MEMS with a comb drive and method for manufacturing it

Abstract

A MEMS comprises a comb drive with a first finger structure comprising a first plurality of electrode fingers and a second finger structure comprising a second plurality of electrode fingers, which form an entangled arrangement parallel to a substrate plane of the MEMS. The comb drive is configured to provide translational relative motion between the first and second finger structures based on an electrostatic force, thus changing the distance between them parallel to the substrate plane. The first and second plurality of electrode fingers are curved perpendicular to the substrate plane.

Description

The present invention relates to a comb-drive MEMS having curved electrode fingers. The present invention further relates to a method of manufacturing such a MEMS, and more particularly to a comb drive having optimized non-linear behavior.Microelectromechanical systems, MEMS, may be implemented for, among other things, actuator and / or sensor operation. For an actuator operation, force members can be provided which provide a force for generating a signal and / or a movement. Thus, a movement within a MEMS can be provided, for example, by a comb drive, in which electrode fingers of finger structures movable relative to one another engage one another and an electrostatic force is generated on the basis of electrostatic forces between the finger structures in order to provide the relative movement.The use of such a comb drive is described, for example, in WO 2021 / 223886 A1, see, for example, FIGS. 12a-d. The document describes a MEMS which is efficient in terms of installation space.WO 02 / 19509 A2 describes a comb drive arrangement having comb drive fingers with non-uniform cross sections which increases the ratio of drive force per applied voltage. The increase in driving force due to the geometry of the comb drive fingers is achieved without the need to increase the tension. In plan view, comb drive fingers can be designed as wedge-shaped structures; in addition, in plan view, the comb drive fingers have frustoconical structures. It is disadvantageous that no change in the counterforce due to the movement due to the finger forces is taken into account, in other words, the force profile is executed continuously, but is not adapted to a characteristic curve of the counterforce.US 2016 / 268927 A1 describes a comb drive device with non-parallel comb fingers, which is intended to be suitable for linearizing the capacitance between corresponding comb finger columns during an arcuate movement. It is disadvantageous that no change in the counterforce due to the movement due to the finger forces is taken into account and is not adapted to the characteristic curve of the counterforce.DE 10 2017 206 183 A1 describes rectangular comb drives as MEMS actuators. A disadvantage of this structure is that the profile of the finger shape does not influence the force characteristic.US 2013 / 009716 A1 describes a MEMS resonator with comb electrodes. Here, too, a profile of the finger shape is not matched to the force characteristic.The drawback of the known solutions to date is that the stiffness of the deformable elements is non-linear with respect to the transmission behavior. In an exemplary audio application of the MEMS, higher harmonics are generated under harmonic excitation by the non-linearities, which lead to non-advantageous distortions of the audio signal.Accordingly, MEMS with comb drives which show a linearized behavior of the force-deflection curve would be desirable.It is therefore an object of the present invention to provide a MEMS and a method for producing the same, in which a comb drive has a linearized ratio of a force deflection curve.This object is achieved by the subject matter of the independent claims.A core idea of the present invention is to provide a comb drive for a translatory movement, in which electrode fingers of both interdigitated finger structures are curved in plan view, i.e. parallel to the substrate plane of the MEMS. The respective curvatures make it possible to adapt the force-deflection behavior. Unlike in WO 02 / 19509 A2 and US 2016 / 268927 A1, both sides of the comb drive are formed curved and a translatory movement, i.e. a movement directed straight toward one another, is simultaneously implemented.According to one exemplary embodiment, a MEMS is provided, which has a comb drive having a first finger structure comprising a first plurality of electrode fingers and having a second finger structure comprising a second plurality of electrodes, which form an interdigitated arrangement with one another parallel to a substrate plane of the MEMS. The comb drive is configured to provide a translatory relative movement between the first finger structure and the second finger structure based on an electrostatic force for changing a distance between the first finger structure and the second finger structure parallel to the substrate plane. The first plurality of electrode fingers and the second plurality of electrode fingers are curved perpendicular to the substrate plane. This advantageously allows the adaptation of a force deflection curve.According to one exemplary embodiment, an electrode finger of the first finger structure and / or of the second finger structure is formed starting from a first electrode finger end toward a second opposite electrode finger end in such a way that an undercut is arranged in a plane perpendicular to the substrate plane. The undercut permits, in conjunction with the translatory movement, a particularly exact and advantageous adaptation of the force-deflection curve.According to one exemplary embodiment, mutually facing sides of mutually engaging electrode fingers are formed congruently with one another at least within a working region. This allows a further optimization of the force-deflection curve. A congruent configuration of mutually facing side surfaces can also be effected independently of the undercut.According to an embodiment, a side surface of an electrode finger of the first finger structure or of the second finger structure has a concave section starting from a first electrode finger end towards a second opposite electrode finger end. The concave section can allow a good adjustment possibility with respect to its radius of the deflection behavior of the comb drive.According to an embodiment, the concave portion is shaped such that a curvature is provided with a radius that is different from a curvature of the electrode finger at a free end of the electrode finger.According to an embodiment, the concave portion is arranged between a first side wall portion of the electrode finger and a second side wall portion of the electrode finger. The first side wall section is inclined at a first angle with respect to a main extension direction of the electrode finger starting from a clamped end of the electrode finger. The second side wall section of the electrode finger is inclined towards a free end of the electrode finger with respect to the main extension direction of the electrode finger at a second angle. The first angle has a value of at most 30 degrees and the second angle has a value of at most 45 degrees. These values result in a particularly high degree of linearity in the deflection behavior.According to one exemplary embodiment, at least one of the electrode fingers has a combination of an undercut on an non-clamped side of the electrode finger and a widening of the electrode finger on a clamped side of the electrode finger. This enables an adaptation by means of the widening of the electrode finger at the clamped end to an undercut of an opposite electrode finger.According to one exemplary embodiment, the at least one electrode finger has a greater electrode finger width on the clamped side than on the non-clamped side.According to one exemplary embodiment, a wave-shaped cutout is arranged between a first side surface of a first electrode finger of the first finger structure and a second side surface of a second electrode finger of the second finger structure facing the first side surface. A waveform allows compensation for mechanical non-linearities.According to one exemplary embodiment, a curvature of curved electrode fingers is adapted to a non-linear stiffness of the comb drive, wherein a curvature-based force variation in the comb drive and along a movement direction of the comb drive compensates for a deflection-based stiffness variation of the comb drive within a tolerance range. This allows the force-deflection curve to be optimized.According to one exemplary embodiment, the MEMS is configured based on the curvature of curved electrode fingers such that a linearized ratio between deflection of the comb drive and generated electrostatic force of the comb drive is obtained, which enables precise actuation of the MEMS.According to an embodiment, the first finger structure and the second finger structure form a first pair of structures. The MEMS has at least one further structure pair which is connected in series to the first structure pair along a force direction of the comb drive. This enables an increase in the generated force in the comb drive.According to one exemplary embodiment, the MEMS is configured such that, starting from a curved region of the electrode finger, a substantially rectangular region is arranged toward a free end or a clamped end.According to one exemplary embodiment, the MEMS is formed as a loudspeaker. Such a loudspeaker can reproduce high quality audio signals, such as by suppressing harmonic noise due to the linearity obtained.According to an embodiment, a method for producing a MEMS comprises arranging a comb drive having a first finger structure comprising a first plurality of electrode fingers and having a second finger structure comprising a second plurality of electrode fingers, such that the first plurality of electrode fingers and the second plurality of electrode fingers form an interdigitated arrangement with the first plurality parallel to a substrate plane of the MEMS. The method is carried out such that the first plurality of electrode fingers and the second plurality of electrode fingers are curved perpendicularly to the substrate plane; and such that an electrode finger of the first finger structure or of the second finger structure, starting from a first electrode finger end toward a second opposite electrode finger end, has an undercut in a plane perpendicular to the substrate plane.Further advantageous embodiments are the subject matter of further patent claims.Particularly preferred embodiments of the present invention will be explained below with reference to the accompanying drawings. The following are shown: FIG. 1 a shows a schematic plan view of a comb drive according to an exemplary embodiment; FIG. 1 bshows an enlarged representation of a part of the comb drive from FIG. 1 a; FIG. 2 shows a schematic exemplary diagram of a drive structure according to an exemplary embodiment, having two comb drives which are connected in series one behind the other in order to enable an active deflection along positive and negative y-directions; FIG. 3 shows a schematic plan view of a part of an electrode finger according to an exemplary embodiment, which can be used, for example, as electrode finger a according to FIGS. 1 aand 1 b; FIG. 4 shows a schematic plan view of a comb drive according to an exemplary embodiment, in which the serial series connection of at least two comb drives along the force direction is shown in schematic fashion; FIG. 5 shows a schematic block diagram of a comb drive according to an exemplary embodiment in a plan view, in which an asymmetrical arrangement is illustrated compared to the symmetrical arrangement in FIG. 4 ; FIG. 6 is a schematic illustration of an electrode finger according to an exemplary embodiment in which the approximated shape of the electrodes is embodied as steps; FIG. 7 ashows a schematic top view of an electrode finger according to an embodiment with an extension at a clamped end; FIG. 7 bshows a schematic plan view of an electrode finger according to an exemplary embodiment with an extension at a fine end; and FIG. 8 shows a schematic flow diagram of a method according to an exemplary embodiment.Before exemplary embodiments of the present invention are explained in more detail below with reference to the drawings, it is pointed out that identical, functionally identical or identically acting elements, objects and / or structures are provided with the same reference numerals in the different figures, with the result that the description of these elements shown in different exemplary embodiments is interchangeable or can be applied to one another.Exemplary embodiments described below are described in connection with a multiplicity of details. However, embodiments may also be implemented without these detailed features. Further, embodiments will be described for convenience using block diagrams to replace a detailed diagram. Furthermore, details and / or features of individual exemplary embodiments can be easily combined with one another, provided that it is not explicitly described to the contrary.FIG. 1 ashows a schematic top view of a comb drive 10 according to an embodiment, wherein some of the details of the comb drive 10 are emphasized in FIG. 1 b. The comb drive 10 has a first finger structure 12 with a plurality of electrode fingers 14 1-146 wherein a number of electrode fingers 14 of the finger structure 12 can have any value of at least 2, for example 3, 4, 5, 6, 10 or more, for example at least 15, at least 20 or more.The comb drive 10 further comprises a second finger structure 16 with a plurality of electrode fingers 18 1-185 in a number that is the same as or different from the finger structure 12. The finger structures 12 and 16 can be arranged completely or partially parallel to a substrate plane of the comb drive or of a MEMS which has the comb drive 10. This means that, starting from one of the two finger structures 12 or 16, the other finger structure 16 or 12 can be arranged parallel to a y-direction parallel to the substrate plane. The fingers 14 1-146 on the one hand and 18 1-185 on the other hand can form an interdigitated arrangement, that is to say an electrode finger of the other electrode structure 16 or 12 can be arranged in each case between two electrode fingers of a finger structure 12 or 16. A potential difference between electrode fingers of the first finger structure 12 and electrode fingers of the second finger structure 16 may cause an electrostatic force that results in a translatory movement along the y-direction between the finger structures 12 and 16 relative to each other.The electrostatic force may be used to change a distance between the finger structures 12 and 16 parallel to the substrate plane along the y-direction.FIG. 1 bshows an enlarged illustration of a part of the comb drive 10 from FIG. 1 a. Therein, it is shown that the first plurality of electrode fingers 14 and the second plurality of electrode fingers 18 are curved perpendicular to the substrate plane x / y. This can be understood to mean that main sides 14A and 18A of the electrode fingers 14 1 and 14 2, which can be arranged perpendicular to the substrate plane x / y, are shaped in a curved manner, in particular when running along the y direction. A cutout 33 between the side surfaces 14A and 18A can be formed in a wave-shaped manner, wherein depending on the geometry of the electrode fingers, at least in the plan view shown, in some embodiments a waveform can also be deviated, in particular a continuous waveform, see for example FIG. 6.The y-direction can be understood as the main extension direction of the electrode fingers starting from attachments 22 of the first finger structure 12 or 24 of the second electrode structure 16. The curvature can be represented in the projection of the electrode fingers 14 1 and 18 1 in a plane parallel to the substrate plane. Further additional curvatures, for example with respect to a y / z plane, which is not recognizable in the view shown in FIG. 1 b, are not excluded, however.The curvatures of the main sides 14A and 14B at least in main side portions of the electrode fingers 14 1 and 18 1 will be explained in detail below. The respective parameterizations can be implemented independently of one another, but also in combination with one another. The described adaptations of the curvatures are in this case related in particular to a working range of the electrode fingers 14 1 and 18 1 or of the finger structures 12 and 16. In connection with the embodiments described herein, a working range is understood to be a deflection range of the comb drive 10, within which the surfaces of the electrode fingers are displaced relative to one another and the main sides are arranged opposite one another. Thus, for example, in order to avoid a mechanical contact of an electrode finger 14 with an opposite fastening region 24 or an electrode finger 18 with an opposite fastening region 22, a remaining distance can be provided, which leads to no overlap with an adjacent electrode finger occurring in parts of the electrode finger adjacent to the fastenings 22 and / or 24. At these locations optimizations may be omitted without causing a negative impact on the adjustment of the deflection behavior described herein.Some of the exemplary embodiments described herein relate to MEMS with a comb drive, in which one or more electrode fingers of the finger structure 12 and / or 16 1 or form an undercut 26 starting from a first electrode finger end, for example adjacent to the fastening region 22 or 24, toward an opposite second electrode finger end, for example the movable or deflectable end. 26 have 2 in a plane perpendicular to the substrate plane. An undercut 26 1 or. 26 2 can be understood to mean that removal of the structure from a one-piece molding tool, for example when an injection molding method is considered as a thought experiment, parallel to the y direction is prevented. Thus, for example, due to the thickening obtained by the undercut or undercut 26 1 toward the movable or free end 28 1 removal along the positive y-direction from the imaginary molding tool can be prevented. Likewise, removal of the electrode finger 18 1 along the negative y-direction can be prevented on account of the thickening toward the free end 28 2.A shape or geometry of the electrode finger and / or the undercut 26 1 and / or 26 2 can have a continuous shape, but can also have a substantially rectangular shape or have a combination of a plurality of substantially rectangular shapes, as is illustrated by steps 32 1-327 by way of example. The step shape allows good compatibility with etching processes, while it is possible, but not necessary, to provide rectangular angles 1-327 between the steps 32. As discussed with reference to FIG. 6, typical sizes of an obtained step shape may be obtained in the range of 300 nm or more, such as up to about 5 μm. Alternatively, a substantially continuous form may also be implemented.Independently, but in particular also in combination with the undercuts 26 1 and 26 2 the mutually facing sides 14A and 18A of the interdigitated electrode fingers 14 1 and 18 1 can be formed congruently. This means that the main side 14A can, at least when viewing the working region, be congruent with the side 18A during a rotation by 180 degrees about the z-axis, optionally with additional translatory displacement.In other words, 1 bshows a comb drive which is optimized for the elimination / reduction of the nonlinear transmission components of a microbeam and / or a membrane.FIG. 2 shows a schematic exemplary diagram of a drive structure with two comb drives 10 1 and 10 2, which are connected in series one behind the other in order to enable an active deflection along positive and negative y-directions. Thus, three states 34 1, 342 and 34 3 are shown by way of example, wherein in state 34 1 a comb drive structure 10 2 is activated and a spacing of the electrode fingers is small to minimal there, while the electrode fingers in the comb drive structure 10 1 have an increased spacing. A state 34 2 has a reference state, such as without actuation, which may correspond to the zero point on a y-axis. A state 34 3 corresponds to a state inverted with respect to state 34 1 in which comb drive structure 10 1 is activated, whereby a deflection y2of the comb drive structure is obtained, which deflection can be opposed to a deflection y1of state 34 1.The diagram shows an exemplary profile of a Coulomb force of an exemplary non-optimized structure. Non-optimized here can be understood to mean the interaction of the force profile of the drive and the counterforce / restoring force of the mechanism. It can also be understood that this is a nearby geometric deflection. Following the prior art, such a close design is a straight course of the finger electrode flanks, in particular without an undercut.In contrast, a curve 38 shows a Coulomb force of the comb drives optimized by means of the curvatures and electrode finger geometries described herein, which force can be adapted to a non-linear stiffness 42 of the mechanical system on account of the adaptation of the electrode finger curvature. This means that the curvature can be used to adapt the electrode fingers in such a way that the Coulomb force 38 corresponds to the non-linear stiffness, as a result of which the force deflection curve can be linearized overall.In the superposition of curves 38 and 42, an embodiment is illustrated in which a curvature of curved electrode fingers is adapted to a non-linear stiffness of the chamber drive and a curvature-based force variation in the comb drive and along a movement direction of the comb drive compensates a deflection-based stiffness variation of the comb drive within a tolerance range of preferably less than 20%, less than 10% or less than 5%. According to such an embodiment, curved electrode fingers may have a linearized ratio between deflection of the comb drive and generated electrostatic force of the comb drive. Linearization is shown in that curve 42 and curve 38 are congruent. This results in linearity for the system behavior, which can also be balanced in such a way that for the same change in path (y) a same response is obtained in force (F), both during drive or deflection and during return.In other words, FIG. 2 shows a deformable element with a geometry deviating from a rectangle and a force-displacement profile matching the nonlinearity of a microbeam.FIG. 3 shows a schematic plan view of a part of an electrode finger 44 according to an exemplary embodiment, which can be used, for example, as electrode finger 14 and / or electrode finger 18. The design parameters described herein can be implemented independently of one another, but also in combination. FIG. 3 shows only a portion of the electrode finger 44 divided along a cut axis 46. Along the x-direction, the electrode finger 44 can be constructed mirror-symmetrically or can deviate from a mirror symmetry, which can depend on the electrode finger arranged adjacent in each case and associated with the opposite finger structure.A side surface 44A of the electrode finger 44 may include a concave portion 52 from a fixed end 48 to an unfixed or free end 28. The concave portion 52 may include a curvature having a radius R 2 different than a curvature R 1 of the electrode finger 44 at the free end 28. Preferably, the radius R 2 is larger than the radius R 1.The concave portion 52 may be disposed between sidewall portions 54 1 and 54 2 respectively. The side wall section 54 1 can be arranged in front of the side wall section 54 2 starting from the clamped end 48 toward the free end 28. The first side wall section 54 1 can be inclined at an angle φ with respect to the main extension direction y of the electrode finger 44. The second side wall portion 54 2 of the electrode finger may be inclined towards the free end 28 of the electrode finger with an angle θ with respect to the main extension direction 28 of the electrode finger. The angle φ preferably has a value of at most 30 degrees and the angle θ has a value of at most 45 degrees.In other words, the angles θ and φ can be selected such that the profiles of the Coulomb force and of the restoring force have similar values, are preferably as exactly as possible with respect to one another or approximately coincide. The angle at the undercut can be designed in such a way that it is in a range of 0 degrees<θ≤30 degrees, preferably 0.5 degrees≤θ≤10 degrees, and the angle at the fastened side with the substrate is in a range of 0 degrees<φ≤45 degrees, preferably 1 degree≤φ≤15 degrees.The contour shown in FIG. 3 can be constructed geometrically / parametrically or else approximately approximated by splines or the like, for example within the scope of a design process, in order subsequently to enable implementation by etching out and / or growth. FIG. 3 likewise shows that both the arrangement of an undercut discussed in FIG. 1 band also a widening of the electrode finger is implemented at the clamped end.According to exemplary embodiments, the electrode finger 44 can have a greater electrode finger width on the clamped side 48 connected to the substrate, i.e. a dimension along the x-direction than on the non-clamped free side 28.In other words, FIG. 3 shows a deformable element with an undercut on the freely movable side and a thickening on the side which is connected to the substrate, wherein an angle θ>0 and φ>0 is provided. An embodiment according to such an embodiment can also be implemented in such a way that the foot of the finger runs at least substantially straight and the thickening at the fingertip is greater than the thickness / width of the finger at the foot, i.e. the clamping.FIG. 4 shows a schematic plan view of a comb drive 40 according to an exemplary embodiment, in which the series connection of at least two comb drives 10 1 and 10 2 which is serial along the force direction y and has already been discussed in FIG. 2 is shown in schematic fashion. The representation of the electrode fingers 14 and 18 is here exemplarily shown as rectangular, wherein the electrode fingers are actually formed in accordance with the comb drive 10, as is represented by the cutout 56 embodied in accordance with FIG. 1 b.The electrode finger structures 12 1 and 12 2 of the comb drives 10 1 and 10 2 can be arranged, for example, comparatively immovably on a substrate 58. In contrast, the finger structures 16 1 and 16 can be arranged movably in 2 and, in a preferred embodiment, form a common movable element 62 or be a part thereof. The finger structures 12 1 and 16 1 can form a first structure pair, wherein at least one further structure pair comprising the finger structures 12 2 and 16 2 can be arranged, which is connected in series to the first structure pair along the force direction y of the comb drive 40. By controlling the comb drive 40 and the symmetrical arrangement of the structure pairs along the force direction, a particularly advantageous movement can be obtained. Optionally, further comb drives 10 and / or 40 can be connected in series or in parallel. The mechanical components can provide both linear influences and non-linear influences. These influences relate to mechanical components. For example, linear elements may provide a constant, non-variable increase in a ratio of force F and deflection y, dF / dy, and vice versa, while non-linear elements may provide a variable increase.In other words, FIG. 4 shows an optimized deformable element embedded in a symmetric push-pull arrangement.FIG. 5 shows a schematic block diagram of a comb drive 50 according to an exemplary embodiment in a plan view, in which, compared to the symmetrical arrangement in FIG. 4, an asymmetrical arrangement of the finger structure 16 arranged movably with respect to the finger structure 12 is illustrated. Here too, the supposedly rectangular shape of the electrode fingers 14 and 18 is actually curved, as the cutout 56 shows.In other words, FIG. 5 shows an optimized deformable element embedded in an asymmetric arrangement.FIG. 6 shows a schematic representation of an electrode finger 64 according to an exemplary embodiment, in which the approximated shape of the fingers or electrodes is embodied as steps 32. Although the step members 32 are only shown as forming a sidewall 64A, the electrode finger 64 is not necessarily hollow or cavity shaped, but is a solid body in accordance with preferred embodiments. At least in the region of the undercut, but possibly also in the further course or other regions of the electrode finger 64, the electrode finger 64 can have one or more rectangular shapes. A plurality of rectangular shapes may form a step shape, wherein a step height of the step shape is constant or variable within the step shape and may have a value of at least 100 nm up to a plurality of μm, for example. The steps do not necessarily have to be arranged discontinuously or at a right angle to one another, but rather can have a curvature between adjacent steps, for example due to etching processes, which curvature can have a radius of at least 200 nm or 300 nm up to approximately 500 μm, for example.That is, the electrode finger shape of the electrode finger 44 may be approximated by one or more rectangular shapes.In other words, FIG. 6 shows an approximated shape with steps.FIG. 7 ashows a schematic top view of an electrode finger 68 according to an embodiment, which can be used as an electrode finger of the first finger structure 12 and / or the second finger structure 16, wherein only one half of the electrode finger is shown in accordance with FIG. 3 and FIG. 6. The electrode finger 68 can have the electrode finger 44 from FIG. 3 or a shape modified therefrom and can be arranged on an extension 72 formed as a rectangular or square, from which the electrode finger 44 emerges along the main extension direction y. The extension 72 may provide an intermediate portion relative to the electrode finger 14 and / or 18 relative to the substrate or mounts 22 and 24, respectively, such as outside of a working range of the electrode fingers. This means that between a fastening 74 of the finger structure and curved and / or undercuts or undercuts approximated by at least one step shape, a section of the electrode finger 68 can be arranged which has a rectangular or square cross section in the x / z plane and can possibly have a cross section that is invariable along the y direction.FIG. 7 bshows a schematic plan view of an electrode finger 76, in which a section 76 starting from the undercut 26 can have a rectangular shape, as is described for the extension 72. This can, for example, avoid a curvature at the free end 28, which can be advantageous, for example, in the case of a mechanical contact with another element. In this embodiment, the extension 72 can also be arranged within the working range of the comb drive.In other words, the geometry of the electrode finger 76' can merge into a rectangular shape starting from the undercut 26. FIGS. 7 aand 7 b show a finger for this purpose, which in each case merges at one of the ends into a rectangular shape. These embodiments can be combined with one another without problems, so that an extension can be arranged at both ends of the finger.FIG. 8 shows a schematic flow diagram of a method 800 according to an embodiment. This has a step 810, in which a comb drive having a first finger structure comprising a first plurality of electrode fingers and having a second finger structure comprising a second plurality of electrode fingers is arranged. This is carried out in such a way that the first plurality of electrode fingers and the second plurality of electrode fingers are curved perpendicularly to the substrate plane and that an electrode finger of the first finger structure or of the second finger structure, starting from a first electrode finger end toward a second opposite electrode finger end, has an undercut in a plane perpendicular to the substrate plane.Exemplary embodiments described herein relate to MEMS components, which can be embodied as layer stacks consisting at least of a substrate layer in which the electrodes and the passive elements are arranged. Further layers relate, for example, to a base, which can also be referred to as a handling wafer, and to a cover, which can also be referred to as a cover wafer. Both cover wafers and handling wafers can be connected to the substrate plane via material-bonding methods, preferably bonding, as a result of which acoustically sealed interspaces can be produced in components. In this intermediate space, which can correspond to the device plane, deformable elements deform, in other words an in-plane deformation can take place, for example triggered by comb drives described herein. This is particularly advantageous for embodiments of the present invention which relate to MEMS which are designed as loudspeakers.The layers may comprise, for example, electrically conductive materials, for example doped semiconductor materials and / or metal materials. The layer-by-layer arrangement of electrically conductive layers enables a simple configuration, since electrodes, for example for deflectable elements and passive elements, can be formed by selective detachment from the layer. If electrically non-conductive materials are to be arranged, this can be done by applying these materials layer by layer by a deposition method.In the MEMS-based loudspeakers subject herein, a classic diaphragm otherwise used is replaced by microbars, as described for example in DE 2017 206 766 A1, for example using passive beams which are deflected with electrostatic comb drives. Both the arrangement with the membrane and with the microbars can require a comparatively large displacement during operation. These large deflections lead to nonlinear effects having a significant influence on the transmission behavior; in particular, the stiffening of the stress plays a major role in this case. As a result of the nonlinearity, higher harmonics are generated under harmonic excitation, which can lead to distortions of the audio signal of the loudspeaker, which is undesirable. With embodiments described herein, the transmission behavior of the comb drive in the case of large displacements is modified to the effect that the non-linearities can preferably be completely eliminated or significantly reduced.The reduction of the nonlinearity can be performed in such a way that the nonlinear stiffness, i.e., the restoring force against the displacement, is reproduced as a function of the Coulomb force, i.e., the electrostatic force. If the curves coincide at least approximately, preferably exactly, the nonlinearity is reduced or even cancelled out and thus the distortions within the electromechanical system are at least partially eliminated. If the curves correspond approximately, a slight residual distortion can remain, which however lies far below the level of a system not optimized thereto and thus nevertheless has advantages.The optimization of such an electromechanical system can be explained with reference to a comb finger. Usually, straight fingers (elements) are used which have a virtually linear transmission behavior but are not capable of cancelling the nonlinearity resulting from the diaphragm / beam. The non-linearity can be cancelled out according to the invention by changing the geometry of the comb finger / deformable element such that, in the event of a deflection, the Coulomb force follows the non-linear restoring force, see FIG. 2, This can be effected, for example, by the combination of an undercut on the non-clamped side of the deformable element / electrode finger with a widening of the deformable element on the fastened side with the substrate. The broadening, i.e. an increase in the dimension b along x, refers to a width of the electrode at the tip of the finger, for instance at the widest point marked by y 1. A factor of broadening is preferably a value of less than factor 2.The deformable element or the comb drive thus has a wave-shaped recess. The dimensions and in particular the angles are selected as discussed in connection with FIG. 3. Previously known solutions describe rectangular or curved microbars. These geometries can lead to distortions of the audio signal due to non-linearities. For eliminating or reducing the non-linear transmission components, the geometry of the microbeam is therefore modified according to the invention so that its rigidity is dependent on the Coulomb force. The microbars have a curvature and, for example, an undercut on the non-clamped side and possibly a widening on the clamped side. This produces a microbeam which can provide a wave-shaped cutout with an adjacent microbeam.Aspects of embodiments described herein relate to MEMS devices and methods directed thereto. Some embodiments relate to a MEMS with a deformable element or electrode finger, characterized in that the deformable element has at least one wave-shaped recess. Some embodiments relate to a MEMS with a deformable element or comb drive, characterized in that the deformable element has a greater extension on the side connected to the substrate than the freely movable side.Some embodiments relate to a MEMS, wherein the angle of the movable element or the movable electrode fingers on the side connected to the substrate is arranged with an angle of 0° to 45°, preferably 1° to 15°, and an angle on the freely movable side is in a range of >0° and ≤ 30°, preferably at least 0.5° and at most 10°.Some embodiments of the present invention provide a MEMS transducer in which the deformable elements or finger structures are embedded in a symmetric arrangement. Other embodiments provide a MEMS transducer in which the deformable elements or finger structures are embedded in an asymmetric arrangement.Some embodiments of the present invention provide a system in which the undercut is replicated by step approximation. Some embodiments of the present invention provide a system in which the undercut changes into a rectangular shape, see FIG. 7 b, or originates therefrom or originates therefrom, for example at the base of the finger element, see FIG. 7 a.Embodiments of a comb drive described herein can be used for the deflection or movement of an element movable for fluidic displacement. This can be an in-plane movement of a fin structure in the same or a different MEMS plane than the comb drive, but alternatively or additionally membrane structures can also be deflected, for example directly or using direction-deflecting lever mechanisms.Although some aspects have been described in connection with a device, it is understood that these aspects also represent a description of the corresponding method, so that a block or a component of a device is also to be understood as a corresponding method step or as a feature of a method step. Analogously, aspects described in connection with or as a method step also represent a description of a corresponding block or detail or feature of a corresponding device.The above-described embodiments are merely illustrative of the principles of the present invention. It is to be understood that modifications and variations of the arrangements and details described herein will be apparent to others skilled in the art. Therefore, it is intended that the invention be limited only by the scope of the following claims and not by the specific details presented herein by way of description and explanation of the embodiments.References included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Patent Literature citedWO 2021 / 223886 A1

[0003] WO 02 / 19509 A2 [0004, 0012]US 2016 / 268927 A1 [0005, 0012]DE 10 2017 206 183 A1

[0006] US 2013 / 009716 A1

[0007] DE 2017 206 766 A1

[0068]

Claims

A MEMS comprising: a comb drive (10; 40; 50) having a first finger structure (12) comprising a first plurality of electrode fingers (14) and having a second finger structure (16) comprising a second plurality of electrode fingers (18) which form an interdigitated arrangement with the first plurality parallel to a substrate plane (x / y) of the MEMS; wherein the first plurality of electrode fingers (14) and the second plurality of electrode fingers (16) are curved perpendicular to the substrate plane; and wherein an electrode finger (14, 18) of the first finger structure or of the second finger structure has an undercut (26) in a plane perpendicular to the substrate plane starting from a first electrode finger end (48) towards a second opposing electrode finger end (28).The MEMS of claim 1, wherein the comb drive is configured to provide a relative translation movement between the first finger structure (12) and the second finger structure (16) based on an electrostatic force for changing a distance between the first finger structure (12) and the second finger structure (16) parallel to the substrate plane.The MEMS of claim 1 or 2, wherein a projection of the undercut (26) into the substrate plane has a substantially rectangular shape; or wherein a projection of the undercut (26) into the substrate plane has a combination of a plurality of substantially rectangular shapes.MEMS according to one of the preceding claims, in which mutually facing sides (14A, 18A) of mutually engaging electrode fingers are formed congruently at least within a working region.MEMS according to one of the preceding claims, wherein a side surface (44A) of an electrode finger (44) of the first finger structure or of the second finger structure has a concave section (52) starting from a first electrode finger end (48) towards a second opposite electrode finger end (28).The MEMS of claim 5, wherein the concave portion (52) comprises a curvature having a radius (R 2) different from a curvature (R 1) of the electrode finger at a free end (28) of the electrode finger.The MEMS according to claim 5 or 6, wherein the concave portion (52) is arranged between a first side wall portion (54 1) of the electrode finger, which starting from a clamped end (48) of the electrode finger is inclined with a first angle (φ) with respect to a main extension direction (y) of the electrode finger, and a second side wall portion (54 2) of the electrode finger, which is inclined with a second angle (θ) with respect to a free end (28) of the electrode finger with respect to the main extension direction (y) of the electrode finger; wherein the first angle (φ) has a value of at most 30° and the second angle (θ) has a value of at most 45°.MEMS according to one of the preceding claims, in which at least one of the electrode fingers has a combination of an undercut (26) on a non-clamped side (28) of the electrode finger and a widening of the electrode finger on a clamped side (48) of the electrode finger opposite the non-clamped side.The MEMS of claim 8, wherein the at least one electrode finger has a greater electrode finger width on the chucked side (48) than on the non-chucked side (28).MEMS according to one of the preceding claims, in which a first side surface (14A) of a first electrode finger (14 1) of the first finger structure (12) and a second side surface (18A) of a second electrode finger (18 1) of the second finger structure (16) facing the first side surface (14A) are formed congruently within a working range of the comb drive.MEMS according to one of the preceding claims, in which a wave-shaped cutout (33) is arranged between a first side surface (14A) of a first electrode finger (14 1) of the first finger structure (12) and a second side surface (18A) of a second electrode finger (18 1) of the second finger structure (18), said second side surface facing the first side surface (14A).MEMS according to one of the preceding claims, wherein a curvature of curved electrode fingers is adapted to a non-linear stiffness of the comb drive (10; 40; 50); wherein a curvature-based force variation in the comb drive and along a movement direction (y) of the comb drive compensates a deflection-based stiffness variation of the comb drive within a tolerance range.The MEMS of claim 12, comprising a linearized relationship between deflection of the comb drive (10; 40; 50)) and generated electrostatic force of the comb drive based on the curvature of curved electrode fingers.The MEMS according to one of the preceding claims, wherein the first finger structure (12 1) and the second finger structure (16 1) form a first structure pair; and the MEMS comprises at least one further structure pair (12 1, 162) which is connected in series to the first structure pair along a force direction (y) of the comb drive.MEMS according to one of the preceding ends, in which, starting from a curved region of the electrode finger, a substantially rectangular region (72, 76) is arranged towards a free end (28) or a clamped end (48).MEMS according to one of the preceding claims, which is formed as a loudspeaker.A method (800) for producing a MEMS, comprising the following steps: arranging (810) a comb drive having a first finger structure comprising a first plurality of electrode fingers and having a second finger structure comprising a second plurality of electrode fingers, such that the first plurality of electrode fingers and the second plurality of electrode fingers form an interdigitated arrangement with the first plurality parallel to a substrate plane of the MEMS; such that the first plurality of electrode fingers and the second plurality of electrode fingers are curved perpendicular to the substrate plane; such that an electrode finger of the first finger structure or of the second finger structure, starting from a first electrode finger end towards a second opposite electrode finger end, has an undercut in a plane perpendicular to the substrate plane.

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