposition or modulation caused by the force F; thus, the functioning as a sensor and the functioning as an actuator can be carried out simultaneously.

[0054] The bending transducer structure 12 can exhibit a structural stiffness that may be based on a material and a geometry of the bending transducer structure. The structural stiffness S1 of the bending transducer structure can provide a nonlinear mechanical stiffness contribution of the bending, that is, based on a changing deflection of the bending transducer structure, an additional force F can cause an increased or decreased deflection amount and / or the deflection behavior may be nonlinear with respect to a linear amplitude of the electrical signal 16.

[0055] The mechanical system 101 has an adaptation structure 18 which is mechanically coupled to the bending transducer structure 12 by means of a mechanical coupling. That is, the adaptation structure 18 is mechanically connected to the bending transducer structure 12. The adaptation structure 18 is configured to provide an adaptation deformation in conjunction with the bending of the bending transducer structure. That is, the force F and / or the electrical signal 16 causes a bending of the bending transducer 12 and thereby the deformation of the adaptation structure 18. A mechanical stiffness S2 of the adaptation structure 12 provides a further nonlinear mechanical stiffness contribution to the bending of the transducer structure based on the mechanical coupling. For example, the adaptation structure 18 can absorb or dissipate a portion of the force F or the force generated by electrical signals 16.The nonlinear behavior of the mechanical stiffness S2 can influence the behavior caused by the mechanical stiffness S1 of the bending converter structure 12, thereby increasing overall linearity compared to the nonlinear contribution of stiffness S1. However, it may be desirable to increase the nonlinearity, which is possible without specific restrictions by selecting a particular mechanical stiffness S2 or its behavior. This can be achieved by selecting a suitable material and / or geometry. Both the bending converter structure 12 and the adaptation structure 18 can be configured to deform. That is, a certain amount of elasticity can be incorporated into both, the bending converter structure 12 and the adaptation structure 18.For MEMS structures, semiconductor-based materials and / or dielectric materials or metal-containing materials may be suitable. For micromechanical systems, in addition to metal or other dielectric or conductive materials, other types of materials such as wood, plastic, or the like may be used.

[0056] At the in Fig. In the example shown, the adaptation structure 18 is adapted to form a mechanical contact at a contact surface 22a and at a contact surface 22b of the bending transducer structure; that is, the contact boundaries are used to ensure mechanical contact. A force generated by the contact between the contact surfaces 22a and 22b can be variable or non-constant during contact formation and with respect to an increase or decrease in amplitude along the bending direction. For example, the size of a contact area where the contact surfaces 22a and 22b make contact can increase or decrease.

[0057] Fig. Figure 1b shows a schematic side view of a mechanical system 102 according to an embodiment, wherein the adaptation structure 18 is adapted to provide the second nonlinear mechanical stiffness contribution without forming any additional contact with the bending converter structure 12 beyond the mechanical coupling or other unchanging or constant connections. While the contact in the contact surfaces 22a and 22b of the mechanical system 101 is such a variable or changing contact, the mechanical system 102 is implemented without such contact surfaces.

[0058] Fig. Figure 1c shows a schematic side view of a mechanical system 104 according to an embodiment. In contrast to the mechanical systems 101 and 102, which have the adaptation structure 18 outside a volume 24 enclosed by the outer sides of the bending transducer structure 12, the mechanical system 103 has a configuration in which the adaptation structure 18 is arranged within the volume 24. This can be understood to mean that the adaptation structure is arranged outside an active area of ​​the bending transducer. In the Fig. In the example provided in Figure 1c, the adaptation structure 12 can be clamped between bending elements 261 and 262, which may be attached to each other at their ends, with optional connections between them not excluded. For example, the bending elements 261 and 262 can be active elements such as electrodes, thermoactive elements, piezoelectric elements, or the like. This can make it possible to obtain pairs of contact surfaces 22a and 22b, 22c and 22d, of which, for example in a scenario like the one illustrated, no contact is formed, or, based on a deflection of the bending transducer structure along a positive or negative bending direction 14, only one of the pair of contact surfaces 22a and 22b on the one hand, or 22c and 22d on the other hand, provides mechanical contact.Instead of implementing mechanical contact in one of the pairs of contact surfaces 22a / 22b or 22c / 22d, it may be possible to form contact in both pairs simultaneously, e.g., based on a sufficient bending amplitude.

[0059] Fig. Figure 1d shows a schematic side view of a mechanical system 104 according to an embodiment comparable to the mechanical system 103, while the adaptation structure 18 is adapted, at least during normal operation, to provide no additional contact surfaces other than the mechanical coupling, which can be implemented, for example, by a clamping 281 and / or 282 at the ends of sections or the entire bending elements 261 and 262.

[0060] The examples of implementation according to Fig. 1a-d can be assigned to different groups of structures. While mechanical systems 101 and 103 provide temporary additional contacts in contact surfaces 22a, 22b, or optionally 22c and 22d, mechanical systems 102 and 104 are formed without such contact formations. This does not preclude constant mechanical couplings.

[0061] Another grouping can be such that the adaptation structure 18 is located outside of volume 24 or inside volume 24.

[0062] Fig. Figure 2a shows a schematic top view of a mechanical system 201 according to an exemplary embodiment. The Cartesian coordinates x, y, and z are shown as a non-restrictive example. According to the illustrated configuration, the bending direction 14 is planar. As can be seen from the structure of the mechanical system 102, the structure can be rotated in space, which also rotates the bending direction 14.

[0063] Bending elements 261 and 262 can have a substantially parallel orientation. In an unactuated state or a reference state of a sensor implementation, the bending elements 261 and 262, which may be formed as bending beams, can, for example, each have curved shapes that are parallel to each other. An unactuated state can be understood as a reference state without the application of an electrical signal 16 in an actuator configuration or a force F in a sensor configuration. The unactuated state can nevertheless allow for some pre-deflection of the bending transducer structure 12.

[0064] A neutral axis 271 of the bending element 261 runs essentially parallel to a neutral axis 272 of the bending element 262. Based on a given configuration, the surfaces 261A and 262B also run essentially parallel to each other, as do the outer surfaces 261B and 262A, as a non-restrictive example.

[0065] As in Fig. As shown in Figure 2a, the bending converter structure 12 can have at least two bending elements 261 and 262 which are mechanically coupled parallel to each other and form a gap 38 with an adjacent bending element of the bending converter structure. The adapting structure 18 can, for example, be arranged in the gap 38, at least partially, to separate the gaps into gaps 381 and 382.

[0066] Clamps 281 and 282 fasten the bending elements 261 and 262 together and provide a gap between them, e.g., as a spacer element. The clamps 281 and 282 can be formed by a single, one-piece element, but can also be formed by several elements, as in Fig. Figure 2a shows that, for example, the clamping device 281 can have spacer elements 28a1 and 28b1, which are part of the bending elements 261 and 262, respectively. For example, the spacer element 28a1 can be formed integrally with the bending element 261, and the spacer element 28b1 can be formed integrally with the bending element 262. This can facilitate simple manufacturing, particularly if the bending elements 261 and 262 are conductive, so that a conductive spacer element 28a1 and 28b1 can provide electrical contact, for example, to be connected to an operating potential shown by GND and +V, which can allow an operating voltage, e.g., B. on the basis of an electrical signal 16, between the bending elements 261 and 262, which can lead to an attractive force between the bending elements 261 and 262 and thus to movement components 341 and 342 of the bending elements 261 and 262 towards each other.

[0067] The adaptation structure 18 can comprise a dielectric material and can be configured to contact at least two elements of the bending converter structure 12 and to insulate them based on the bending, e.g., the bending elements 261 and 262. Preferably, an insulator 361 is arranged between the conductive spacer elements 28a1 and 28b1. Similarly, it is preferred to arrange an insulator 362 between the spacer elements 28a2 and 28b2 to prevent short circuits between the respective spacer elements. According to another example, however, at least the spacer elements 28a2 and 28b2 can be implemented using a dielectric material, thus eliminating the need for the insulator 362. If the mechanical system 201 is produced as a layered structure, it is still possible to provide the insulator 361 / 362 as a layer of the system without complicated additional steps.

[0068] One of the advantages provided by the adaptation structure 18 as a separate layer in the electrostatic air gap, instead of being produced directly on the electrodes 261 and / or 262, is that the areas with interfaces between conductor / metal and dielectric / insulator material are significantly reduced. Such interfaces, particularly in typical material systems and production processes in the field of MEMS and nanoelectromechanical systems (NEMS), are known from the literature to be good charge traps, which can increase the dielectric charging effect and thus the static friction probabilities between contact surfaces, especially with frequent contact-based actuation. Reducing these interfaces can help to reduce the hysteresis of the system response and to exhibit better functional reliability and reproducibility of the system response.

[0069] Since the dielectric layer is isolated in the cell space, the overall internal stress in the thin-film structures of the cell due to production, especially for MEMS and NEMS applications, can be significantly lower than in cases where dielectric layers are on the electrodes, particularly for non-uniform (e.g., Fig. 3b) Configuration, due to a reduced interface area between two or more different types of material systems (conductor / metal to dielectric / insulator material). This can simplify the design, as more complex techniques for compensating for self-stressing are not required, and cells exhibit negligible pre-deflection after release of structures during production.

[0070] On the other hand, the production of such isolated dielectric layers as structure 18, especially in the MEMS and NEMS fields, at the minimum resolution limits of the production process (i.e., at the smallest electrostatic air gaps that can be produced for the lowest possible operating voltages), can be accompanied by a comparatively increased complexity, and it is difficult to adequately control their dimensions in practice during production at such resolution limits.

[0071] Furthermore, maintaining structural integrity and sufficient robustness of isolated dielectric / insulator layers 18 at reduced thicknesses can be challenging for a given design, particularly at the resolution limits of production processes in the MEMS and NEMS fields. Therefore, a minimum thickness of the structure 18 can be applied to maintain the shape of a thin, isolated dielectric layer, especially to withstand high electrostatic pressure forces repeatedly during operation, without mechanical and / or electrical failure. This can limit the minimum thickness of the structure 18 that can be used even if an electrical breakdown voltage limit has not been reached for the dielectric layer at the required operating voltage.This in turn can limit the downward scaling of the system to usable minimum air gaps, and thus require a higher voltage for actuation compared to cases where dielectric layers are directly on the electrodes (e.g. ). Fig. 3a-c, etc.), in which case the minimum thickness of the dielectric layer on the electrode is limited only by the limit of electrical breakdown at the required operating voltage (since the required structural integrity and robustness comes from the electrodes on which a dielectric layer is produced).

[0072] The adaptation structure 18 can be clamped between the bending elements 261 and 262, as illustrated for the mechanical systems 103 and 104. The adaptation structure 18 can be formed integrally with the insulators 361 and / or 363. An insulating property of the adaptation structure 18 can be advantageous, but is optional in a case where the bending elements 261 and / or 262 are electrically insulated, for example, if they have an insulating layer arranged on them and / or if they are operated non-electrically, e.g., thermally.

[0073] Based on actuation using the electrical signal 16 and / or responding to the force F, the gaps 381 and 382 can change their dimensions. For example, the gaps 381 and 382 can become smaller, at least in a region of the contact surfaces 22a / 22b between the bending element 261 and the adaptation structure 18 and / or between the adaptation structure 18 and the bending element 262 in the contact surfaces 22c and 22d.

[0074] Starting from a vertex of the progression, for example a position where the plane AA' is located, the contact surfaces 22a-d can increase along contact evolution directions 441 and 442. An increase in the contact area can enable an increase in the mechanical resistance provided by the adaptation structure 18 through its mechanical stiffness contribution, in order to counteract nonlinearities in the possible electrostatic actuation of the bending elements 261 and 262.

[0075] The mechanical system 201 can be used as a single actuator / sensor, but it can also be used in conjunction with other mechanical systems, for example, as a group of them. In other words, it shows Fig. 2a an exemplary basic cell configuration with an insulating layer 18 between the electrodes, instead of the electrostatic air gap 381 / 382, in a top view of a planar bend or a side view of an off-planar bend.

[0076] The exemplary basic cell configuration can refer to an electrostatic bending actuator (NED) for response modulation based on contact formation between the electrodes (261, 262) in the electrostatic interstitial space via a detached dielectric / insulator layer (18), which is connected to a cell geometry at the spacer regions (28) by electrical insulation (361, 362) of the electrodes. When a potential difference is applied to the electrodes, the cell bends in direction 14 (based on the NED principle) along the neutral axis of the cell geometry. The greatest movement in the electrodes 261, 262 will occur in the center of the cell (AA plane) along directions 341 and 342, respectively. Beyond a certain voltage (not necessarily an attractive voltage of the cell geometry), based on cell design parameters such as electrode thickness, length, cell topography angle, etc., the cell geometry will flex.The electrodes will come into contact with the dielectric layer (18), resulting in initial contact formation and thus initiating the transition to a region of modulated response. After initial contact formation, contact evolution along the cell length will occur in directions 5a and 5b, resulting in increased stiffness of the cell geometry, particularly in the cell bending direction. This counteracts the nonlinearity of the cell response when an actuation voltage signal is applied. Cell symmetry (along the AA plane) facilitates simpler design and control of the actuator but is not essential for the principle to function. The geometry can be realized both planarly and extraplanarly using various production processes, such as batch micromachining, surface micromachining, 3D printing, etc., or combinations thereof.

[0077] Fig. Figure 2b shows the schematic top view of a mechanical system 2001, which comprises a plurality of cells 201 according to Fig. 2a. The cells 201 are arranged in series, one along the other, and connected at the respective clamp 282 of a previous cell. This allows the amplitude of a deflection along the bending direction 14 at an unclamped end 46 to be increased compared to a single cell. Fig. Figure 2c shows a schematic top view of a mechanical system 2002 according to an embodiment, wherein a second half 842 of cells 201 is rotated, for example, by 180 degrees. While, for example, all of the cells of the mechanical system 201 may have a curvature along the +y-direction, half 481 of the cells of the mechanical system 2002 is arranged accordingly, and the second half 482 has curvatures along the -y-direction. Compared to the mechanical system 2001, a so-called s-configuration can thus be obtained, which makes it possible to avoid at least partial rotation and at least partial rectilinear movement of the end 46. The groups or halves 481 and 482 can also be arranged in reverse and / or cells with a curvature along the +y-direction and along the -y-direction can be arranged alternately. Furthermore, any sequence or type of grouping can be implemented.

[0078] Fig. Figure 2d shows a schematic top view of a mechanical system 2003 that has a double-clamped configuration, i.e., both ends of the chain of cells are clamped. This can make it possible to obtain a deflection of the mechanical system 2003 along the bending direction 14 more strongly at a midpoint or center of the mechanical system 2003.

[0079] Fig. Figure 2e shows a schematic top view of another mechanical system 2004 according to an embodiment. Starting from a center 48 of the mechanical system 2004 or the deflectable part thereof, a symmetrical number of, for example, two cells 201 are preferably arranged in such a way that the curvature occurs along the y-direction, followed by a preferably symmetrical number of cells 201 that have an alternative curvature along the +y-direction. The number of cells exhibiting the direction of curvature along the +y-direction and along the -y-direction can be the same. Embodiments also provide structures in which, starting from the center 48, the cells are arranged asymmetrically with respect to the number of cells and / or the structure of the cells and / or their orientation.

[0080] Although the mechanical systems 2001 to 2004 are illustrated as having eight cells, the number can vary, for example, at least 2, at least 3, at least 4, at least 8, or even more. Mechanical systems according to the embodiments can have different implementations of individual cells, with these cells being implemented similarly or differently. That is to say, each mechanical system described herein can be used individually or in combination with at least one cell or a greater number of cells, with the cells being of the same type or embodiment, or of a different type or embodiment. Identical or different configurations can be combined in any way or with any concept.

[0081] In other words, they show Fig. 2b to 2e are exemplary bending beam configurations. Fig. 2b shows a jam-free configuration, Fig. 2c shows a jam-free S-configuration, Fig. Figure 2D shows a double-clamped configuration, and Fig. Figure 2e shows a double-clamped S-configuration, in top view for planar bending or in side view for extraplanar bending. Fig. Figures 2b-2e show basic bending actuator beam configurations for the example cell shown in Fig. 2a is shown: (i) clamp-free configuration: all cells bend in the same direction, resulting in a bending movement in a direction 14 of the free end of the beam; (ii) clamp-free S-configuration: cells of group 481 and cells of group 482 bend in opposite directions to form an S-configuration when actuated, in order to avoid rotation of the free end of the beam and to allow rectilinear movement in direction 14; (iii) double-clamped configuration: all cells bend in the same direction, resulting in movement in direction 14 of the beam center; (iv) double-clamped S-configuration: cells bending along +y and cells bending along -y bend in opposite directions to form an S-configuration on each side of the beam center when actuated, in order to achieve rectilinear movement in direction 14.

[0082] Fig. Figure 2f shows a schematic top view of a mechanical system 202, which, in comparison to the mechanical system 201, has a multilayered adaptation structure in which a plurality of layers 181 and 182, optionally additional layers, each have a gap 383 between adjacent layers 181 and 182, wherein the gap 383 is partially closed in a deflected state of the bending converter structure 12. The adaptation structure 18 can have a layered structure that is arranged planarly between the first bending element 261 and the second bending element 262. The different layers 181 and 182 can have a continuous gap between them or can have a discontinuous gap, for example, if they are contacted with each other at discrete positions.

[0083] In other words, it shows Fig. Figure 2f shows an exemplary basic cell configuration with multiple insulating layers between the electrodes in the electrostatic air gap to enable the formation of multiple contacts in a top view for planar bending and in a side view for off-planar bending. The exemplary basic cell configuration features multiple detached dielectric / insulator layers (181, 182) between the electrodes (261, 262) in the electrostatic air gaps (381-383) to enable the formation of multiple contacts during actuation. The stiffness (thickness, modulus of elasticity, etc.) of the dielectric layers in the bending direction and the positioning of the separate insulating layers relative to a neutral axis of the cell geometry (i.e.,Depending on the requirements (how far the dielectric layer will expand or contract relative to the electrodes), different configurations for contact formation and evolution can be achieved. Contact formation and evolution only between the insulating layers 181 and 182 is also possible through their movement in directions 34a3 and 34b3, with contact evolution in directions 44a3 and 44b3. This helps to reduce the probability of dielectric charging, since electrodes with a potential will not be in contact with the surfaces of the dielectric layer for the nonlinear stiffening of a cell via contact formation during actuation.Alternatively, contact formation of all electrodes (261, 262) and the dielectric layers (181, 182) can be achieved with contact evolution in the cell bending directions (44) to obtain a higher cell stiffness when a voltage signal is applied, together with higher available electrostatic forces.

[0084] The configuration from Fig. 2f provides advantages, e.g. compared to Fig. 2a, since even with the same cell, different linear regimes with different inclinations can be obtained based on the occurrence of different regimes for contact formation and propagation and their superposition, simply by increasing the actuation voltage. The dimensions of electrodes, dielectric layers, and air gaps can be of the same order of magnitude as in Fig. 2a, however, the overall stiffness of the cell must be reduced accordingly or the actuation voltage must be increased in order to achieve this. Fig. 2f same bending range as in Fig. 2a, since the presence of multiple layers and air gaps increases the total gap between electrodes 261 and 262 (especially at the production resolution limits of the manufacturing process used), which will reduce the overall electrostatic forces (which can be compensated for by reducing the overall cell bending stiffness or by increasing the actuation voltage). The cell bending stiffness can usually be reduced by using thinner and / or longer electrode / dielectric layers with higher dome angles.

[0085] Fig. Figure 2g shows a schematic top view of a mechanical system 203 according to an embodiment, wherein the adaptation structure 18 has a variable distance to at least one bending element 261 and / or 262 of the bending converter structure 12, for example when comparing the mechanical system 203 with the mechanical system 201, a layer 52 of the adaptation structure 18 can have one or more protrusions 541, 542 on one or both sides of the layer 52, wherein a position of a protrusion 541 and / or 542 can be symmetrical or asymmetrical with respect to the side facing the bending element 261 and the side facing the bending element 262, and / or along the direction x.This means that the number of protrusions 541, 542 on a first side 52A and on a second, opposite side 52B of layer 52 can be the same or different, and the height of the protrusions 541 and 542 can be the same or different based on the design criteria. The protrusions 541 and 542 allow for a variable distance between the adaptation structure and at least one of the bending elements 261 and 262 along an axial direction.

[0086] The protrusions 541 and / or 542 can be made of the same material as layer 52 or of a different material. Making layer 52 and the protrusions 541 and 542 from the same, possibly dielectric, material can simplify fabrication. The protrusions 541 and 542 can reduce static friction effects by decreasing the contact area. Alternatively, the contact area 22a / 22b and / or 22c / 22d can be separated or structured.

[0087] Fig. Figure 2g thus shows an exemplary basic cell configuration with a structured insulating layer in an electrostatic air gap between the electrodes to reduce contact points during actuation, in a top view for planar bending or a side view for extraplanar bending.

[0088] In other words, the exemplary basic cell configuration features a structured dielectric / insulator layer 52 in the electrostatic air gap between the electrodes to reduce the effective contact area between the dielectric layer 52 and the electrodes 261 and 262 during contact formation and evolution in directions 441, 442 upon actuation.

[0089] A key advantage of the configuration according to Fig. 2g, for example, compared to Fig. 2a or Fig. 2f, may be due to a low number of contact points, which can greatly reduce the static friction probabilities and also the dielectric charging of the dielectric layers due to the changing contact with the electrodes. The configuration of Fig. 2g can achieve a reduction in cell response nonlinearity solely through initial contact at the AA' plane and electrode expansion in the bending direction. To achieve this, continuous contact propagation is not required, and other structured areas are not essential for reducing response nonlinearity. The other contact sites (541 and / or 542) can be used for improved guidance and increased stiffness if contact is established at these sites, while generating a higher electrostatic force due to a higher effective relative permittivity.

[0090] Alternatively, the two electrodes 261 and 262 can also be structured (in a tongue-and-groove configuration) to have a reduced contact area for simpler production. The electrical layer and the electrodes can even be tongue-and-groove simultaneously or manufactured to surfaces with higher roughness (e.g., using DRIE etching processes of crystalline silicon to create deep corrugations on the sidewalls of Si electrodes and Si trenches that are filled with the conformal dielectric material, for example Al2O3, using an atomic layer deposition (ALD) process to conform to the shape of the trench and, upon release, exhibit a high surface roughness).

[0091] The dimensions of the electrodes, dielectric layers, and air gaps can be arranged in the same size order as in Fig. 2a, however, the overall stiffness of the cell must be reduced accordingly, or an actuation voltage must be increased in order to achieve this. Fig. 2g same bending range as with Fig. 2a, since the presence of structured dielectric layers and air gaps will increase the total gap between electrodes 261 and 262 (especially at the production resolution limits of the production process used, which will reduce the total electrostatic forces), which can be compensated for by reducing the overall flexural stiffness of the cell or increasing the actuation voltage. The cell flexural stiffness can usually be reduced by using thinner and / or longer electrode / dielectric layers with higher dome angles.

[0092] Fig. Figure 3a shows a schematic top or side view of a mechanical system 301, which, in comparison to, for example, the mechanical system 202, has layers 181 to 184 of the adaptation structure 18 to cover the bending elements 261 and / or 262 on both sides, which may result in, for example, a total of four layers. That is, instead of a plurality of spaces, as has the mechanical system 202, a single space 38 can be obtained.

[0093] In other words, it shows Fig. 3a An exemplary basic cell configuration with a dielectric / insulator layer on all sides of the electrodes, shown in a top view for planar bending and a side view for off-planar bending. The exemplary basic cell configuration features a dielectric / insulator layer on all sides of the electrodes for a high dielectric constant in an electrostatic gap (for higher forces) and for complete and reliable electrical insulation (even with an adjacent outer beam electrode). Furthermore, the inherent stress in such a configuration is inherently lower, particularly in the case of a homogeneous dielectric layer, which can be achieved via conformal deposition processes such as atomic layer deposition (ALD). For a system with a compact stacking of the bending cell beams ( Fig. 2b-e) In a parallel manner, contact formation with external electrodes of cells of adjacent beams can also be achieved using a cell geometry such as that described in Fig. 3a is shown, manufactured (via the outermost insulating layer on electrodes) to modulate the stiffness of the entire stack of actuator beams (in addition to contact formation and evolution in the electrostatic interspace of the cell).

[0094] The structure according to Fig. In addition to those already mentioned, 3a provides, for example, in comparison to Fig. 2a or Fig. 2f, for further benefits.

[0095] For example, it enables simpler and better controllable production of dielectric layers (18 1-4) with a required thickness on the electrodes, particularly using standard MEMS and NEMS production processes and materials. Based on conformal deposition processes such as ALD, the dielectric layers can also be deposited to achieve much smaller air gaps than the production resolution limits by coating the cell geometry after production to exhibit lower actuation voltages.

[0096] Furthermore, the limit of structural integrity is not a limiting factor on the required minimum thickness of the dielectric layer; the only main limit is the electrical breakdown limit at the maximum operating voltage.

[0097] However, the number of surfaces with interfaces between conductor / metal and dielectric / insulator material is significantly higher, which can lead to greater electrical charge buildup and increased frictional adhesion probabilities between contact surfaces. For higher charge buildup effects that lead to frictional adhesion problems, which can be addressed through design features such as stiffer electrodes with electrostatic attraction and / or repulsion effects (pull-in or pull-out) for contact formation or easier opening, conformal anti-stick coatings, such as an ALD-applied FOTS (perfluorodecyltrichlorosilane) layer, can be used. Alternatively, the system can be operated via amplitude-modulated AC electrical signals at a much higher frequency than the maximum mechanical response frequency of a cell to rapidly discharge the cells and reduce any charge buildup effects.

[0098] Fig. Figure 3b shows a schematic view of a mechanical system 302 in which, compared to the mechanical system 301, only the inner adaptation structure layers 181 and 182 are arranged, as a non-restrictive example. The second nonlinear mechanical stiffness contribution may therefore differ compared to the mechanical system 301. However, the electrical insulation can still be maintained.

[0099] In other words, it shows Fig. 3b An exemplary basic cell configuration with an insulating layer on electrodes only on the side of the electrostatic gap between the electrodes to reduce dielectric charging, shown in a top view for planar bending and a side view for off-planar bending. The exemplary basic cell configuration has an insulating layer on electrodes only on the side of the electrostatic gaps between the electrodes to reduce the probabilities of possible dielectric charging and associated static friction probabilities, while maintaining a high dielectric constant in the electrostatic gap (for higher forces) and the required electrical insulation.

[0100] In comparison to the structures from Fig. 2a, Fig. 2f and / or Fig. 3a. Advantages of the structure according to Fig. 3b, in addition to those already mentioned, lies in the fact that the structure represents an intermediate compromise configuration between Fig. 2a and Fig. 3a is - which has less charging, static friction and interfaces compared to Fig. 3a exhibits, while it continues to exhibit the mechanical structural integrity of dielectric layers originating from the electrodes, in contrast to Fig. 2a. However, due to the absence of counteracting self-stresses from reverse interfaces, the same will have a higher total self-stress than Fig. 2a and Fig. 3 exhibit,.

[0101] Fig. Figure 3c shows a schematic view of a mechanical system 303 which, starting from the mechanical system 302, has only one of the adaptation structures 181 and 182, for example, adaptation structure 181. This can further reduce the dielectric charge while still providing insulation between the electrodes 261 and 162. The second nonlinear stiffness contribution can advantageously be applied to one of the bending elements 261 and 162, thus providing an additional degree of freedom. In contrast to the mechanical system 201, where the adaptation structure 18 is symmetrical between the bending elements 261 and 262, different distances can be implemented with respect to the bending elements 261 and 262, with one of the distances possibly being reduced to zero, as shown for the mechanical system 303.

[0102] In other words, it shows Fig. Figure 3c shows an exemplary basic cell configuration with an insulating layer on only one electrode, on the side of the electrostatic gap between the electrodes, to reduce dielectric charge, in a top view for planar bending and a side view for off-planar bending. The exemplary basic cell configuration features an insulating layer on only one electrode, on the side of the electrostatic gap between the electrodes, to further reduce the probabilities of potential dielectric charging and associated static friction probabilities, while allowing for a high dielectric constant in the electrostatic gap (for higher forces) and the necessary electrostatic insulation.

[0103] Instead of applying a single adaptation structure 181 to the bending element 261, the layer can also be applied to its outer side and / or to the inner or outer side of the bending element 262.

[0104] Compared to Fig. 3b can the structure from Fig. 3c advantageously results in fewer interface areas and thus less charging, as well as typically lower overall self-stress in the cell for the same design parameters (since self-stress at interfaces is usually more dominant). Furthermore, even better structural integrity and robustness of the dielectric layer can be achieved for lower thickness values, particularly at the resolution limits of production processes in the MEMS and NEMS fields, compared to Fig. 3b, since to maintain the same level of electrical breakdown strength (which determines the maximum applicable voltage) the thickness of the dielectric layer on an electrode Fig. 3c the total thickness on each electrode Fig. It should be 3b.

[0105] Conversely, the increased required thickness of the dielectric layer on one electrode would lead to higher local stress on that specific electrode due to the greater thickness. Therefore, local machining to compensate for this stress might be necessary for certain electrode designs. Furthermore, using conventional conformal but slow deposition processes like ALD to deposit the dielectric layer will double the deposition time required to achieve the same level of dielectric thickness on one side of the electrode.

[0106] Fig. Figure 3d shows a schematic view of a mechanical system 304 according to an embodiment in which a single adaptation structure layer is applied as described for the mechanical system 303, wherein the single layer is structured such that it forms an interrupted structure which is arranged between the first bending element 261 and the second bending element 262.

[0107] In comparison to the mechanical system 303, structuring the adaptation layer 181, which, as a non-restrictive example, is arranged in the mechanical system 304 at the bending element 262, enables the implementation of a defined behavior of the nonlinear mechanical stiffness contribution on the one hand and a further reduced dielectric charge on the other, together with a low frictional adhesion risk. The adaptation elements 561, 562, ..., obtained by structuring the adaptation structure 18, can be arranged on a single bending element 262 and / or at least partially on an opposite side, e.g., the bending element 261.

[0108] In other words, it shows Fig. Figure 3D shows an exemplary basic cell configuration with a structured insulating layer applied only to one electrode on the side of the electrostatic gap between the electrodes to reduce dielectric charging and contact points during actuation, in a top view for planar bending and a side view for off-planar bending. The exemplary basic cell configuration features a structured insulating layer applied only to one electrode on the side of the electrostatic gap between the electrodes to further reduce dielectric charging and static friction probabilities by reducing the required dielectric material and contact points during actuation.

[0109] Compared to Fig. 3c can form the structure from Fig. 3D design advantageously results in fewer interface surfaces and less dielectric base material, thus reducing charge buildup. It can also reduce the number of contact points with the other potential electrode. This leads to a significant overall reduction in the probability of static friction. Furthermore, lower overall internal stress within the cell can be achieved for the same design parameters due to the interrupted interfaces and reduced amount of base material.

[0110] However, due to the structured dielectric layer, which results in dielectric islands / areas (561, 562), the probabilities of delamination between the electrode and the dielectric areas are higher compared to a continuous dielectric layer, since during contact formation and propagation in each cycle all contact forces will be concentrated locally directly at the base of each area and must be endured by the local interface between the electrode and the dielectric area.

[0111] For the same cell design, the electrostatic forces at a given voltage will be reduced because the effective relative permittivity (compared to the continuous dielectric layer) in the electrostatic space will be lowered due to a reduced amount of dielectric material with a higher relative permittivity than air.

[0112] Fig. Figure 3e shows a schematic view of a mechanical system 305 according to an embodiment, wherein a groove structure with one or more grooves 581 is arranged in the space 38, and wherein a spring structure with one or more springs 62 is arranged. The groove structure and the spring structure can form mechanical contact in a deflected state of the mechanical system 304 and prevent relative movement of the spring structure and the groove structure relative to each other along the x-direction, which is perpendicular to the bending direction 14 of the bending converter structure. With an increase in bending along the bending direction 14, an increasing number of springs can form mechanical contact with the opposite groove, which can be understood, for example, as a discrete number of steps of contributions to the nonlinear stiffness behavior.

[0113] The groove structure and / or the spring structure can be formed, for example, by the adaptation structure 18, e.g., the adaptation elements 56 of the mechanical system 304, whereby the grooves can also be implemented in a continuous or interrupted layer, such as in layer 181 or 182 of the mechanical system 302.

[0114] The groove structure and / or the spring structure can be formed from a material of one of the bending elements, for example, the bending element 261. Springs 581 and / or 582 can be made of the same material and can be formed integrally with the bending elements 261 and 262. In an implementation in which the bending elements 261 and 262 are charged with an electrical potential, preferably at most one of the groove structure or the spring structure is formed by the electrode material of the bending element 261 or 262, respectively, or alternatively or additionally, an insulating material is arranged between them.

[0115] On the other hand, both the groove structure and the spring structure can be formed from a continuous or interrupted layer of the adaptation structure, for example from layers 181 and 182 of the mechanical system 302.

[0116] In other words, an exemplary base cell configuration with a structured insulator layer on one electrode and a structured opposing electrode for a bending locking mechanism is shown in a top view for planar bending and in a side view for off-planar bending. This configuration features a structured insulator layer on one electrode and a structured opposing electrode for a bending locking mechanism. This mechanism improves contact locking and increases stiffness effectively through contact spreading, while simultaneously reducing dielectric charging and contact points during actuation.

[0117] The structure made up of Fig. 3e can be compared to Fig. 3D ensures increased displacement robustness, even if the same is true compared to Fig. 3D requires a larger gap between the cell electrodes to produce the necessary structures within that space. Therefore, the overall stiffness of the cell must be reduced, or the actuation voltage must be increased to achieve this. Fig. 3e same bending range as Fig. to obtain 3D. Compared to Fig. 3D can create the structure from Fig. 3e can be manufactured more easily.

[0118] Fig. Figure 3f shows a schematic view of a mechanical system 306 which, compared to the mechanical system 305, has additional connecting elements 641, 642, ... that further contribute to the second nonlinear stiffness. The connecting elements 64 can be made of the same material as the adapting elements 56, e.g., a dielectric material.

[0119] In other words, it shows Fig. Figure 3f shows an exemplary basic cell configuration with structured and linked insulator layer elements on one electrode and a structured opposing electrode for bend locking to improve contact locking and increase effective stiffness with contact spreading, while simultaneously reducing dielectric charging and contact points during actuation. This is shown in a top view for planar bending and a side view for off-planar bending. The exemplary basic cell configuration features a structured and linked insulator layer on one electrode and a structured opposing electrode for a bend locking mechanism to improve contact locking and increase effective stiffness with contact spreading, while simultaneously reducing dielectric charging and contact points during actuation.

[0120] Compared to Fig. 3e can it structure according to Fig. 3f enable the probability of delamination due to mechanical bonding of the dielectric layer to be reduced, even compared to Fig. 3e and / or Fig. 3d, since the contact forces are now also distributed along the cell length up to the edge insulator 36 and are divided by side linking elements (while these still have a reduced area of ​​interfaces), instead of simply concentrating locally directly at the base of each region (as in Fig. 3e and Fig. 3d). However, this effect can cause the following compared to Fig. 3e A larger gap between the cell electrodes is required to produce the necessary structures in the gap with the bending layer 64, especially at the minimum production resolution limits of typical MEMS and NEMS production processes. Thus, the overall stiffness of the cell must be reduced or an actuation voltage must be increased to achieve this. Fig. 3e same bending range as with Fig. to obtain 3D. Compared to Fig. 3f can derive the structure from Fig. 3e can be manufactured more easily.

[0121] Fig. Figure 3g shows a schematic view of a mechanical system 307 according to an embodiment in which the connecting elements 64 are formed from a different material compared to the adapting elements 56, e.g., a conductive material, such as that used for the bending elements 261 and 262. Since, in this example, contact is provided exclusively in the area of ​​the grooves 58 and springs 62, the risk of a short circuit is prevented while maintaining a low level of dielectric charging. Optionally, a material of the connecting elements 64, which are insulated from the bending elements 261 and 262 by an insulating material at the clamping 281 and 282, can be arranged in a region of the insulator 361 and 362.

[0122] In other words, it shows Fig. 3g an exemplary basic cell configuration with a structured insulating layer on one electrode, linked with floating electrodes, and a structured opposing electrode (spring structure) for a bending locking mechanism for better contact locking and to improve an effective increase in stiffness with contact spreading and a simultaneous reduction of dielectric charging and contact points when actuated in a top view for planar bending or in a side view for extraplanar bending.The exemplary basic cell configuration features a structured insulator layer on one electrode, linked with floating electrodes 64 (which can be used to charge and / or discharge the linked insulator structures to stabilize / modulate a system response in or after / before each operating cycle), and a structured opposite electrode for a bending locking mechanism to improve contact locking and enhance effective stiffness increase with contact spreading while simultaneously reducing dielectric charging and contact points upon actuation.

[0123] Compared to Fig. 3f can derive the structure from Fig. 3g advantageously provides better performance due to a mechanical linkage of dielectric regions / islands via standard electrode material, which usually exhibits better mechanical properties such as higher fracture toughness, elasticity, reduced plastic deformation or creep, etc., compared to standard dielectric materials (compared to Fig. 3f), especially in the MEMS and NEMS area, and thus a well-defined behavior can be obtained.

[0124] However, the structure can be made of Fig. 3g exhibit mechanical connections based on an electrode / dielectric interface between island-linking bends (compared to Fig. 3f, where the same dielectric material is used), and thus the probabilities of delamination may be higher (compared to Fig. 3f), especially at the minimum production resolution limits of typical MEMS and NEMS production processes. Furthermore, the effective relative permittivity will be lower due to less dielectric material. Therefore, the overall stiffness of the cell must be reduced or an actuation voltage must be increased to compensate for this. Fig. 3g same bending range as in Fig. To obtain 3f, which is a basis for a compromise. Compared to Fig. 3g can produce the structure according to Fig. It should be 3f simpler.

[0125] The embodiments described herein relate, among other things, to a mechanical coupling of the bending converter structure and the adaptation structure. Such a mechanical coupling can comprise a fixed arrangement of one element to another, for example, by using the stiffness of a substrate 66 and / or an insulating material and / or another material that adapts different elements to one another. The mechanical coupling between the adaptation structure and the bending converter structure can be adapted to combine the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution to obtain the bending of the bending converter structure based on a combination of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution. In the Fig. In the examples provided in 2a to 3g, the first nonlinear mechanical stiffness contribution and / or the second nonlinear mechanical stiffness contribution can be based on mechanical contact between a first element and a second element of the mechanical system, for example, between the bending transducer structure and the adaptation structure. Other contacts are possible and are described herein. The mechanical contact can cause a variable magnitude of mechanical forces acting on the bending transducer structure and / or the adaptation structure, with an increase in a bending amplitude, for example, along or opposite to direction 14.

[0126] With regard to the hereinto in connection with Fig. In the embodiments described in 2a to 3g, a mechanical system can be configured to provide mechanical contact between the bending transducer structure 12 and the adaptation structure 18, for example by contacting opposing contact surfaces 22. The bending transducer structure 12 and the adaptation structure 18 are arranged to increase their contact area with each other when the bending of the transducer structure increases, the contact area formed between the adaptation structure and the bending transducer structure being, for example, Fig. 2a, and / or between a first element of the adaptation structure connected to the first element of the bending transducer structure and a second element of the adaptation structure connected to the second element of the bending transducer structure, as for example in Fig. 3b is shown.

[0127] As in Fig. As shown in Figures 2a to 3g, in a non-displaced state of the bending converter structure, a first neutral axis of the first bending element 261 can be substantially parallel to a second neutral axis of the second bending element 262, particularly in a case where both elements have a similar shape and are parallel to each other. Alternatively or additionally, a surface of the bending element 261 facing the bending element 262 can be substantially parallel to a surface of the element 262 facing the bending element 261.

[0128] As in Fig. As shown in Figures 2a to 3g, the adaptation structure 18 can be arranged partially or completely between a first section of the bending converter structure and a second section of the bending converter structure, each formed, for example, by a respective bending element 261 and 262. The adaptation structure can be arranged between them along a bending direction of the bending converter structure. As shown, for example, in Fig. As shown in Figure 2a, the bending converter structure can have at least two bending elements 261 and 262 which are mechanically coupled in parallel and form a gap 38 or more gaps with an adjacent bending element of the bending converter structure or the adaptation structure, or a part thereof. At least a part of the adaptation structure is arranged in the gap and mechanically coupled in parallel to the adjacent bending elements via mechanical contact. The bending of the bending converter structure along direction 14 can cause mechanical contact between the adaptation structure 18 and at least one of the adjacent bending elements in the gap, either directly with the element or with a layer attached to it.For example, starting with the mechanical system 201, a mechanical system according to exemplary embodiments can also have three or more bending elements 26 that are mechanically coupled in parallel to form at least one first gap between a first bending element and a second bending element, and at least one other gap between the second bending element and a third bending element. For example, the mechanical system 201 can have at least one third bending element 263, which is arranged, for example, to clamp the bending element 262 between the bending element not shown and the bending element 261. Different parts of the adaptation structure can be arranged in the different gaps to form different contacts, either simultaneously or at different times.

[0129] Fig. Figure 4a shows a schematic view of a mechanical system 401 according to an embodiment. Compared to other mechanical systems described herein, for example, mechanical systems 201 or 301, the bending elements 261 and 262 can have different shapes and / or different properties. Although the neutral axes of the bending elements 261 and 262 in the example from Fig. 4a do not run parallel, the sides 261 A and 262 B of the bending elements 261 and 262 run essentially parallel in the unactuated state shown.

[0130] Similar to other embodiments, actuation and / or an external force F can cause contact to be formed in the contact surfaces 22a / 22b between the adaptation structure layers 181 and 182, which increases along directions 441 and 442 with an increase in deflection.

[0131] In other words, it shows Fig. 4a An exemplary cell configuration with fully insulated electrodes and electrodes with a flat base for downward bending along direction 14, shown in a top view for planar bending and in a side view for extraplanar bending. The term downward bending refers to a viewing direction in Fig. 4a and is not necessarily linked to an orientation of the mechanical system 401 in space. It is obvious to those skilled in the art that terms such as up, down, left, right, front, back, or the like can change arbitrarily in space when a mechanical system 401 or other embodiments are rotated.

[0132] Despite the presence of a planar or straight element 262, the bending direction 14 can be influenced, at least to some extent, by the shape or structure of the bending element 261. The exemplary cell configuration features fully insulated electrodes and flat-bottomed electrodes for downward bending. A geometry with straight electrodes is particularly useful for generating non-planar S-configuration bending beams, since an ordinary flat-bottomed electrode can be used to generate upward and downward bending cells in the cell beam for easier production. Furthermore, the use of deposition-based conformal dielectric layers, required for insulation-based contact formation (341 and 342) and its evolution (441 and 442) in an electrostatic gap, reduces the achieved effective air gap much more than the typical production limit of the physical air gap.This significantly increases the electrostatic forces due to an increase in the effective dielectric constant in the electrostatic gap. It also improves the system's electrical reliability against short circuits between electrodes and against accidental contact formation. The flat electrode side (planar and extraplanar) can also be used directly when required for certain applications, such as those requiring well-defined border formation based on a flat wall, as in micropumps, microvalves, microspeakers, etc., to effectively control fluid pressure distribution.

[0133] Fig. Figure 4a shows, among other things, another embodiment of the present invention, according to which the inventive concept is not limited to a geometry of curved electrodes / dome electrodes. Other advantages provided include, for example, that this type of geometry can be more easily produced at the wafer level compared to curved electrodes / dome electrodes in order to obtain an extraplanar, e.g., downward-curved, bending system using standard MEMS production processes at the wafer level (e.g., wafer bonding and structuring of the electrodes via batch micromachining processes) due to the planar nature of the electrode geometry. Due to the use of wafer bonding and batch micromachining processes, the prestressing in these structures can be significantly lower compared to extraplanar configurations formed by surface micromachining, which requires thin-film deposition.A general design constraint (which is not absolute, however) for effective bending behavior is that the local electrode thickness in certain areas is so small that bending in that particular direction is facilitated.

[0134] Fig. Figure 4b shows a schematic view of a mechanical system 402 according to an embodiment that can be considered complementary to the mechanical system 401. While the mechanical system 401 may have increased stiffness at the center of the bending element 261 along an axial path, the bending element 262 may have a thinning 68 at its center, thereby locally weakening the structure or reducing its mechanical stiffness. Compared to the mechanical system 401, the bending direction 14 is reversed. While the bending element 261 of the mechanical systems 401 and 402 may have complementary properties, the bending element 262, as a non-limiting example, is planar in both ways, and a non-planar implementation for the mechanical systems 401 and 402 may also be selected and implemented.

[0135] In both configurations, the bending transducer structure can have at least two bending elements 261 and 262, which can be attached to one another at discrete positions, for example, the clamps 281 and 282. Along a bending direction 14, along which the bending transducer structure 12 is configured to provide the bending, the stiffness of one of the bending elements differs from that of the other bending element. That is, a local stiffness can vary from section to section of the electrodes to achieve upward or downward bending, while a specific desired topology of a planar electrode is present on one side of the transducer element.

[0136] In other words, it shows Fig. 4b An exemplary configuration with fully insulated electrodes and flat-bottomed electrodes for upward bending, shown in a top view for planar bending and in a side view for extraplanar bending. The exemplary cell configuration features fully insulated electrodes and one flat-bottomed electrode for upward bending. The cell configuration from Fig. 4a can be used together with this configuration to create a bending beam with an extraplanar / planar S-configuration using an ordinary flat-bottom electrode.

[0137] Fig. Figure 4b illustrates a further embodiment of the present invention, according to which the concept is not limited to a geometry of curved electrodes / dome electrodes. Further advantages gained include the fact that this type of geometry can be more easily produced at the wafer level (compared to curved electrodes / dome electrodes) to obtain an extraplanar, e.g., upward, bending system using standard MEMS production processes at the wafer level (e.g., wafer bonding and structuring of the electrodes via batch micromachining processes) due to the planar nature of the electrode geometry. Because of the use of wafer bonding and batch micromachining processes, the prestressing in these structures can be significantly lower compared to extraplanar configurations formed by surface micromachining, which requires thin-film deposition.A general design constraint (which is not absolute, however) for effective bending behavior is that the local electrode thickness in certain areas is so small that bending in that particular direction is facilitated.

[0138] While other embodiments have been described as having one or more bending elements with a curved profile between a first end and a second end of the bending element 261 / 262 in a non-displaced state of the mechanical system in order to define the direction 14 of the bending, it is also possible to implement angular profiles, as for example in Fig. Figure 5a illustrates a schematic view of a mechanical system 501. Curved, but possibly straight, elements of the bending elements 261 and 262 are arranged symmetrically or asymmetrically with an angle α between them, where the angle α is, for example, less than 170° or more than 190°. Compared, for example, to the mechanical system 201, this can lead to contact formation on two separate surfaces 22a / 22b on the one hand and 22c / 22d on the other, in addition to a median plane A-A', defined by the planes BB' and C-C'. This allows the magnitude of the second nonlinear mechanical stiffness contribution to be adjusted, e.g., increased.

[0139] A strong dependence of α can be observed with respect to the distance of the contact-forming planes BB' and CC' from the plane of symmetry AA' (as well as with the bending effect / bend curvature achieved under applied stress). For example, as α increases (and other dimensions remain nearly constant), the B-B' and C-C' planes can move closer to the A-A' plane (at one point they will almost overlap, as in Fig. 2a, when the system becomes “flat enough”, and the first contact will occur almost at the A-A' symmetry plane. However, this is only a general case and there may be exceptions for asymmetrical designs or extreme α values.

[0140] In other words, to show another embodiment of the present invention, according to which the concept is not limited to a geometry of dome electrodes / straight electrodes or to formations of centralized single-point contacts and their distribution, shows Fig. 5a An exemplary cell configuration with fully insulated electrodes and multiple non-centralized physical contact points and contact distribution is shown in a top view for planar bending and in a side view for off-planar bending. The exemplary cell configuration features fully insulated electrodes and multiple non-centralized physical contact points and a contact distribution. Although symmetrical for the given geometry (about the A-A' plane), the contact points do not need to be symmetrical for the stiffening principle to function and to allow a reduction of one order of magnitude of nonlinearity in the system responses. The contact points and contact distribution can be modified asymmetrically based on cell geometry (e.g., asymmetrical cell design) and / or by changing the load conditions (e.g.,asymmetrical load distribution on the cell structure).

[0141] Fig. Figure 5b shows a schematic view of a mechanical system 502 according to an embodiment. In comparison to the mechanical system 501, the findings associated with the mechanical systems 401 and 402 are combined, i.e., at least one of the bending elements 261 and 262 can have a variable stiffness and / or a variable thickness along the axial profile along the x-direction.

[0142] A key difference between the structures from Fig. 5b and Fig. 5a may consist of increasing the stiffness of the bottom electrode by making it thicker (filling an empty roof), as a possible way to further shift the contact formation planes towards the quarter length of the cell (since the regimes of higher stiffness can then usually be reached much faster) in order to modulate the contact spreading lengths on both sides of the contact plane in order to match the ranges of linear regimes as required.

[0143] It should be noted that a ground electrode with bending systems (as in Fig. 8a shown by elements 841 and 842) or a different roof angle α can also be used to change the position of the plane of contact formations.

[0144] For a given air gap, the increase in the stiffness of the bottom electrode can be compensated for by a corresponding reduction in the overall stiffness of the cell, or the actuation voltage must be increased to achieve this. Fig. 5b same bending range as in Fig. to obtain 5a.

[0145] In other words, it shows Fig. 5b An exemplary cell configuration with fully insulated electrodes and multiple non-centralized physical contact points and a distribution of contacts due to a bottom electrode geometry in a top view for planar bending and in a side view for off-planar bending. The exemplary cell configuration has fully insulated electrodes and multiple non-centralized physical contact points and a distribution of contacts that, compared to Fig. 5a are symmetrically shifted (C-C' and B-B' planes), with the cell design based on a bottom electrode geometry of the cell.

[0146] Fig. Figure 6a shows a schematic view of a mechanical system 601, which has three, optionally a higher number, bending elements 261, 262 and 263 as components of the bending converter structure. Between adjacent bending elements 261 and 262 on the one hand and 262 and 263 on the other, adaptation structure layers 181 and 182 are arranged, which provide for a respective contact formation area 221 and 222 with an increase in a movement 34 11 up to 34 22This allows, for example, the presence of three electrodes, which can be connected to different or grouped potentials, such as a reference potential GND at the outer electrodes 261 and 263 and a potential difference thereof at an inner element 262. Any other configuration is also possible. This can enable jointly or selectively controlled pairs of electrodes 261 and 262 on the one hand, and 262 and 263 on the other. The pairs of elements 261 and 262 on the one hand, and 262 and 263 on the other, can each form a dome-like structure, resulting in at least a two-coupling structure.

[0147] Although the bending elements 261, 262 and 263 are shown to have a curved shape along the axial direction x, they can alternatively or in combination have an angular shape.

[0148] In other words, it shows Fig. Figure 6 shows an exemplary two-coupling base cell configuration with insulating layers between the electrodes for both electrostatic air gaps 381 / 382 and 383 / 384 in a top view for planar bending and a side view for off-planar bending. The exemplary two-coupling base cell configuration features insulating layers between the electrodes for both electrostatic air gaps. A two-coupling cell design experiences higher bending curvatures and deliverable forces for a given voltage and chip area compared to standard single-coupling structures with two dome-shaped air gaps used in a compact form factor.By using contact formations and their evolution based on a deposited dielectric layer in the electrostatic spaces, even higher bending curvatures and available forces can be obtained, along with a reduced order of magnitude of nonlinearity in the system's response.

[0149] A structure according to Fig. 6a provides the advantage that, in practice, two-coupling cells can best be used in planar NED structures for numerous components due to their high performance.

[0150] Fig. Figure 6b shows a schematic diagram with a normalized stress on the abscissa and a normalized curvature of a mechanical system, for example, mechanical system 601, on the ordinate. Curves 741 and 742 show different behaviors, with curve 742 showing a nonlinear response of the bending converter structure, i.e., coupled bending elements 261 and 262, without forming contact with the matching structure. This can be achieved, for example, by an insufficient thickness of the insulating layer in the air gaps. In contrast, diagram 741 shows an increased thickness of the insulating layer, which allows contact between the matching structure and the bending converter structure. It is evident that the linearized behavior of version 2, starting from the initial contact formation at a normalized stress of 0.8, is higher than in the case of the first curve. Fig. Figure 3 shows the linearized behavior after initial contact formation at a normalized voltage of 0.5.

[0151] The term “sufficient” insulator thickness can refer to a thickness that can withstand the voltage applied across it throughout the entire operating range without electrical breakdown upon contact formation and its distribution.

[0152] For a given cell configuration, contact formation can always be achieved at a certain higher voltage (with / without attraction) until the insulator thickness allows such a particularly high voltage to be applied across it without electrical breakdown. The only things that change are the location of the first contact formation with respect to the applied voltage and the length of the linear regime. If contact formation at lower voltages is desired, the stiffness of the cell electrodes can be reduced to allow easier movement of the electrodes towards each other at lower voltages, or narrower gaps between the electrodes can be used (for higher electrostatic forces to attract the electrodes and for less distance the electrodes must travel before contact with the insulating layer occurs).

[0153] The general optimal thickness of the insulating layer may be a minimum value at a given location or tolerance range that can withstand the maximum possible operating stress of the entire regime, while also possessing the structural integrity and mechanical robustness required to withstand the high compressive forces during contact formation and propagation without mechanical breakage (and thus possible electrical breakdown).

[0154] For a fixed gap between the electrodes (usually as small as possible, ideally the minimum value at the production resolution limit), the thicker the electrical insulation, the less the electrodes need to move to achieve contact and transition to a linearization regime. In the case of dielectric layers, the total electrostatic forces increase with layer thickness due to an increase in the effective dielectric constant of the electrostatic gap, which also contributes to faster contact formation for a given voltage. Therefore, the insulator thickness can be used to control contact formation and the extent of contact propagation allowed before electrical breakdown occurs.

[0155] To achieve a smooth / abrupt transition to a linear regime: Normally, an insulator / dielectric layer thickness of more than 2 / 3 of the total gap between the electrodes can be used to establish contact before an attraction phenomenon occurs, ensuring a smooth transition to a linear regime. If attraction is desired for the reasons mentioned above, larger air gaps can be used if the insulator thickness is already at the limit of electrical breakdown or mechanical structural integrity and cannot be reduced for the required maximum operating voltage.

[0156] It should be noted that contact formation and spreading, in addition to the insulator thickness, also depends on a local stiffness of the contact surface during bending (which depends on the electrode thickness, length, geometric topology, topology angle (if any), etc.) and on the actuating forces generated in the area of ​​contact formation and spreading (which depends on the applied voltage, the electrostatic air gap, the effective dielectric constant, etc.).

[0157] A similar principle for combining nonlinear behavior can be implemented in any other mechanical system described herein. That is, a mechanical system according to exemplary embodiments can have a bending transducer structure configured to nonlinearly deform based on bending in response to an applied electrical signal and / or to nonlinearly provide an electrical signal in response to an applied external force causing the bending. The mechanical system has a matching structure mechanically coupled to the bending transducer structure, wherein the bending and a deformation of the matching structure are causally correlated, the deformation of the matching structure providing a nonlinear force to the bending transducer structure that reduces the magnitude of the nonlinearity in the overall response of the mechanical system, for example, linearizing the bending.This results in a linear spring or ensures a desired nonlinearity. In the case of spring configurations, linearization is not necessarily maintained for the entire response regime. However, compared to systems without a spring, i.e., springless systems, there is a reduction in nonlinearity in the overall response.

[0158] In other words, it shows Fig. 6b An exemplary cell bending curvature compared to an actuation voltage (normalized with respect to maximum values) from a finite element method (FEM) simulation of identical twin-coupling cell geometries with sufficient (T2) / insufficient (T1) thicknesses of the insulating layer in the air gaps to achieve contact formation / lack of contact formation in the range of the applicable voltage. The exemplary cell bending curvature is then compared to the actuation voltage (normalized with respect to maximum values) from FEM simulations of identical twin-coupling cell geometries (same cell as in Fig. Figure 6a shows a system with sufficient (T2) / insufficient (T1) thicknesses of dielectric / insulator layer in the identical air gaps and a cell geometry to achieve contact formation / no contact formation in the range of the applied voltage. It is important to note that for most of the operating voltage range, the curvature achieved in the contact formation region is higher due to contact-based operation through a sufficiently thick dielectric layer (T2) compared to a system without contact formation (T1), even with a linearized response.

[0159] Fig. 6c shows a schematic diagram that is similar to the diagram from Fig. 6b resembles, with an additional curve 743 representing a version 2 of the two-domed cell geometry. Fig. Figure 6b represents the version which does not make contact due to insufficient thickness of the insulating layer, which is referred to as version 1, and curve 741, which shows high linearity, is represented as version 3.

[0160] In other words, it shows Fig. Figure 6c shows an exemplary cell bending curvature compared to an actuation stress (normalized with respect to maximum values) from an FEM simulation of different versions of twin-coupling cells, in order to obtain a design-based adjustable position of first contact formation within the range of the applicable stress. The exemplary cell bending curvature is shown against the actuation stress (normalized with respect to maximum values) from FEM simulations of different versions of twin-coupling cells to demonstrate a design-based adjustable position of first contact formation within the range of the applicable stress. Versions 1 and 3 correspond to cell designs T1 and T2. Fig. 6b, while version 2 has a similar cell design to version 3, but with larger air gaps to shift the first contact point with respect to the applied voltage. This exemplary case demonstrates the high degree of flexibility regarding the design possibilities of the present configurations of this invention for easily adjusting the system's response.

[0161] Fig. Figure 6d shows a schematic diagram with the normalized stress on the ordinate and the normalized curvature on the abscissa to illustrate the behavior of a produced test pattern of the two-coupling cell, as in Fig. Figure 6a illustrates this with regard to deformation hysteresis. As can be seen, there is only a small difference between the start-up behavior in a positive cycle, shown in curve 781, and the run-down behavior in the positive cycle, shown in curve 782; that is, there is a small hysteresis, which is consistent with the FEM simulation illustrated in curve 783. Curves 781, 782, and 783 refer, for example, to version 3 from Fig. 6c.

[0162] In other words, it shows Fig. Figure 6d shows an exemplary cell bending curvature compared to an actuation stress (normalized with respect to maximum values) from an FEM simulation and experimental measurements of produced test samples of a two-coupling cell, demonstrating a negligible curvature hysteresis in the forward and backward evolution of a contact during stress application and de-energization. The exemplary cell bending curvature is shown against the actuation stress (normalized with respect to maximum values) from an FEM simulation and experimental measurements of a produced test sample of a two-coupling cell (same geometry as the Fig. 6a, Fig. 6b-T2 and Fig. 6c, Version 3) demonstrates a negligible bending hysteresis in forward and reverse evolution of a contact with voltage start and release. The experimental results practically show that the expected negligible motion hysteresis (which usually occurs due to static friction between contacting surfaces or charging problems during zipper function cycles and zipper function release) is achieved, and also illustrate the reproducibility and reliability of the system's performance.

[0163] Fig. Figure 6e shows a schematic diagram, again showing the normalized stress on the ordinate and the normalized curvature of the mechanical system 601, curves 781 and 782 from Fig. 6d, shows. In other words, shows Fig. 6e An exemplary cell bending curvature compared to an actuation voltage (normalized with respect to maximum values) of test samples of a two-coupling cell produced from experimental measurements, which demonstrates a negligible charging effect in successive starts of positive and negative voltage cycles. The exemplary cell bending curvature is shown in comparison to the actuation voltage (normalized with respect to maximum values) of test samples of a two-coupling cell produced from experimental measurements (same geometry as Fig. 6a, Fig. 6b-T2 and Fig. 6c, Version 3), which demonstrates a negligible charging effect in successive attempts of positive and negative voltage cycles.

[0164] While at least some of the embodiments described above show the adaptation structure 18 being arranged at least partially or even completely within the volume 24 defined by the bending converter structure, such an implementation is not necessary, as is the case, for example, in connection with Fig. 1a and Fig. 1b is described.

[0165] Fig. Figure 7a shows a schematic view of a bending transducer or a mechanical system 701 according to an embodiment in which the adaptation structure 18 is arranged at least partially outside the volume 24 or an active region of the transducer. For example, the adaptation structure 18 can have one or more bending beam structures 841, 842 of the same or different thickness, i.e., extending along the y-direction. Both ends of these are connected to the bending transducer structure 12, which includes, for example, the presence of the common areas of the clamps 281 and 282, wherein at least a first end 861, which is connected to or part of the clamp 281, can also be connected to the common substrate 66 without losing the advantages of the present invention.Even though end 861 is in contact with substrate 66, this should still be understood to mean that end 861 is connected to the bending converter structure 12, for example via substrate 66. The adaptation structure 18 is configured to provide the adaptation formation, e.g., bending, as a bend of the bending beam structures 841 and 842.

[0166] As described in other embodiments for contact formation between the adaptation structure and the bending converter structure, contact formation in the mechanical system 701 between the bending beam structures 841 and 842 can occur based on movements 341 and 342 along the same direction (+y), for example, to ensure contact formation at plane AA', which increases along contact evolution directions 441 and 442. At a point of contact formation in contact surfaces 22a / 22b, for example, plane A-A', the bending elements 261 and 262 can move towards each other, as shown by the direction of movement arrows 881 and 882. The bending elements 261 and 262 can, for example, provide contact between them, but this is not necessary.Whether a contact is provided or not can depend at least partially on the amplitude of the deflection along the bending direction 14 and / or a size of the gap 38, for example a distance between the bending elements 261 and 262 along the +y direction.

[0167] It is a general requirement that 842 should be thinner than 841. For example, the outermost bend of 842, due to its position furthest from a neutral fiber of the cell (especially compared to 841), can experience the maximum compressive bending moment, and thus its inward bending will be greater than that of 841, particularly if it has a lower bending stiffness than 841. If 842 is thinner, it will have a much lower stiffness towards bending, and thus its inward bending will be significantly greater than that of 841, resulting in reliable and rapid contact with 841 upon bending (which, in turn, is necessary to increase cell stiffness nonlinearly upon bending).

[0168] The air gap 92 will influence two important points: 1) The larger the gap 92 is, the greater the compressive bending moment 842 experiences with respect to 841 (and thus the inward deflection magnitude for a fixed bending stiffness of each bend / flexion), on the other hand: 2) The larger the gap is, the more the bend 842 must move inwards with respect to 841 in order to achieve initial contact.

[0169] Typically, the most effective case for cell bending and contact formation occurs when both gaps 92 and 38 are as small as possible (depending on the manufacturing process used), and one gap 92 is smaller than 38. This allows contact formation to occur at lower voltages and generate higher electrostatic forces, and thus a higher bending moment, at lower applied voltages (for gap 38). Furthermore, the inward deflection of 842 is significantly increased by using a much thinner 842 with a longer length compared to 841, resulting in faster and more reliable contact formation. This is also evident in Fig. 7a.

[0170] A gap 92, arranged between the bending elements 841 and 842 of the adaptation structure 18, can be adapted with respect to the distance between the bending beams 841 and 842 along the +y direction to determine the deflection amplitude that provides initial contact and thus the linearization effect. During bending of the bending converter structure 12, the adaptation structure 18 is configured to form contact between the bending beam structures 841 and 842 in a contact area 22a / 22b, which increases with an increase in the bending amplitude of the bending converter structure along the bending direction. Contacting the ends 861 and 862 with the clamping and / or with the material of a bending element 261 or 262 can ensure that the bending beam elements 841 and / or 842 are at the same potential compared to the adjacent bending element 261, 262.However, this is not a problem, as a mechanical contact does not lead to short circuits or the like.

[0171] In other words, it shows Fig. 7a an exemplary cell configuration with a dedicated structure for contact formation and evolution outside the electrostatic air gap and an avoidance of a mandatory insulator-based contact for flexible design options and a further reduction of friction probabilities between contact surfaces due to any direct charging in a top view for planar bending or in a side view for extraplanar bending.The exemplary cell configuration features a dedicated structure for contact formation and evolution outside the electrostatic gap, avoiding a mandatory insulator-based contact for flexible design options and further reducing the probability of static friction between contact surfaces due to dielectric layer charging or electrostatic charging of a contact surface, since contact surfaces without any intervening dielectric layer will be at the same voltage. During cell flexion upon actuation, both structural beams 841 and 842 bend inwards (341 and 342, respectively). The inward movement of 842 (342) will be greater than that of 841 (341), as 842 is designed to have much lower stiffness (with reduced width, longer length, etc.).) exhibits a greater degree of flexion than 841, and is also positioned further from the neutral axis of the cell geometry compared to 841, and is thus subject to greater bending in the direction of 342 compared to 841. This results in contact formation at a required actuation voltage level due to cell bending. The contact formation and its propagation (441 and 442) during cell actuation and subsequent cell bending results in an increase in the overall cell stiffness, which can be used to counteract the nonlinearity arising from the increasing electrostatic forces in the electrostatic space 38 when an actuation voltage is applied.In this case, the contact surfaces exhibit significantly reduced probabilities of static friction because there is no dielectric between them and they are held at the same voltage level, thus negating static friction probabilities due to dielectric charging or electrostatic forces arising from any retained potential difference. Static friction due to adhesion between the contact surfaces can, if necessary, be reduced by using structured surfaces (similar to the structuring described in...). Fig. 3D, Fig. 3e, Fig. 3f or Fig. (3g is shown) can be further reduced to limit the effective contact surface.

[0172] Fig. Figure 7b shows a schematic view of a mechanical system 702 that has shorter bending beams 841 and 842 compared to the mechanical system 701. This can lead to offsets 941 and / or 942, so that the adaptation structure 18 contacts the bending converter structure 12 closer to a center, for example, closer to the A-A' plane. The offsets 941 and 942 can be implemented independently; that is, only one or both offsets can be present, and / or the offsets 941 and 942 can differ in magnitude. This can provide a further degree of freedom with regard to the normalization of a combination of cells 702, for example, in combination with other cells.

[0173] In other words, it shows Fig. 7b An exemplary cell configuration with a shifted position of the dedicated contact structure outside the electrostatic air gap 38 to modify the occurrence of the first contact and its evolution with the applied actuation voltage, shown in a top view for planar bending and in a side view for extraplanar bending. The exemplary cell configuration features a shifted position of the dedicated contact structure outside the electrostatic air gap to shift the occurrence of the first contact and its evolution with the applied actuation voltage.This is achieved with the help of a cumulative effect of the positional displacement of the bending beams 841 and 842 with respect to a neutral fiber of the cell and a direct influence on the bending of the bottom electrode at the applied voltage, since the contact formation and spreading (441 and 442) will also limit the bending deformation of the bottom electrode 1b at the applied voltage, especially at the highest deformation of the electrostatic gap (38) on the plane AA in the direction 882.This affects the system response mainly in two ways: firstly, due to an increase in the overall cell stiffness upon contact formation and propagation, and secondly, by limiting the generation of the electrostatic force in the space 38 by limiting the local space reduction, particularly from the direction 882 at the AA' plane, compared to cases where there is no direct feedback from mechanical coupling with cell bending to limit the localized deformation of the bottom electrode, and thus of the electrostatic space, as in . Fig. 7a.

[0174] It can be seen as a difference between the structures made up of Fig. 7b and Fig. 7a can be seen as the total bending stiffness of the cell being determined by Fig. 7b (compared to Fig. 7a) can increase more non-linearly with respect to an applied voltage (provided that contact formation occurs at the same voltage as in Fig. 7a occurs, by reducing the stiffness of the contacting bends), while in addition the reduction rate of the gap between the electrodes at higher voltage is reduced due to mechanical feedback to the bottom electrode, so that a growth rate of the generated electrostatic forces is also reduced - thus, by shifting the dedicated structure position inwards, regimes with higher stiffness can usually be obtained, while a rate of generated electrostatic forces is also limited - this helps to modulate the regimes of reduced-order nonlinearities as required in the same cell area (compared to Fig. 7a). Furthermore, cell bars can be compared to Fig. 7a can be stacked closer together in parallel, thus providing optimal space utilization and better compactness at the system level.

[0175] With regard to the mechanical systems 701 and 702, the number of two bending beams 841 and 842 coupled in parallel is chosen only as an example. The number can differ, for example, be more than two, such as 3, 4, 5, or a higher number. According to one embodiment, the number of bending elements can also be 1 if, for example, a spring structure is included, as in connection with Fig. Figure 7c describes a schematic view of a mechanical system 703, wherein the adaptation structure 18 comprises the bending beam structures 841 and 842 arranged in series and an intermediate spring structure 96. The spring structure 96 can be adapted to locally reduce the distance to the bending converter structure 12 in a non-displaced state of the mechanical system, for example, by locally pointing it towards the bending converter structure 12. For example, the spring structure 12 can have two or more curved deformable elements 961, 962, which, for example, have a curved shape. The curved shapes can contact each other such that they form a point in the contact area, with the point, in the example shown, pointing towards the bending converter structure 12.

[0176] The spring structure 96 can exhibit linearized spring properties, for example, by implementing a double-curved design, as shown with a zipper contact surface in the space 92. The spring structure 96 can be configured to form mechanical contact with the bending converter structure 12, for example, by ensuring that the amplitude of the deflection along the bending direction 14 is sufficiently high. From the configuration shown, a deflection along the bending direction 14, based on the mechanical coupling with the adaptation structure 18, can lead to bending of spring elements 961 and 962 due to the transport of forces via the bending beams 841 and 842. It should be noted that the elements 841 and 842 are advantageously flexible to ensure that the mechanical system 703 has high strength, but that a rigid structure can also be arranged to transport forces to the spring structure 96.Bending the bending converter structure 12 along the bending direction 14 can cause movements 341 and 342 of the spring elements 961 towards each other in order to increase the contact area 22. Simultaneously, the spring structure, for example a tip thereof, can move along a direction 44 towards the bending converter structure 12, for example until mechanical contact occurs, whereby mechanical contact is possible but not necessary.

[0177] In other words, it shows Fig. Figure 7c shows an exemplary cell configuration with a dedicated structure for contact formation outside the electrostatic air gap 38, featuring guided contact formation and an evolution for faster initial contact formation at the applied actuation voltage. This is shown in a top view for planar bending and in a side view for extraplanar bending. The exemplary cell configuration has a dedicated structure (for contact formation outside the electrostatic air gap) with guided contact formation and evolution for faster initial contact formation at the applied actuation voltage. The guidance in the beam structure (841 / 842) facilitates a smooth and rapid transition to contact formation (341 and 342) and contact distribution (44) in the gap 92.Based on the guided shape curvature and thickness 841 / 842, contact formation and spreading and their effect on cell bending stiffness can be regulated.

[0178] One advantage of the structure according to the Fig. 7c compared to the Fig. 7a-b may be due to the fact that the contact formation is demonstrated by elements 961, 962 and is faster, resulting in the same magnitude of bending deflection as in Fig. 7a-b to achieve. Furthermore, the rate of increase in stiffness with bending during contact spreading is determined in relation to Fig. 7a for similar thickness bends will usually be higher.

[0179] Fig. Figure 7d shows a schematic view of a mechanical system 704 according to an embodiment. In contrast to the mechanical system 703, a further bending beam 843 is arranged between the bending beams 841 and 842, with a spring structure 96 on one side and the bending converter 12 on the other. This can be equivalent to the arrangement of the spring structure 96 in the bending beam element 842 of the mechanical system 702, possibly in conjunction with an increased distance between the bending beams 841 and 842 therein. In contrast to the mechanical system 703, the spring structure 96 may not contact the bending converter structure 12, but rather the bending beam element 843, to provide the second nonlinear mechanical stiffness contribution. The spring structure 96 of the mechanical system 703 and 704 can have two bending elements 961 and 962 facing each other and connected to each other at a connection area 98.The spring structure 96 is configured to increase a contact area between the two bending elements 961 and 962 with an increase in the bending of the bending traveling structure 12, for example starting from the connection area 98.

[0180] The adaptation structure 18, which has a spring structure, can be mechanically attached to the bending transducer structure 12 and supported by the substrate 66 that carries the bending transducer structure 12. This can be achieved, for example, if the bending transducer structure 96 is incorporated into the adaptation structure 18, which contacts the bending transducer structure 12 or the substrate 66, in order to be mechanically contacted in parallel with the bending transducer structure 12.

[0181] In other words, it shows Fig. Figure 7d shows an exemplary cell configuration with a dedicated structure for contact formation outside the electrostatic gap 38 through contact formation and evolution for faster initial contact formation and with mechanical bending coupling to a bending electrode to restrict faster propagation of contact evolution and increase an order of magnitude of nonlinearity of cell stiffening upon actuation, in a top view for planar bending and in a side view for extraplanar bending. The exemplary cell configuration has a dedicated structure (for contact formation outside the electrostatic air gap) with guided contact formation and evolution for faster initial contact formation and with mechanical bending coupling to a bending electrode to restrict faster propagation of contact evolution and increase an order of magnitude of nonlinearity of cell stiffening upon actuation.The beam structure 843 restricts the generation of the electrostatic force in the space 38 during bending by limiting the local reduction of the space, particularly from the direction 882 on the A-A' plane, due to direct coupling with the bottom electrode 262. In comparison to . Fig. 7c the structure according to 7d ensures an advantageous integration of mechanical feedback.

[0182] Fig. Figure 8 shows a schematic view of a mechanical system 801 according to an embodiment that illustrates a different implementation of a spring structure 102. The spring structure 102 can be implemented as a bending beam structure coupled in parallel to at least one bending beam structure 261 or 262 of the bending converter structure 12. In the examples of the mechanical system 801, the bending beam structure formed by a series connection of different bending beams 841, 842, and 843 can exhibit local stiffening, for example, based on increased stiffness of the bending beam element 842. This allows the bending beam element 842 to be stiffer compared to the bending beam elements 841 and 843. A similar or complementary behavior can be obtained to implement local weakening instead of local stiffening between the ends 861 and 862.

[0183] The local stiffening implemented in the beam element 842 can make it possible to avoid contact formation with the bending converter structure 12.

[0184] In other words, it shows Fig. Figure 8a shows an exemplary basic cell configuration with a nonlinear spring configuration 102, which consists of a structural material of the electrode / cell, in the cell geometry to generate a nonlinear stiffening of the cell without contact formation or contact evolution in a top view for planar bending and in a side view for extraplanar bending. The exemplary basic cell configuration features a nonlinear spring configuration 102, which consists of a structural material of the electrode / cell, in the cell geometry to generate a nonlinear stiffening in the cell without contact formation or contact evolution. The nonlinearity of the spring configuration can be controlled in the bending direction by different design parameters of the spring configuration, for example, by the thickness and length of sections 841, 843, and 842.This configuration is particularly useful when the stiffness of the cell needs to be increased without contact-based operation, for example, when no disturbance in the frequency response of the cell is required that may occur due to sudden contact formation or its propagation, while counteracting the non-linearity of the cell's response upon actuation.

[0185] Fig. Figure 8b shows a schematic view of a mechanical system 802 according to an embodiment. In comparison to the mechanical system 801, a spring structure 102' has a plurality of layered bending beam structures or a layered arrangement of bending beam structures, wherein the arrangement is contacted between supporting bending beams 841 or 842 and the bending converter structure.

[0186] Connecting elements 1041 to 1043 can be adapted to connect different layers of the bending beam elements 841 / 842 on the one hand and 843 on the other, and / or to connect bending beams to the bending converter structure. The connecting elements 1041 to 1045 can be flexible or rigid. A gap between bending beam elements 841 and 842, which is closed extraplanarly by the bending beam element 843, allows edges 1061 and 1062 of the bending beam elements 841 and 842 to move diagonally or inclined along directions 1081 and 1082, respectively.

[0187] In other words, it shows Fig. 8b An exemplary cell configuration with a nonlinear spring configuration consisting of structural material of the electrode / cell, in the cell geometry with a mechanical bending coupling to bending electrodes for generating a nonlinear stiffening in cells without contact formation or contact evolution in a top view for planar bending and in a side view for extraplanar bending. The exemplary cell configuration features a nonlinear spring configuration 102', consisting of structural material of the electrode / cell, in the cell geometry with a mechanical bending coupling to the bending electrode for generating a nonlinear stiffening in the cell without contact formation or contact evolution.The mechanical coupling (841 and 842) has a direct influence on the bending of the bottom electrode at the applied voltage and limits the bending deformation of the bottom electrode 262 at the applied actuation voltage, particularly at the highest deformation of the electrostatic gap (38) at the plane AA' in the direction 882. This again affects the system response mainly in two ways: firstly, due to an increase in the overall cell stiffness when the nonlinear spring bends, and secondly, by limiting the generation of the electrostatic force in the gap 38 by restricting the localized gap reduction, particularly from the direction 882 at the A-A' plane, compared to cases where there is no direct mechanical coupling feedback with cell bending to limit the localized deformation of the bottom electrode and thus of the electrostatic gap, for example, as in . Fig. 8a.

[0188] Fig. Figure 8c shows a schematic diagram comparing curves 1121 and 1122, illustrating bending curvatures over a normalized stress on the abscissa and normalized curvature on the ordinate of the diagram. While curve 1121 shows a coupled bending thickness T1 that is smaller than a coupled bending thickness T2 in curve 1122 and relates to the mechanical system 802, it is evident that the strongly nonlinear response of the smaller thickness T1 in curve 1122 becomes more linear, resulting in linear regions 1141 and 1142 where the behavior is strongly linear. Although this results in a lower amplitude of curvature, the behavior is advantageously linear.

[0189] In other words, it shows Fig. 8c a cell bending curvature compared to an actuation stress normalized with respect to maximum values, from FEM simulations of the in Fig. The exemplary cell configurations shown in Figure 8b feature identical cells but mechanical bending couplings of smaller and larger thicknesses to change the magnitude of a nonlinearity response within a required stress range. The bending couplings refer, for example, to elements 841 and 842. The exemplary cell bending curvature is shown in comparison to the actuation stress (normalized with respect to the maximum values) from FEM simulations of a [missing information]. Fig. Figure 8b shows an exemplary cell configuration with identical cells, but mechanical bending couplings (841 and 842) of uniformly smaller (T1) and larger (T2) thicknesses to modify the magnitude of the response nonlinearity within a required stress range. The mechanical coupling can be designed to have different thicknesses and contact points of its parts to modulate the reduction in the nonlinearity magnitude as required within a specific range. Although the resulting bending curvature is always smaller for these structures in the case of reduced nonlinearity (since there is no dielectric / insulator-based contact formation in the electrostatic gap used), it is important to note that the magnitude of the nonlinearity can be substantially reduced while there is no contact-based operation, i.e.,without any possibility of problems due to static friction or dielectric charging, along with higher stiffness when an actuation signal is applied.

[0190] Fig. Figure 8d shows a schematic view of a mechanical system 804 according to an embodiment. Compared to the mechanical system 802, a plurality of spring structures 102' are arranged, for example, three spring structures 102'1 to 102'3. These can be connected via a bending beam structure 841, which can have a straight or, as shown, a curved curvature. Because the bending beam element 841 connects and supports the spring structures 102'1 to 102'3 as a curved structure, possibly substantially parallel to the bending beam elements 261 to 262, movements 1161, 1162, and 1163, for example, of base sections of the spring elements 102'1 to 102'3, can be directed substantially towards the normal of the bending converter structure 12.

[0191] The number of spring elements 102' can be 1, 2, or 3, or a higher number. As shown, the adapting structure 18 can have a spring structure that is mechanically attached to the bending transducer structure 12 and supported by a bending beam structure 841 adapted to bend together with the bending transducer structure 12. The bending transducer structure 12, in turn, can have a conductive material, just like the adapting structure 18. The materials can be the same or at least comparable.

[0192] In other words, it shows Fig. Figure 8d shows an exemplary cell configuration with a distributed nonlinear spring configuration, consisting of a structural material of the electrode / cell, in the cell geometry with a mechanical bending coupling to bending electrodes to generate a nonlinear stiffening in a cell without contact formation or contact evolution in a top view for planar bending and in a side view for extraplanar bending. The exemplary cell configuration features a distributed nonlinear spring configuration, consisting of a structural material of the electrode / cell, in the cell geometry with a mechanical bending coupling to a bending electrode to generate a nonlinear stiffening in the cell without contact formation or contact evolution. Due to the distributed structures (842 - 844 and 841), the mechanical feedback can be transferred with increasing bending deformation as required (e.g.,(in directions 1161-1163) to extend the feedback effect on the localized deformation of the bottom electrode, and thus on the localized deformation of the electrostatic gap, in addition to increasing the structural cell stiffness. The geometries of the distribution structures can be modified for a more uniform / non-uniform distribution of the mechanical feedback as required and / or used with higher numbers.

[0193] Compared to Fig. 8b ensures the structure according to Fig. 8d for an advantageous integration of conformal bending with a mechanical feedback coupling. Conformal springs / structures offer the advantage that the cell beams can be stacked more closely parallel compared to non-conformal spring configurations, thus providing optimal space utilization and improved compactness at the system level.

[0194] Fig. Figure 8e shows a schematic view of a mechanical system 805 according to an embodiment, which has a symmetrical arrangement of an adaptation structure 18 outside the bending converter structure 12. Starting from the space 38 as an inner section of the mechanical system 805, there is a sequential arrangement of thinner bending elements 841 and thicker elements 842, which provide local stiffening, as in conjunction with Fig. As described in Figure 8a, the elements are arranged along a curved path to, for example, exhibit essentially constant gaps 921 and 923 on one side of the bending elements 261 and 262 opposite the gap 38. This can be understood as a sequential arrangement of spring elements 102 along a curved path. In other words, it shows Fig. 8e An exemplary basic cell configuration with a nonlinear spring configuration conforming to the electrode geometry and consisting of a structural material of the electrode / cell, in the cell geometry to generate nonlinear stiffening in a cell without contact in a top view for planar bending and in a side view for off-planar bending. The exemplary basic cell configuration has a nonlinear spring configuration conforming to the electrode geometry and consisting of a structural material of the electrode / cell, in the cell geometry to generate nonlinear stiffening in a cell without contact. The cell stiffening is achieved due to a higher strain / bending of bends (841) with respect to electrodes, since these will experience the greatest bending (they are furthest from the neutral fiber of the cell).The conformal shape of the bends helps to optimize cell area utilization, and the parallel cell beam stacking can be made more compact. It is important to note that contact between the bends (841) and electrodes (261, 262) can always be used to further modulate cell stiffness during actuation.

[0195] In comparison to the structure from Fig. 8d can be a structure according to Fig. 8e provide the advantage of better shape adaptability and lower surface area utilization, along with the possibility of closer stacking (accompanied by the possibility of contact formation, as in conjunction with Fig. (as described in section 8f). Conformal springs / structures offer the advantage that cell beams can be stacked more closely parallel compared to non-conformal spring configurations, thus providing optimal space utilization and better compactness at the system level.

[0196] Fig. Figure 8f shows a schematic view of a mechanical system 806 according to an embodiment. In contrast to the mechanical system 805, the external bending elements 841 and 842 can, for example, have a continuous or constant thickness and / or stiffness. At discrete locations 1181 and 1182, the bending elements 841 and 842 of the adapting structure 18 can be mechanically attached to or contact the bending beam elements 261 and 262, respectively. This allows for relative bending or movement 116 towards the bending converter structure with a maximum amplitude between the attached locations, e.g., at planes BB' or C-C'.

[0197] The bending transducer structure 12 can have a first and a second element 261 and 262, which are coupled in parallel. The adaptation structure 18 can have at least one first adaptation element 841 and a second adaptation element 841 or 842, optionally the other element shown. These adaptation elements can be mechanically coupled in parallel to the bending element 261 or 262, respectively, while forming the same spaces 921 and / or 922. The mechanical system 906 can be implemented with or without contact formation at the planes BB' and / or CC'. Contact formation can be used, for example, in the spaces 921 and 922 to modify the change in cell stiffness during bending (increasing or decreasing it depending on the contact formation), a spreading, and its effect on the increase of the electrostatic gap 38 due to mechanical feedback from the outer structure pressing against the inner electrodes.Due to mechanical pressure, the local air gap in the electrostatic gap 38 can decrease at a given point, thereby increasing the nonlinearity rather than decreasing it, since the local minimization of the gap due to contact will dominate more strongly than the increase in mechanical stiffness after a certain time period. For example, in a normal operating configuration, an alternative implementation might not utilize contact formation. In such a configuration, there would only be extensible conformal springs to increase stiffness in a linear or nonlinear manner with mechanical expansion (the outermost / innermost structures will expand the most) due to bending.

[0198] Non-contact operation can be understood as normal operation in which the configuration or mechanical elements without contact (e.g., merely as expandable conformal springs) are to be used to increase stiffness (linear / non-linear) under mechanical expansion (outermost / innermost structures will expand the most) due to bending.

[0199] Conforming springs / structures offer the advantage that cell beams can be stacked closer together in parallel compared to non-conforming spring configurations, thus providing optimal space utilization and better compactness at the system level.

[0200] However, contact formation in these gaps can also be used to modify the change in cell stiffness during bending. Whether the nonlinearity of the response will increase or decrease in a given operating range depends on contact formation, propagation, and its effect on the reduction of the electrostatic gap 921 due to mechanical feedback from an external structure pressing against the internal electrodes. Due to mechanical pressure, the local air gap in the electrostatic gap region may decrease at a given point, thereby increasing the nonlinearity rather than decreasing it, since the local minimization of the gap due to contact will, after a certain time, dominate more than the increase in mechanical stiffness.The change in the overall response depends strongly on the geometric design of the cell (air gaps used, electrode thickness, spring design, etc.), the applied voltage, the localized contact formation, the local pressure and its effect on 921, etc. Based on this, the non-linearity of the response can be adjusted to be more or less pronounced for a specific range of applied voltage after contact formation.

[0201] If the designs of a conformal spring configuration (e.g. Fig. 8f or Fig. 8e) with designs of contact-forming cells (e.g. as in Fig. 2a or Fig. (as shown in 6a) are to be combined, then alternatively, contact formation in outer spring gaps can be used to generate initial contact formation in the electrostatic gap 921 more quickly (since the pressure on the local air gaps helps to achieve contact earlier), while higher overall cell stiffness on bending can be achieved due to contact formation and propagation in the outer spring and in an inner electrostatic gap, thus ensuring even faster and more effective linearization. However, the advantage of reduced charging from Fig. 8f will be at least partially lost.

[0202] In other words, it shows Fig. Figure 8f shows an exemplary basic cell configuration with a nonlinear spring configuration conforming to the electrodes and with a direct structural connection to bending electrodes, consisting of structural material of the electrode / cell within the cell geometry to generate nonlinear stiffening in the cell without contact, in a top view for planar bending and in a side view for off-planar bending. The exemplary basic cell configuration includes a nonlinear spring configuration conforming to the electrodes and a direct structural connection to bending electrodes, consisting of structural material of the electrode / cell within the cell geometry to generate nonlinear stiffening in the cell without contact.Cell stiffening is achieved mainly by a higher strain / bending of bends (841, 842) with respect to electrodes, since they experience the greatest bending (they are furthest from the neutral phase of the cell), and with a faster transition to a regime of nonlinear bending stiffness due to a structural connection with electrodes (1181, 1182) that can act as quasi-clamps, compared to cases without these, e.g. Fig. 8e. The conformal shape of the bends helps to optimize cell area utilization, and the parallel stacking of the cell beams can be more compact. It is important to note that contact between the bends (841, 842) and electrodes (261, 262) can always be used to further modulate cell stiffness during actuation.

[0203] In comparison to the structure from Fig. 8e ensures the structure from Fig. 8f for the advantage that a higher rate of increase in stiffness during bending can be obtained for similar dimensions and / or nonlinearity regimes of reduced magnitude can be better tailored to the requirements (together with the possibility of contact formation at multiple points as well as due to a structural connection with electrodes, as in connection with Fig. 8f is described).

[0204] Fig. Figure 8g shows a schematic view of a mechanical system 807, which has a stacked configuration of bending elements 84 of the adaptation structure 18. That is, several layers of bending elements can form an adaptation structure on one or both sides of the bending converter structure 12. Although mechanical systems 806 and 807 are shown to have parts of the adaptation structure on both sides of the bending converter structure, it can also be arranged on only one or on both sides.

[0205] Based on an increased bending amount, the further outwards the elements of the adaptation structure are arranged, the less stiffness they can provide in one embodiment, for example by implementing them more thinly compared to inner elements, as shown, for example, by comparing beam elements 841 and 843 or elements 842 and 844.

[0206] The multiple layers can be connected with a single discrete element at positions 1181 and 1182, or with separate elements. Furthermore, additional elements can be arranged along the path of the bending elements 261 and 262.

[0207] In other words, it shows Fig. Figure 8g is an exemplary basic cell configuration with several parallel nonlinear spring configurations conforming to the geometry of the electrodes and structural connection with the electrodes, and consisting of structural material of the electrode / cell within the cell geometry to generate a nonlinear stiffening in the cell without contact formation; however, contact formation is also possible. The illustration from Fig. Figure 8g is a top view for planar bending or a side view for off-planar bending. The different layers shown for mechanical system 807 can have the same configuration, as shown, but can also implement different configurations. For example, the inner or outer layer, or even an additional layer, can have a configuration according to Fig. 8e or the like. An additional arrangement of spring elements is also possible. The exemplary basic cell configuration comprises several parallel nonlinear spring configurations conforming with respect to the geometry of the electrodes and a structural connection with the electrodes consisting of structural material of the electrode / cell within the cell geometry to generate nonlinear stiffening in the cell without contact formation. The cell stiffening is achieved mainly due to a higher strain / bending of bends (841-844) with respect to the electrodes, since they experience the most bending (as they are furthest from the neutral fiber of the cell), and with a faster transition to a regime of nonlinear bending stiffness due to a structural connection with the electrodes (1181, 1182), which can act as quasi-clamps, compared to cases without them, for example, in Fig. 8e. The conformal shape of the bending points helps to optimally utilize the cell area, and the parallel stacking of the cell beams can be made more compact. It is important to note that contact formation between the bending points (841-844) and / or electrodes (261, 262) can always be used to further modulate the cell stiffness. Different possibilities for contact formation and evolution in the air gaps 921, 922 (without feedback to the bending electrodes) and / or 923, 924 (with feedback to the bending electrodes), especially at the CC' and / or B-B' planes, can be established based on a bending point design (thickness, length, topology, etc.).

[0208] In comparison to the structure from Fig. 8f ensures the structure from Fig. 8g for the advantage that a higher rate of stiffness increase during bending can be obtained for similar dimensions and / or nonlinearity regimes with reduced magnitude can be better tailored to the requirements (together with multiple contacts as well as due to a structural connection with the electrodes and multiple bending layers).

[0209] Fig. Figure 9a shows a schematic view of a mechanical system 901 according to an exemplary embodiment. The bending converter structure can have a first converter section 12a, which, for example, includes bending elements 26. 11 together with bending elements 26 12 exhibits, for example, as described for mechanical system 801. A second converter section 12b can be arranged, which, for example, includes bending elements 26. 21 and 26 22exhibits components that can operate according to converter section 12a. Converter section 12a and / or converter section 12b can be arranged symmetrically or asymmetrically relative to each other.

[0210] The converter sections 12a and 12b can be independently controlled by using electrical signals 161 and 162 by applying a potential, designated V1 and V2, simultaneously or at different times, in comparison to the illustration from Fig. 9a an assignment of different electrode elements 26 11 up to 26 22 It can be switched to a reference potential GND or a control potential.

[0211] In comparison to the mechanical system 801, the adaptation structure 18 can be modified by the use of insulators 362, 363, 366 and 367 of internal electrodes 26. 12 and 26 22be isolated. However, these elements are optional, but can make it possible to detect a deflection of the adaptation structure 18, for example, when using piezoelectric materials as bending element 842 or bending elements 841 or 843, or in different components thereof. This can make it possible to obtain a readout signal 163 (V read-out). The mechanical system 901 combines two modifications. On the one hand, the bending transducer structure 12 of the mechanical system 801 can be combined with a second section of the obtained structure, for example, the transducer structure 12b, to provide a different, for example, opposite bending direction 141 and 142. Furthermore, a deflection in one or more of the elements of the adaptation structure 18 can be detected by using a respective electrical signal 163, which, for example, can also be implemented in the mechanical system 801 by using suitable materials and by isolating any electrodes used from the bending transducer structure 12.

[0212] As in Fig. As shown in 9a, the adaptation structure 18 can have a bending transducer structure that is mechanically coupled in parallel to the first transducer section 12a and second transducer section 12b and between both sections 12a and 12b.

[0213] Optionally, the bending converter structure of the adaptation structure 18 can have a local stiffening 842, for example in a middle area of ​​the bending converter structure.

[0214] A deflection or bending of the bending transducer structure 18 can be detected, for example, by using capacitive movements and / or piezoelectric measurements or other principles.

[0215] In other words, it shows Fig. 9a An exemplary base cell beam configuration with identical electrodes for bending in both directions and nonlinear spring configurations consisting of the electrode / cell material within the cell geometry to generate nonlinear stiffening of the cell without contact formation or evolution in a top view for planar bending and in a side view for extraplanar bending. The exemplary bimorphic base cell configuration optionally features a configuration of identical electrodes for bending in both directions and a nonlinear spring configuration consisting of the structural material of the electrode / cell within the cell geometry to generate nonlinear stiffening in the cell without contact formation or evolution in the electrostatic gap. For cell bending in direction 141 or 142, a corresponding cell part is actuated with V1 or V2 actuation signals.While one side is actuated, the other side of the cell acts as a passive load, which can also be designed to be a nonlinear load in the bending direction in addition to the bends (841, 842, 843). Alternatively, the passive cell part (for a specific bending direction) can also be partially actuated to make it an active load, which can be used to further counteract the nonlinearity in the cell's response in the bending direction. The deformation in the bend (841, 842, 843), which is electrically isolated from the cell's electrodes, can be used for detection purposes using materials in a bending region that exhibit piezoresistive and / or piezoelectric effects. The bends can be configured to provide a detection signal (V. read-out) to generate a state that is linear or exhibits a lower order of magnitude of nonlinearity at applied actuation voltages (V1, V2). It is important to note that there are always possibilities for insulator / dielectric-based contact formation and evolution between the cell electrodes (bending elements26). 11 -26 22 ) in the electrostatic air space (381, 382) can be used to further modulate cell stiffness during actuation, while also achieving higher actuation forces.

[0216] Fig.Figure 9b shows a schematic view of a mechanical system 902 according to an exemplary embodiment. In comparison to the mechanical system 901, the adaptation structure 18 has two opposing bending beam elements 841 and 842, which are implemented to have a conductive material to form electrodes, at least in a portion of the bending elements 841 and 842. To prevent short circuits, an insulator 122 can be arranged at least in a central region of the adaptation structure 18 between the bending beam elements 841 and 842, for example, in areas where mechanical contact could occur in the absence of the insulator 122. A similar function is implemented by the use of insulators 363 and 368 in the area of ​​the clamps 281 and 282, whereby it could be advantageous to implement a gap 92 at least partially between the electrodes to improve the deflection of the adaptation structure 18.

[0217] The adaptation structure 18 can have an electrode structure comprising electrodes 841 and 842 and an insulating material 122 between them. The electrode structure can form at least part of the bending beam structure of the adaptation structure, and the adaptation deformation can lead to a deformation of the electrode structure, wherein the mechanical system 902 can be adapted to provide one or more electrical signals according to the adaptation deformation. By using two electrodes isolated from each other, such a signal 163 can generate a difference between the potential V read-out and V read-out_GND be, which can change due to the deflection.

[0218] In other words, it shows Fig. 9b an exemplary bimorphic base cell configuration with a configuration of identical electrodes for bending in both directions 141 and 142 and nonlinear spring configurations with multiple isolated bending points consisting of the electrode material for generating a nonlinear stiffening in a cell together with a possibility of feedback by capacitive sensing to estimate a bending deformation for active control of a cell deformation, in a top view for planar bending or in a side view for extraplanar bending.The exemplary bimorphic base cell configuration comprises a configuration of identical electrodes for bending in both directions and a nonlinear spring configuration with multiple isolated bending points consisting of the electrode material to generate nonlinear stiffening in the cell, along with a means of capacitive feedback to estimate bending deformation for active control of cell deformation. The change in capacitance between bends 3n and 3o can be measured using the readout signals V. read-out and V read-out_GND can be detected. The bending points can be designed to exhibit a change in capacitance that is linear or of a lower order of nonlinearity under applied actuation stresses (V1, V2).

[0219] Both systems 901 and 902 enable the control of an actuator configured to deflect upon electrical signals 161 and / or 162. As mentioned, a measurement principle that enables control, among other things, can be implemented in another system described herein by providing the functionality accordingly, preferably in the adaptation structure 18.

[0220] Fig. Figure 9c shows a schematic view of a mechanical system 903 in which the bending transducer section 12b is formed asymmetrically compared to the bending transducer section 12a, which allows for different deflection behavior compared to signals 161 and 162 with the same amplitude, and thus provides an additional degree of freedom. Furthermore, by forming an asymmetric relationship between the distances 12a and 12b, external effects such as gravity or a permanent load can be taken into account, for example with regard to a desired reference deflection.

[0221] According to exemplary embodiments, the bending transducer structures described herein can be configured to bend in response to an applied electrical signal, wherein the mechanical system includes a control unit 115 configured to provide the electrical signal. This can enable at least parts of the mechanical system to be used as an actuator. Alternatively or additionally, the mechanical system can be implemented such that the bending transducer structure is configured to provide the electrical signal in response to the applied external force F causing the bending, and the mechanical system includes a readout circuit 117 configured to provide the electrical signal. The control unit 115 and / or the readout circuit 117 can be part of or connected to other mechanical systems described herein.The control unit 115 and the readout circuit 117 can be part of the same unit, for example a control unit or the like.

[0222] In other words, in Fig. Figure 9c shows a bimorphic exemplary basic cell configuration with a configuration of different electrodes for bending in both directions and a compensation of the nonlinearity in the respective other response for a given bending direction for the same applied stress, together with a nonlinear spring configuration with multiple isolated bends consisting of the electrode material to generate a nonlinear stiffening of the cell and a possibility of feedback by capacitive sensing to estimate a bending point deformation for active control of a cell deformation, shown in a top view for planar bending and in a side view for extraplanar bending.

[0223] Fig. Figure 10a shows a schematic view of a mechanical system 1001 having a configuration in which the bending transducer structure 12 comprises bending elements 26'1 and 26'2, which have an electrothermal material that can be configured to expand or contract in response to the electrical signal 161 and / or 162. For such a purpose, clamps 281 and 282 can also have a conductive material to transport electrical charges to the electrothermal material. Although clamp 282 is shown to have a reference ground potential, it should be noted that this potential can also be a supply voltage, i.e., the signal 161 and / or 162 for a base cell connected to the mechanical system 1001, as shown, for example, in Fig. 2b-2e is shown.

[0224] The adaptation structure can include bending elements 841 and 842, which may have a structural electrode material, i.e., a conductive material, such as a conductive MEMS semiconductor material or a metal material. A gap 38 can allow relative movement of bending elements 26'1 and 26'2 relative to each other when bent along the bending direction 141 or 142. A structural dielectric insulator material 36 can provide electrical and thermal insulation.

[0225] In other words, it shows Fig. 10a An exemplary bimorphic base cell configuration based on an electrothermal bending actuator principle and fully insulated electrodes for contact formation and evolution, enabling capacitive sensing in a top view for planar bending and in a side view for extraplanar bending. The exemplary bimorphic base cell configuration is based on an electrothermal bending actuator principle and fully insulated electrodes for contact formation and evolution, enabling capacitive sensing in the electrostatic space 38. The electrothermal actuator electrodes 26'1 or 26'2 can be actuated to bend in directions 141 and 142, respectively, using appropriate actuation voltages (V1, V2).For example, when V1 is activated (V2 is off), electrode 26'1 expands (due to thermal expansion) and, for contact formation and evolution, 841 moves towards 341, while 842 moves towards 342 (passive contraction) (in directions 441 and 442). The capacitance readout electrodes (841, 842) come into contact and modulate the stiffness of the entire cell to match the generated usable actual force and capacitance change (for detection) at the applied actuation voltage signal.

[0226] Fig. Figure 10b shows a schematic view of a mechanical system 1002 which, in comparison to the mechanical system 1001, incorporates a piezoelectric material instead of an electrothermal material to implement an actuator and / or sensor function. That is, the bending elements 26'1 and 26"2 can, at least partially, incorporate a piezoelectric material. The piezoelectric material can preferably be covered on two opposite sides with conductive layers 124 to apply the voltage to activate and / or evaluate the contraction or expansion of the piezoelectric material.

[0227] In other words, it shows Fig. Figure 10b shows an exemplary bimorphic base cell configuration based on a piezoelectric bending actuator principle and fully insulated electrodes for contact formation and evolution to enable capacitive sensing in a top view for planar bending and in a side view for extraplanar bending. The exemplary bimorphic base cell configuration is based on the piezoelectric bending actuator principle and fully insulated electrodes for contact formation and evolution to enable capacitive sensing in the electrostatic space 38. The piezoelectric actuator electrodes (1241 to 1244) can be actuated to bend in directions 141 and 142, respectively, using appropriate actuation voltages (V1, V2).For example, when V1 is activated (V2 is off), the piezoelectric material (26"1) expands (due to the piezoelectric effect), and, for contact formation and evolution, electrode 841 moves towards 341, while 842 moves (in directions 441 and 442) towards 342 (passive contraction). The capacitance readout electrodes (841 and 842) come into contact and modulate the stiffness of the entire cell to match the generated usable actual force and capacitance change (for detection) at the applied actuation voltage signal. Since it is a piezoelectric actuation system, the piezoelectric material layers 26'1 and / or 26"2 can also be designed to contract, depending on the design requirements.

[0228] Fig. Figure 10c shows a schematic view of a mechanical system 1003, which can essentially correspond to the mechanical system 1002, wherein a dielectric elastomer material is arranged in the bending elements 26'''1 and 26'''2 instead of a piezoelectric material.

[0229] In other words, it shows Fig. Figure 10c shows an exemplary bimorphic base cell configuration based on an actuator principle for bending a dielectric elastomer and fully insulated electrodes for contact formation and evolution to enable capacitive sensing in a top view for planar bending and in a side view for extraplanar bending. The exemplary bimorphic base cell configuration is based on an actuator principle for bending a dielectric elastomer and on fully insulated electrodes for contact formation and evolution to enable capacitive sensing in the electrostatic interspace 38. The DEA electrodes (1241 to 1244) can be actuated to bend in directions 141 and 142, respectively, using appropriate actuation voltages (V1, V2).For example, when V1 is activated (V2 is off), the dielectric elastomer material (26'''1) expands (depending on the actuation principle of the dielectric elastomer) and, for contact formation and evolution (in directions 441 and 442), the electrodes 841 move in the direction of 341, while 842 moves in the direction of 342 (passive contraction). The capacitance readout electrodes (841, 842) come into contact and modulate the stiffness of the entire cell to match the generated usable actual force and capacitance change (for detection) at the applied actuation voltage signal.

[0230] The embodiments described herein make it possible to combine a first nonlinear contribution of a deflection, provided by the bending converter structure, with a second nonlinear contribution, provided by a deflection of the adaptation structure. The combination of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution can be implemented to achieve, compared to the first nonlinear contribution, as described, for example, in Fig. 6b, Fig. 6d and Fig. 6e in combination with Fig. As shown in section 6e, this ensures high linearity.

[0231] The mechanical systems described herein feature a bending transducer structure to exhibit an electrostatic configuration, a piezoelectric configuration, an electrothermal configuration, and / or an electroactive polymer configuration. As shown in Fig. 10a, Fig. 10b and Fig. As can be derived from Section 10c, the implementation of the bending transducer structure can be applied to any structure of the mechanical system described herein, regardless of the configuration described herein. That is, the mechanical systems described herein in connection with an electrostatic or electrodynamic configuration can be implemented without difficulty with other configurations of actuator / sensor principles. The electrostatic configurations described herein refer to a combination of electrode structures. Whether these structures are used to be excited electrostatically or electrodynamically may depend on the specific design.

[0232] Some embodiments described herein relate to a mechanical system that is a micromechanical system (MMS), in particular a MEMS. As described herein, the bending transducer structure can be adapted to provide bending planar with respect to a layer array or extraplanar with respect to a layer array.

[0233] For example, in Fig. As shown in Figures 2b-2e, a mechanical system described herein may, according to exemplary embodiments, comprise several cells mechanically arranged in series, each cell being configured according to the exemplary embodiments described herein. Cells may be configured to be identical or similar, but this is not required.

[0234] The basic concept for counteracting nonlinearity in a transducer system response using nonlinear mechanical stiffening is known from the prior art and publications [1-5]. However, most of these solutions are highly design-specific with limited applicability and performance levels. For example, bending transducer systems that rely on nonlinear stiffening through contact formation and evolution, such as electrostatically actuated zipper actuators, typically suffer from motion hysteresis due to contact formation and rupture [4, 6-9], electrostatic attraction instabilities [4, 6-8], static friction problems, abrupt response changes [6, 8, 10], a design necessarily based on complicated self-stressing machining [7], dedicated requirements for external structures [1-3, 5, 11], etc.

[0235] In most zipper configurations, a direct peak deflection or movement of a specific structural area is used instead of bending curvature of the entire cell / component geometry. Simultaneous modulation / linearization of the different system responses (bending curvature, bending moment, available force, capacitance change, motion resolution, frequency response, etc.) to an actuation signal in such configurations is difficult (usually only one or two responses are modulated in a given design). Furthermore, electrostatic zipper actuators exhibit attraction instabilities, which make their control challenging

[12] .

[0236] Some embodiments relate to a desired cost-effective application (approximately 20 claims). The possible claim points are as follows: • An actuator and / or sensor mechanism with stiffness modulation based on an elementary design, when an actuation signal is applied in the direction of bending / movement, to counteract nonlinearity in the cell's response and / or to linear / nonlinear loads. Bending of the entire cell is used with respect to the neutral axis of the elementary cell. • Stiffness modulation via contact formation and its evolution based on an insulator / dielectric layer in the electrostatic space (for electrostatic actuator / capacitive readout) with cell bending during actuation. • Insulation layer and / or electrode configurations in the electrostatic gap (centered, ALD-coated, etc.) can be used to modulate the occurrence of contact formation and its evolution upon actuation signal before contacting of an entire zipper-capable electrode length or a breakdown voltage of the insulating layer is achieved. • Elementary design based on the stiffness of electrodes and / or insulators to enable contact formation prior to electrode attraction for a continuous, smooth transition to a linearized cell response or a cell response with reduced-order nonlinearity. Alternatively, a sudden transition can be achieved by utilizing attraction. • The contact-based concepts in electrostatic gaps enable actuation and movement across electrode attraction voltages, increasing an achievable overall curvature (at a given voltage due to a higher relative permittivity, particularly useful in the case of a minimum air gap due to a production constraint). • The static friction effect can be counteracted by: increased surface roughness of contact surfaces (e.g. curvatures), structured electrode surfaces (contact points, etc.) to reduce an effective contact area, structuring of insulator / dielectric material (minimized volume, minimized material interfaces, etc.) to reduce contact area, and retained electrostatic charges, and / or by ALD-based anti-static friction coating (e.g. FDTS). • Stiffening of a cell during actuation by using springs / bending systems - with contact formation outside the electrostatic gap. • Stiffening of a cell during actuation by using springs / bending systems - without contact formation. • Bending system in cell design with feedback of a bending movement based on mechanical coupling for deformation of electrodes - to increase stiffness and limit localized reduction of the electrostatic gap, especially at the points of highest electrode bending / deformation. • Stiffening based on complementing the bending section on the opposite side in the cell (can be set to active or inactive based on the design). • Use of multiple insulating layers in the electrostatic gap for contact-based stiffening functions with different contact formation possibilities, e.g. insulator-insulator / electrode-insulator-electrode, etc. • Use of multiple coated cell electrodes with air gaps for bending and / or contact-based stiffening options. • The concept is also applicable to different cell geometries, actuation principles, and combinations of different stiffness-enhancing methods set out in the invention are possible.

[0237] Although some aspects have been described in the context of a device, it is evident that these aspects also constitute a description of the corresponding process, where a block or device corresponds to a process step or a feature of a process step. Similarly, aspects described in the context of a process step also provide a description of a corresponding block, element, or feature of a corresponding device.

[0238] The embodiments described above are merely illustrative of the principles of the present invention. It is evident that modifications and variations of the arrangements and details described herein are obvious to those skilled in the art. Furthermore, it is intended that these modifications and variations are to be limited only by the scope of the appended claims and not by the specific details set forth herein in the description and explanation of the embodiments. bibliography [1] B. Rivlin, S. Shmulevich, Inbar Hotzen and D. Elata, “A gap-closing electrostatic actuator with a linear extended range,” 2013 Transducers & Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII), pp. 582-585, 2013. [2] J. Li, „Electrostatic zipping actuators and their applications to MEMS,“ MASSACHUSETTS INSTITUTE OF TECHNOLOGY, 2004. Accessed: 14. Juni 2021. [Online]. Verfügbar: https: / / dspace.mit.edu / handle / 1721.1 / 33678 [3] Jian Li, M. P. Brenner, J. H. Lang, A. H. Slocum und R. Struempler, „DRIE-fabricated curved-electrode zipping actuators with low pull-in voltage,“ in TRANSDUCERS '03. 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers (Cat. No.03TH8664), 2003, 480-483 Ausgabe 1. [4] R. Legtenberg, J. Gilbert, S. D. Senturia und M. Elwenspoek, „Electrostatic curved electrode actuators,“ Journal of Microelectromechanical Systems, Ausgabe 6, Nr. 3, S. 257-265, 1997, DOI: 10.1109 / 84.623115. [5] X. Xiang, X. Dai, K. Wang, Z. Yang, Y. Sun und G. Ding, „A Customized Nonlinear Micro-Flexure for Extending the Stable Travel Range of MEMS Electrostatic Actuator,“ J. Microelectromech. Syst., Ausgabe 28, Nr. 2, S. 199-208, 2019, DOI: 10.1109 / JMEMS.2019.2894669. [6] P. Gebbers, C. Grätzel, L. Maffli, C. Stamm und, H. Shea, „Zipping it up: DEAs independent of the elastomer's electric breakdown field,“ Proceedings of SPIE - The International Society for Optical Engineering, Ausgabe 8340, 61-, 2012, DOI: 10.1117 / 12.915020. [7] J. Felder, E. Lee und D. L. DeVoe, „Large Vertical Displacement Electrostatic Zipper Microstage Actuators,“ J. Microelectromech. Syst., Ausgabe 24, Nr. 4, S. 896-903, 2015, DOI: 10.1109 / JMEMS.2014.2358294. [8] L. Maffli, S. Rosset und H. R. Shea, „Zipping dielectric elastomer actuators: characterization, design and modeling,“ Smart Mater. Struct., Ausgabe 22, Nr. 10, p. 104013, 2013, DOI: 10.1088 / 0964-1726 / 22 / 10 / 104013. [9] R. Horning, „PolyMEMS Actuator: A Polymer-Based Microelectromechanical (MEMS) Actuator with Macroscopic Action,“ Fort Belvoir, VA, 2002.

[10] S. H. Pu et al., „RF MEMS Zipping Varactor With High Quality Factor and Very Large Tuning Range,“ IEEE Electron Device Lett., Ausgabe 37, Nr. 10, S. 1340-1343, 2016, DOI: 10.1109 / LED.2016.2600264.

[11] B. Rivlin and D. Elata, „Design of nonlinear springs for attaining a linear response in gap-closing electrostatic actuators,“ International Journal of Solids and Structures, Ausgabe 49, Nr. 26, S. 3816-3822, 2012, DOI: 10.1016 / j.ijsolstr.2012.08.014.

[12] R. S. Diteesawat, A. Fishman, T. Helps, M. Taghavi und J. Rossiter, „Closed-Loop Control of Electro-Ribbon Actuators,“ Frontiers in Robotics and Al, Ausgabe 7, S. 144, 2020, DOI: 10.3389 / frobt.2020.557624.

[13] H. Conrad et al., „A small-gap electrostatic micro-actuator for large deflections,“ Nature communications, Ausgabe 6, S. 10078, 2015, DOI: 10.1038 / ncomms10078.

[14] H. Conrad, H. Schenk, C. Schirrmann, T. Sandner, F. Zimmmer und J. U. Schmidt, „MICROMECHANICAL COMPONENT,“ WO2012095185 (A1), WO WO2011EP50483 20110114, 19.7.2012.

[15] H. Schenk, B. Kaiser und L. Ehrig, „BENDING TRANSDUCER AS AN ACTUATOR, BENDING TRANSDUCER AS A SENSOR, BENDING TRANSDUCER SYSTEM,“ WO2020078541 (A1), WO WO2018EP78298 20181016, 23.4.2020.

Claims

[1] A mechanical system that has the following features: a bending transducer structure (12) configured to provide a bending response to an applied electrical signal (16) and / or to provide an electrical signal (16) responding to an applied external force (F) causing the bending, wherein a structural stiffness (52) of the bending transducer structure (12) provides a first nonlinear mechanical stiffness contribution with respect to the bending; an adaptation structure (18) which is mechanically coupled to the bending converter structure (12) by mechanical coupling in order to provide an adaptation deformation together with the bending, wherein a structural stiffness (52) of the adaptation structure (18) provides for a second nonlinear mechanical stiffness contribution with respect to the bending based on the mechanical coupling during deformation; wherein the adaptation structure (18) has a bending beam structure (84) which is coupled in parallel to a bending beam structure (26) of the bending converter structure (12) and which has a local stiffening between a first end and a second end of the bending beam structure (84) of the adaptation structure (18); and / or wherein at least one of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution is based on a mechanical contact between a first element and a second element of the mechanical system, wherein the mechanical contact provides a variable magnitude of mechanical forces acting on the bending converter structure (12) and / or the adaptation structure (18) upon an increase in a bending amplitude; and wherein the mechanical system is configured to provide the mechanical contact between the bending converter structure (12) and the adaptation structure (18), wherein the bending converter structure (12) and the adaptation structure (18) are arranged such that they increase a contact area between each other upon an increase in the bending of the bending converter structure (12), wherein the contact area between is formed from the following: • the adaptation structure (18) and the bending transducer structure (12); • a first element of the adaptation structure (18) connected to a first bending element (261) of the bending converter structure (12); and a second element of the adaptation structure (18) connected to a second bending element (262) of the bending converter structure (12). [2] The mechanical system according to claim 1, wherein the mechanical coupling is adapted to combine the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution to obtain the bending of the bending converter structure (12) based on a combination of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution. [3] The mechanical system according to claim 1 or 2, wherein in a non-displaced state of the bending transducer structure (12) a first neutral axis of a first bending element (261) of the bending transducer structure (12) is substantially parallel to a second neutral axis (272) of a second bending element (262) of the bending transducer structure (12); or wherein in a non-displaced state of the bending transducer system a first surface of the first bending element (261) pointing towards the second bending element (262) is substantially parallel to a second surface of the second bending element pointing towards the first bending element (261). [4] The mechanical system according to one of the preceding claims, wherein the adaptation structure (18) has an interrupted structure arranged between a first bending element (261) and a second bending element (262) of the bending converter structure (12). [5] The mechanical system according to one of the preceding claims, wherein the adaptation structure (18) comprises a dielectric material; wherein the adaptation structure (18) is configured to contact at least two elements of the bending transducer structure (12) and to insulate them from each other on the basis of bending. [6] The mechanical system according to one of the claims, wherein the adaptation structure (18) has a layered structure arranged planarly between the first bending element (261) and the second bending element (262). [7] The mechanical system according to claim 6, wherein the adaptation structure (18) has a plurality of layers which have a gap (383) between adjacent layers which is partially closed in a deflected state of the bending transducer structure (12). [8] The mechanical system according to one of the preceding claims, wherein the adaptation structure (18) has a variable distance to at least one bending element (261, 262) of the bending converter structure (12). [9] The mechanical system according to one of the preceding claims, wherein a groove structure (58) and an opposing spring structure (62) are arranged in an intermediate space (38) between the first bending element (261) and the second bending element (262); wherein the groove structure and the spring structure form a mechanical contact in a deflected state of the mechanical system and prevent a relative movement of the spring structure (62) and the groove structure relative to each other along a direction perpendicular to a bending direction (14) of the bending converter structure (12). [10] The mechanical system according to claim 9, wherein the adaptation structure (18) comprises connecting elements (64) between adjacent groove structures (58) which have a conductive or insulating material. [11] The mechanical system according to one of the preceding claims, wherein the adaptation structure (18) is arranged at least partially between a first section of the bending transducer structure (12) and a second section of the bending transducer structure (12) along a bending direction (14) of the bending transducer structure. [12] The mechanical system according to claim 11, wherein the bending converter structure (12) has at least two bending elements (261, 262) which are mechanically coupled in parallel and form a gap (38) with an adjacent bending element of the bending converter structure (12), wherein at least a part of the adaptation structure (18) is arranged in the gap (38) and is mechanically coupled in parallel to the adjacent bending elements via the mechanical contact; wherein the bending of the bending converter structure causes a mechanical contact between the adaptation structure (18) and at least one of the adjacent bending elements in the gap. [13] The mechanical system according to claim 12, comprising at least three bending elements which are mechanically coupled in parallel to form at least a first gap between a first bending element and a second bending element and to form a second gap between the second bending element and a third bending element; wherein a first part of the adaptation structure (18) is arranged in the first gap to form a first contact and a second part of the adaptation structure (18) is arranged in the second gap to form a second contact. [14] The mechanical system according to one of the preceding claims, wherein the bending transducer structure (12) comprises a first transducer section and a second opposing transducer section, wherein the first transducer section and the second transducer section are convex with respect to a central region between the first transducer section and the second transducer section, wherein the adaptation structure (18) comprises a bending beam structure (26; 84) which is mechanically coupled in parallel to the first transducer section and the second transducer section and is coupled between the first transducer section and the second transducer section. [15] The mechanical system according to claim 14, wherein the local stiffening is arranged in a central region of the bending beam structure. [16] The mechanical system according to claim 14 or 15, wherein the adaptation structure (18) comprises an electrode structure with a first electrode (841), a second electrode (842) and an insulating material in between, wherein the electrode structure forms at least a part of the bending beam structure (84); wherein the adaptation deformation leads to a deformation of the electrode structure; wherein the mechanical system is adapted to provide an electrical signal (16) according to the adaptation deformation. [17] The mechanical system according to any one of claims 14 to 16, wherein the first converter section (12a) and the second converter section (12b) are arranged symmetrically or asymmetrically with respect to each other. [18] The mechanical system according to one of the preceding claims, wherein the adaptation structure (18) is arranged at least partially outside a volume (24) enclosed by outer sides of the bending transducer structure (12). [19] The mechanical system according to claim 18, wherein the adaptation structure (18) comprises a first bending beam structure (841) and a second adjacent bending beam structure (842), both ends (86) of the same being connected to the bending converter structure; wherein the adaptation structure (18) is configured to provide the adaptation formation as a bending of the first bending beam structure (841) and the second bending beam structure (842), wherein during the bending of the bending converter structure (12) the adaptation structure (18) is configured to form a contact between the first bending beam structure (841) and the second bending beam structure (842) in a contact area (22) which increases with an increase in a bending amplitude of the bending converter structure (12). [20] The mechanical system according to claim 18 or 19, wherein the adaptation structure (18) comprises a first bending beam structure (841), a second bending beam structure arranged in series with the first bending beam structure (841), and a spring structure arranged between the first bending beam structure (841) and the second bending beam structure, wherein the spring structure (96; 102) is adapted to locally reduce a distance to the bending converter structure (12) in a non-displaced state of the mechanical system; wherein the spring structure (96; 102) has a linearized spring property and is arranged to form mechanical contact with the bending converter structure (12) or with another bending beam structure (26; 84) of the adaptation structure (18) to provide the second nonlinear mechanical stiffness contribution. [21] The mechanical system according to claim 20, wherein the spring structure (96; 102) has two bending elements which are opposite each other and are connected to each other at a connecting section; wherein the spring structure is configured to increase a contact area between the two bending elements by increasing the bending of the bending converter structure (12). [22] The mechanical system according to one of claims 18 to 21, wherein the adaptation structure (18) comprises a spring structure (96; 102) which is mechanically attached to the bending transducer structure (12) and is supported on a substrate which supports the bending transducer structure (12). [23] The mechanical system according to claim 22, wherein the spring structure (96; 102) comprises a plurality of layered bending beam structures. [24] The mechanical system according to one of claims 18 to 21, wherein the adaptation structure (18) comprises a spring structure (96; 102) which is mechanically attached to the bending transducer structure (12) and is supported by a bending beam structure (26; 84) which bends together with the bending transducer structure (12). [25] The mechanical system according to any one of claims 18 to 24, wherein the bending transducer structure comprises a conductive material, and wherein the adaptation structure (18) comprises the conductive material. [26] The mechanical system according to one of claims 18 to 25, wherein the adaptation structure (18) has a bending beam structure (26; 84) which is coupled in parallel to a bending beam structure of the bending converter structure (12). [27] The mechanical system according to claim 26, wherein the bending beam structure (26; 84) has at least a local stiffening or a local weakening between a first end and a second end of the bending beam structure. [28] The mechanical system according to claim 26 or 27, wherein the bending converter structure (12) comprises a first bending element and a second bending element (262) coupled in parallel to the first bending element (261); wherein the adaptation structure (18) comprises at least a first adaptation element (181) mechanically connected in parallel to the first bending element (181) while forming a first gap; and at least a second adaptation element (182) mechanically connected in parallel to the second bending element while forming a second gap (922). [29] The mechanical system according to one of the preceding claims, wherein the second nonlinear contribution at least partially counteracts the first nonlinear contribution, wherein the combination of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution exhibits higher linearity compared to the first nonlinear mechanical stiffness contribution. [30] The mechanical system according to one of the preceding claims, wherein the bending converter structure (12) comprises a first bending element (261) and a second bending element (262) which are attached to each other at discrete positions (118), wherein along a bending direction (14) along which the bending converter structure (12) is configured to provide the bending, the stiffness of the first bending element (261) differs from that of the second bending element (262). [31] The mechanical system according to one of the preceding claims, wherein in a non-displaced state of the mechanical system a bending element of the bending converter structure (12) has a curved or angular profile between a first end and a second end of the bending element to define a direction of bending. [32] The mechanical system according to one of the preceding claims, wherein the bending transducer structure (12) comprises at least the following: • an electrostatic or electrodynamic configuration; • a piezoelectric configuration; • an electrothermal configuration; and / or • an electroactive polymer configuration. [33] The mechanical system according to one of the preceding claims, wherein the bending transducer structure (12) is configured to bend in response to the applied electrical signal (16); wherein the mechanical system includes a control unit configured to provide the electrical signal (16). [34] The mechanical system according to one of the preceding claims, wherein the bending transducer structure (12) is configured to provide the electrical signal (16) in response to the applied external force (F) causing the bending; wherein the mechanical system includes a readout circuit configured to provide the electrical signal (16). [35] The mechanical system according to any of the preceding claims, wherein the mechanical system is a micromechanical system. [36] The mechanical system according to any one of claims 1 to 35, wherein the bending transducer structure (12) is adapted to provide the bending in a planar manner with respect to a layer arrangement comprising the mechanical system. [37] The mechanical system according to claims 1 to 35, wherein the bending converter structure (12) is adapted to provide the bending in an extraplanar manner with respect to a layer arrangement comprising the mechanical system. [38] A mechanical system arrangement comprising several cells which are mechanically arranged in series, wherein each cell is configured according to one of the preceding claims. [39] A mechanical system which has the following features: a bending transducer structure (12) configured to nonlinearly deform with respect to a deflection and / or deflection behavior responding to an applied electrical signal (16) based on a bending and / or to nonlinearly provide an electrical signal (16) responding to an applied external force (F) causing the bending, an adaptation structure (18) that is mechanically coupled to the bending transducer structure (12); wherein the bending and a deformation of the adaptation structure (18) are causally correlated, wherein the deformation of the adaptation structure (18) provides a nonlinear force for the bending transducer structure (12) that reduces the magnitude of a nonlinearity in an overall response of the mechanical system; wherein the bending converter structure (12) has at least two bending elements (261, 262) which are mechanically coupled in parallel and a space (38) is formed between the two bending elements (261, 262). [40] Method for providing a mechanical system, the method comprising the following steps: Providing a bending transducer structure (12) such that it is configured to provide a bending response to an applied electrical signal (16) and / or to provide an electrical signal (16) responding to an applied external force (F) causing the bending, such that a structural stiffness (52) of the bending transducer structure provides a first nonlinear mechanical stiffness contribution of the bending; mechanical coupling of an adaptation structure (18) to the bending converter structure (12) in a mechanical manner to provide an adaptation deformation together with the bending, so that a structural stiffness (52) of the adaptation structure (18) provides for a second nonlinear mechanical stiffness contribution to the bending based on the mechanical coupling during deformation; such that the adaptation structure (18) has a bending beam structure (84) that is coupled in parallel to a bending beam structure (26) of the bending converter structure (12), which has a local stiffening between a first end and a second end of the bending beam structure (84) of the adaptation structure (18); and / or such that at least one of the first nonlinear mechanical stiffness contribution and the second nonlinear mechanical stiffness contribution is based on a mechanical contact between a first element and a second element of the mechanical system, wherein the mechanical contact provides a variable magnitude of mechanical forces acting on the bending converter structure (12) and / or the adaptation structure (18) upon an increase in a bending amplitude; and such that the mechanical system is configured to provide the mechanical contact between the bending converter structure (12) and the adaptation structure (18), such that the bending converter structure (12) and the adaptation structure (18) are arranged to increase a contact area between them upon an increase in the bending of the bending converter structure (12), wherein the contact area between is formed from the following: • the adaptation structure (18) and the bending transducer structure (12); • a first element of the adaptation structure (18) connected to a first bending element (261) of the bending converter structure (12); and a second element of the adaptation structure (18) connected to a second bending element (262) of the bending converter structure (12). [41] Method for providing a mechanical system, the method comprising the following steps: Providing a bending transducer structure (12) such that it is configured to nonlinearly deform based on bending in response to an applied electrical signal (16) and / or to nonlinearly provide an electrical signal (16) in response to an applied external force (F) causing the bending, wherein the bending transducer structure (12) has at least two bending elements (261, 262) that are mechanically coupled in parallel and a space (38) is formed between the two bending elements (261, 262), mechanical coupling of an adaptation structure (18) with the bending transducer structure (12); such that the bending and a deformation of the adaptation structure (18) are causally correlated, so that the deformation of the adaptation structure (18) provides a nonlinear force for the bending transducer structure (12) which reduces the magnitude of a nonlinearity of the overall response of the mechanical system.

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