Microelectromechanical systems inertial switch and method of forming the same

Abstract

Various embodiments may relate to a MEMS inertial switch including a proof mass including an upper portion and one or more lower portions, a z-axis movable electrode at a center portion of the proof mass, and a corresponding z-axis stationary electrode such that the z-axis movable electrode is configured to contact with the corresponding z-axis stationary electrode for detecting out-of-plane acceleration. The MEMS inertial switch may further include a plurality of in-plane movable electrodes at edge portions of the proof mass, and a corresponding plurality of in-plane stationary electrodes such that each of the plurality of in-plane movable electrodes is configured to contact with a corresponding in-plane stationary electrode for detecting in- plane acceleration. A contact gap between the z-axis movable electrode and the corresponding z-axis stationary electrode may be less than a contact gap between each of the plurality of in- plane movable electrodes and the corresponding in-plane stationary electrode.

Description

MICROELECTROMECHANICAL SYSTEMS INERTIAL SWITCH AND METHODOF FORMING THE SAMECROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of Singapore application No. 10202401956P filed July 3, 2024, the contents of it being hereby incorporated by reference in its entirety for all purposes.TECHNICAL FIELD

[0002] Various embodiments of this disclosure may relate to a microelectromechanical systems (MEMS) inertial switch. Various embodiments of this disclosure may relate to a method of forming a microelectromechanical systems (MEMS) inertial switch.BACKGROUND

[0003] The microelectromechanical systems (MEMS) inertial switch is an on-off sensor for the detection of an external acceleration FIG. 1 shows (a) a simplified block diagram of the microelectromechanical systems (MEMS) inertial switch; and (b) plots of acceleration as a function of time, and output voltage as a function of time illustrating the working principle of the MEMS inertial contact switch when detecting acceleration. As shown in FIG. 1(a), a MEMS inertial contact switch includes a suspended mass, connected to fixed anchor through springs. A moveable electrode is attached to the suspended mass and a fixed electrode is placed at a contact gap from the moveable electrode. The suspended mass with moveable electrode moves towards the fixed electrode when an acceleration is applied to the suspended mass. If the acceleration exceeds the threshold of the switch, the moveable electrode on the suspended mass makes contact with the fixed electrode, thereby generating an electrical signal as output,provided that the fixed anchor is biased with a battery. Note that no output signal is generated as long as the applied acceleration is less than the threshold of the switch. The threshold level determines the minimum acceleration to be detected by the inertial contact switch.

[0004] In some applications, MEMS acceleration switches may be required to detect accelerations along all 3 axes to determine direction and amplitude of the applied acceleration. Typically, such 3-axis acceleration sensing requires three separate proof masses. FIG. 2 shows a schematic of a switch including one proof mass (moving mass 1) for in-plane (along x / y-axis) acceleration detection, and another proof mass (moving mass 2) for out-of-plane (along z-axis) acceleration detection.

[0005] Acceleration sensitivity (S) scales with the mass (AT) of a proof mass according to the following relation:S = - = - (1)Here a is the applied acceleration, x is the displacement under applied acceleration, and k is the spring constant of the springs attached to the proof mass. The acceleration threshold at) can be determined as a function of the contact gap (<7) according to the following relation: / \(2)

[0006] Triaxial inertial switches commonly use side contacts (along x-y plane) to detect accelerations along x and y axes, and vertical contacts (along z-axis) to detect accelerations along z-axis. Side contact gaps are normally large (> 10 pm) resulting in a large threshold acceleration (> 40g) Additionally, the side contact areas are normally irregular, unoptimized and large (> 100 pm2), which can increase adhesion or stiction during switch contact resulting in a reduced reliability for multiple cycle switching. FIG. 3 shows (left) a schematic illustrating irregular, rough surfaces of side contact areas of the proof mass and sidewalls; and (right) a scanning electron microscopy (SEM) image showing released electroplated structures defining the sidewalls. Unreleased sidewalls have also been used as side contacts. However, unreleasedsidewalls may result in stiffer stationary electrodes, which can increase bouncing when the proof mass contacts the stationary electrodes. Such bouncing can significantly reduce the contact time of a switch. Sufficient contact time is essential to wake up or turn on the background circuit which is normally electrically connected to a switch. FIG. 4 shows (a) a scanning electron microscopy (SEM) image of an unreleased sidewall contact; (b) a schematic of the switch with the unreleased sidewall contact; (c) a plot of switch output and applied acceleration as a function of time illustrating switching characteristics with bouncing of the unreleased sidewall contact; and (d) a plot of switch output and applied acceleration as a function of time illustrating switching characteristics without bouncing. FIG. 4 shows an effect of bouncing resulting in reduced contact time (Tc) at stiffer unreleased sidewalls. FIG. 4(c) shows that there are two peaks in the switch output graph. The 1stpeak appears due to first switch contact, and the 2ndpeak appears due to second switch contact due to bouncing of the moveable electrode on the stiffer stationary electrode during switch contact. Comparing the two switch output graphs in FIG. 4(c) - (d), switch output in FIG. 4(d) yields longer contact time (TC2) due to no bouncing during switch contact as compared to FIG. 4(c), where bouncing reduces contact time (Tci) of the first switch contact.SUMMARY

[0007] Various embodiments may relate to a microelectromechanical systems (MEMS) inertial switch. The MEMS inertial switch may include a proof mass including an upper portion and one or more lower portions. The MEMS inertial switch may also include a z-axis movable electrode at a center portion of the proof mass. The MEMS switch may also include a corresponding z-axis stationary electrode such that the z-axis movable electrode is configured to contact with the corresponding z-axis stationary electrode for detecting out-of-plane acceleration. The MEMS inertial switch may further include a plurality of in-plane movableelectrodes at edge portions of the proof mass. The MEMS inertial switch may also include a corresponding plurality of in-plane stationary electrodes such that each of the plurality of inplane movable electrodes is configured to contact with a corresponding in-plane stationary electrode for detecting in-plane acceleration. A contact gap between the z-axis movable electrode and the corresponding z-axis stationary electrode may be less than a contact gap between each of the plurality of in-plane movable electrodes and the corresponding in-plane stationary electrode.

[0008] Various embodiments may relate to a method of forming a microelectromechanical systems (MEMS) inertial switch. The method may include forming a proof mass including an upper portion and one or more lower portions. The method may also include forming a z-axis movable electrode at a center portion of the proof mass. The method may further include forming a corresponding z-axis stationary electrode such that the z-axis movable electrode is configured to contact with the corresponding z-axis stationary electrode for detecting out-of- plane acceleration. The method may also include forming a plurality of in-plane movable electrodes at edge portions of the proof mass. The method may additionally include forming a corresponding plurality of in-plane stationary electrodes such that each of the plurality of inplane movable electrodes is configured to contact with a corresponding in-plane stationary electrode for detecting in-plane acceleration A contact gap between the z-axis movable electrode and the corresponding z-axis stationary electrode may be less than a contact gap between each of the plurality of in-plane movable electrodes and the corresponding in-plane stationary electrodeBRIEF DESCRIPTION OF THE DRAWINGS

[0009] In the drawings, like reference characters generally refer to the same parts throughout the different views. The drawings are not necessarily drawn to scale, emphasis instead generally being placed upon illustrating the principles of various embodiments. In the following description, various embodiments of the invention are described with reference to the following drawings.FIG. 1 shows (a) a simplified block diagram of the microelectromechanical systems (MEMS) inertial switch; and (b) plots of acceleration as a function of time, and output voltage as a function of time illustrating the working principle of the MEMS inertial contact switch when detecting acceleration.FIG. 2 shows a schematic of a switch including one proof mass (moving mass 1) for in-plane (along x / y-axis) acceleration detection, and another proof mass (moving mass 2) for out-of- plane (along z-axis) acceleration detection.FIG. 3 shows (left) a schematic illustrating irregular, rough surfaces of side contact areas of the proof mass and side walls, and (right) a scanning electron microscopy (SEM) image showing released electroplated structures defining the side walls.FIG. 4 shows (a) a scanning electron microscopy (SEM) image of an unreleased sidewall contact; (b) a schematic of the switch with the unreleased sidewall contact; (c) a plot of switch output and applied acceleration as a function of time illustrating switching characteristics with bouncing of the unreleased sidewall contact; and (d) a plot of switch output and applied acceleration as a function of time illustrating switching characteristics without bouncing.FIG. 5 shows a general illustration of a microelectromechanical systems (MEMS) inertial switch according to various embodiments.FIG. 6 shows a general illustration of a method of forming a microelectromechanical systems (MEMS) inertial switch according to various embodiments.FIG. 7A shows a simplified top view schematic of a microelectromechanical systems (MEMS) inertial switch according to various embodiments.FIG. 7B shows a cross-sectional view along line section AA’ of the microelectromechanical systems (MEMS) inertial switch shown in FIG. 7A according to various embodiments.FIG. 8 shows (a) a cross-sectional schematic of the proof mass undergoing torsional motion due to in-plane acceleration according to various embodiments; (b) a cross-sectional schematic of the proof mass undergoing linear motion due to out-of-plane acceleration according to various embodiments; and (c) a cross-sectional schematic combining (a) and (b) and illustrating the microelectromechanical systems (MEMS) inertial switch according to various embodiments, similar to the schematic shown in FIG. 7B.FIG. 9A shows a simplified top view schematic of a triaxial microelectromechanical systems (MEMS) inertial switch according to various embodiments.FIG. 9B shows a cross-sectional schematic of the triaxial microelectromechanical systems (MEMS) inertial switch as shown in FIG. 9A according to various embodiments along line section AA’ (i.e., along or parallel to x-axis).FIG. 9C shows a cross-sectional schematic of the triaxial microelectromechanical systems (MEMS) inertial switch as shown in FIG. 9A according to various embodiments along line section BB’ (i.e., along or parallel to y-axis).FIG. 9D shows a cross-sectional schematic of the triaxial microelectromechanical systems (MEMS) inertial switch as shown in FIG. 9A according to various embodiments along diagonal line section CC’.FIG. 10 shows the torsional motion of the cross-section as shown in FIG. 9B when an acceleration is applied along x-axis according to various embodiments.FIG. 11 shows the torsional motion of the cross-section as shown in FIG. 9C when an acceleration is applied along y-axis according to various embodiments.FIG. 12 shows the linear motion of the cross-section as shown in FIG. 9D when an acceleration is applied along z-axis according to various embodiments.FIG. 13A shows a three-dimensional (3D) schematic of the finite element (FE) model with zoomed in images showing [A] the torsion spring for x-axis acceleration detection and vertical contact structure for y-axis acceleration detection, [B] the torsion spring for y-axis acceleration detection and vertical contact structure for x-axis acceleration detection, and [C] linear springs for z-axis acceleration detection according to various embodiments.FIG. 13B shows a top view schematic of the finite element (FE) model according to various embodiments.FIG. 13C shows a perspective bottom view schematic of the finite element (FE) model according to various embodimentsFIG. 14 shows the first four vibration mode shapes with respective resonant frequencies, where (a) the first vibration mode shape is used to detect x-axis acceleration, (b) the second vibration mode shape is used to detect y-axis acceleration, (c) the third vibration mode shape is used to detect z-axis acceleration, and (d) the fourth vibration mode shape is an unwanted mode shape according to various embodimentsFIG. 15A shows a plot of displacement (in nanometers or nm) as a function of acceleration along x axis (in g, free-fall acceleration under gravity) illustrating acceleration sensitivity (Sx) of the x-axis acceleration detection vertical contact structures according to various embodiments.FIG. 15B shows a plot of displacement (in nanometers or nm) as a function of acceleration along y axis (in g, free-fall acceleration under gravity) illustrating acceleration sensitivity Sy) of the y-axis acceleration detection vertical contact structures according to various embodiments.FIG. 15C shows a plot of displacement (in nanometers or nm) as a function of acceleration along z axis (in g, free-fall acceleration under gravity) illustrating acceleration sensitivity (Sz) of the z-axis acceleration detection vertical contact structures according to various embodiments.FIG. 16A is a scanning electron microscopy (SEM) image showing a top planar view of a portion of the microelectromechanical systems (MEMS) inertial switch with a vertical contact structure including a stationary top electrode and a movable bottom electrode according to various embodiments.FIG. 16B is a scanning electron microscopy (SEM) image showing a cross-sectional side view of a vertical contact structure with the stationary top electrode having a metal indent.FIG. 16C shows a plot of switch output (in volts or V) as a function of time (in milli-second or ms) showing the switching characteristics of the vertical contact structure including a stationary top electrode having a metal indent according to various embodiments.FIG. 16D shows a plot of maximum output at each cycle (in volts or V) as a function of the number of cycles illustrating a 10% reduction in switch output of the vertical contact structure (including a stationary top electrode having a metal indent) according to various embodiments at the 100th cycle as compared to the 1st cycle.DESCRIPTION

[0010] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details and embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized, and structural, logical, and electrical changes may be made without departing from the scope of the invention. The variousembodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

[0011] Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments. Features that are described in the context of an embodiment may correspondingly be applicable to the other embodiments, even if not explicitly described in these other embodiments. Furthermore, additions and / or combinations and / or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0012] In the context of various embodiments, the articles “a”, “an” and “the” as used with regard to a feature or element include a reference to one or more of the features or elements.

[0013] Tn the context of various embodiments, the terms “about” or “approximately” as applied to a numeric value encompasses the exact value and a reasonable variance, e g. within 10% of the specified value.

[0014] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items.

[0015] By “comprising” it is meant including, but not limited to, whatever follows the word “comprising”. Thus, use of the term “comprising” indicates that the listed elements are required or mandatory, but that other elements are optional and may or may not be present.

[0016] By “consisting of’ is meant including, and limited to, whatever follows the phrase “consisting of’. Thus, the phrase “consisting of’ indicates that the listed elements are required or mandatory, and that no other elements may be present.

[0017] According to Equation (2), it may be required to increase a mass of a proof mass to reduce acceleration threshold for a particular contact gap. Therefore, a single proof mass which is able to achieve 3-axis acceleration sensing (i.e., tri-axial acceleration sensing) may be desirable due to reduced die space which leads to better form factor at reduced cost. Moreover,for a certain die space, a single proof mass for tri-axial sensing may allow for a larger proof mass as compared to 3 separate proof masses for individual axis sensing.

[0018] Various embodiments may relate to a tri-axial MEMS inertial switch for detecting acceleration along all 3 axes with a single proof mass. Triaxial sensing with a single proof mass may benefit from a compact form factor due to reduced size. Various embodiments may relate to a switch for detecting in-plane accelerations (along x / y-axis) and out-of-plane acceleration (along z-axis) using vertical contact gaps. Various embodiments may relate to vertical contact structures with tunable vertical contact gaps along z-axis to control the acceleration threshold for acceleration detection along different individual axes, while reducing or minimizing any unwanted contact due to cross-axis sensitivity. It is worth noting that vertical contact gaps may be precisely tuned (down to sub-pm or nm-level), and the contact area may be well optimized for performance.

[0019] FIG. 5 shows a general illustration of a microelectromechanical systems (MEMS) inertial switch according to various embodiments. The MEMS inertial switch may include a proof mass 502 including an upper portion 502a and one or more lower portions 502b. The MEMS inertial switch may also include a z-axis movable electrode 504a at a center portion of the proof mass 502. The MEMS switch may also include a corresponding z-axis stationary electrode 504b such that the z-axis movable electrode 504a is configured to contact with the corresponding z-axis stationary electrode 504b for detecting out-of-plane acceleration. The MEMS inertial switch may further include a plurality of in-plane movable electrodes 506a, 508a at edge portions of the proof mass 502. The MEMS inertial switch may also include a corresponding plurality of in-plane stationary electrodes 506b, 508b such that each of the plurality of in-plane movable electrodes 506a, 508a is configured to contact with a corresponding in-plane stationary electrode (i.e., of the plurality of in-plane stationary electrodes 506b, 508b) for detecting in-plane acceleration. A contact gap between the z-axismovable electrode 504a and the corresponding z-axis stationary electrode 504b may be less than a contact gap between each of the plurality of in-plane movable electrodes 506a, 508a and the corresponding in-plane stationary electrode (i.e., of the plurality of in-plane stationary electrodes 506b, 508b).

[0020] In other words, the microelectromechanical systems (MEMS) inertial switch may include a proof mass 502 with an upper portion 502a (alternatively referred to as a first portion) and one or more lower portions 502b (alternatively referred to as a second portion). The switch may also include movable electrodes 504a, 506a, 508a on or over the proof mass 502, with corresponding stationary electrodes 504b, 506b, 508b. The movable electrode 504a may be located at a center portion of the proof mass 502, while movable electrodes 506a, 508a may be located at edge portions of the proof mass 502. Tn the absence of acceleration (i .e., at rest), a contact gap between the electrodes 504a, 504b may be smaller than a contact gap between the electrodes 506a, 506b, as well as a contact gap between the electrodes 508a, 508b.

[0021] For avoidance of doubt, FIG. 5 seeks to illustrate some features of a MEMS inertial switch according to various embodiments, and is not intended to limit e.g., the shape, size, orientation, dimensions and / or number of the features. For instance, while FIG. 5 shows two in-plane stationary electrodes 506b, 508b, various embodiments may include any suitable number of in-plane stationary electrodes, e.g., four, as described in further detail below

[0022] Each pair of movable electrode and corresponding stationary electrode (e.g., pairs 504a-b, 506a-b and 508a-b) may form a vertical contact electrode pair (alternatively referred to as vertical contact structure). Each of the stationary electrodes 504b, 506b, 508b may be part of or in contact with a structure (e.g., an anchor) which is stationary during operation. The stationary electrodes 504b, 506b, 508b may be suspended directly over the movable electrodes 504a, 506a, 508a, respectively. For instance, the corresponding z-axis stationary electrode 504b may be suspended directly over the z-axis movable electrode 504a.

[0023] An “edge portion” as described herein may generally refer to an off-center portion of the proof mass 502. As described in more detail below, a proof mass may include a plurality of frames. An “edge portion” of the proof mass 502 may refer to a region of any of the frames that is adjoining an edge of the frame. For instance, in some cases, the “edge portion” may refer to a region of the outermost frame adjoining an edge of the outermost frame, while in other cases, the “edge portion” may refer to a region of the second outermost frame or the middle frame that is adjoining the edge of that frame.

[0024] In various embodiments, the proof mass 502 may be mechanically coupled to a plurality of anchors.

[0025] In various embodiments, each of the one or more lower portions 502b of the proof mass 502 may have a thickness greater than a thickness of the upper portion of the proof mass 502. A surface area of a main surface of each of the one or more lower portions 502b of the proof mass 502 may be smaller than a surface area of a main surface of the upper portion 502a. A width / lateral dimension of each of the one or more lower portions 502b of the proof mass 502 may be smaller than a width / lateral dimension of the upper portion 502a. Consequently, the center of mass may be asymmetric along the z axis. In various embodiments, the one or more lower portions 502b of the proof mass 502 may result in a center of mass being at the one or more lower portions 502b of the proof mass 502 (or at a level of the one or more lower portions 502b). As such, the one or more lower portions 502b of the proof mass 502 may allow for torsional motion of the proof mass 502 in response to in-plane acceleration (i.e., along x- axis and / or y axis), thereby allowing for detection of in-plane acceleration using vertical contact electrode pairs. In other words, in-plane acceleration may be detected via torsional motion of the proof mass 502. In addition, the one or more lower portions 502b of the proof mass 502 may help reduce acceleration threshold.

[0026] In various embodiments, the upper portion 502a and the one or more lower portions 502b may be different layers (of the same material or of different materials), while in various other embodiments the upper portion 502a and the one or more lower portions 502b may be parts of a single monolithic structure or layer.

[0027] In various embodiments, the proof mass 502 may include a pair of torsional springs along an axis in y-direction passing through the center portion of the proof mass 502, the pair of torsional springs configured to allow torsional motion of the proof mass 502 in response to acceleration along an axis in x-direction (which is 90° to the axis in y-direction). In various embodiments, the proof mass 502 may include a pair of torsional springs along an axis in x- direction passing through the center portion of the proof mass 502, the pair of torsional springs configured to allow torsional motion of the proof mass 502 in response to acceleration along an axis in y-direction. In various embodiments, the torsional springs may be included in the upper portion 502a.

[0028] In various embodiments, out-of-plane acceleration (i.e., along an axis in z-direction, which is 90° to the axis in the x-direction and also 90° to the axis in the y-direction) may be detected via linear motion of the proof mass 502. The MEMS inertial switch may also include one or more linear springs to allow for linear motion of the proof mass 502 along an axis in the z-direction. The one or more linear springs may be configured to increase a resonant frequency of unintended vibration in form of in-plane motions.

[0029] In various embodiments, the corresponding z-axis stationary electrode 504b may have an indented surface facing the proof mass 502 and the corresponding z-axis moveable electrode 504a. In various embodiments, each of the corresponding plurality of in-plane stationary electrodes 506b, 508b may have an indented surface facing the proof mass 502 and the corresponding in-plane moveable electrodes 506a, 508a. In various embodiments, the z-axis movable electrode 504a may have an indented surface facing the corresponding z-axisstationary electrode 504b. In various embodiments, each of the plurality of in-plane movable electrodes 506a, 508a may have an indented surface facing the corresponding in-plane stationary electrode 506b, 508b. The indented surface or surfaces may help to reduce adhesion force when a movable electrode comes into contact with a stationary electrode, thereby improving reliability for multiple switching cycles.

[0030] Tn various embodiments, the contact gap between a movable electrode 504a, 506a, 508a and a corresponding electrode 504b, 506b, 508b may be defined as the shortest distance between the movable electrode and the corresponding electrode in the absence of any acceleration (i.e., at rest). For instance, if the stationary electrode has an indented surface with an indent (i.e., protruding portion), while the movable electrode has a flat, planar surface, the contact gap is between the indent (i.e., protruding portion) of the stationary electrode, and the flat, planar surface of the movable electrode. Conversely, if the stationary electrode has an indented surface with an indent (i.e., protruding portion), while the movable electrode also has an indented surface with an indent (i.e., protruding portion), the contact gap is between the indent (i.e., protruding portion) of the stationary electrode, and the indent (i.e., protruding portion) of the movable electrode.

[0031] In various embodiments, as shown in FIG. 5, the plurality of in-plane movable electrodes 506a, 508a may include a first in-plane movable electrode 506a at a first edge portion of the proof mass 502 (and e.g., along an axis in the x-direction passing through the center portion of the proof mass 502), as well as a second in-plane movable electrode 508a at a second edge portion of the proof mass 502 opposite to the first edge portion relative to the center portion of the proof mass 502 (and e.g., along the axis in the x-direction passing through the center portion of the proof mass 502). The first in-plane movable electrode 506a, a corresponding first in-plane stationary electrode 506b, the second in-plane movable electrode 508a and acorresponding second in-plane stationary electrode 508b may be configured to determine acceleration along an axis, e.g., an axis in x-direction.

[0032] In various embodiments, as mentioned above, the plurality of in-plane movable electrodes may also include a third in-plane movable electrode at a third edge portion of the proof mass 502 (and e.g., along an axis in the y-direction passing through the center portion of the proof mass 502), as well as a fourth in-plane movable electrode at a fourth edge portion of the proof mass 502 opposite to the third edge portion relative to the center portion of the proof mass 502 (and e.g., along the axis in the y-direction passing through the center portion of the proof mass 502). The third in-plane movable electrode, a corresponding third in-plane stationary electrode, the fourth in-plane movable electrode and a corresponding fourth in-plane stationary electrode may be configured to determine acceleration along an axis, e g., an axis in y-direction.

[0033] In various embodiments, the contact gap between the z-axis movable electrode 504a and the corresponding z-axis stationary electrode 504b may be less than a contact gap between the third in-plane movable electrode (or fourth in-plane movable electrode) and the corresponding third in-plane stationary electrode (or corresponding fourth in-plane stationary electrode) for y-axis acceleration detection, which may in turn be less than a contact gap between the first in-plane movable electrode (or second in-plane movable electrode) and the corresponding first in-plane stationary electrode (or corresponding second in-plane stationary electrode) for x-axis acceleration detection.

[0034] In various embodiments, as mentioned above, the proof mass 502 may include a plurality of frames. The plurality of frames may be arranged in a concentric arrangement. In various embodiments, the first in-plane movable electrode 506a may be at the first edge portion located at an outermost frame, and the second in-plane moveable electrode 508a may be at the second edge portion located at the outermost frame. In various embodiments, the third first in-plane movable electrode 506a may be at the third edge portion located at a middle frame, and the fourth in-plane moveable electrode 508a may be at the fourth edge portion located at the middle frame. The z-axis movable electrode 504a may be at or on an innermost frame of the plurality of frames.

[0035] FIG. 6 shows a general illustration of a method of forming a microelectromechanical systems (MEMS) inertial switch according to various embodiments. The method may include, in 602, forming a proof mass including an upper portion and one or more lower portions. The method may also include, in 604, forming a z-axis movable electrode at a center portion of the proof mass. The method may further include, in 606, forming a corresponding z-axis stationary electrode such that the z-axis movable electrode is configured to contact with the corresponding z-axis stationary electrode for detecting out-of-plane acceleration. The method may also include, in 608, forming a plurality of in-plane movable electrodes at edge portions of the proof mass. The method may additionally include, in 610, forming a corresponding plurality of inplane stationary electrodes such that each of the plurality of in-plane movable electrodes is configured to contact with a corresponding in-plane stationary electrode for detecting in-plane acceleration. A contact gap between the z-axis movable electrode and the corresponding z-axis stationary electrode may be less than a contact gap between each of the plurality of in-plane movable electrodes and the corresponding in-plane stationary electrode.

[0036] For avoidance of doubt, FIG. 6 seeks to illustrate steps of forming a microelectromechanical systems (MEMS) inertial switch according to various embodiments, and is not intended to limit the sequence of the various steps. For instance, steps 604 and 608 may occur at the same time, while steps 606 and 610 may occur at the same time (which may be before or after steps 604, 608).

[0037] Various embodiments may relate to a method of forming a microelectromechanical systems (MEMS) inertial switch including the proof mass, the z-axis movable electrode, thecorresponding z-axis stationary electrode, the plurality of in-plane movable electrodes at edge portions of the proof mass, and the corresponding plurality of in-plane stationary electrodes. The proof mass may be formed by semiconductor fabrication techniques such as lithography and etching. In one example, the upper portion of the proof mass may be formed from a top silicon device layer of a silicon-on-insulator (SOI) wafer, while the one or more lower portions of the proof mass may be formed from a bottom silicon substrate of the SOI wafer. The z-axis movable electrode, the corresponding z-axis stationary electrode, the plurality of in-plane movable electrodes at edge portions of the proof mass, and the corresponding plurality of inplane stationary electrodes may also be formed by semiconductor fabrication techniques such as deposition and etching.

[0038] In various embodiments, each of the one or more lower portions of the proof mass may have a thickness greater than a thickness of the upper portion of the proof mass. A surface area of a main surface of each of the one or more lower portions of the proof mass is smaller than a surface area of a main surface of the upper portion.

[0039] In various embodiments, in-plane acceleration may be detected via torsional motion of the proof mass.

[0040] In various embodiments, the proof mass may include a pair of torsional springs along an axis in y-direction passing through the center portion of the proof mass, the pair of torsional springs configured to allow torsional motion of the proof mass in response to acceleration along an axis in x-direction.

[0041] In various embodiments, the proof mass may include a pair of torsional springs along an axis in x-direction passing through the center portion of the proof mass, the pair of torsional springs configured to allow torsional motion of the proof mass in response to acceleration along an axis in y-direction.

[0042] In various embodiments, out-of-plane acceleration may be detected via linear motion of the proof mass.

[0043] In various embodiments, the proof mass may include one or more linear springs configured to increase a resonant frequency of unintended vibration in form of in-plane motions.

[0044] In various embodiments, the corresponding z-axis stationary electrode may have an indented surface facing the proof mass. Each of the corresponding plurality of in-plane stationary electrodes may have an indented surface facing the proof mass.

[0045] In various embodiments, the z-axis movable electrode may have an indented surface facing the corresponding z-axis stationary electrode. Each of the plurality of in-plane movable electrodes may have an indented surface facing the corresponding in-plane stationary electrode.

[0046] The contact gap between movable electrodes and stationary electrodes may be determined by a thickness of a sacrificial layer, e g., sacrificial oxide layer. In various embodiments, the sacrificial oxide layer may be formed via deposition after formation of the movable electrodes. Accordingly, the contact gap may be defined precisely, even if the electrode(s) have indented surfaces.

[0047] In various embodiments, the plurality of in-plane movable electrodes may include a first in-plane movable electrode at a first edge portion of the proof mass and along an axis in the x-direction passing through the center portion of the proof mass, and a second in-plane movable electrode at a second edge portion of the proof mass opposite to the first edge portion relative to the center portion of the proof mass and along the axis in the x-direction passing through the center portion of the proof mass.

[0048] In various embodiments, the plurality of in-plane movable electrodes may further include a third in-plane movable electrode at a third edge portion of the proof mass and along an axis in the y-direction passing through the center portion of the proof mass, and a fourth in-plane movable electrode at a fourth edge portion of the proof mass opposite to the third edge portion relative to the center portion of the proof mass and along the axis in the y-direction passing through the center portion of the proof mass.

[0049] The first in-plane movable electrode, a corresponding first in-plane stationary electrode, the second in-plane movable electrode and a corresponding second in-plane stationary electrode may be configured to determine acceleration along an axis in x-direction. The third in-plane movable electrode, a corresponding third in-plane stationary electrode, the fourth in-plane movable electrode and a corresponding fourth in-plane stationary electrode may be configured to determine acceleration along an axis in y-direction.

[0050] FIG. 7A shows a simplified top view schematic of a microelectromechanical systems (MEMS) inertial switch according to various embodiments. FIG 7B shows a cross-sectional view along line section AA’ of the microelectromechanical systems (MEMS) inertial switch shown in FIG. 7A according to various embodiments. Line section AA’ in FIG. 7A is drawn through the middle of the structure along x-axis, while line section BB’ in FIG. 7A is drawn through the middle of the structure along y-axis. FIGS. 7A - B are used to describe the working principle of the MEMS inertial switch according to various embodiments As seen from FIG. 7B, an additional proof mass portion 702b (proof mass 2) is attached to the underside of the main proof mass portion 702a (proof mass 1). The thickness of proof mass portion 702b (h) may be required to be higher than the thickness of proof mass portion 702a (L), and the surface area for proof mass portion 702b may be required to be smaller than the surface area of proof mass portion 702a. Proof mass portion 702b may be attached to proof mass portion 702a around the center (i.e., vertical axis passing through center of mass) of proof mass portion 702a. The combination of the portions 702a, 702b may result in the overall proof mass to be asymmetric along z-axis. Provided proof mass portion 702a (proof mass 1) has mass of M and proof massportion 702b (proof mass 2) has mass of Mi, the threshold acceleration in Equation (2) can be modified to:

[0051] Here, total mass is: M = M1+ M2. Proof mass portion 702a and proof mass portion 702b may be of the same structural layer, or may be of different structural layers. There may be three vertical contact structures: the contact structure in the center 704 may be used for out- of-plane (z-axis) acceleration detection, and the contact structures 706, 708 around the edges may be used for in-plane (x-axis according to FIG. 7A) acceleration detection. Here, the vertical contact gaps may be varied. As illustrated in FIGS. 7A - B, the vertical contact structure 704 may include a bottom electrode 704a (also referred to as z-axis movable electrode) and a top electrode 704b (also referred to as z-axis stationary electrode). The vertical contact structure 706 may include a bottom electrode 706a (also referred to as in-plane movable electrode) and a top electrode 706b (also referred to as in-plane stationary electrode). The vertical contact structure 708 may include a bottom electrode 708a (also referred to as in-plane movable electrode) and a top electrode 708b (also referred to as in-plane stationary electrode).

[0052] The contact gaps may be such that gap 2 (di) < gap 1 (di). As seen from FIG. 7A, springs 714a, 714b may be attached to proof mass portion 702a (proof mass 1) along the central line section BB’. The springs 714a, 714b may attach proof mass portion 702a to anchors 716a, 716b. The springs 714a, 714b may be torsional springs.

[0053] FIG. 8 shows (a) a cross-sectional schematic of the proof mass undergoing torsional motion due to in-plane acceleration according to various embodiments; (b) a cross-sectional schematic of the proof mass undergoing linear motion due to out-of-plane acceleration according to various embodiments; and (c) a cross-sectional schematic combining (a) and (b) and illustrating the microelectromechanical systems (MEMS) inertial switch according to various embodiments, similar to the schematic shown in FIG. 7B.

[0054] FIG. 8(a) shows the out-of-plane torsional motion of the proof mass under an inplane acceleration along x-axis. For better understanding of the working principle, the contact structure for out-of-plane detection (in the center of the proof mass) is omitted in FIG. 8(a). The maximum displacement due to such torsional motion can be seen around the edges of the proof mass with one edge moving up (will contact the top electrode) and other edge is moving down (going away from the top electrode). The minimum displacement can be seen around the pivot point located around the center of the proof mass as shown in FIG. 8(a). Provided kt denotes stiffness of the torsional springs, acceleration threshold (a^) for torsional motion can be derived from Equation (3):

[0055] FIG. 8(b) shows the linear out-of-plane motion of the proof mass under an out-of- plane acceleration along z-axis. For better understanding of the working principle, the contact structures for in-plane detection are omitted in FIG. 8(b). As the pivot point for torsional motion in FIG. 8(b) is located around the center of the proof mass, placing the contact structure for out- of-plane acceleration detection around the center of the device may reduce cross-axis sensitivity due to torsional motion under in-plane acceleration. For detecting the displacement (given by the vertical gap) under in-plane acceleration, any displacements of the contact structure for out- of-plane acceleration detection may be due to cross-axis sensitivity. Given that gap 2 (di) is smaller than gap 1 (di), under linear motion as shown in FIG. 8(b), the contact gap in the center (i .e., contact gap of the vertical contact structure for out-of-plane acceleration detection) may first be closed. Provided ki denotes stiffness of the springs for linear motion, acceleration threshold (at,i) for linear motion can be derived from equation (3):

[0056] Combining structures from FIGS. 8(a) - (b) form the cross-section given in FIG. 8(c), which resembles the proposed cross-section in FIG. 7(b).

[0057] FIG. 9A shows a simplified top view schematic of a triaxial microelectromechanical systems (MEMS) inertial switch according to various embodiments. The MEMS inertial switch may include vertical contact structures 904, 906, 908, 910, 912 for acceleration detection along all 3 axes (i.e., x, y, and z axes). FIG. 9B shows a cross-sectional schematic of the triaxial microelectromechanical systems (MEMS) inertial switch as shown in FIG. 9A according to various embodiments along line section AA’ (i.e., along or parallel to x-axis) FIG 9C shows a cross-sectional schematic of the triaxial microelectromechanical systems (MEMS) inertial switch as shown in FIG. 9A according to various embodiments along line section BB’ (i.e., along or parallel to y-axis). FIG. 9D shows a cross-sectional schematic of the triaxial microelectromechanical systems (MEMS) inertial switch as shown in FIG. 9A according to various embodiments along diagonal line section CC’.

[0058] As shown in FIG. 9A, the bottom metal electrodes 904a, 906a, 908a, 910a, 912a may be attached to the proof mass or moving structure 902, resulting in the bottom metal electrodes 904a, 906a, 908a, 910a, 912a being moveable electrodes. For each of top metal electrodes 904b, 906b, 908b, 910b, 912b, a stationary bridge may be formed between two portions of anchors 916c, 916d, 916e, 916f, 916g by the top metal electrode 904b, 906b, 908b, 10b, 912b over the moveable bottom electrode 904a, 906a, 908a, 910a, 912a (see also FIG. 9B). As the anchors 916c, 16d, 916e, 916f, 916g remain stationary during operation, the top metal electrodes 904b, 906b, 908b, 910b, 912b held by the anchors 916c, 916d, 916e, 916f, 916g may remain stationary. Vertical contact structure 904 may thereby include movable bottom metal electrode 904a (also referred to as z-axis movable electrode) and stationary top metal electrode 904b (also referred to as z-axis stationary electrode). Further, each vertical contact structure 906, 908, 10, 912 may include a movable bottom metal electrode (respectively 906a, 908a, 910a, 912a, also referred to as in-plane movable electrode) and a stationary top metal electrode (respectively 906b, 908b, 910b, 912b, also referred to as in-plane stationary electrode). 1

[0059] As seen from FIG. 9B, a pair of additional proof mass portions 902b (proof mass 2) may be attached to the underside of the main proof mass portion 902a (proof mass 1) along the line section AA’. The pair of proof mass portions 902b can alternatively be attached to main proof mass portion 902a along the line section BB’, with no proof mass portions 902b being attached to main proof mass portion 902a along the line section AA’. The proof mass portions 902b may be attached to proof mass portion 902a within the outer edges of frame 3 (i.e., the innermost frame). As such, the proof mass portions 902b may be used for acceleration detection along all 3 axes to improve the sensitivity, thereby reducing the acceleration threshold according to Equation (3). The proof mass 902, more specifically upper proof mass portion 902a, may include torsional springs 914a, 914b, 914c, 914d and linear springs 914e, 914f, 914g, 914h. The upper proof mass portion 902a may also include a plurality of frames. As shown in FIG. 9A, the upper proof mass portion 902a may include three frames - frame 1 (outermost frame), frame 2 (middle frame), and frame 3 (innermost frame).

[0060] In terms of fabrication, the top silicon device layer of a silicon-on-insulator (SOI) wafer can form proof mass portion 902a, while the bottom silicon substrate of the SOI wafer can form proof mass portions 902b. The springs 914a - h with respective lateral dimensions can be obtained by etching the structural layer (i.e., the top silicon device layer of the SOI wafer) of proof mass portion 902a along its thickness. Proof mass portions 902b can be defined by selectively etching the silicon substrate of the SOI wafer from the backside of the wafer.

[0061] FIG. 9A shows that a pair of torsional springs 914a, 914b attached to the outer edge of frame-1 (i.e., the outermost frame) of proof mass portion 902a along line section BB’ (along y-axis). The pair of torsional springs 914a, 914b may be dedicated to x-axis acceleration detection. The in-plane movable electrodes 906a, 908a to detect the accelerations along x-axis may be placed along the free edges or edge regions of frame-1 and along the line section AA’.FIG. 10 shows the torsional motion of the cross-section as shown in FIG. 9B when anacceleration is applied along x-axis according to various embodiments. As seen from FIG. 10, under torsional motion, the center of the proof mass 904 (where the torsional springs 914a, 914b are attached to the proof mass 902 along line section BB’) may have minimum displacement, while the free edge regions of the proof mass 902 (i.e., of frame-1, where in-plane movable electrodes 906a, 908a are placed) may have maximum displacement. Frame-2 and frame-3 may also undergo torsional motion with frame-1 in response to x-axis acceleration. Acceleration threshold (tfe) for x-axis acceleration detection can be derived from equation (3): )Here, dxdenotes the vertical gap for contact gap 1 and kxdenotes the stiffness of the torsional springs 914a, 914b under the intended torsional motion (in FIG. 10) for x-axis acceleration detection.

[0062] FIG. 9A shows another pair of torsional springs 914c, 914d which are attached to frame-2 (i.e., middle frame) of proof mass portion 902a along the line section AA’ (along x- axis). FIG. 11 shows the torsional motion of the cross-section as shown in FIG. 9C when an acceleration is applied along y-axis according to various embodiments. As the maximum displacement occurs around the edge regions of frame-2, the contact structures for y-axis acceleration detection may be attached to the edge regions of frame-2 as shown in FIG. 9A and aligned to y-axis along line section BB’. The outermost frame- 1 may remain stationary, while frame-3 may undergo torsional motion with frame-2 in response to y-axis acceleration. Given the torsional motion under x-axis acceleration yields minimum displacement along the line section BB’, as seen from center region in FIG. 11, placing the in-plane movable electrodes 910a, 912a for y-axis acceleration detection along the line section BB’ allows reduced crossaxis sensitivity under x-axis acceleration for the in-plane movable electrodes 910a, 912a. Similarly, placing the torsional springs 914c, 914d for y-axis acceleration detection along the line section AA’ allows minimum displacement along line section AA’ under y-axisacceleration, as seen from the center region in FIG. 11. By placing the in-plane movable electrodes 906b, 908b for x-axis acceleration detection along the line section AA’, cross-axis sensitivity under y-axis acceleration may be significantly reduced for the in-plane movable electrodes 906b, 908b. Acceleration threshold (aty) for y-axis acceleration detection can be derived from equation (3):Here, dydenotes the vertical gap for contact gap 2 and kydenotes the stiffness of the torsional springs under the intended torsional motion (in FIG. 11) for y-axis acceleration detection.

[0063] FIG. 9A shows two pairs of linear springs, i.e. linear springs 914e, 914f, 914g, 914h, attached to frame-3 (i.e., innermost frame) of proof mass portion 902a. One pair of linear springs 914e, 914f may be aligned along x-axis, and another pair of linear springs 914g, 914h may be aligned along y-axis. The spring combination and spring constant of linear springs 914e, 914f, 914g, 14h may act as a means to push the resonant frequency of unintended vibration motions (in particular, the in-plane motion(s) along x-y plane) much higher than the resonant frequency of the intended linear out-of-plane motion (along z-axis). The details may be as provided below with evidence from finite element modelling (FEM). FIG. 12 shows the linear motion of the cross-section as shown in FIG. 9D when an acceleration is applied along z-axis according to various embodiments. All three frames (i.e., frame-1, frame-2, and frame-3) may undergo linear motion due to z-axis acceleration. The z-axis movable electrode 904a for z-axis acceleration detection may be placed at the center of the proof mass portion 902a as the torsional motions under respective x-axis and y-axis accelerations produce minimum displacements around the center of the proof mass portion 902a. As such, the cross-axis sensitivity of z-axis movable electrode 904a due to accelerations applied along x-axis and / or y-axis may be reduced. Acceleration threshold (atz) for z-axis acceleration sensing can be derived from equation (3):Here, dzdenotes the vertical gap for contact gap 3 and kzdenotes the overall stiffness of the linear springs 914e, 914f, 914g, 914h under the intended linear motion (in FIG. 12) for z-axis acceleration sensing. In various embodiments, the contact gaps may be such that contact gap 1 (dx) > contact gap 2 (dy) > contact gap 3 (tZz). Output voltage may be read from bond pads 918a, 918b as shown in FIG. 9C.

[0064] Simulation and discussions

[0065] The schematic in FIG. 9A may be implemented using a defined structure (with overall area < 2.8 mm x 2.8 mm) with springs. The structure is further analyzed using FEM in COMSOL. FIG. 13A shows a three-dimensional (3D) schematic of the finite element (FE) model with zoomed in images showing [A] the torsion spring for x-axis acceleration detection and vertical contact structure for y-axis acceleration detection, [B] the torsion spring for y-axis acceleration detection and vertical contact structure for x-axis acceleration detection, and [C] linear springs for z-axis acceleration detection according to various embodiments. Note that a pair of lower proof mass portions (proof mass 2) is attached to an upper proof mass portion (proof mass 1) in the FE model similar to the cross-section in FIG. 9B. Single crystal silicon may be used as the structural layer for both proof mass 1 and proof mass 2, and no bottom and top metal electrodes are considered in the FE model to reduce complexity. The structure is aligned to <110> crystal axis of the single crystal silicon for silicon wafer along (100) direction. FIG. 13B shows a top view schematic of the finite element (FE) model according to various embodiments. The width and length conventions for torsional and linear springs are illustrated in FIG. 1 B. The fixed boundary conditions are applied along the exterior boundary of each anchor as shown in FIG. 13B. FIG. 13C shows a perspective bottom view schematic of the finite element (FE) model according to various embodiments. The pair of lower proof mass portions (proof mass 2) is attached to frame-3 as shown in FIG. 13C. Table 1 lists all the designed parameters for the FE model described in FIGS. 13A - C.

[0066] Table 1: Designed parameters for the FE model

[0067] First, eigenfrequency analysis in COMSOL to obtain the vibration mode shapes and corresponding resonant frequencies ( „) related to the vibration mode shapes. FIG 14 shows the first four vibration mode shapes with respective resonant frequencies, where (a) the first vibration mode shape is used to detect x-axis acceleration, (b) the second vibration mode shape is used to detect y-axis acceleration, (c) the third vibration mode shape is used to detect z-axisacceleration, and (d) the fourth vibration mode shape is an unwanted mode shape according to various embodiments.

[0068] The fourth vibration mode shape in FIG. 14(d) is an unwanted vibration mode, and it is intended to increase the resonant frequency of this vibration mode. In the FE model, the resonant frequency of this unwanted vibration mode in FIG. 14(d) is ~3 times higher than the resonant frequency of the intended third vibration mode in FIG 14(c).

[0069] Next, the acceleration sensitivities ( ) are simulated using stationary study in COMSOL. Acceleration sensitivity for a particular axis is simulated by applying gravity or acceleration (a) along that specific axis and the displacement (x) due to the applied acceleration (a) is derived from the contact structure for that particular detection axis. The vertical contact structures for respective axis of detection are illustrated in FIG. 13 A FIG. 15 A shows a plot of displacement (in nanometers or nm) as a function of acceleration along x axis (in g, free-fall acceleration under gravity) illustrating acceleration sensitivity (Sx) of the x-axis acceleration detection vertical contact structures according to various embodiments. FIG. 15B shows a plot of displacement (in nanometers or nm) as a function of acceleration along y axis (in g, free-fall acceleration under gravity) illustrating acceleration sensitivity (5y of the y-axis acceleration detection vertical contact structures according to various embodiments. FIG. 15C shows a plot of displacement (in nanometers or nm) as a function of acceleration along z axis (in g, free-fall acceleration under gravity) illustrating acceleration sensitivity Sz) of the z-axis acceleration detection vertical contact structures according to various embodiments. FIGS. 15A - C show the sensitivity for respective detection axis. The respective threshold accelerations atx,, atzmay be determined from Equations 6 - 8.

[0070] Table 2 summarizes the simulated output parameters of the designed 3 -axis MEMS inertial switch.

[0071] Table 2: FE simulated output of the designed 3-axis MEMS inertial switch

[0072] Values of contact gaps for the respective detection axis may be chosen to design a 3- axis MEMS inertial switch such that the switch exhibits similar levels of acceleration thresholds for all 3 detection axes. To obtain cross-axis sensitivity under an acceleration along a specific axis, first the displacements are obtained from the contact structures for the other two axes; for which axes the accelerations have not been applied. For example, to obtain cross-axis sensitivity of contact structure for y-axis detection (Sw) under x-axis acceleration, a varying acceleration is applied along x-axis, and out-of-plane displacements are recorded around contact structure for y-axis detection. The slope of the graph may thus provide Syx. Given that the contact gaps are tunable, cross-axis acceleration threshold may be defined as a normalized term to compare the cross-axis sensitivities for all 3 axes. Cross-axis acceleration in Table 2 may be defined as the ratio of the contact gap for a particular axis to the cross-axis sensitivity for that particular axis. For example, cross-axis threshold for contact structure for y-axis detection (atyx) under x- axis acceleration is defined by the ratio of contact gap 2 ( to true cross-axis sensitivity for y- axis detection contact structure (Syx) under x-axis acceleration:%Cross-axis sensitivity in Table 2 may be defined as the ratio of cross-axis acceleration sensitivity to the true acceleration sensitivity for a specific axis (along which the acceleration is applied). For example, under x-axis acceleration, given that the cross-axis acceleration sensitivity of contact structure for y-axis detection is Syx, and true acceleration sensitivity for contact structure for x-axis detection is Sx, then the %cross-axis sensitivity (° / oSyx) can be defined as:

[0073] Reducing the thickness ratio (t2 / ti ) of proof mass 2 to proof mass 1 by 50% (reducing h from 720pm to 360pm while keeping t\ = 30pm), acceleration threshold for x-axis detectionincreases by -74%, acceleration threshold for y-axis detection (a^) increases by -74%, and acceleration threshold for z-axis detection (ate) increases by -14.4%. This increase in acceleration thresholds is due to -12.7% reduction in the overall mass (My+ M2) of the structure. Reducing the length to width ratio (Lx / Wx) for torsional tethers for x-axis detection by 50% (increasing Wxfrom 5pm to 10pm, while keeping Lx= 50pm) increases resonant frequency (fn) corresponding to the mode shape in FIG. 14(a) by -57.8% and increases acceleration threshold for x-axis detection (citx) by -82.2%, primarily due to -82.2% increase in spring constant for the torsional springs (kx). The acceleration thresholds for the contact structures for the other two axes (y and z) remain at similar levels. Reducing the length to width ratio (Ly / Wy) for torsional tethers for y-axis detection by 50% (increasing Wyfrom 5pm to 10pm, while keeping Ly= 50pm) increases resonant frequency (fn) corresponding to the mode shape in FIG. 14(b) by -57.7% and increases acceleration threshold for y-axis sensing (city) by -82.2% primarily due to -82.2% increase in spring constant for the torsional springs (ky). The acceleration thresholds for the contact structures for the other two axes (x and z) remain at similar levels. Reducing the length to width ratio (Lz / Wz) for torsional tethers for y-axis detection by 50% (increasing Wzfrom 10pm to 20pm, while keeping Lz= 200pm) does not show any significant increase of resonant frequency (fn) corresponding to the mode shape in FIG. 14(c) as well as acceleration threshold for z-axis detection (atz) primarily due to no significant change in spring constant for the linear springs (kz). The acceleration thresholds for the contact structures for the other two axes (x and y) also remain at similar levels.

[0074] Vertical contact structure characteristics

[0075] As mentioned above, the electrodes of the vertical contact structures according to various embodiments may have indents to reduce adhesion, thereby increasing contactreliability for multiple cycles. The vertical contact gap may be tuned to sub-micron range with contact area of the order 6.25 pm2(~16x smaller than typical lateral contact area). FIG. 16A is a scanning electron microscopy (SEM) image showing a top planar view of a portion of the microelectromechanical systems (MEMS) inertial switch with a vertical contact structure including a stationary top electrode and a movable bottom electrode according to various embodiments FIG. 16B is a scanning electron microscopy (SEM) image showing a cross- sectional side view of a vertical contact structure with the stationary top electrode having a metal indent. FIG. 16C shows a plot of switch output (in volts or V) as a function of time (in milli-second or ms) showing the switching characteristics of the vertical contact structure including a stationary top electrode having a metal indent according to various embodiments. FIG. 16D shows a plot of maximum output at each cycle (in volts or V) as a function of the number of cycles illustrating a 10% reduction in switch output of the vertical contact structure (including a stationary top electrode having a metal indent) according to various embodiments at the 100th cycle as compared to the 1st cycle. The results as shown in FIGS. 16C-D are based on a MEMS inertial switch operated in ambient condition without packaging. The contact reliability may be further improved by using packaging to package the MEMS inertial switch to introduce a vacuum inside the package.

[0076] In various embodiments, with vertical contact structures, the contact gap may be reduced by more than 7x as compared to > 10 pm contact gaps for conventional sidewall contacts. The acceleration threshold for in-plane axis (i.e., x- or y-axis) can be reduced by more than 4.5x as compared to > 40g acceleration threshold for conventional sidewall contacts.

Claims

Claims1. A microelectromechanical systems (MEMS) inertial switch comprising: a proof mass comprising an upper portion and one or more lower portions; a z-axis movable electrode at a center portion of the proof mass; a corresponding z-axis stationary electrode such that the z-axis movable electrode is configured to contact with the corresponding z-axis stationary electrode for detecting out-of-plane acceleration; a plurality of in-plane movable electrodes at edge portions of the proof mass; and a corresponding plurality of in-plane stationary electrodes such that each of the plurality of in-plane movable electrodes is configured to contact with a corresponding in-plane stationary electrode for detecting in-plane acceleration, wherein a contact gap between the z-axis movable electrode and the corresponding z-axis stationary electrode is less than a contact gap between each of the plurality of in-plane movable electrodes and the corresponding in-plane stationary electrode.

2. The microelectromechanical systems (MEMS) inertial switch according to claim 1, wherein each of the one or more lower portions of the proof mass has a thickness greater than a thickness of the upper portion of the proof mass, and wherein a surface area of a main surface of each of the one or more lower portions of the proof mass is smaller than a surface area of a main surface of the upper portion.

3. The microelectromechanical systems (MEMS) inertial switch according to claim 1, wherein in-plane acceleration is detected via torsional motion of the proof mass.

4. The microelectromechanical systems (MEMS) inertial switch according to claim 3, wherein the proof mass comprises a pair of torsional springs along an axis in y- direction passing through the center portion of the proof mass, the pair of torsional springs configured to allow torsional motion of the proof mass in response to acceleration along an axis in x-direction.

5. The microelectromechanical systems (MEMS) inertial switch according to claim 3, wherein the proof mass comprises a pair of torsional springs along an axis in x- direction passing through the center portion of the proof mass, the pair of torsional springs configured to allow torsional motion of the proof mass in response to acceleration along an axis in y-direction.

6. The microelectromechanical systems (MEMS) inertial switch according to claim 1, wherein out-of-plane acceleration is detected via linear motion of the proof mass.

7. The microelectromechanical systems (MEMS) inertial switch according to claim 1, wherein the proof mass comprises one or more linear springs configured to increase a resonant frequency of unintended vibration in form of in-plane motions.

8. The microelectromechanical systems (MEMS) inertial switch according to claim 1, wherein the corresponding z-axis stationary electrode has an indented surface facing the proof mass and the corresponding z-axis moveable electrode; andwherein each of the corresponding plurality of in-plane stationary electrodes has an indented surface facing the proof mass and the corresponding in-plane moveable electrode.

9. The microelectromechanical systems (MEMS) inertial switch according to claim 1, wherein the z-axis movable electrode has an indented surface facing the corresponding z-axis stationary electrode; and wherein each of the plurality of in-plane movable electrodes has an indented surface facing the corresponding in-plane stationary electrode.

10. The microelectromechanical systems (MEMS) inertial switch according to claim 1, wherein the plurality of in-plane movable electrodes comprises: a first in-plane movable electrode at a first edge portion of the proof mass and along an axis in the x-direction passing through the center portion of the proof mass; a second in-plane movable electrode at a second edge portion of the proof mass opposite to the first edge portion relative to the center portion of the proof mass and along the axis in the x-direction passing through the center portion of the proof mass; a third in-plane movable electrode at a third edge portion of the proof mass and along an axis in the y-direction passing through the center portion of the proof mass, and a fourth in-plane movable electrode at a fourth edge portion of the proof mass opposite to the third edge portion relative to the center portion of the proof mass and along the axis in the y-direction passing through the center portion of the proof mass;wherein the first in-plane movable electrode, a corresponding first inplane stationary electrode, the second in-plane movable electrode and a corresponding second in-plane stationary electrode are configured to determine acceleration along an axis in x-direction; and wherein the third in-plane movable electrode, a corresponding third inplane stationary electrode, the fourth in-plane movable electrode and a corresponding fourth in-plane stationary electrode are configured to determine acceleration along an axis in y-direction.

11. A method of forming a microelectromechanical systems (MEMS) inertial switch, the method comprising: forming a proof mass comprising an upper portion and one or more lower portions; forming a z-axis movable electrode at a center portion of the proof mass; forming a corresponding z-axis stationary electrode such that the z-axis movable electrode is configured to contact with the corresponding z-axis stationary electrode for detecting out-of-plane acceleration; forming a plurality of in-plane movable electrodes at edge portions of the proof mass; and forming a corresponding plurality of in-plane stationary electrodes such that each of the plurality of in-plane movable electrodes is configured to contact with a corresponding in-plane stationary electrode for detecting in-plane acceleration; wherein a contact gap between the z-axis movable electrode and the corresponding z-axis stationary electrode is less than a contact gapbetween each of the plurality of in-plane movable electrodes and the corresponding in-plane stationary electrode.

12. The method according to claim 11, wherein each of the one or more lower portions of the proof mass has a thickness greater than a thickness of the upper portion of the proof mass; and wherein a surface area of a main surface of each of the one or more lower portions of the proof mass is smaller than a surface area of a main surface of the upper portion.

13. The method according to claim 11, wherein in-plane acceleration is detected via torsional motion of the proof mass.

14. The method according to claim 13, wherein the proof mass comprises a pair of torsional springs along an axis in y- direction passing through the center portion of the proof mass, the pair of torsional springs configured to allow torsional motion of the proof mass in response to acceleration along an axis in x-direction.

15. The method according to claim 13, wherein the proof mass comprises a pair of torsional springs along an axis in x- direction passing through the center portion of the proof mass, the pair of torsional springs configured to allow torsional motion of the proof mass in response to acceleration along an axis in y-direction.

16. The method according to claim 1 1, wherein out-of-plane acceleration is detected via linear motion of the proof mass.

17. The method according to claim 11, wherein the proof mass comprises one or more linear springs configured to increase a resonant frequency of unintended vibration in form of in-plane motions.

18. The method according to claim 11, wherein the corresponding z-axis stationary electrode has an indented surface facing the proof mass and the corresponding z-axis moveable electrode; and wherein each of the corresponding plurality of in-plane stationary electrodes has an indented surface facing the proof mass and the corresponding in-plane moveable electrode.

19. The method according to claim 11, wherein the z-axis movable electrode has an indented surface facing the corresponding z-axis stationary electrode; and wherein each of the plurality of in-plane movable electrodes has an indented surface facing the corresponding in-plane stationary electrode.

20. The method according to claim 11, wherein the plurality of in-plane movable electrodes comprises:a first in-plane movable electrode at a first edge portion of the proof mass and along an axis in the x-direction passing through the center portion of the proof mass; a second in-plane movable electrode at a second edge portion of the proof mass opposite to the first edge portion relative to the center portion of the proof mass and along the axis in the x-direction passing through the center portion of the proof mass; a third in-plane movable electrode at a third edge portion of the proof mass and along an axis in the y-direction passing through the center portion of the proof mass, and a fourth in-plane movable electrode at a fourth edge portion of the proof mass opposite to the third edge portion relative to the center portion of the proof mass and along the axis in the y-direction passing through the center portion of the proof mass; wherein the first in-plane movable electrode, a corresponding first inplane stationary electrode, the second in-plane movable electrode and a corresponding second in-plane stationary electrode are configured to determine acceleration along an axis in x-direction; and wherein the third in-plane movable electrode, a corresponding third inplane stationary electrode, the fourth in-plane movable electrode and a corresponding fourth in-plane stationary electrode are configured to determine acceleration along an axis in y-direction.

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