Description

Technical Field

Embodiments of the present disclosure relate to MEMS actuators. Further embodiments relate to methods for controlling a MEMS actuator.

Some embodiments of the present disclosure relate to expanding and contracting bending actuator configurations for single or multiple dimensions motion and force generation.

Embodiments are related to microsystems or micro electromechanical systems (MEMS). Embodiments include bending elements based on electrostatic actuation, piezoelectric actuation, thermal actuation, electromagnetic actuation or a combination of any of them, as an active element. In particular, some embodiments relate to nanoscopic electrostatic drive (NED) cells as described in [1] as an active element. Embodiments comprise arrangements of bending cells in series and/or in parallel that can be used to create expanding configurations, contracting configurations and/or combinations of both. Embodiments of the present disclosure may include expanding and contracting configurations which are designed to be in synchronization, or which are designed for intended non-synchronization for the required motions and for surveillance.

Embodiments relate to actuator configurations which are usable for applications such as micro-positioning of objects (in-plane and/or out-of-plane), active elements of microspeakers, micro-pumps, micro-valves, micro-grippers, micro-optical benches, microsystem assemblies, etc.

Background

Various types of actuation elements are known in the state of the art, including, for example, nanoscopic electrostatic drive [1]. Further known actuation elements include thermal and piezoelectric bending elements. Further, thermal actuators [2, 3, 4] and piezoelectric actuators [5, 6] have been used for designing expanding and contracting arrangements of MEMS actuators, providing for both in-plane or out-of-plane positioning. For example, US 2007/103029 A1 and WO 2005/001863 A1 show systems which are based on electrothermal actuation of stacked electrodes in a contracting configuration. The shown systems rely on residual stress engineering in the stacked electrodes to create the required space for motion upon release. WO 2000/067268 A1 shows a further example of a system which is based on electrothermal actuation of electrodes in a contracting and expanding configuration. US 7420318 B1 and US 2008/061916 A1 show systems which are based on piezoelectric actuation of electrodes for creating and expanding a configuration. Further, US 2010/033788 A1 , US 2011/292490 A1 , US 2019/039881 A1 and US 2020/096761 A1 show systems which are based on electrothermal actuation of stacked electrodes for out of plane contracting configurations which rely on residual stress engineering in the stacked electrodes to create the required space for motion upon release.

Summary

Despite the existing solutions, it is desirable to have a concept for a MEMS actuator which provides an improved trade of between an accurate positioning, a large positioning range, an energy-efficient actuation and design flexibility, for example, so as to provide for linear and/or rotational movement.

An embodiment of the present disclosure provides a MEMS actuator comprising at least one actuator cell. The actuator cell comprises a first connecting piece and a second connecting piece. A mechanical connection between the first connecting piece and the second connecting piece comprises at least one connector unit. The connector unit comprises a first beam and a second beam being serially connected with the first beam so as to provide for a meandered shape. At least the first beam comprises a serial arrangement of a plurality of actuator elements configured to change a bending of the first beam upon actuation.

Due to the meandered shape provided by the first and the second beams, the change of the bending of the first beam allows for applying a force between the first connecting piece and the second connecting piece in a direction which is least partially parallel to an axial direction of the actuator cell, along which the first and the second connecting pieces may be arranged. For example, the force may provide for a linear movement of the second connecting piece relative to the first connecting piece or for a change of a relative orientation between the first and second connecting pieces. An increase of an average bending of the first beam and/or the second beam may provide for an expanding force between the first and the second connecting units, while a decrease of an average bending of the first beam and/or the second beam may provide for a contracting force between the first and the second connecting units The serial arrangement of actuator elements of the first beam allows for a flexible design of the connector unit. For example, the actuator elements may be arranged so as to provide one or more of a linear motion, an angular motion, a rotary motion and/or multidirectional motions, wherein different types of motions and/or motions towards different directions may be performed independently to each other or simultaneously. Furthermore, the serial arrangement of actuator elements allows to design the first beam so as to reduce or even to avoid stress within the first beam, independently of whether one or more or all actuator elements of the first beam are actuated or not. In other words, the serial arrangement of the actuator elements may provide for a stress-free motion or a low stress motion. Avoiding stress in the first beam increases the usable force of the MEMS actuator, a travel range and an energy efficiency of the MEMS actuator. Also, due to the low stress in the first beam, the MEMS actuator may provide for a high motion frequency and a high motion resolution. For example, due to low stress, examples may provide for an expansion or a contraction of an actuator cell from few nanometers to hundreds of pm, in particular over 10 pm.

The serial arrangement of actuator elements further allows to design the first beam in an expanding configuration, that is, the actuator elements may be configured to provide for an increase of a distance between the first connecting piece and the second connecting piece upon actuation. Further, the serial arrangement of actuator elements allows for the design of a contracting configuration, that is, the actuator elements are configured to provide a decrease of a distance between the first connecting piece and the second connecting piece upon actuation. The possibility to design both expanding and contracting configurations together with a high design flexibility for the serial arrangement of actuator elements in the first beam further allows for designing a MEMS actuator, in which an interplay between an expanding configuration and a contracting configuration causes particularly low stress, or even no stress. In other words, the disclosed concept allows to design expanding configurations and contracting configurations so that motions of the expanding configurations and the contracting configurations upon actuation is synchronized. In other words, besides allowing both individual and/or joined control of the expanding and contracting configurations sections, the concept also simplifies the synchronization establishment between the expanding and contracting configurations due to the design principle and the driving mechanism. Further, the serial arrangement of actuator elements allows for an arrangement of contracting configurations without necessarily relying on residual stress engineering.

According to an embodiment, the connector unit is a first connector unit, and the mechanical connection comprises a second connector unit. For example, the second connector unit may comprise a first beam and a second beam being serially connected with the first beam so as to provide for a meandered shape. For example, the first beam of the second connector unit comprises a serial arrangement of a plurality of actuator elements configured to change a bending of the first of the second connector unit upon actuation. In other words, in examples, the second connector unit may comprise equivalent features as the first connector unit. In other examples, the second connector unit may be inactive, or may comprise actuator elements which are arranged differently from the description of the first connector unit. The second connector unit is arranged symmetric to the first connector unit with respect to the first and second connecting pieces. Thus, a symmetric actuation of the actuator elements of the first actuator unit and the second actuator unit may, for example, result in a linear movement of the second connecting piece with respect to the first connecting piece along an axial direction of the actuator cell. For example, an asymmetric actuation may result in a change of an orientation between the first and second connecting pieces. Having a second connector unit provides for an increased force of the MEMS actuator, an increased stability. Further, having a first connector unit and a second connector unit increases a flexibility in the implementation of different motion types, such as rotational and linear motions. An increased stability of the actuator cell may increase a motion accuracy of the actuator cell.

A further embodiment according to the disclosure provides a MEMS actuator. The MEMS actuator comprises at least a first actuator cell and a second actuator cell, each comprising a first connecting piece and a second connecting piece. A mechanical connection between the first connecting piece and the second connecting piece comprises at least one connector unit. The connector unit comprises at least one beam, wherein the beam comprises a serial arrangement of a plurality of actuator elements. The actuator elements of the first actuator cell are configured to decrease the bending of the beam of the first actuator cell upon actuation. The actuator elements of the second actuator cell are configured to increase the bending of the beam of the second actuator cell upon actuation. Functionalities and advantages described for the previous embodiments may, if applicable, optionally apply to this embodiment. As the MEMS actuator comprises the first actuator cell having a contracting configuration and the second actuator cell having an expanding configuration, it may provide for an interplay between expanding and contracting configurations.

The following embodiments may refer to any of the MEMS actuators as described before.

According to an embodiment, the actuator cells of the first connector unit are addressable independently from actuator elements of the second connector unit. Thus, for example, in dependence on an individual actuation of the first and the second connector units a linear movement or a change of orientation, that is a rotation, of the first connecting piece with respect to the second connecting piece may be performed.

According to an embodiment, the serial arrangement of actuator elements of the first connector unit and a serial arrangement of actuator elements of the second connector unit are configured so as to provide a movement of at least one of the first and the second connecting piece. The movement comprises one or more of an on-axis movement of the second connecting piece with respect to the first connecting piece along an axial direction, an off-axis movement of at least one of the first and second connecting pieces in a direction different from the axial direction, and an in-plane rotation of at least one of the first and the second connecting pieces with respect to a MEMS substrate.

The axial direction may be a direction, along which the first and second connecting pieces are arranged at least for a predetermined actuation state, for example an unactuated or a fully actuated actuation state, of the first and second connector units. For example, an off- axis movement may comprise a change of orientation between the first connecting piece and the second connecting piece.

According to embodiments, the first beam and the second beam are arranged so that upon actuation of the actuator elements, a position and/or an orientation of the second connecting piece is moved with respect to the first connecting piece. For example, the position is moved along an axial direction, for example an in-plane direction.

According to embodiments, a first end of the first beam is connected with a first end of the second beam. For example, the first ends may be connected directly or indirectly, for example via a connector. The second end of the first beam is connected with one of the first and the second connecting pieces and the second end of the second beam is connected with the other one of the first and the second connecting pieces. The first ends of the first beam and the second beam are positioned outside of a connecting line between the first and the second connecting pieces, so as to implement the meandered shape.

According to embodiments, the first beam and the second beam are arranged so that an actuation of the actuator elements or MEMS results in a change of a distance between the respective second ends of the first beam and the second beam. For example, the first and second beams are arranged substantially perpendicular to a connecting line between the first and second connecting pieces. For example, the serial arrangement of the actuator elements is arranged along a direction between the first and the second ends of the first beam.

According to embodiments, the first and second connecting pieces and the first and second beams are arranged in-plane with respect to a MEMS substrate. The first ends of the first and second beams are movable at least in one or more in-plane directions. For example, the first ends are movable in a direction parallel to the connecting line between the first and second connecting pieces. As the first ends are movable, both the first and the second beam may contribute to a movement of the first connecting piece with respect to the second connecting piece. Thus, a larger travel distance may be reached.

According to embodiments, the first beam is configured at least one section of the first beam is bent in a first bending direction when being in an unactuated state, and wherein the section of the first beam is bent in a second bending direction, which is opposite to the first bending direction, when being in a predetermined actuated state. Thus, the first beam may provide for a symmetric or asymmetric motion around a straight position, which the first beam may have when being in a further actuation state. For example, such a motion may be advantageous for pump or sound generation.

According to embodiments, the first and second connecting pieces and the first and second beams are arranged in-plane with respect to a MEMS substrate. The actuation of the actuator elements of the first beam results in a change of an in-plane bending of the first beam. Due to the in-plane bending, an in-plane position of the second connecting piece relatively to the first connecting piece is moved, thus allowing to implement linear and/or rotational movements within the plane of the substrate.

According to embodiments, the serial arrangement of the actuator elements comprises at least a first section of actuator elements and a second section of actuator elements. The first section is configured for bending in a first bending direction. The second section is configured for bending in a second bending direction which is opposite of the first bending direction. For example, a bending direction may refer to a curvature of the respective beam. For example, the serial arrangement of actuator elements may have, at least in one of an actuated state or an unactuated state, an S-like shape. Having the first and the second section with different bending directions allows for a movement of the first connecting piece with respect to the second connecting piece while avoiding mechanical stress at a connecting point between the first connecting piece and the first beam and a connecting point between the second connecting piece and the second beam and possibly also at a connection point between the first and the second beam. Avoiding stress improves the durability of the actuator cell and increases an energy efficiency for an operation of the actuator cell. For example, S-like shape may provide for a particular rectilinear motion.

According to embodiments, the second beam comprises at least a first section of actuator elements and a second section of actuator elements. The first section of actuator elements of the second beam is arranged opposite to the first section of actuator elements of the first beam. The second section of actuator elements of the second beam is arranged opposite to the second section of actuator elements of the first beam. A bending direction for which the actuator elements of the first section of the second beam are configured is opposite to the bending direction for which the actuator elements of the first section of the first beam are configured. A bending direction for which the actuator elements of the second section of the second beam are configured is opposite to the bending direction for which the actuator elements of the second section of the first beam are configured. In other words, both the first beam and the second beam may have, at least in one of an actuated state and an unactuated state, an S like shape. Thus, a large travel distance may be reached while keeping mechanical stress low.

According to embodiments, the actuator elements of the first beam comprise a first actuator element and a second actuator element. The second actuator element is addressable independently from the first actuator element. An independent actuation of different actuator elements of a beam allows for a flexible control of the movement of the first connecting piece with respect to the second connecting piece. For example, a rotation of an orientation of the first connecting piece with respect to the second connecting piece may be realized, for example, without a movement of a position of the first connecting piece and the second connecting piece. According to embodiments, at least the first beam comprises a parallel arrangement of a plurality of serial arrangements of actuator elements. Optionally, also the second beam may comprise a parallel arrangement of a plurality of serial arrangements of actuator elements. A parallel arrangement of a plurality of serial arrangements of actuator elements may increase the force which is generated by the actuator cell and/or may increase a stability of the actuator cell.

According to embodiments, each of the actuator elements comprises a first surface and a second surface arranged opposite of the first surface. A first end of the first surface is arranged opposite of a first end of the second surface. A second end of the first surface is arranged opposite of a second end of the second surface. The actuator element is configured to change an amount of a distance between the first and the second ends of the first surface relative to an amount of a distance between the first end and the second end of the second surface, so that a change of a bending of the actuator element may be achieved. Within the serial arrangement of actuator elements, the actuator elements are arranged such that the first ends of the first and second surfaces of one of the actuator elements are arranged opposite to the first or the second ends of the first and second surfaces of the subsequent actuator element of the one actuator element. For example, arranged opposite means adjacent to each other, or with a spacer element in between them. Thus, due to the serial arrangement, the change of the bending of the first beam (or the second beam) may be a result of the individual changes of the bending of the individual actuator elements. Thus, the configuration of the individual actuator elements of the serial arrangement allows for a flexible design of the actuation properties of the actuator cell. In particular, a bending behavior of the first beam and/or the second beam is designable in dependence on an application of the actuator cell. Further, having individual actuator elements allows to introduce inactive elements in between one or more of the actuator elements which further increases the designed flexibility for the actuator cell.

According to embodiments, the actuator element comprises one or more of electrostatic actuators, thermal actuators, for example thermoelectric actuators, and piezoelectric actuators. Compared to thermal or piezoelectric actuators, electrostatic actuators, for example NEDs, have the advantage of a lower power consumption, a larger displacement stroke, a higher response frequency, CMOS compatibility at least in the exemplary NED case, smaller area footprint for a given target displacement and/or force no hysteresis. As the material of electrostatic actuator elements may optionally be fabricated from single crystal material, at least on the exemplary case, they may provide for a higher lifetime, for example due to the absence of creeps.

According to embodiments, the actuator cell is a first actuator cell and the MEMS actuator further comprises a second actuator cell. For example, the features as described with respect to the actuator cell equally apply to the second actuator cell, however, the first actuator cell and the second actuator cell may be implemented differently. The actuator elements of the first actuator cell are configured to decrease the bending of the first beam of the first actuator cell upon actuation, for example, so as to decrease the distance between the first and second connecting pieces. Actuator elements of the second actuator cell are configured to increase the bending of the first beam of the second actuator cell upon actuation, for example, so as to increase the distance between the first and the second connecting pieces of the second actuator cell. In other words, the first actuator cell may have a contracting configuration, and the second actuator cell may have an expanding configuration. An interplay between an expanding actuator cell and the contracting actuator cell may allow a uniformed distribution of a force on an object to be moved, so that a motion may be performed very smoothly. In other examples, an interplay between an expanding configuration and a contracting configuration may be used for generating a rotational movement. As the first actuator cell may expand upon actuation and the second actuator cell may contract upon actuation a common control signal may be used for the first actuator cell and the second actuator cell for arrangements, in which a contracting and an expanding configuration is to be implemented.

According to embodiments, a length of a path along the first beam of the first actuator cell in an actuated state of the first actuator cell substantially equals length of a path along the first beam of the second actuator cell in an actuated state of the second actuator cell. In other words, a path along the first beam (an optionally also the second beam) of the first and second actuator cells is equal in the respective bent states of the first and the second actuator cells. Designing the first beam (and optionally also the second beam) in this way allows for a synchronized movement of the first actuator cell and the second actuator cell, that is for a synchronized movement of a contracting configuration and an expanding configuration. The synchronized movement may, for example, allow to apply the same control signal to the actuator elements of the first actuator cell and the second actuator cell, for example, without the need to adapt a control signal provided to one of the first and the second actuator cells with respect to a control signal provided to the other one of the first and the second actuator cells. According to embodiments, the actuator elements of the first actuator cell equal the actuator elements of the second actuator cell. That is, the actuator elements of the first actuator cell are of the same type and of the same dimension as the actuator elements of the second actuator cell. Having equal actuator cells provides for an equal response of the first and the second actuator cells to a common control signal, so that an easy synchronization of a movement of the first actuator cell and the second actuator cell may be realized.

According to embodiments, the actuator elements of the first and second actuator cells are configured to actuate in response to a control signal, for example, a voltage or a current. The MEMS actuator is configured to provide the actuator elements of the first actuator cell with the same control signal as the actuator elements of the second actuator cell. Providing the same control signal to the first and the second actuator cells provides for an easy implementation and enables a synchronous movement of the first and the second actuator cells. Further, mechanical stress in the arrangement comprising the first and the second actuator cells may be avoided, even in the case of noise on the control signal.

According to embodiments, the MEMS actuator further comprises a moveable structure, for example a stage. A first boundary of the moveable structure is connected with the second connecting piece of the first actuator cell at a first connection point. A second boundary of the movable structure, which is opposite of the first boundary, is connected with the second connecting piece of the second actuator cell. An axial direction of the first actuator cell, along which the first and the second connecting pieces are arranged, is antiparallel to an axial direction along which the first and second connecting pieces of the second actuator cell are arranged. Thus, by expanding the first actuator cell and contracting the second actuator cell the moveable structure may be moved along the axial direction of the first and the second actuator cells. Beneficially, these embodiments are combined with the feature that the first actuator cells and the second actuator cells are contracting and expanding configurations, respectively.

According to embodiments, the first actuator cell is part of a first actuator unit. The second actuator cell is part of a second actuator unit. Each of the first and the second actuator units comprises a series of actuator cells arranged along an axial direction of the actuator unit, for example an in plane direction. The first connecting piece of the first actuator cell of the series of actuator cells is connected with a base piece of the MEMS actuator. The second connecting piece of one of two subsequent actuator cells is connected with the first connecting piece of the other one of the two subsequent actuator cells. Thus, for example, actuations of one or more actuator elements of one or more of the actuator cells result in an accumulated movement of a position and/or an orientation of the second connecting piece of the last actuator cell relative to the base piece. Arranging multiple actuator cells in a series allows to provide for a large travel distance while keeping the dimensions of the MEMS actuator small and providing a high mechanical stability of the MEMS actuator.

According to embodiments, the MEMS actuator comprises at least one actuator unit which comprises a series of actuator cells arranged along an axial direction of the actuator unit. The first connecting piece of the first actuator cell of the series of actuator cells is connected with a base piece of the MEMS actuator. The second connecting piece of one of two subsequent actuator cells is connected with a first connecting piece of the other of the two subsequent actuator cells.

According to embodiments, a first actuator cell of the series of actuator cells is addressable independently from a second actuator cell of the series of actuator cells. For example, a first actuator cell may provide for a linear movement along an axial direction of the actuator unit and a second actuator cell may provide for a rotational movement or a change of an orientation between the second connecting piece of the last actuator cell and the base piece. An independent addressability of the individual actuator cells of the series of actuator cells allows to realize a plurality of different kinds of movements with the actuator unit.

According to embodiments, the first actuator cell of the actuator unit is configured to provide, in response to a predetermined actuation, a movement of its second connecting piece with respect to its first connecting piece along a connecting line between its first and second connecting piece. A second actuator cell of the actuator unit is configured to provide, in response to a predetermined actuation, a change of the orientation between its second connecting piece and its first connecting piece.

According to embodiments, the MEMS actuator comprises a rotatably supported structure which is connected, at a point which is spaced apart from a rotation center of the rotatably supported structure, to the second connecting piece of the last actuator cell of the at least one actuator unit. Thus, a contraction or an expansion of the actuator unit along its axial direction may be translated into a rotation of the rotatably supported structure. According to embodiments, the MEMS actuator further comprises a stage which is mounted to be movable in a first direction and in a second direction of a plane of the MEMS actuator. The MEMS actuator comprises at least first and second actuator units each configured to change, upon actuation, a distance between the first connecting piece of a first actuator cell and the second connecting piece of a last actuator cell along an axial direction of the respective actuator unit. The first and second actuator units are arranged so that an actuation of the first actuator unit results in a position change of the stage along the first direction and an actuation of the second actuator unit results in a positon change of the stage along the second direction. The first direction and the second direction are different from each other. For example, the first direction is perpendicular to the second direction. Thus, the stage is movable within the plane of the MEMS actuator in two different directions.

According to embodiments, the MEMS actuator further comprises a functional element, for example, a probe micro positioner, a tip, or a micro gripper. The at least one actuator unit is part of a serial arrangement of a plurality of actuator units which further comprises a second actuator unit. That is, for example, the base piece of one of the actuator units is connected with a second connecting piece of a previous actuator cell of the one actuator unit. The serial arrangement of actuator units is connected with the functional element. The axial direction of the first actuator unit is different from the axial direction of the second actuator unit. Thus, for example, an actuation of the first actuator element results in a change of a position and/or orientation of the functional element in a first direction, and an actuation of the second actuator element results in a change of a position and/or orientation of the functional element in a second direction which is different from the first direction. Thus, the functional element may be positioned precisely by actuating one or more of the actuator units of the serial arrangement of actuator units.

Further embodiments of the disclosure provide a method for controlling the MEMS actuator as described above. The method comprises providing a control signal to the actuator elements.

Brief Description of the Figures

In the following, embodiments of the present disclosure are described in more detail with respect to the figures, among which:

Fig. 1 illustrates an example of a MEMS actuator, Fig. 2 illustrates an example of an actuator cell,

Fig. 3a illustrates an example of a MEMS actuator in a first actuation state,

Fig. 3b illustrates the MEMS actuator of Fig. 3a in a second actuation state,

Fig. 4 illustrates another example of MEMS actuator,

Fig. 5 illustrates another example of MEMS actuator,

Fig. 6 illustrates an example of an angular motion of an actuator unit,

Fig. 7 illustrates another example of an actuator unit,

Fig. 8 illustrates another example of an actuator unit,

Fig. 9 illustrates another example of an actuator unit,

Fig. 10 illustrates another example of an actuator unit,

Fig. 11 illustrates examples of actuator elements and serial arrangements thereof,

Fig. 12 illustrates further examples of serial arrangements of actuator elements,

Fig. 13 illustrates another example of a MEMS actuator,

Fig. 14 illustrates examples of electrostatic actuator elements,

Fig. 15 illustrates examples of electrothermal and piezoelectric actuator elements,

Fig. 16 illustrates another example of a MEMS actuator,

Fig. 17 illustrates another example of a MEMS actuator,

Fig. 18 illustrates another example of a MEMS actuator, Fig. 19 illustrates another example of a MEMS actuator,

Fig. 20 illustrates another example of a MEMS actuator,

Fig. 21 illustrates another example of a MEMS actuator,

Fig. 22 illustrates another example of a MEMS actuator,

Fig. 23a illustrates another example of a MEMS actuator,

Fig. 23b illustrates another example of a MEMS actuator,

Fig. 24 illustrates an example of a parallel arrangement of actuator elements,

Fig. 25 illustrates another example of a MEMS actuator,

Fig. 26 illustrates an example of a method for operating a MEMS actuator.

Detailed description of illustrative embodiments

In the following, embodiments are discussed in detail, however, it should be appreciated that the embodiments provide many applicable concepts that can be embodied in a wide variety of MEMS actuators. The specific embodiments discussed are merely illustrative of specific ways to implement and use the present concept, and do not limit the scope of the embodiments. In the following description, a plurality of details is set forth to provide a more thorough explanation of embodiments of the disclosure. However, it will be apparent to one skilled in the art that other embodiments may be practiced without these specific details. In other instances, well-known structures and devices are shown in form of a block diagram rather than in detail in order to avoid obscuring examples described herein. In addition, features of the different embodiments described herein may be combined with each other, unless specifically noted otherwise.

In the following description of embodiments, the same or similar elements or elements that have the same functionality are provided with the same reference sign or are identified with the same name, and a repeated description of elements provided with the same reference number or being identified with the same name is typically omitted. Hence, descriptions provided for elements having the same or similar reference numbers or being identified with the same names are mutually exchangeable or may be applied to one another in the different embodiments.

Fig. 1 illustrates a MEMS actuator 100 according to an embodiment. The MEMS actuator 100 comprises an actuator cell 110. The actuator cell 110 comprises a first connecting piece 111 and a second connecting piece 112. The first connecting piece 111 and the second connecting piece 112 are mechanically connected via a connector unit 121. The connector unit 121 comprises a first beam 131 and a second beam 132. The first beam 131 comprises a serial arrangement 141 of a plurality of actuator elements 140. The actuator elements 140 are configured to change a bending of the first beam 131 upon actuation.

That is, for example, each of the actuator elements 140 is configured to change the bending of the first beam 131 at a position at which the respective actuator element is located in the first beam 131 upon actuation of the respective actuator element. Thus, an overall bending of the first beam 131 may result from bending contributions of the individual actuator elements 140 of the first beam 131. Consequently, the bending of the first beam 131 may be uniform or may vary along the serial arrangement of actuator elements 140 in accordance with a distribution of the actuator elements 140 along the serial arrangement 141 and/or individual bending states of the actuator elements 140. Further, a direction of the change of the bending of the individual actuator elements 140 may be uniform or may be individual for the actuator elements 140, or may be specific to one or more groups of actuator elements of the plurality of actuator elements 140.

For example, the first connecting piece 111 , the second connecting piece 112 and the connector unit 121 may be arranged in a plane which, for descriptive purposes, is labelled as a x-y-plane, as indicated in Fig. 1. An actuation of one of the actuator elements 140 may result in a change of the bending of the beam 132 within the x-y-plane. In other words, a curvature of the first beam 132 at the position of the one actuator element may change within the x-y-plane upon actuation of the one actuator element. Subsequent actuator elements of the serial arrangement of actuator elements 140 may be arranged adjacent to each other or may be spaced apart from each other. For example, spacer elements, e.g. as described with respect to Fig. 11 , may be arranged between individual actuator elements of the plurality of actuator elements 140. For example, the first beam 131 and the second beam 132 are arranged so that an actuation of the actuator elements results in a force between the second end 135 of the first beam 131 and the second end 136 of the second beam. As the second end 135 is connected with the first connecting piece 111 , and the second end 136 is connected with the second connecting piece 112, the force may in examples result in a decrease or an increase of a distance between the first connecting piece and the second connecting piece, that is, in a contraction or an expansion of the actuator cell 110, respectively. In other examples, e.g. if the mechanical connection between the first and the second connecting pieces comprises a further connection, e.g. a second connector unit, the force may, for example, result in a rotation, that is, a change of an orientation between the first and the second connecting pieces 111 , 112 (cf. Fig. 2).

Thus, in examples, the first beam 131 and the second beam 132 are arranged so that an actuation of the actuator elements results in a change of a distance between the respective second ends of the first beam 131 and the second beam 132.

In Fig. 1 , the first connecting piece 111 and the second connecting piece 112 are exemplarily arranged along the x direction. The first beam 131 and the second beam 132 are, at least for one predetermined actuation state, arranged substantially along the y direction perpendicular to the x direction, although the directions of the first beam 131 and the second beam 132 may change upon actuation. As the first beam 131 and the second beam 132 provide, at least partially, for a connection between the first connecting piece 111 and the second connecting piece 112, and the first beam 131 and the second beam 132 may be substantially arranged along the y direction, the first beam 131 and the second beam 132 provide for a meandered shape. In other words, the first beam 131 and the second beam 132 may be arranged mainly outside a connecting line between the first connecting piece 111 and the second connecting piece 112.

For example, a first end 133 of the first beam 131 is connected with a first end 134 of the second beam 132. Further, a second end 135 of the first beam 131 may be connected with a first connecting piece 111 . A second end 136 of the second beam 132 may be connected with the second connecting piece 112. The first ends 133, 134 of the first and second beams 131 , 132 are positioned outside of a connecting line between the first connecting piece 111 and the second connecting piece 112, so that the first beam 131 and the second beam 132 provide for a meandered shape. The first ends 133 and 134 may be connected directly, or may be connected via a connector. The second beam 132 may optionally comprise a serial arrangement 142 of a plurality of actuator elements 140. The second serial arrangement 142 is configured to change a bending of the second beam 132 upon actuation. For example, the serial arrangement 142 may have properties as described with respect to the actuator elements 140. In examples, the second beam 132 is configured to be symmetric to the first beam 131 with respect to a plane perpendicular to the x direction. For example, actuator elements of the second beam 132 may be configured to provide for an opposite change of the bending of the second beam 132 compared to respective oppositely arranged actuator elements 140 of the first beam 131.

Fig. 2 illustrates a further embodiment of the actuator cell 110. According to this embodiment, the actuator cell 110 further comprises a second connector unit 222. The second connector unit 222 provides, as the first connector unit 121, a mechanical connection between the first connecting piece 111 and the second connecting piece 112.

In examples, the second connector unit 222 is inactive. For example, the second connector unit 222 may be a spring. In other examples, the second connector unit 222 is implemented similarly to the first connector unit 121. For example, the second connector unit 222 is arranged in the x y plane. The second connector unit 222 may comprise a first beam 231 and a second beam 232. The first and the second beams 231 , 232 may provide for a meandered shape. The first beam 231 and the second beam 232 may comprise respective serial arrangements of pluralities of actuator elements, as described with respect to the first connector unit 121. In some examples, the second connector unit 222 may be configured so as to be symmetric to the first connector unit 121 with respect to the connecting line between the first connecting piece 111 and the second connecting piece 112. It is noted that, for simplicity, the following description is concentrated on the first beam 131 of the first connector unit 121 as described with respect to Figs. 1 and 2. However, the description of the first beam 131 may optionally also apply to the second beam 132 and the first and the second beams 231, 232 of the second connector unit 222, wherein directions and bending directions may optionally be adapted according to these symmetries.

Continuing in the description of Fig. 1 , a change of the bending of the first beam 131 may result in a change of a relative position between the first connecting piece 111 and the second connecting piece 112. The change of the relative position may be a linear movement, for example, along the x direction, which may be referred to as a rectilinear movement. In particular, if the second beam 132 is symmetric to the first beam 131 with respect to a plane perpendicular to the x axis, e.g., a plane through a connection between the first beam 131 and the second beam 132 at the first ends 133, 134, and the first beam 131 and the second beam 132 are actuated symmetrically with respect to this plane, a relative movement between the first connecting piece 111 and the second connecting piece 112 may be linear along the x axis.

For example, if the first beam 131 and the second beam 132 are actuated asymmetrically, or if the first beam 131 and the second beam 132 are asymmetric to each other, a relative orientation between the first connecting piece and the second connecting piece 111 , 112 may change.

With respect to Fig. 2, a change of a relative orientation between the first connecting piece 111 and the second connecting piece 112 may be achieved, by actuating the first connector unit 121 asymmetrically with respect to the second connector unit 222.

A relative movement between the first connecting piece 111 and the second connecting piece 112 along the x axis may be referred to as an on axis movement, while other movements may be referred to as off axis movements. For example, a change of the relative orientation between the first connecting piece 111 and the second connecting piece 112 may be referred to as an in-plane rotation, provided that the movements of the first connecting piece 111 and the second connecting piece 111 is within the xy plane.

For example, actuator elements 140 of the second connector unit 222 may be addressable independently from the actuator elements of the first connector unit 121 , Thus, on-axis movement, off-axis movement and/or in-plane rotation may be realized by different actuation states of the first connector unit 121 and the second connector unit 222.

Thus, the serial arrangement 141 of actuator elements of the first connector unit and a serial arrangement of actuator elements of the second connector unit are configured so as to provide a movement of at least one of the first connecting piece 111 and the second connecting piece 112. The movement may comprise one or more of an on-axis movement of the second connecting piece with respect to the first connecting piece along an axial direction, e.g. the x-direction, along which the first and second connecting pieces are arranged at least for a predetermined actuation state of the first and second connector units, an off-axis movement of at least one of the first and second connecting pieces in a direction different from the axial direction, and an in-plane rotation of at least one of the first and the second connecting pieces with respect to a MEMS substrate.

Continuing the description of Fig. 1 , the MEMS actuator may optionally comprise or may be implemented on a substrate, also referred to as a MEMS substrate.

For example, the first connecting piece 111 may be fixed at the MEMS substrate, while the second connecting piece 112 is connected to a structure which is moveable with respect to the MEMS substrate. For example, the first and the second beams 131 , 132 and, in particular, the first ends 133, 134 of the first beam 131 and the second beam 132 may be moveable with respect to the MEMS substrate. For example, the first ends 133, 134 may be movable at least in one direction, for example in the x direction, so that a linear relative movement between the first connecting piece 111 and the second connecting piece 112 may be realized.

For example, the first and second connecting pieces 111 , 112 and the first and second beams 131 , 132 are arranged in-plane with respect to the MEMS substrate, and the first ends 133, 134 of the first and second beams are movable at least in one in-plane direction, e.g. a direction parallel to the connecting line between the first and second connecting pieces 111 , 112. For example, an actuation of the actuator elements of the first beam 131 results in a change of an in-plane bending of the first beam 131.

A change of the actuation of the actuator elements of the first beam 131 and optionally the second beam 132 so that a distance between the second end 135 of the first beam 131 and the second end 136 of the second beam 132 increases may be referred to as an expansion of the first connector unit 121. Accordingly, a change of the actuation of the actuator elements of the first beam 131 and optionally the second beam 132 so that the distance between the second ends 135, 136 decreases may be referred to as a contraction.

Fig. 3a illustrates a MEMS actuator 300 according to an embodiment. For example, the MEMS actuator 300 corresponds to the MEMS actuator 100. The MEMS actuator 300 comprises an actuator unit 302 which includes a serial arrangement of a plurality of actuator cells 110a, 110b, 110c. Each of the actuator cells 110a-c may, for example, correspond to the actuator cell 110 as described with respect to Fig. 1. The first connecting piece 111a of the first actuator cell 110a is connected with a base piece 309. The second connecting piece 112a of the first actuator cell 110 is connected with the first connecting piece 111 b of the second actuator cell 110b. The second connecting piece 112b of the second actuator cell 110b is connected with the first connecting piece 111 c of the actuator cell 110c. In other words, the actuator cells 110a-c are arranged serially. That is, a relative movement of the second connecting piece 112c of the last actuator cell 110c of the serial arrangement of actuator cells relative to the first connecting piece 111 a of the first actuator cell 110a of the serial arrangement of actuator cells results from accumulated movements of the individual actuator cells 110a to 110c. The second connecting piece 112c of a last actuator cell of the actuator unit 302 may be referred to as second connecting piece of the actuator unit. The number of three actuator cells is exemplary. Other serial arrangements of actuator cells may have a higher or a lower number of actuator cells. The following description of the actuator cell 110c is to be understood exemplarily for the actuator cells 110a-c. Further, features described in the following with respect to the actuator cell 110a may also be implemented in the actuator cell 110 of Fig. 1 and Fig. 2.

The first beam 131 and the second beam 132 of the first connector unit 121 of the actuator cell 110c comprises a first section 351 of actuator elements and comprises a second section 352 of actuator elements. The first section 351 is configured to change a bending of the first section 351 of the first beam 131 in a first bending direction. The second section 352 is configured to change a bending of the second section 352 of the first beam 131 to a second direction upon actuation. The first direction is opposite to the second direction.

For example, the first direction is a negative bending direction and the second direction is a positive bending direction. In other words, the first section 351 may be configured for a negative bending and the second section 352 may be configured for a positive bending.

The second beam 132 of the first connector unit 121 may comprise a first section 353 and a second section 354 of actuator elements. The first section 353 of the second beam 132 is arranged opposite of the first section 351 of the first beam 131 . The second section 354 of the second beam 132 is arranged opposite of the second section 352 of the first beam 131. The first section 353 is configured for changing its bending into the second bending direction. The second section 354 is configured for changing its bending into the first bending direction upon actuation.

For example, the first section 351 of the first beam 131 and the second section 354 of the second beam 132 comprise actuator elements 343. The actuator elements 343 are configured for changing the bending of the respective beams into the first bending direction. The second section 352 of the first beam 131 and the first section 353 of the second beam 132 may comprise actuator elements 344 which are configured for changing a bending of the respective beams into the second bending direction.

For example, an actuation state of the MEMS actuator 300 as depicted in Fig. 3a may be an unactuated state. Fig. 3b illustrates the MEMS actuator 300 of Fig. 3a in an actuation state which is different from the actuation state shown in Fig. 3a. For example, the actuation state of the MEMS actuator 300 shown in Fig. 3b may be an actuated actuation state.

For example, the actuator elements 343, 344 may increase the bending upon actuation. Thus, upon actuation the actuation cells 110 may expand along the x direction which may, for example, be considered a direction perpendicular to the arrangement of the actuators. Based on the expansion of the actuator cells 110, a translation of the last connecting piece 112c of the last actuator cell 110c along the x direction may be achieved.

The actuator cells 110a-c as shown in Figs. 3a and 3b may optionally comprise edge connectors 360 for providing the serial arrangement of the first and the second beam of each of the connector units 121 , 222. Due to the arrangement of the actuator elements 343, 344 in sections having opposite bending directions which, for example, deform and expand in opposite and complimenting manner, the expansion of the actuator cells 110a-c may be clamped free or free of mechanical stress, for example at the edge connectors 360 and/or the first and second connecting pieces 111a-c, 112a-c. A mechanical connection between the first connecting piece 111 of an actuator cell and the second connecting piece 112 of a subsequent actuator cell may be referred to as a central connector of the actuator unit 302.

In other words, for example, the first beam 131 and the second beam 132 comprise complimentary sections of positive and negative bending beams which are attached end to end with an edge connector 360. Actuator cells may also be referred to as units. Actuator elements may also be referred to as bending elements.

For avoiding stress at the connection points between the first sections 351 , 353 and the second sections 352, 354 of the first and the second beams 131 , 132 and at the edge connectors 360 as well as at the first and second connecting pieces 111 , 112, the first sections 351 , 353 and the second sections 352 and 354 may be configured according to the following scheme: The following considerations are based on values for the curvature and the length of each of the first and second sections of the first beam and the second beam of the first connector unit and the second connector unit. The curvature is denoted with Cx, wherein the length of the section is denoted with Lx, wherein x denotes the index of the section as indicated exemplarily for the actuator cell 110c in Fig. 3b.

For a S-bending without having a discontinuity and slope at the S junction for curvature transition between positive and negative bending sections, the first and the second beams of the first connector unit and the second connector unit may, for example, fulfil, at least approximately, the following equations:

(set 1) Cl * L1 = —C2 * L2 ; C5 * L5 = -C6 * LG

C3 * L3 = — C4 * L4 ; C7 * L7 = -C8 * L8

In some embodiments, the following equations may apply for providing rectilinear motion: (set 2) (Cl * L1) + (-C2 * L2) = (C5 * L5) + (-C6 * L6)

(C3 * L3) + (-C4 * L4) = (C7 * L7) + (-C8 * L8)

In some embodiments, the following equations may apply:

(set 3) Cl = -C2 = C3 = — C4 = C5 = — C6 = C7 = -C8 L1 = L2 = L3 = L4 = L5 = L6 = L7 = LB

For example, the values of Cx (Curvature of section x) and Lx (Length of section x) can be varied as per requirement till they are satisfying one or more of the above sets of equations (not necessarily the case always though). The variation in Cx and Lx may optionally be used to modulate the volume covered by the expanding unit configurations (cf. Fig. 4). This is in particular helpful in designing of micro-pump or micro-speaker systems where fluid volume displaced is critical.

For example, by varying the values of Cx and Lx, a volume covered by the expanding actuator cell may be adjusted, so as to adjust the MEMS actuator to a specific application period. This may, for example, be helpful in designing of micropumps or microspeaker systems in which a displaced fluid volume may be critical.

Fig. 4 illustrates a further embodiment of the MEMS actuator 300. The left panel illustrates the MEMS actuator 300 in a first actuation state which may, for example, correspond to an unactuated state. The right panel of Fig. 4 illustrates an example of the MEMS actuator 300 in a second actuation state, for example an actuated actuation state. Compared to the example of the MEMS actuator 300 shown in Figs. 3a and 3b, in Fig. 4 a relative length of the first section 351 , 353 of the first and second beams 131 , 132 with respect to the second sections 352, 354 of the first and second beams 131 , 132 is decreased. As illustrated in the right panel of Fig. 4, the decreased length of the first sections 351 , 353 with respect to the second sections 352, 354 may result in an increased displacement upon actuation. Consequently, the difference in volume required by the serial arrangement of actuator cells in the first actuation state and in the second actuation state is larger compared to the configuration shown in Figs. 3a and 3b.

For example, a displacement or change of distance between the first connecting piece and the second connecting piece of a single actuator cell 110 may be directly proportional to the square of the length of the first beam 131 and the second beam 132, and may be proportional to the curvature of the first and the second beams in the expanded state. Thus, by connecting multiple actuator cells in series, a total displacement or a total expansion which achievable may be increased. In a serial connection of actuator units, the displacement or expansion of each of the actuator cells 110 accumulate while a deliverable force of the actuator cells remains the same. Consequently, a desired target maximum displacement value may, for example, be achieved by configuring the combination of length and curvature of the first and second beams and the number of actuator cells 110 used in series. As the actuator cell 110 allows for configuring the length and the curvature of the individual sections of the first and second beams based on a suitable choice of the arrangement of the actuator elements, the MEMS actuators 110, 300 allow to minimize a footprint area required by the MEMS actuator while achieving the target maximum displacement in an efficient way. For example, typical values for a maximum displacement or expansion of an actuator unit comprising a serial arrangement of actuator cells may be up to 10 mm. However, also higher values may be reached. For example, typical maximum displacement or expansion of a single actuator cell is up to 1 mm.

In other words, in examples, the serial arrangement 141 comprises a S-junction with different length and curvature configurations (C1*L1 = C2*L2). This allows to optimize the volume that gets displaced by expanding or contracting configurations, which may be useful for pump or sound generation. Fig. 5 illustrates a MEMS actuator 500 according to an embodiment. The MEMS actuator 500 is an alternative implementation of the MEMS actuator 300. In the MEMS actuator 500, the first section 351 and the second section 345 of the first beam 131 and the second beam 132 comprise actuator elements 543, e.g. instead of the actuator elements 343 of the MEMS actuator 300. Similarly, the second section 352 and the first section 353 of the first beam 131 and the second beam 132 comprise actuator elements 544, e.g. instead of the actuator elements 344. The actuator elements 543, 544 are configured for decreasing the bending of the respective beam upon actuation. Consequently, for example, the left panel of Fig. 5 illustrates an unactuated state of the MEMS actuator 500, while the right panel of Fig. 5 illustrates an actuated state of the MEMS actuator 500. In other words, the MEMS actuator 500 may have a contracting configuration. Thus, upon actuation, the MEMS actuator 500 contracts so that a distance between the first connecting piece 111 a and the second connecting piece 112c decreases upon activation.

In other words, the MEMS actuator 500 may be converse to exemplary configurations of the MEMS actuator 300, which are configured for expanding upon actuation. Thus, the concepts described with respect to Figs. 3a, 3b and 4 for the MEMS actuator 300 may optionally apply, for example, in a reverse manner, to the MEMS actuator 500.

In other words, the examples of the actuator unit 302 shown in Figs. 3a, b, 5 may be configured for expanding or for contracting, and may comprise bending element cells in S- configuration with stacking in units that can be optimized for displacement, force, chip area, motion frequency. In examples, an actuation of the sections and/or beams may be controlled individually (for linear, rotational and/or trajectory trace motions).

Also, some embodiments may include both contracting and expanding configurations. For example, connections between contracting and expanding configurations may be implemented by direct mechanical connections, spring system based mechanical connections (for soft deformable connections during pulling action) or use of grapple hooklike structures to create pulling possible upon contraction. For example, an actuator unit which contracts upon actuation, such as the actuation cell shown in Fig. 5, may be labelled as a pre-angled (PA) unit.

In some embodiments, an actuator cell in a contracting configuration may be configured for bending the first and the second beams further up to a position, in which the first and the second beams are perpendicular to the x axis. That is, for example, a distance between the first and the second connecting pieces 111 , 112 may even be shorter as shown in the right panel of Fig. 5 in an actuated state of the MEMS actuator 500. For such a configuration, it may be beneficial if the edge connectors 360 have a particularly large dimension in the x direction, so that more space for contracting is provided. Such a configuration may be particularly useful for applications which require a large volume of fluid displacement about a mean straight position (e.g., micropumps, microspeakers, etc.), especially when combined with a concept shown in Fig. 4 in a reverse manner for contracting configurations. Contracting configurations may also be very suitable for applications that need a higher chip area fill in an actuated positon (e.g., in comparison with the expanding configurations) while ensuring the required large free space for motion period. Contracting configurations may also be useful for fabrication processes (e.g., Bosch deep reactive ion etching process) that are sensitive towards large open areas or chips with low fill factor during fabrication, i.e. , in an actuated position.

In other words, Fig. 5 may illustrate an example of a configuration of bending actuators in the exemplary case of a contracting configuration to achieve translation in the direction perpendicular to the central connectors’ position. It may be converse to the expanding configuration concept (exemplary case shown in Fig. 3a, 3b). The bending beams 131 , 132 (e.g. NED beams), formed by a series of basic bending elemental cells (e.g. NED bending cells, piezoelectric bending cells, thermal bending cells, etc.), may be arranged in sections 351 , 352, 353, 354 to deform and contract in the opposite and complementing manner so as to provide clamped-free movement in the direction of motion upon actuation (cf. right panel of Fig. 13). The actuation cells 110a-c) may contain complementary sections of positive and negative bending pre-angled beams as described with respect to Fig. 11 , that are attached end-to-end with the edge connectors, and are termed as a “Pre-Angled (PA) unit” (as shown in the left panel of Figure 13). For a pre-angled bending S-beam (to have rectilinear contracting motion) without having a discontinuity in curvature transition between positive to negative bending sections (to avoid stress generation at the transition point and spending of excess energy), it may follow equation-sets (1), (2) in a exemplary case.

As shown in Figs. 3a, 3b and 5 described in the following by the means of Fig. 3b, the first beam 131 and/or the second beam 132 may comprise a parallel arrangement of a plurality of serial arrangements 141 of actuator elements. For example, in Fig. 3b, the first beam 131 and the second beam 132 each comprise a number of three serial arrangements 141 of actuator elements, which are arranged in parallel to each other. For example, the parallely arranged serial arrangements 141 of the first beam 131 may be connected with each other at the first end 133 of the first beam 131 , and/or at the second end 135. Optionally, the beam may also comprise further connections between the parallel arrangements 141 of actuator elements between the first end 133 and the second end 135. For example, having a parallel arrangement of a plurality of serial arrangements 141 of actuator elements may be particularly beneficial in the S configuration as shown in Figs. 3a to 5, because in such an S configuration, a length of a path along each of the serial arrangements 141 between the first end 133 and the second end 135 may remain constant during movement of the beam. Thus, mechanical stress at the first end and the second end may be avoided.

For example, a total deliverable force of the actuator cell 110 may be proportional to a moment generated in the actuator elements 140 and may further be proportional to the number of parallely arranged serial arrangements of actuator elements in a beam or a beam section. Thus, a parallel arrangement of serial arrangements of actuator elements within an actuator cell section or beam allows a higher deliverable force, which is achievable by the actuator cell 110.

According to embodiments, the actuator elements of the first beam 131 comprise a first actuator element and a second actuator element which is addressable independently from the first actuator element. Alternatively or additionally, the actuator elements 140 of the first connector unit 121 are addressable independently from the actuator elements of the second connector unit 222. Alternatively or additionally, a first actuator cell of the series of actuator cells is addressable independently from a second actuator cell of the series of actuator cells.

In embodiments, an electrical connection to the actuator elements 140 of the actuator cells 110 of the actuator unit 302 is provided via the first and the second connecting pieces 111 , 112, via the first and the second beams 131 , 132 and via a connection between the first and the second beams, for example, the edge connector 360. For example, the actuator elements 140 of the first connector units 121 of the actuator cells 110 of the actuator unit 302 may be connected in a series, so that the first connector units 121 are actuated simultaneously. Equivalently, the actuator elements 140 of the second connector units 222 of the actuator unit 302 may be electrically connected in series, so that the second connector units 222 are actuated simultaneously. In other examples, all actuator elements 140 of the actuator unit 302 are connected with the same control signal input, so that all actuator elements 140 of the actuator unit 302 are actuated simultaneously. In further examples, each of the actuator cells 110a-c is electrically connected individually. Optionally, within each of the actuator cells 110a-c, the first connector unit 121 and the second connector unit 222 is electrically connected individually. Optionally, one or more of the sections of the beams of the actuator cells 110a-c are electrically connected individually. Optionally, individual actuator elements are electrically connected individually.

In other words, the electrical connections to the serial arrangements 141 of actuator elements, that is, the bending beams, which may be arranged in series and/or in parallel, within one actuator cell 110 may be provided via the central edge connectors, as shown for example in Fig. 3a, 3b, 4, 5. In a series of actuator cells 110, each of the actuator cells 110 can be individually provided with electrical connections, for example, by using dedicated electrical connections passing via the central and edge connectors. Although those central connections may in some examples require more chip area, an electrically connection via the central connectors may provide a high electrical reliability. Alternatively, particular sections, or all sections, of the actuator cells 110 may be connected electrically in series, which may provide for a particularly low required chip barrier. In some examples, the right and the left halves of the actuator cells, that is the first connector unit 121 and the second connector unit 222 connected in a series may have individual electrical connections. This allows to actuate one half of the units independently at a time, which may provide more electrical reliability. For example, in case of electrical short cut on one side, the other actuatable side may still provide the target deflection, but at a reduced net deliverable force. An individual electrical connection to the first connector unit 121 and the second connector units 222 provide for an angled motion. For example, the beams, for example the unactuated halves, may be designed to act as passive springs in their unactuated or partially actuated state.

Fig. 6 illustrates an angular motion created by the actuator unit 302 according to an embodiment. According to the examples shown in Fig. 6, the first and second beams of the actuator unit 302 are configured to act as passive springs, at least in one of an unactuated state, a partially actuated state and an actuated state. The middle panel of Fig. 6 shows a first actuation state of the actuator unit 302. The first connector units of the actuator unit 302 are referred to as a first portion 621 of the actuator unit 302. The second connector units 222 of the actuator unit 302 are referred to as a second portion 622 of the actuator unit 302. The left panel of Fig. 6 shows a second actuation state of the actuator unit 302. In the second actuation state the actuator elements of the second portion 622 are actuated so as to provide for an expansion of the second portion 622. As the beams are configured to act as passive springs, although the first portion 621 expands, however, to a lower extent than the second portion 622. Therefore, the actuation of the second portion 622 results in a rotational movement, wherein each of the actuator cells 110a-c provides for a rotation angle 681 , 682, 683. A total rotation angle, which describes a change of an orientation between the first first connecting piece 111a and the last second connecting piece 112c may correspond to a sum of the individual contributions 681 , 682, 683 of the actuator cells 110a-c, e.g. according to the following equation: where describes the angular rotation of the n-th actuator unit.

The right panel of Fig. 6 shows a third actuation state of the actuator unit 302, in which the first portion 621 is actuated. In this case, each of the actuator cells 110a-c provides for a contribution 681 682’, 683’ to a total change of orientation between the first first connecting piece 111 a and the last second connecting piece 112c.

Optionally, the unactuated half acting as passive spring, e.g. portion 621 in the left panel of Fig. 6 or portion 622 in the right panel of Fig. 6 can also be actuated partially (i.e. at a lower voltage) to adapt the in-plane rotation angle (by deforming more in the direction of motion) at a particular actuation voltage (applied to the normally actuated side). This allows to finely control the net rotation angle. Conversely, one half (e.g. portion 621 or 622) of the unit can be designed to bend and move in opposite to the direction of motion (i.e. generate backwards rather than forward motion) upon actuation to greatly increase the rotation angle (compared to a passive case). This helps in creating a greater in-plane rotation angle, though at cost of reduced net deliverable force in the direction of forward motion that normally would have been delivered in the exemplary case (in Figurel ). This loss can be compensated by increasing the net force delivered by the section actuating in forward direction, e.g., by increasing the number of bending beams stacked in parallel in the forward bending section, increasing actuation voltage, etc.

Although the example of Fig. 6 is illustrated by the means of an expanding configuration of the beams, a rotational movement may equivalently be implemented by means of a contracting configuration. In examples, the individual contributions 681 , 682, 683, 681 ’, 682’, 682’, 683’ to the change of orientation, provided by the individual actuator cells 110a-c, are equivalent.

As demonstrated in the Figs. 3a-6, the actuator unit 302 may be configured to allow for both an in plane rotation and a linear motion. The rotation angle may be controlled by the voltage applied to the first and second portions 621 , 622, in particular, by the voltage that is applied to the inactivated or partially actuated unit halves, that is the first portion 621 in the left panel and the second portion 622 in the right panel. Further, the rotation angle may be controlled by the distance moved. This may, for example, be particularly useful for applications wherein plane angular tilt corrections are required during and/or after a certain distance motion. Examples of such applications are micro-opto electronical micro systems (MOEMS) based Fabry-Perot optical filters, MOEMS based optical banches, MOEMS interferometers, etc., where parallelization of optical surfaces during actuation is required. For example, tilt corrections are required to compensation the errors coming from fabrication, assembling, vibrations, etc.

In alternative to the example shown in Fig. 6, where all of the actuator cells 110a-c are configured for performing a rotational motion, in other examples a set of actuator cells of the actuator cells 110a-c or an individual actuator cell may be implemented for performing a rotational motion, while other actuator cells may be configured for performing a linear motion, for example, exclusively a linear motion.

Fig. 7 illustrates another example of the actuator unit 302. In this embodiment, the actuator cell 110c is configured for performing a rotational motion upon actuation, while the actuator cells 110a, 110b are configured for performing a linear motion upon actuation. For example, the middle panel of Fig. 7 illustrates an actuated state of the actuator unit 302. The left panel shows a first actuation state of the actuator unit 302, in which the actuator cells 110a and 110b are actuated so as to perform a linear motion along the x direction. The first connector unit 121 of the actuator cell 110c is unactuated or less actuated as the second connector unit 222 of the actuator cell 110c. The second connector unit 222 of the actuator cell 110c is actuated, so as to provide for a rotational movement. The right panel of Fig. 7 shows a second actuation state of the actuator unit 302, in which the actuation states of the first connector unit 121 and the second connector unit 222, as compared to the left panel, are exchanged, so as to provide for a rotational movement in the opposite direction. It is noted that electrical connections of the actuator unit 302 may be configured so that the actuator unit 302 allows, in dependence on one or more control signals applied to the actuator unit 302, for both types of movements as described with respect to Figs. 6, 7 and following Fig. 8.

For example, the configuration shown in Fig. 7 may be beneficial for controlling an angle created by individual actuator cells or a set of actuator cells, thus allowing a better control over the location and extent of rotation created. For example, the rotation movement of the actuator cell 110c may provide for a tilt correction required after moving a target along a linear distance, for example, by the actuation of the actuator cells 110a and 110b.

Fig. 8 illustrates another example of the actuator unit 302 according to an embodiment. According to this embodiment, the first connector unit 121 of the actuator cell 110c is asymmetric with respect to the second connector unit 222 of the actuator cell 110c. For example, a curvature Cx and/or a length Lx of one or more of sections of the beams of the first connector unit 121 is asymmetric with respect to an oppositely arranged section of the beams of the second connector unit 222 of the actuator cell 110c. Thus, upon actuation of the actuator cell 110c, for example by using an identical control signal for both the first connector unit 121 and the second connector unit 222, an expansion (or in alternative implementations a contraction) may be asymmetric, so as to provide a rotational motion of the second connecting piece 112c with respect to the first connecting piece 111c. For example, the first connector unit 121 has a different maximum deflection compared to the second connector unit 222. This implementation has the advantage that a dedication separate electrical connection to the sections of the actuator cell 110c, or to the first connector unit 121 and the second connector unit 222 of the actuator cell 110c may not be required to generate an angular motion/rotation.

In some embodiments, a variation of the curvature and length of the sections of the beams may be configured so as to provide for a specific stiffness of the first connector unit 121 and/or the second connector unit 222, for example, in an unactuated state, so as to allow for a better tuning of a linear and/or rotational motion.

In general, rotational motion may be achieved by configuring the first connector unit 121 and the second connector unit 222 so that the first connector unit extends or contracts to a different extent compared to the second connector unit 222 upon actuation. Fig. 9 illustrates another example of the actuator unit 302 according to an embodiment. According to this embodiment, in the actuator cell 110c, a length of the first and the second beams of the first connector unit 121 is different from a length of the first and the second beams of the second connector unit 222. The left panel of Fig. 9 shows a first actuation state of the actuator unit 302, while the right panel shows a second actuation state. As illustrated in the right panel, in the second actuation state, in which the beams are expanded, the first connector unit 121 and the second connector unit 222 of the actuator cell 110c provide for a different distance between the first and the second connecting pieces 111 c and 112c. this difference results in a rotation 863’ of the first connecting piece 112c with respect to the second connecting piece 111 c.

In other words, the second connector unit 222 may provide for a different forward motion compared to the first connector unit 121 .

As described with respect to the previous Figures, embodiments may provide for angular motion, tilt and/or rotation configurations (in and/or out of plane) based on expanding configurations, contracting configurations or combination of both (with/without linear motion possibility along with it.

Fig. 10 illustrates an alternative implementation of the actuator unit 302 according to an embodiment. This embodiment allows for an implementation of the first beam 131 and the second beam 132 of the actuator cells 110 without an S configuration in a expanded state of the first beam 131 and the second beam 132. In this example, the first beam 131 is connected with the second beam 132 via a flexible connector 1013. Further, the second beam 131 is connected with the second connecting piece 112 via a flexible connector 1015. The flexible connectors 1013 and 1015 allow to avoid stress, or to reduce mechanical stress, during actuation of the actuator cell 110, although the first beam 131 and the second beam 132 may comprise only one section of actuator elements, the actuator elements within this one section being configured for a bending in a uniform direction.

Fig. 11 illustrates actuator elements and serial arrangements of actuator elements according to embodiments. A first type of actuator elements 1171 comprises a first surface 1172 which is arranged opposite of a second surface 1176 of the actuator element 1171 . A first end 1173 of the first surface 1172 is arranged opposite of a first end 1177 of the second surface 1176. A second end 1174 of the first surface 1172 is arranged opposite of a second end 1178 of the second surface 1176. For example, the first ends 1173, 1177 and the second ends 1174, 1178 indicate opposite ends of their respective surfaces 1172, 1176 along a direction, along which a plurality of the actuator elements 1171 is arranged in a serial arrangement of actuator elements, for example, the y direction referred to in the previous figures. The actuator element 1171 is in a first actuation state, for example an unactuated state. An illustration of the actuator element 1171 referenced with reference sign 1171 ’ represents an actuated, or in comparison with the actuator element 1171 , more actuated, actuation state of the actuator element 1171. Upon actuation, a distance between the first end 1173 of the first surface 1172 and the second end 1174 of the first surface 1172 increases relative to a distance between the first end 1177 of the second surface 1176 and the second end 1178 of the second surface 1176. That is, the distance between the first end 1173 and the second end 1174 increases and/or the distance between the first end 1177 and the second end 1178 decreases. Thus, the actuator element 1171 is configured for increasing the bending upon actuation. A change of a volume of the actuator element 1171 upon actuation may be described by a deformation triangle 1168. An orientation of a secondary surface of the actuator element 1171 , the secondary surface connecting the first surface 1172 with the second surface 1176, may, for example, change by an angle 1169 upon actuation.

For example, within one section, e.g. sections 343, 344, 543, 544 of Fig. 3a, b, 5, of actuator elements, or within the serial arrangement 141 , 142 of actuator elements, the actuator elements are arranged such that the first ends 1173, 1177 of the first and second surfaces 1172, 1176 of one of the actuator elements are arranged opposite, e.g. adjacent to, or with a spacer element in between, to the first ends 1173, 1177 of the first and second surfaces 1172, 1176 or opposite to the second ends 1174, 1178 of the first and second surfaces 1172, 1176 of the subsequent actuator element of the one actuator element.

As illustrated in Fig. 11 , according to embodiments, a second type of actuator cell 1191 is based on the first type of actuator element 1171 , but has a modified thickness in the y direction. For example, the actuator element 1191 has a structure which corresponds, in a first actuation state of the actuator element 1191 , e.g., an unactuated state, to a structure of the first type of actuator element 1171 combined with structural elements 1179, 1179’. The structural elements 1179, 1179’ may have the same material as the actuator element 1171 , so that in the actuator element 1191 the structural elements 1179, 1179’, in examples, may not be identified. The combination of the actuator element 1171 with the structural elements 1179, 1179’ may in these examples to be understood as describing a volume or an outer shape of the actuator element 1191 in comparison with the actuator element 1171. In other examples, the structural elements 1179, 1179’ may be of a different material, for example, the structural elements 1179, 1179’ may comprise an inactive material which does not change its shape substantially upon actuation of the actuator element 1191. In these examples, the structural elements 1179, 1179’ may be referred to as spacer elements. In some examples the structural elements may comprise an electrically isolating material.

Thus, according to embodiments, the first beam 131 and/or the second beam 132 comprise one or more inactive elements 1179, 1179’, 1199, which are, for example, substantially rigid, i.e. , which do not bend substantially upon actuation of any of the actuator elements of the first beam 131 and/or the second beam 132. For example, one or the inactive elements is arranged between two subsequent actuator elements of the serial arrangement of actuator elements.

The structural element 1179 is positioned between a first end 1193 of a first surface 1192 of the actuator element 1191 and a first end 1197 of a second surface 1196 of the actuator element 1191. The first surface 1192 is arranged opposite of the second surface 1196. The structural element 1179’ is positioned between the second end 1194 and the second end 1198. An illustration of the actuator element 1191 referenced with reference sign 1191 ’ represents a second actuation state of the actuator element 1171 , e.g. an actuated state with a higher actuation than the first actuation state. In the actuated actuator element 1191 ’, the structure of the structural elements 1179, 1179’ provides for the circumstance that a distance between the first end 1193 and the second end 1194 equals, at least substantially, the distance between the first end 1173 and the second end 1174 of the first surface 1172 of the actuator element 1171 in the unactuated state. Similarly, in the actuated actuator element 1191 ’, a distance between the first end 1197 and the second end 1198 of the second surface 1196 equals, at least substantially, a distance between the first end 1177 and the second end 1178 of the second surface 1176 of the unactuated actuator element 1171. As, due to the structural elements 1179, 1179', the distance between the first end 1193 and the second end 1194 is larger than the distance between the first end 1197 and the second end 1198 in the first actuation state compared to the second actuation state, a serial arrangement 1146 of a plurality of actuator elements 1191 in the first actuation state is bent. Upon actuation of the first actuation state of the serial arrangement 1146 of the actuator elements 1191 , a bending of the serial arrangement 1146 decreases. Thus, in the second actuation state of the serial arrangement 1146, e.g. represented by the serial arrangement 1146’, the serial arrangement may be straight. A third type of actuator element 1181 comprises a shape which may be described as a combination of the actuator element 1171 and structural elements 1199, which may be understood similar as the structural element 1179. A first structural element 1199 is arranged between a first end 1183 of a first surface 1182 and a first end 1187 of a second surface 1186 of the actuator element 1181. A second structural element 1199 is arranged between a second end 1184 of the first surface 1182 and a second end 1199 of the second surface 1186. The first end 1183 is arranged opposite of the first end 1187. The second end 1184 is arranged opposite of the second end 1188. For example, the structural elements 1199 extend a dimension of the first end second surfaces 1182, 1186 by and equal length along the y direction. For example, the structural elements 1199 may extend the distance between the first end 1183 and the second end 1184, as well as between the first end 1187 and the second end 1188, compared to the actuator element 1171 , by the same amount as the structural elements 1179, 1179', extend the distance between the first end 1197 and the second end 1198 of the actuator element 1191. Thus, in a second actuation state (e.g. an actuated state) of the actuator element 1181 , illustrated as actuator element 1181 ’, the distance between the first end 1183 and the second end 1184 may equal the distance between the first end 1197 and the second end 1198 of the second surface 1196 of the actuator element 1191. Equivalently, in the actuated actuator element 1181’, the distance between the first end 1187 and the second end 1188 of the second surface 1186 may equal the distance between the first end 1193 and the second end 1194 of the first surface 1192 of the actuator element 1191. Therefore, in an actuated state of a serial arrangement 1147’ of actuator elements 1181 , a length along a path along the actuated, bent serial arrangement 1147’ equals, at least substantially, a length along a path along the serial arrangement 1146 in the unactuated, bent state, provided that a number of actuated elements 1191 of the serial arrangement 1146 equals a number of actuator elements 1181 of the serial arrangement 1147’. In other words, in a bent state of the serial arrangement 1146, which in case of the serial arrangement 1146 is an unactuated state, the length of the path of the serial arrangement 1146 equals the length of the path of the serial arrangement 1147’ in a bent state, which in case of the serial arrangement 1147’ corresponds to an actuated state.

As the length of the path along the serial arrangement 1146 equals the length of the path along the serial arrangement 1147’, a simultaneous actuation of the serial arrangement 1146 and the serial arrangement 1147’ allows for a movement, in which an actuator cell which is based on one or more of the serial arrangements 1146, upon actuation, contracts by the same extent, to which an actuator cell designed on the basis of one or more of the serial arrangements 1147 expands upon actuation. The serial arrangement 1146 may also be referred to as a pre-angled configuration or a pre-angled beam. Accordingly, the actuator element 1191 may be referred to as pre-angled (PA) actuator element or pre-angled bending cell. For example, the pre-angled configuration contracts upon actuation. The serial arrangement 1147 may be regarded as a normal angled configuration or normal angled beam. The normal angled arrangement 1147 may expand upon actuation. Accordingly, the actuator element 1181 may be referred to as normal angled (NA) actuator element or normal angled bending cell. For example, the pre-angled configuration 1146 decreases its bending, e.g. deforms into a straight position, upon actuation.

In other words, the disclosed concept may comprise to add the actual structural material triangle in reverse flipped position to an unactuated bending cell that is equal to the deformation triangle of that bending cell at a specific actuation voltage and a load point. Consequently, when a same voltage and load point is applied to the cell a straight positioned bending cell can be achieved. Placing the pre-angled actuator elements 1191 adjacent to each other in a series logic 1146 the pre-angled beam of any length can be formed which will bend into a straight position upon actuation.

For example, synchronous motion of contracting configuration may be derived from the concept described with respect to Fig. 11. In other words, Fig. 11 shows schematically a method of formation of pre-angled bending beam 1146 and normal-angled bending beam 1147 from a selected bending cell whose deflections are complementary to each other and may be synchronized w.r.t actuation voltage applied. The synchronization is achieved based on the designing principle of making the total length of the two beam types nearly equal (L), curvature (C) been already same as they are formed from the same bending cell (or at a fixed offset for materials with anisotropic elastic modulus). This may result in a synchronized tip deflections (or at a fixed offset for material with anisotropic elastic modulus) upon actuation for both the beam types that are complementary to each other as tip deflection is K (C*L ² ).

Fig. 12 illustrates multiple actuation states of different serial arrangements of pre-angled actuator elements according to embodiments. As illustrated in Fig. 12(a), a first example of a serial arrangement 1246a of pre-angled actuator elements 1191 has a first bending direction in a first actuation state which is shown on the left panel. In a second actuation state, the serial arrangement 1246a is straight. In a third actuation state, shown in the right panel, the serial arrangement 1246a has a second bending direction, which is opposite to the first bending direction. For example, the beam 1246a is configured to create positive and negative deflection about a mean position for a target voltage and load point. As illustrated in Fig. 12(b), a second example of a serial arrangement 1246b of pre-angled actuator elements 1191 has, in a first actuation state which is shown in the left panel, an S like shape. In the first actuation state, a first section 1251 b of the serial arrangement 1246b is bent towards the first direction, which is opposite to a second direction into which a second section 1252b of the serial arrangement 1246b is bent. In the second actuation state, shown in the center panel, the serial arrangement 1246b is straight. In a third actuation state, shown in the right panel, the first section 1251 b is bent towards the second direction, while the second section 1252b is bent towards the first direction. For example, the pre-angled bending beam S-configuation 1246b is configured to create highly linear positive and negative deflections about a mean position for a target voltage and load point. As illustrated in Fig. 12(c), a third example of a serial arrangement 1246c of pre-angled actuator elements 1191 comprises a serial arrangement of sections 1251c, 1252c, 1253c, 1254c which are bent, in a first actuation state which is shown in the left panel, in alternating bending directions. That is, a first section 1251c and a third section 1253c are bent towards a first bending direction which is opposite to a second bending direction towards which a second section 1252c and a fourth section 1254c are bent. In a second actuation state, shown in the center panel, the serial arrangement 1246c is straight. In a third actuation state, shown in the right panel, the first and the third sections 1251 c, 1253c are bent towards the second bending direction and the second and the fourth sections 1252c, 1254c are bent towards the second bending direction. For example, in Fig. 12c, the left panel illustrates an unactuated state, the center panel illustrates a partially actuated state, and the right panel illustrates an actuation state with a higher actuation than that of the center panel. For example, the right panel illustrates a completely actuated state. For example, the beam 1246c is implemented as pre-angled bending beam with multiple S-configuations to create highly linear positive and negative deflections about a mean position for a target voltage and load point.

For example, in Fig. 3a, 3b, actuator elements 343, 344 may optionally correspond to the actuator elements 1181. For example, in Fig. 5, actuator elements 543, 544 may optionally correspond to the actuator elements 1191.

According to examples, e.g. as described with respect to Fig, 12, at least one section of the first beam 131 is bent in a first bending direction when being in an unactuated state, and wherein the section of the first beam is bent in a second bending direction, which is opposite to the first bending direction, when being in a predetermined actuation state.

For example, in the predetermined actuation state, the bending of the beam 131 is symmetric to the unactuated state with respect to a straight position of the beam, and wherein the predetermined actuation state is a maximal actuated state.

In other words, the pre-angled beams may be configured to bend beyond the straight position. For that purpose, for example, the deformation triangle, e.g., the structural elements 1179, 1179’ may be adapted accordingly. Thus, embodiments include beams which may be actuated around a mean straight position, based on applied voltage, which is required for some applications.

The actuator elements may be arranged in a pre-angled serial arrangement, for example, in sections which are configured to bend in complimentary manner in an S configuration. Thus, a linear translation at a free end of the beam may be achieved while moving to a straight position, or beyond, as shown for the case of the serial arrangement 1246b. it should be noted that the serial arrangements 1246a-c may be configured to deflect more in one direction than into the other direction. That is, a maximum bending may be asymmetric with respect to the straight position. This may be achieved by the choice of the structural elements 1179, 1179’, and applied voltage in a load point.

In examples, structural materials with anisotropic elasticity (such as crystalline silicon) may be used for the beams or for the MEMS actuator. In this case, the pre-angle created via deformation triangle may change the average elastic modulus value of the particular bending cell due to the angle and position it is placed at in the pre-angled beam. This change in elastic modulus may lead to a difference in curvature of the bending cells for the different positions in the same pre-angled beam if same cell geometry is used for all the bending cells (actuator elements) at a particular actuation voltage. This change, if not negligible/acceptable for the required performance, can be compensated by changing the bending cell second-area-moment value corresponding to its angle and position (by changing the geometry of bending cell as per its position and angle, such as cell thicknesses, etc.), by adapting the applied voltage to get the required deflection for the particular load point for the entire pre-angled beam, etc. Another solution is to create multiple S-configuration pairs within the pre-angled beam sections as shown in Figure 12(c). The advantage of such a configuration is that the individual S-configurations don’t get angled due to their position in the pre-angled beam and thus a negligible/acceptable change in elastic modulus value of the bending cells can be achieved. This simplifies the designing and the actuation control while without posing any limitation to the displacement of the preangled beam tip as any number of S-configurations can be cascaded together to achieve a target displacement in unactuated state (which provides more distance for pre-angled beam to contract) without changing the bending cells angle outside a S-configuration due to their position. The individual S-configuration length (based on number of cells in it), curvature of each section within the individual S-configuration, etc. can be optimized with respect to the chip area to achieve a required displacement and force value for the entire pre-angled beam. This concept of multiple S-configurations in a single beam can also be applied to normally-angled beams as well to have more designing freedom for achieving required displacement and force values in an optimum chip area for the entire normally-angled beam. The advantage of this construction method for contracting beams is that it provides a large degree of designing freedom, optimum chip area use, high fill factor, etc. for achieving a target force, displacement, actuation frequency, motion resolution, etc. Also, there is no need to rely on accurate stress based engineering (similar to one used in [2][3] for out-of- plane) to create pre-curvature for contraction, which is known to be harder to design and control in MEMS devices and is highly sensitive towards fabrication process errors (thus reproducibility of identical pre-stressed curvatures during fabrication process is difficult) and also very sensitive towards ambient operation conditions such as temperature, thus reducing device performance reliability during operation.

Thus, according to examples, the serial arrangement 141 comprises a plurality of first sections 1251 c, 1253c and a plurality of second sections 1252c, 1254c, wherein the first sections and second sections are arranged alternatingly in the serial arrangement. Each of the first sections is configured to change a bending of the first section towards a first bending direction upon actuation. Each of the second sections is configured to change a bending of the second section towards a second bending direction upon actuation. The first bending direction is opposite to the second bending direction. Optionally, the first and second sections are bent in an unactuated state. These examples allow for a compensation of anisotropic elasticity, e.g. by multiple S-configurations in a single beam, thus simplifying designing and allowing for optimization of contraction area.

Fig. 13 illustrates a MEMS actuator 1300 according to an embodiment. The left panel illustrates a first actuation state, for example an unactuated state, and the right panel illustrates a second actuation state, for example an actuated or a completely actuated actuation state. The MEMS actuator 1300 comprises a movable stage 1361. Further, the MEMS actuator 1300 comprises a first actuator unit 302a, which may be an example of the actuator unit 302. The actuator unit 302a comprises actuator cells 1310a, which may be examples of the actuator cell 110. The actuator cells 1310a are configured to contract upon actuation (e.g. along the x-direction as shown in Fig. 13). For realizing a contraction upon actuation, the first beam 1331a and the second beam 1332a of each of the actuator cells 1310a comprise serial arrangements of pre-angled actuator elements, for example, serial arrangements of pre-angled actuator elements 1191 arranged according to the concept of the serial arrangement 1146. For example, the first beam 1331a and the second beam 1332a comprise serial arrangements 1246b which are S shaped in the first actuation state. The MEMS actuator 1300 further comprises a second actuator unit 302b which comprises actuator cells 1310b which may be examples of the actuator cell 110. The actuator cells 1310b are configured to expand upon actuation (e.g. along the x-direction). An axial direction of the actuator unit 1302b, along which the actuator unit 1302a is to expand, is antiparallel to an axial direction of the actuator unit 1302a, along which the actuator unit 1302a is to contract (that is, a direction from the first connecting pieces to the second connecting pieces of the actuator cells of the respective actuator units is antiparallel). Thus, upon actuation, the second connecting piece 112a of the actuator unit 1302a may move in the same direction, and by the same amount, as the second connecting piece 112b of the actuator unit 1302b. Each of the actuator cells 1310b comprises a first beam 1331b and a second beam 1332b which may be examples of the first beam 131 and the second beam 132, respectively. For example, the first beam 1331b and the second beam 1332b each comprise serial arrangements of actuator elements according to the concept of the serial arrangement 1147 of actuator elements 1181. For example, the first beam 1331b and the second beam 1332b are configured to have an S like shape in a bended state, for example in the second actuation state. The first beams 1331a, 1331 b and the second beams 1332a, 1332b may be examples of the first beam 131 and the second beam 132, respectively. The actuator cells 1310a and 1310b are adapted to each other so as to provide for a synchronized movement upon actuation of the actuator units 302a and 302b. That is, upon actuation, a contraction of the actuator unit 302a corresponds, at least substantially, to an expansion of the actuator cell 302b. The second connecting piece 112a of the actuator unit 302a is connected to a first boundary surface of the movable structure 1361. The second connecting piece 112b of the actuator unit 302b is connected to a second boundary surface of the moveable structure 1361 which is arranged opposite of the first boundary surface of the movable structure 1361. For example, a length of a path along the first beam 1331 a of the first actuator cell 1310a in an unactuated state of the first actuator cell, e.g. left panel of Fig. 13, substantially equals a length of a path along the first beam 1331 b of the second actuator cell 1310b in an actuated state of the second actuator cell, e.g. right panel of Fig. 13. Thus, upon actuation the first actuator cells 1310a may contract synchronous to an expansion of the second actuator cells 1310b.

For example, the actuator elements of the first actuator cell 1310a equal the actuator elements of the second actuator cell 1310b, thus allowing for an easy synchronous implementation.

For example, a control signal is applied to the first and the second actuator units 302a, 302b, e.g. a voltage level or a current. The actuator elements of the first and second actuator cells may actuate in response to the control signal, e.g. as explained with respect to Fig. 14, 15. Due the synchronous behavior of the actuator units 302a, 302b upon actuation, the same control signal may be provided to the first and the second actuator units 302a, 302b, still enabling a synchronous movement.

In other words, the first actuator cell 1310a (or the first actuator unit 302a) and the second actuator cell 1310b (or the first actuator unit 302b) are configured for an inherently synchronized motion upon actuation.

Although the concept of synchronous motion of expanding and contracting actuator cells is shown in Fig. 13 by means of actuator units 302a, b comprising a serial arrangement of actuator cell (which may, in examples comprise a single actuator cell 1310a, 1310b), the concept is applicable to a pair of single actuator cells, parallel arrangements of actuator cells, or combinations of parallel and serial arrangements of actuator cells.

Accordingly, in examples, the actuator cell 1310a is a first actuator cell, and wherein the actuator cell 1310b is a second actuator cell. The actuator elements of the first actuator cell 1310a are configured to decrease the bending of the first beam 1331 a of the first actuator cell 1310a upon actuation, and wherein actuator elements of the second actuator cell 1310b are configured to increase the bending of the first beam 1331 b of the second actuator cell upon actuation. In other words, the MEMS actuator 1300 may represent a exemplary case of synchronized expanding and contracting configurations linked via a load stage 1361 to achieve linear translation of the stage in direction of the expansion and contraction of the NA (302a) and PA (302b) units respectively. The NA and PA units are formed using synchronized preangled and normal-angled bending beams (e.g. formed as shown in Figure 11) sections. Due to the design based synchronization of beam sections and equal number of NA and PA units, the extent of expansion is equal to the extent of contraction in the direction of the motion for the same actuation voltage (or at a certain offset between voltages applied to NA and PA units for materials with anisotropic elastic modulus). The advantages of such a configuration are that they have greatly enhanced out-of-plane stiffness (compared to a system with either just expanding configuration or only contracting configuration), thus, higher motion frequency and lower out-of-plane sagging (thus no support structures required underneath and a contact-less operation is possible which will be free from any kind of stiction issues). Thus, the net deliverable force may be effectively doubled (in the exemplary case) due to the synchronization (as pulling force and pushing force act in synchronization on the load stage), high chip area fill factor, low sagging etc. Also, the synchronization obtained based on the design itself greatly simplifies the drive control required for the actuation.

The synchronization between the expanding and contracting configurations, apart from using synchronized beam types and same number of NA and PA units, can also be achieved by using combination of different numbers of NA and PA units, with different lengths of the NA and PA units’ sections, etc. to achieve same extent of contraction or expansion motion upon actuation at either same voltage or at a particular voltage offset applied to the NA and PA units.

All the concepts mentioned herein for expanding and/or contracting configurations can be applied to the combination of the expanding and contracting configurations as well (whether synchronized or not). For example, in case of higher loads when the enhanced out-of-plane stiffness due to linked expanding and contracting configurations is not sufficient, supporting sliding surfaces underneath the stages can be used as well (similar to as shown in Figs. 17, 18).

In general, MEMS actuators according to embodiments comprise actuator cells 110 arranged in series, as described with respect to the actuator units 302, or in parallel (e.g. Fig. 18). Embodiments include serial arrangements of parallel arrangements of actuator cells 302, and/or parallel arrangements of serial arrangements of actuator cells 302.

For example, the total deliverable force is also directly proportional to number of units or actuator cells used in parallel (while the maximum displacement remains the same). A target force value can be achieved from the combination of length of bending beams, the generated moment in bending elements, the number of bending beams stacked in parallel in a unit and the number of units in parallel. For NED based bending elements, typical range of maximum deliverable force is around 0 to 10 mN (typical maximum deliverable force value is around 1 mN) and the typical motion frequency range is around 0 to 100 kHz.

Based on the parameters such as length, curvature, generated moment, number of bending elements in a section (e.g. of the beams), number of units placed in series and/or in parallel, etc. a target force and displacement configuration can be achieved within an optimum chip area as per the requirement. The bending elements (e.g. NED cells) allow an analog control thus based on the driving voltage applied, nanometer range of displacement resolution can be achieved while maintaining a travel range in millimeters.

In the following, different exemplary implementations of the actuator elements 140, 343, 344, 543, 544, 1171 are described, which comprise one or more of electrostatic actuators, thermal actuators, e.g. thermoelectric actuators, and piezoelectric actuators.

Fig. 14 illustrates different types of electrostatic actuator elements according to embodiments. The actuator elements shown in Fig. 14 are examples of the actuator elements 140, 343, 344, 543, 544, 1171. Panel A of Fig. 14 shows an example of a first type of actuator element 1440 according to an embodiment. The left panel illustrates the actuator element 1440 in a first actuation state, for example an unactuated actuation state. The right panel illustrates the actuator element 1440 in a second actuation state, for example an actuated actuation state. A first electrode 1441 , for example a top electrode, is separated from a second electrode 1443, for example a bottom electrode, by an electrostatic gap 1442. The first electrode 1441 is connected with the second electrode

1443 via insulating regions 1444, so that the first electrode 1441 is electronically isolated from the second electrode 1443. Two mechanical connections via the insulating regions

1444 between the first electrode 1441 and the second electrode 1443 are positioned at opposite ends of the first electrode 1441. For example, the opposite ends, at which the mechanical connections to the second electrode are provided, are arranged along the y direction. When a voltage is applied between the first electrode 1441 and the second electrode 1443, the first electrode 1441 and the second electrode 1443 are attracted to each other. At least one of the electrodes is bent along a direction between the two mechanical connections between the two electrodes, so that the attraction between the two electrodes translates into a force along the y direction. Consequently, upon application of the voltage between the two electrodes, the actuator element 1440 may expand at the position of the mechanical connection between the first and the second electrodes. As a consequence, a distance between a first end 1473 and a second end 1474 of a first surface 1472 increases relative to a distance between a first end 1477 and a second end 1478 of a second surface 1476 which is arranged opposite of the first surface 1472 upon application of a voltage between the two electrodes, that is upon actuation. Thus, actuation results in a deformation triangle 1468, which may correspond to the deformation triangle 1168. Examples of the actuator element 1440 are NED bending cells in unimorph configuration with one electrostatic gap.

Panel B shows a second type of electrostatic actuator element 1450 according to an example. Compared to the electrostatic actuator element 1440, the actuator element 1450 comprises an additional third electrode 1455 which is arranged between the first electrode 1441 and the second electrode 1443. The third electrode 1455 is separated from the first electrode 1441 by a first electrostatic gap 1 52 and by insulating regions 1444. Further, the third electrode 1455 is separated from the second electrode 1443 by a second electrostatic gap 1454 and by further insulating regions 1444. The function of the electrostatic actuator element 1450 is similar to the function of the actuator element 1440. Having a third electrode may increase a force of the actuator element 1450. Examples of the actuator element 1450 are NED bending cells in unimorph configuration with two electrostatic gaps.

Panel C shows a third type of actuator element 1460 according to an example. The left panel shows a first actuation state, the middle panel shows a second actuation state, and the right panel shows a third actuation state. Compared to the actuator element 1450, the actuator element 1460 is symmetric with respect to the third electrode 1455. For example, the actuator element 1460 is configured for individually applying a voltage either between the first and the third electrode, or between the second and the third electrode. For example, applying a voltage between the first electrode 1441 and the third electrode 1452 may provide for an actuation according to the actuation state shown in the center panel, while an application between the second electrode 1443 and the third electrode 1455 may provide for an actuation according to the actuation state shown in the right panel. For example, the second actuation state and the third actuation state are actuations in opposite directions. Thus, the actuator element 1460 may provide for either a bending in a first bending direction or a bending in a second bending direction, the first bending direction being opposite to the second bending direction, in dependence on whether a voltage is applied between the first electrode and the third electrode or between the second electrode and the third electrode. Examples of the actuator element 1446 are NED bending cells in bimorph configuration with two electrostatic gaps, which may provide a better curvature control compared to unimorph configurations.

Fig. 15 illustrates different types of actuator elements 1540, 1550, 1560 according to embodiments. The actuator elements 1540, 1550, 1560 may be examples of the actuator elements 140, 343, 344, 543, 544, 1171. Panel A of Fig. 15 shows a first type of actuator element 1540. The actuator element 1540 may be an example of a electrothermal actuator element or electrothermal bending cell. The left panel illustrates a first actuation state of the actuator element 1540, for example an unactuated actuation state. The actuator element 1540 comprises a first electrode 1541 , a second electrode 1543, and a insulating layer 1542, which is arranged between the first electrode 1541 and the second electrode 1543 so as to isolate the first electrode 1541 from the second electrode 1543 thermally and electrically. The middle panel illustrates a second actuation state of the actuator element 1540, for example an actuated state, in which the first electrode is actuated. In the second actuation state, the first electrode 1541 is heated, for example, electrically, so that the first electrode 1541 expands thermally. In the second actuation state, the second electrode 1543 is cold, and may, for example, be cooled, so as to contract. Due to expansion of the first electrode 1541 and/or contraction of the second electrode 1543, the actuator element 1540 bends towards a first direction. The right panel shows a third actuation state, for an example an actuated state, in which the actuator element 1540 bends towards a second bending direction, which is different from the first bending direction. In the third actuation state, the first electrode 1541 is cold and/or the second electrode 1543 is hot, so as to provide for a contraction and/or expansion, respectively. Deformation of the actuator element 1540 upon actuation provides for a deformation triangle 1568, which may correspond to the deformation triangle 1168 as described with respect to Fig. 11.

Panel B illustrates an example of a piezoelectric actuator element or a piezoelectric bending cell according to an embodiment. The left panel shows a first actuation state, for example an unactuated state. The actuator element 1550 comprises a first electrode 1551 and a second electrode 1553. The first electrode 1551 comprises a piezoelectric active layer. The second electrode 1553 comprises a passive conductive layer. The first electrode 1551 is separated from the second electrode 1553 by an insulating layer 1552 which isolates the first electrode 1551 electrically from the second electrode 1553. The right panel of panel B illustrates a second actuation state of the piezoelectric actuator element 1550, for example, an actuated state. Upon actuation, the piezoelectric actuator element 1550 deforms. The deformation may be described by the deformation triangle 1568. Panel C of Fig. 15 illustrates a further example of a piezoelectric actuator 1560. The left panel illustrates a first actuation state, for example an actuated state. Compared to the actuator element 1550, the actuator element 1560 comprises a third electrode 1555. The second electrode 1553 is arranged between the first electrode 1551 and the third electrode 1555. The second electrode 1553 is separated from the third electrode 1555 by an insulating layer 1554 which provides an electric isolation of the second electrode 1553 from the third electrode 1555. The middle panel illustrates a second actuation state which is an actuated state in which the first electrode 1551 is actuated so as to provide for a bending of the actuator element 1560 in a first bending direction. The right panel illustrates a third actuation state of the actuator element 1560, in which the third electrode 1555 is actuated, so as to provide for a bending of the actuator element 1560 in a second bending direction, which is opposite of the first bending direction.

The actuator elements 1440, 1450, 1460, 1540, 1550, 1560 may be examples of the actuator element 1171 , and thus may provide a basis for the pre-angled serial arrangement 1146 and/or the normal angled serial arrangement 1147. A geometric change of the actuator elements upon actuation may thereby be represented by the deformation triangle 1168, 1468, 1568.

In the following, several possible applications of the actuator unit 302 as described before will be described.

For example, to create out-of-plane angular motion, e.g., a design based sagging of the linked stage (e.g. due to the load weight on it, the weight of the system itself, different out- of-plane stiffness’s of the PA and NA sides, etc.) can be introduced. The sagging can be made symmetrical or asymmetrical around the load stage based on different out-of-plane stiffness's of the contracting and expanding units on each side of the stage, number of units used, etc. to create, e.g., a pendulum motion of the load stage upon actuation. The system can also be designed to create out-of-plane motions by generating torque around load stage (with or without stage sagging) via applying different voltages to NA and PA units (at a varying offset, frequency, etc.) to create unsynchronized motion of expanding and contracting configurations.

Fig. 16 illustrates examples of MEMS actuators 1600, 1601 according to embodiments. The MEMS actuator 1600, illustrated in the upper panel of Fig. 16, comprises an actuator unit 302 the second connecting piece 112 of which is connected with a rotatably supported structure 1604. The rotatably supported structure 1604 is connected with a rigid or fixed part 1605 of the MEMS actuator 1600 via a flexible connection 1606, for example, a spring. The left panel shows a first actuation state of the MEMS actuator 1600, for example, an unactuated state. The right panel shows a second actuation state, for example an actuated state of the MEMS actuator 1600. As the rotatably supported structure 1604 is connected with the rigid part 1605 via a flexible connection 1606, an expansion of the actuator unit 302 results in a rotation of the rotatably supported structure 1604.

The lower panel of Fig. 16 illustrates a MEMS actuator 1601 according to an embodiment. In comparison with the MEMS actuator 1600, the MEMS actuator 1601 comprises two actuator units 302. The second connecting pieces 112 of the actuator units 302 are connected to opposite ends of the rotatably supported structures 1604. Thus, upon actuation, the rotatably supported structure 1604 rotates around a rotation center 1607 of the rotatably supported structure 1604.

In other words, the MEMS actuator 1600, 1601 may represent examples for MEMS actuators, which use a combination of parallel expanding actuator units 302 and/or supporting structures 1606 to generate torque and thus rotational motion.

Fig. 17 illustrates a MEMS actuator 1700 for performing a linear motion according to an embodiment. The left panel shows a first actuation state, the right panel shows a second actuation state. The MEMS actuator 1700 comprises a stage 1704 connected to the second connecting piece of an actuator unit 302. The actuator unit 302 is configured for expanding and/or contracting along the X-direction. The MEMS actuator 1700 comprises sidewalls 1702 along the X-direction, the sidewalls 1702 having sliding surfaces 1703. Support structures 1708 are connected with this stage 1704 and/or with the first and/or second connecting pieces connecting actuator cells of the actuator unit 302. The support structure 1708 is configured for sliding along the sliding surfaces 1703 when the stage 1704 is in motion due to an actuation of the actuator unit 302. Fig. 18 illustrates another example of the MEMS actuator 1700. According to the example shown in Fig. 18, instead of a serial arrangement of actuator cells as provided by the actuator unit 302, actuator cells are arranged in parallel so as to move one of the support structures 1708. In this example, the MEMS actuator 1700 comprises a serial arrangement of parallel arranged actuator cells 110. One of the support structures 1708 is arranged between each of subsequent parallel arrangements of actuator cells 110. Such an arrangement may provide high mechanical stability. For example, Fig. 18 is an example for multiple expanding configurations in honeycomb setup with loading stage and guiding structures.

Figs. 17 and 18 may represent examples, in which translation motion could be restricted to be highly linear and in-plane by use of support structures that allow motion based on sliding in one direction while restricting motion in the other directions. This may be achieved by using sliders and support structures (e.g. sliding surface, side-walls, loading stage, etc.). The use of multiple expansion configuration in parallel can be used, for example, in a honeycomb setup (with or without sliders) to increase total deliverable force, out-of-plane and/or in-plane stiffness, higher motion frequency, etc. The support frame structures (see Figure 8) can be made of passive elements and/or active elements (to provide locking at a particular position after displacement, e.g., with the help of contacting the side walls upon their actuation, locking into the ridges in side walls upon actuation, etc.). An in-plane rotation (based on schemes described earlier) can also be allowed by use of active support frame structures and/or adaptation of side walls to allow the space required for rotational motion. The support frame structures can be sandwiched with a top cover to provide complete out- of-plane locking for them (in case of flipping of the system can occur). The sliding surfaces can be covered with low friction and anti-stiction coatings (e.g. FDTS coating) to avoid high friction forces and stiction. Alternatively, these systems can also be implemented using hybrid assembly of support structures that are separately processed so that they don’t have stiction and low friction between contacting surfaces.

Alternatively, the system can be left to translate unrestricted in multiple directions to achieve certain degree of motion out-of-plane and in-plane directions, torsional movements, etc. based on the angle that can be introduced by designing, actuation scheme, loading or a combination of all.

Fig. 19 illustrates a MEMS actuator 1900 according to an embodiment in various actuation states. The MEMS actuator 1900 comprises a functional element 1901 , for example a probe micro positioner or a probe tip. The MEMS actuator 1900 comprises a serial arrangement of a plurality of actuator units 302 comprising a first actuator unit 302a and a second actuator unit 302b. The first actuator unit 302a is configured for contracting and/or expanding along a first axial direction, for example the x-direction. The second actuator unit 302b is configured for expanding and/or contracting along a second direction, for example the y- direction. The first direction is different from the second direction.

Fig. 20 illustrates an alternative implementation of the MEMS actuator 1900 according to an embodiment. In this embodiment, the functional element 1901 is a micro grip. Further, this embodiment comprises a third actuator unit 302c, which is configured for expanding and/or contracting in a third axial direction, which is different from the first and different from the second axial direction.

Fig. 19 may illustrate an example for an expanding configuration with active individual actuation control in both ±x and ±y directions for a probe micro-positioning. Fig. 20 may illustrate an example for expanding configurations with active individual actuation control for a trajectory travel for a micro-gripper. These may be examples for cases, in which translation in a particular angle or trajectory is required. For example, the units can be controlled individually or in sections positioned at an angle to form the required angle/trajectory based on, e.g., the angles and positions that can be introduced by varying the shape (L-shape, T-shape, C-shape, arc-shape, etc.) and dimensions (length and width in particular) of the joining central connectors.

As exemplarily illustrated in Figs. 19 and 20, embodiments provide for different trajectories (circular path, different shape paths, etc.) based on expanding configurations, contracting configurations or combination of both.

Fig. 21 illustrates a MEMS actuator 2100 according to an embodiment. The MEMS actuator 2100 comprises a first parallel arrangement 2101 of actuator units 302, which are arranged for expanding and/or contracting along the X-direction. The parallel arrangement 2101 is connected with a first load stage frame 2103, which is arranged to move along the X- direction upon actuation of the first parallel arrangement 2101. The first load stage frame 2103 has connected therewith a second parallel arrangement 2102 of actuator units 302. The parallel arrangement 2102 is connected with the load stage frame 2103, so as to move along the X-direction together with the load stage frame 2103 upon actuation of the first parallel arrangement 2101. The second parallel arrangement 2102 is configured for expanding and/or contracting along a second direction for example the Y-direction. A second load stage frame 2104 is connected with the second parallel arrangement 2102 so as to move along the Y-direction upon actuation of the parallel arrangement 2102. The second load stage frame 2104 is to move with the first load stage frame 2103 along the X- direction upon actuation of the first parallel arrangement 2101.

Fig. 22 illustrates an alternative example of the MEMS actuator 2100, which additionally comprises sliding surfaces 2105 so as to facilitate a smooth movement of the first load stage 2103 and the second load stage 2104. Thus, the second load stage 2104 is movable in both x and y directions with respect to a MEMS substrate. The sliding surfaces provide for a reduced contact area (design and/or fabrication based). Highly conformal anti-stiction & low friction coatings usage (e.g. FDTS via ALD) as well as hybrid assembly with coatings may be applied.

Accordingly, some embodiments comprise a stage 2104 which is mounted to be movable in a first direction (x) and in a second direction (y) of a plane of the MEMS actuator 2100. The MEMS actuator 2100 comprises at least first and second actuator units 302, each configured to change, upon actuation, a distance between the first connecting piece (2111) of a first actuator cell and the second connecting piece (2112) of the last actuator cell along an axial direction of the respective actuator unit. The first and second actuator units are arranged so that an actuation of the first actuator unit results in a position change of the stage 2104 along the first direction and an actuation of the second actuator unit results in a position change of the stage 2104 along the second direction.

For example, expanding configurations can be used to generate highly rectilinear X-Y 2D- motion as well based on different arrangements (with or without support structures) as shown in Figures 21 , 22. The electrical connections to the inner expanding configurations can be provided, for example, via the outer stage expanding configuration (used in Figure 21 , 22 configurations), via dedicated soft springs, wireless power transfer, etc. The same systems, based on, e.g., selective actuation of units sections, can be used to generate inplane rotation (or out-of-plane rotation, e.g. load and/or units position based sagging) as well along with the highly rectilinear X-Y motion.

Fig. 23a illustrates another example of the MEMS actuator 2100 according to an embodiment. According to this embodiment, the MEMS actuator 2100 comprises a third parallel arrangement 2107 of actuator units 2302a. Further, the first parallel arrangement 2101 is a parallel arrangement of actuator units 2302b. Actuator units 2302a are configured for expanding upon actuation, whereas actuator units 2302b are configured for contracting upon actuation. The first parallel arrangement 2101 and the third parallel arrangement 2107 are configured for contracting and/or expanding along the X-direction. Further, the MEMS actuator 2100 comprises a fourth parallel arrangement of actuator elements 2108, which is configured for expanding and/or contracting along the Y-direction. The fourth parallel arrangement 2108 comprises one or more actuator units 2302a, while the second parallel arrangement 2102 comprises one or more actuator units 2302b. The parallel arrangement

2102 and the parallel arrangement 2108 are configured for moving the second load stage 2104 along the Y-direction relative to the first load stage 2103. The parallel arrangements 2101 , 2107 are configured for moving the second load stage 2104 along the X-direction with respect to a rigid part of the MEMS actuator. Optionally, the MEMS actuator 2100 comprises capacitive displacement sensing mechanisms 2107 for measuring a position of the first load stage 2103 and the second load stage 2104. Electrical connection springs 2109 provide an electrical connection to the second load stage 2104, for example for actuating the arrangement 2102, 2108. The MEMS actuator 2100 may optionally comprise stopper structures 2165, which may be configured to prevent a movement of the first load stage 2103 beyond a predetermined position. As shown in Fig. 23a, the parallel arrangements of actuator units 2101 , 2102, 2107, 2108 may each comprise one single, or alternatively, multiple actuator units, as shown in Fig. 22.

In other words, examples comprise capacitive sensing based on dedicate structures (linked to stage) with mechanical stoppers to ensure no contact.

Fig. 23b shows a more detailed illustration of the example of the MEMS actuator 2100 shown in Fig. 23a. For example, the MEMS actuator 2100 may comprise guides 2367 (or sidewalls) to guide a movement of the first load stage and/or the second load stage. For example, the beams of the actuator units 2302a, 2302b may comprise sections, each comprising a parallel arrangement of actuator units 2301.

Fig. 24 illustrates a parallel arrangement 2401 of actuator elements 140 according to an embodiment, as it may be implemented in the actuator units 2302a, 2302b as examples of the section 2301.

In other words, the synchronized expanding and contracting configurations can be used to generate 2D-motion as well based on different arrangements (with or without support structures), e.g., as shown in Figs. 23a, 23b. The electrical connections to the inner expanding configurations can be provided, for example, via the outer stage expanding configuration, via dedicated soft springs (which may be used in Figure 23a configurations), wireless power transfer, etc. The same systems, based on, e.g., selective actuation of units sections, can be used to generate in-plane rotation (or out-of-plane rotation, e.g. load and/or units position based sagging) as well along with the highly rectilinear X-Y motion. In an exemplary case, capacitive position sensing mechanism based on dedicated structures such as comb-fingers (as shown in Figure 16) which are directly linked to the load stage (inner and/or outer) can also be implemented for a reliable closed-loop control. Such dedicated sensing structures can easily be designed to have linear capacitance variation with the position change. Also, based on sensing structures design and their location in the system a differential capacitance sensing mechanism can also be established which can be used to determine not just linear translation more reliably but also the rotation angle, tilt, etc. This significantly simplifies the control system circuitry while also greatly enhancing the sensing system reliability.

The support structures such as sliding surfaces underneath and/or above (with help of a top cover to lock the entire load stage in between two surfaces), mechanical stoppers (to block the unwanted translation in one direction after a certain distance when translation in other direction is taking place), position-locking mechanisms, etc. can optionally always be used or removed as per the requirement (e.g. high load structures). A typical example when such dedicated structures might be required will be when a large system with area equal or more than the 2D micro-positioning system itself, e.g., a CCD image sensor chip, is to be displaced using the micro-positioning system. The sensor chip can be, for example, placed and glued on top of the load stage at a certain height using fine-placer while the entire micro-positioning system remains hidden underneath it, thus saving considerable in-plane chip area. In such cases, where large loads need to be carried and displaced by the micropositioning system, the support structures can restrict the unwanted in-plane and out-ofplane movements, both during positioning and in maintaining the position. The sliding surfaces can be covered with low friction and anti-stiction coatings (e.g. FDTS coating) to avoid high friction forces and stiction. Alternatively, these systems can also be implemented using hybrid assembly of support structures that are separately processed so that they don't have stiction and low friction between contacting surfaces.

Thus, as described with respect to the previous figures, an angled/rotation motion (in-plane and/or out-of-plane) of a stage can be created by using concepts explained herein for expanding configurations (some cases shown in Figure 6-9 and 16 to 20) that are applicable to contracting configurations as well in a complementary manner. For example, the described MEMS actuators may be realized using contracting actuator cells and/or expanding actuator cells. For example, if left side of NA units are expanded (similar to as shown in Figure 4), then to create same angled motion on both the side of the load stage, the left side of the linked PA units have to contract in the same extent and manner. Also, NA and PA units positions can be misaligned (e.g. rather at the center they can be attached at the opposite corners of the load stage) to create a torque and rotation motion via difference in contraction and expansion motions levels and corresponding forces levels exerted on the stage (can be achieved, e.g., applying different actuation voltages to NA an PA units/sections, different number of NA & PA units, different unit sections length, different number of stacked beams in each unit, etc.).

Fig. 25 illustrates a MEMS actuator 2500 according to an embodiment. The MEMS actuator 2500 comprises a first actuator cell 2510a and a second actuator cell 2510b. The first actuator cell 2510a comprises a first connecting piece 2511 a and a second connecting piece 2512a. A mechanical connection between the first connecting piece 2511a and the second connecting piece 2512a comprises a connector unit 2521 a. The connector units 2521 a comprises a beam 2531 a, which comprises a serial arrangement 2541a of a plurality of actuator elements 2540a. The actuator elements 2540a of the first actuator cell 2510a are configured to decrease a bending of the beam 2531 a of the first actuator cell 2510a upon actuation, for example, so as to decrease a distance between the first and the second connecting pieces 2511a, 2512a. The second actuator cell 2510b comprises a first connecting piece 2511 b and a second connecting piece 2512b. A mechanical connection between the first connecting piece 2511b and the second connecting piece 2512b comprises a connector unit 2521 b, which comprises a beam 2531 b. The beam 2531 b comprises a serial arrangement 2541 b of a plurality of actuator elements 2540b. The actuator elements 2540b of the second actuator cell 2510b are configured to increase a bending of the beam 2531 b of the second actuator cell 2510b upon actuation, for example, so as to increase a distance between the first connecting piece 2511 b and the second connecting piece 2512b. For example, the first actuator cell 2510a is configured for contracting upon actuation. For example, the second actuator cell 2510b is configured for expanding upon actuation.

The actuator cell 2510a, 2510b may optionally correspond any of the configurations of the actuator cell 110 described before, and the MEMS actuator 2500 may optionally correspond to any of the configurations of the MEMS actuator 100. All features, concepts, and functionalities explained with respect to the Figs. 1-24 may accordingly, optionally, be combined with or implemented in the MEMS actuator 2500 and/or the actuator cells 2510a, 2510b.

Fig. 26 illustrates a method 2600 according to an embodiment. The method 2600 comprises a step 2601 of providing a control signal to the actuator elements of any of the previously described MEMS actuators.

Although some aspects have been described as features in the context of an apparatus it is clear that such a description may also be regarded as a description of corresponding features of a method. Although some aspects have been described as features in the context of a method, it is clear that such a description may also be regarded as a description of corresponding features concerning the functionality of an apparatus.

In the foregoing Detailed Description, it can be seen that various features are grouped together in examples for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed examples require more features than are expressly recited in each claim. Rather, as the following claims reflect, subject matter may lie in less than all features of a single disclosed example. Thus the following claims are hereby incorporated into the Detailed Description, where each claim may stand on its own as a separate example. While each claim may stand on its own as a separate example, it is to be noted that, although a dependent claim may refer in the claims to a specific combination with one or more other claims, other examples may also include a combination of the dependent claim with the subject matter of each other dependent claim or a combination of each feature with other dependent or independent claims. Such combinations are proposed herein unless it is stated that a specific combination is not intended. Furthermore, it is intended to include also features of a claim to any other independent claim even if this claim is not directly made dependent to the independent claim.

The above described embodiments are merely illustrative for the principles of the present disclosure. It is understood that modifications and variations of the arrangements and the details described herein will be apparent to others skilled in the art. It is the intent, therefore, to be limited only by the scope of the pending patent claims and not by the specific details presented by way of description and explanation of the embodiments herein. References

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