A method for calculating the squeeze film damping of a MEMS device with microbumps

Abstract

The present application relates to a kind of microprojection structure MEMS device containing film damping calculation method, the method is: the center projection surface film damping force of the center position of MEMS device is subtracted from the film damping force of the same position without containing projection structure, the increment of the overall film damping caused by center projection to MEMS device is obtained, the increment of the film damping increment generated by each projection structure is approximately expressed, and it is multiplied by the total number of projection contained in MEMS device to obtain the total film damping increment generated by all projection structures, the film damping of MEMS device without any projection structure is added to total film damping increment to obtain the total film damping value of microprojection structure MEMS device;The calculation method is simple and efficient, can accurately calculate the film damping of microprojection structure MEMS device while guaranteeing the calculation efficiency, accurately predict the dynamic performance of such MEMS structure, greatly save the calculation time and design cost.

Description

Technical Field

[0001] This invention relates to the field of microelectromechanical systems (MEMS) technology, and in particular to a method for calculating the pressure film damping of MEMS devices with micro-bump structures. Background Technology

[0002] Micro-Electro-Mechanical Systems (MEMS), also known as micro-electromechanical systems or microsystems, are micro-integrated devices or systems with millimeter-scale dimensions and micrometer-scale resolution, formed by the integration of micromechanical technology and integrated circuit technology. MEMS continuously explores new principles and functions of components and systems through miniaturization and integration, opening up a new technological field and industry. The advantage of MEMS lies in its ability to perform tasks that large-scale electromechanical systems cannot, and its ability to be embedded in large-scale systems to improve the automation, intelligence, and reliability of the entire system. In the 21st century, MEMS will gradually move from the laboratory to practical applications, having a significant impact on fields such as industry, agriculture, information technology, environment, bioengineering, medicine, space technology, and national defense.

[0003] Damping has a significant impact on the dynamic performance of MEMS devices, such as the bandwidth and frequency response of MEMS accelerometers, the sensitivity of MEMS resonant cavities, and the response time of MEMS switches and damping shock absorbers. Many MEMS devices rely on the vibration or relative motion of certain core components within them for operation, such as MEMS accelerometers, MEMS resonators, MEMS gyroscopes, MEMS pressure sensors, and MEMS microphones. When these MEMS devices are in a non-vacuum environment, the compression and suction effects of the internal fluid medium within the vibrating device generate pressure-damping forces.

[0004] Existing research has found that when the system size is reduced to a certain scale, many physical phenomena will differ significantly from those in the macroscopic world. In the micro-scale domain where MEMS devices are located, the pressure film damping caused by the vibration of MEMS devices will surpass thermoelastic damping, surface loss, and support damping to become the main dissipation form of MEMS devices.

[0005] As the functions of MEMS devices continue to expand, the structures of MEMS devices also become more diverse. Various array bump structures have been introduced into MEMS devices to improve their penetration, sensitivity, or absorption performance, such as medical probes, MEMS data acquisition devices, and capacitive sensors. Therefore, microarray bump structures have become a typical structure in MEMS devices.

[0006] The reason why there is currently no method for calculating the pressure film damping of MEMS devices with micro-bump structures is that the protrusions in MEMS devices affect airflow, increase the complexity and uncertainty of airflow, and make it impossible for traditional theoretical models to accurately calculate the internal fluid behavior of MEMS devices.

[0007] Based on the above analysis, a method for calculating the pressure damping force of MEMS devices with micro-bump structures is developed, which plays an important role in the prediction and analysis of the dynamic performance of MEMS devices, structural optimization, and performance improvement. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method for calculating the pressure damping force of MEMS devices with micro-bump structures. This method makes up for the inability of the prior art to accurately predict the influence of the protrusion structure on the damping of MEMS devices. Under the premise of ensuring calculation efficiency, it realizes the accurate calculation of the pressure damping of MEMS devices with micro-bump structures.

[0009] The technical solution adopted in this invention is a method for calculating the pressure film damping of a MEMS device with a micro-bump structure. The MEMS device includes two parallel plates that can move relative to each other in the vertical direction. One of the two parallel plates is a fixed plate, and the other is a movable plate. The inner surface of the fixed plate or the inner surface of the movable plate is provided with an array of protrusions. The array of protrusions includes a central protrusion located at the center of the inner surface of the fixed plate or the inner surface of the movable plate. The method includes the following steps:

[0010] S1. When two parallel flat plates move relative to each other in the vertical direction, calculate the surface pressure F exerted on the central protrusion. a ;

[0011] S2. When neither the inner surface of the fixed plate nor the inner surface of the movable plate contains any protrusions, and the two parallel plates move relative to each other in the vertical direction, calculate the surface pressure F exerted on the area occupied by the original central protrusion. b ;

[0012] S3, Apply the surface pressure F obtained in step S1 a The surface pressure F obtained in step S2 b Subtracting the two values ​​yields the incremental pressure damping force ΔF generated by the central protrusion on the overall MEMS device; this incremental pressure damping force ΔF is used to approximately represent the incremental pressure damping force generated by each of the other protruding structures.

[0013] S4. Multiply the pressure film damping force increment ΔF obtained in step S3 by the total number N of protrusions in the MEMS device to obtain the total pressure film damping increment ΔF generated by all protrusions. n ;

[0014] S5. Calculate the pressure damping force F of the MEMS device without any protrusions. p ;

[0015] S6: Calculate the total pressure film damping increment ΔF obtained in step S4. n The pressure damping force F calculated in step S5 p Adding them together, we obtain the pressure damping force F of the MEMS device containing any number of protrusions. d The damping force F of the pressure membrane d Dividing by the relative velocity v of the two plates yields the pressure damping coefficient C of the MEMS device with micro-bumps. d .

[0016] The beneficial effects of this invention are as follows: The above-mentioned method for calculating the pressure damping of MEMS devices with micro-bump structures has high calculation accuracy, and the calculation error can be controlled within 10% in most cases. Furthermore, the calculation method of this invention is relatively simple, and it can achieve accurate calculation of the pressure damping of MEMS devices with micro-bump structures while ensuring computational efficiency. This invention simplifies the complexity of the target problem, obtains a large dataset of different bump structure parameters and their corresponding pressure damping values ​​through numerical calculation methods, constructs the relationship between bump structure parameters and the number of bumps and pressure damping, and expands and supplements upon traditional theory. While solving technical problems, this invention possesses a certain degree of reliability and scientific validity. It fills the gap in the calculation method for pressure film damping of MEMS devices with micro-bump structures, providing an effective means for damping evaluation of such devices. The overall technical solution of this invention forms a relatively complete analytical method, which can provide solutions for other technical problems with certain similarities to those addressed by this invention. In its design process, this invention considers many extreme cases that MEMS devices may encounter, making its calculation method applicable to the damping evaluation needs of most MEMS devices with micro-bump structures, thus ensuring the universality of the calculation method.

[0017] Preferably, in step S5, the pressure damping force F of the MEMS device without any protrusions is... p The expression is: Where μ represents the airflow viscosity coefficient, L represents the length of the plate, ω represents the width of the plate, and h represents the initial distance between the moving plate and the motion plate.

[0018] Preferably, the type of the protrusion structure is any one of cone, frustum, or column; the protrusion structures distributed in the same array are of the same type; by adopting this structure, the calculation method of the present invention can be applied to the damping evaluation needs of most MEMS devices with micro-protrusion structures, thus ensuring the universality of the calculation method.

[0019] In step S1, the surface pressure F experienced by the calculation center protrusion a The specific process includes the following steps:

[0020] S11: Calculate the surface pressure F on the central protrusion when the inner surface of the fixed plate or the inner surface of the movable plate contains only the central protrusion. sa ;

[0021] S12: When the inner surface of a fixed plate or the inner surface of a movable plate contains an array of protrusions, the surface pressure F of the central protrusion is defined. a Divide by the surface pressure F obtained in step S11, which only contains the pressure exerted on the central protrusion. sa For the normalized center convex surface pressure

[0022] S13: When calculating the total projected area S of the array of protrusions on the inner surface of a fixed plate or a movable plate, where the inner surface contains an array of protrusions. n Calculate the inner surface area S of the flat plate containing the array of protrusions. p The total projected area S n Divide by the inner surface area S p The normalized projected area of ​​the array of protrusions on the plane is obtained.

[0023] S14: Create normalized center convex surface pressure Normalized projected area of ​​the array protrusion structure on the plane The linear expression is used to calculate the surface pressure F on the central protrusion. a The linear expression is: The slope of the linear relationship can be determined by both the convex structure parameters and the flat plate structure parameters, as shown in the following expression: in, The ratio of the protrusion height H to the initial spacing h of the flat plate; This is the ratio of the equivalent upper base radius r1 to the equivalent lower base radius r2; It is the ratio of the convex height H to the equivalent lower base radius r2.

[0024] Preferably, in step S11, when the central protrusion is a cone, the surface pressure F on the central protrusion is... saThe calculation method is as follows: The surface pressure of a single cone is divided into two parts: the surface pressure in the region of rapid pressure change and the surface pressure in the region of stable pressure. The region below two-thirds of the cone height is defined as the stable pressure region, and the average surface pressure in this part is determined by the pressure p at the bottom of the cone. u An approximation is that the surface pressure in the pressure stabilization region is equal to the pressure p at the bottom of the cone. u The product of the pressure stability region and the projected area on the plane containing the pressure stability region; the region above two-thirds of the cone height is defined as the region of rapid pressure change, where the change can be approximated as linear. Let the pressure at the cone apex be p. ct The pressure at two-thirds of the height of the cone is approximately equal to the pressure p at the base of the cone. u , Adding the pressure in the region of rapid pressure change to the pressure in the region of stable pressure yields the surface pressure F of the cone-shaped structure containing a single cone plane. sa F sa expression:

[0025]

[0026] Preferably, in step S11, when the central protrusion is a platform, the surface pressure F on the central protrusion is... sa equal to the pressure p at the center of the upper bottom surface of the platform. tt The product of the area of ​​the upper base and the pressure p at the bottom edge of the platform u The product of the area of ​​the tectonic platform's side surface projected onto the plane; its expression is: Where r1 represents the equivalent radius of the upper bottom surface of the platform, and r2 represents the equivalent radius of the lower bottom surface of the platform;

[0027]

[0028] Preferably, in step S11, when the central protrusion is a column, the surface pressure F on the central protrusion is... sa equal to the pressure p at the center of the top base of the column bt The product of the area of ​​the prism's top base and the area of ​​its upper base; its expression is: Where r2 represents the equivalent radius of the cylinder. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a MEMS device with a micro-bump structure according to the present invention;

[0030] Figure 2 This is a schematic diagram of the array of protrusions on the fixed plate in this invention;

[0031] Figure 3This is a schematic diagram of the structure of the fixed plate after reducing the number of frustums by uniformly surrounding the central frustum in this invention;

[0032] Figure 4 A comparison chart showing the pressure film damping coefficient of MEMS devices with different numbers of frustum microstructures calculated using the calculation method of the present invention and the calculation results calculated using Fluent numerical simulation software.

[0033] As shown in the figure: 1. Moving plate; 2. Fixed plate; 3. Raised structure; 4. Air film between the two inner surfaces; 5. Movable plate at the maximum displacement; 6. Central frustum; 7. The upper surface of the frustum is equivalent to a circle with the same area; 8. The lower surface of the frustum is equivalent to a circle with the same area. Detailed Implementation

[0034] The invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can implement it based on the description. The scope of protection of the invention is not limited to these specific embodiments.

[0035] Those skilled in the art should understand that, in the disclosure of this invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0036] Furthermore, the terms "first," "second," and "third" are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0037] In the description of the embodiments of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0038] This invention provides a method for calculating the pressure damping of a MEMS device with a micro-bump structure. The MEMS device includes two parallel plates that are capable of relative movement in the vertical direction. One of the parallel plates is a fixed plate, and the other is a movable plate. The inner surface of either the fixed or movable plate is provided with an array of protrusions, including a central protrusion located at the center of the inner surface of either the fixed or movable plate. The method includes the following steps:

[0039] S1. When two parallel flat plates move relative to each other in the vertical direction, calculate the surface pressure F exerted on the central protrusion. a ;

[0040] S2. When neither the inner surface of the fixed plate nor the inner surface of the movable plate contains any protrusions, and the two parallel plates move relative to each other in the vertical direction, calculate the surface pressure F exerted on the area occupied by the original central protrusion. b ;

[0041] S3, Apply the surface pressure F obtained in step S1 a The surface pressure F obtained in step S2 b Subtracting the two values ​​yields the incremental pressure damping force ΔF generated by the central protrusion on the overall MEMS device; this incremental pressure damping force ΔF is used to approximately represent the incremental pressure damping force generated by each of the other protruding structures.

[0042] S4. Multiply the pressure film damping force increment ΔF obtained in step S3 by the total number N of protrusions in the MEMS device to obtain the total pressure film damping increment ΔF generated by all protrusions. n ;

[0043] S5. Calculate the pressure damping force F of the MEMS device without any protrusions. p ;

[0044] S6: Calculate the total pressure film damping increment ΔF obtained in step S4. n The pressure damping force F calculated in step S5 p Adding them together, we obtain the pressure damping force F of the MEMS device containing any number of protrusions. d The damping force F of the pressure membrane d Dividing by the relative velocity v of the two plates yields the pressure damping coefficient C of the MEMS device with micro-bumps. d .

[0045] The beneficial effects of this invention are as follows: The above-mentioned method for calculating the pressure damping of MEMS devices with micro-bump structures has high calculation accuracy, and the calculation error can be controlled within 10% in most cases. Furthermore, the calculation method of this invention is relatively simple, and it can achieve accurate calculation of the pressure damping of MEMS devices with micro-bump structures while ensuring computational efficiency. This invention simplifies the complexity of the target problem, obtains a large dataset of different bump structure parameters and their corresponding pressure damping values ​​through numerical calculation methods, constructs the relationship between bump structure parameters and the number of bumps and pressure damping, and expands and supplements upon traditional theory. While solving technical problems, this invention possesses a certain degree of reliability and scientific validity. It fills the gap in the calculation method for pressure film damping of MEMS devices with micro-bump structures, providing an effective means for damping evaluation of such devices. The overall technical solution of this invention forms a relatively complete analytical method, which can provide solutions for other technical problems with certain similarities to those addressed by this invention. In its design process, this invention considers many extreme cases that MEMS devices may encounter, making its calculation method applicable to the damping evaluation needs of most MEMS devices with micro-bump structures, thus ensuring the universality of the calculation method.

[0046] Furthermore, the type of the protrusion structure can be any one of a cone, a frustum, or a cylinder; protrusion structures distributed in the same array are of the same type, and the protrusion structure parameters of protrusion structures distributed in the same array are consistent; by adopting this structure, the calculation method of the present invention can be applied to the damping evaluation needs of most MEMS devices with micro-protrusion structures, ensuring the universality of the calculation method.

[0047] Further, in step S1, the surface pressure F experienced by the calculation center protrusion... a The specific process includes the following steps:

[0048] S11: Calculate the surface pressure F on the central protrusion when the inner surface of the fixed plate or the inner surface of the movable plate contains only the central protrusion. sa ;

[0049] S12: When the inner surface of a fixed plate or the inner surface of a movable plate contains an array of protrusions, the surface pressure F of the central protrusion is defined. a Divide by the surface pressure F on the central protrusion obtained in step S11 sa For the normalized center convex surface pressure

[0050] S13: When calculating the total projected area S of the array of protrusions on the inner surface of a fixed plate or a movable plate, where the inner surface contains an array of protrusions. n The total projected area Sn This refers to the sum of the projected areas of all the protruding structures; the projected area of ​​a single central protrusion is the area of ​​its lower base. Calculate the inner surface area S of a flat plate containing an array of protruding structures. p The total projected area S n Divide by the inner surface area S p The normalized projected area of ​​the array of protrusions on the plane is obtained. The projected area of ​​a single central protrusion on the plane is defined as S1. The projected area S1 of a single central protrusion is divided by the total area of ​​the plane, S... p The normalized projected area of ​​a single central protrusion on the plane is obtained. When the inner surface of a fixed plate or the inner surface of a movable plate contains only a central protrusion, the normalized projected area...

[0051] S14: Normalized central convex surface pressure Normalized projected area of ​​the array protrusion structure on the plane There is a linear relationship, and the slope k of this linear relationship is determined by the parameters of the convex structure: when the convex structure is a cone, the slope k is determined by the radius (or side length) of the cone's base and the height of the cone; when the convex structure is a frustum, the slope k is determined by the radius (or side length) of the upper base (or side length) of the frustum, the radius (or side length) of the lower base (or side length) of the frustum, and the height of the frustum; when the convex structure is a cylinder, the slope k is determined by the radius (or side length) of the cylinder's base and the height of the cylinder; normalized central convex surface pressure is then established. Normalized projected area of ​​the array protrusion structure on the plane The linear expression is used to calculate the surface pressure F on the central protrusion. a The linear expression is: The slope of the linear relationship can be determined by both the convex structure parameters and the flat plate structure parameters, as shown in the following expression:

[0052] in, The ratio of the protrusion height H to the initial spacing h of the flat plate; The ratio of the equivalent upper base radius r1 to the equivalent lower base radius r2 of the convex structure; It is the ratio of the convex height H to the equivalent lower base radius r2.

[0053] Furthermore, when a MEMS device contains only one protrusion structure, equal Since the value is equal to 1, an expression for the linear relationship can be derived. This linear expression allows us to calculate the surface pressure F of the central protrusion on a plane containing an array of protrusions. a .

[0054] Furthermore, in step S11, when the central protrusion is a cone, the surface pressure F on the central protrusion... sa The calculation method is as follows: The surface pressure of a single cone is divided into two parts: the surface pressure in the region of rapid pressure change and the surface pressure in the region of stable pressure. The region below two-thirds of the cone height is defined as the stable pressure region, and the average surface pressure in this part is determined by the pressure p at the bottom of the cone. u An approximation is that the surface pressure in the pressure stabilization region is equal to the pressure p at the bottom of the cone. u The product of the area projected onto the plane where the pressure stability region lies; the region located above two-thirds of the cone's height is defined as the region of rapid pressure change, and the pressure at the cone's apex is p. ct The pressure at two-thirds of the height of the cone is approximately equal to the pressure p at the base of the cone. u , Adding the pressure in the region of rapid pressure change to the pressure in the region of stable pressure yields the surface pressure F of the cone-shaped structure containing a single cone plane. sa F sa The expression is:

[0055] Furthermore, in step S11, when the central protrusion is a platform, the average pressure on the bottom surface of the platform is equal to the pressure p at the center of the bottom surface of the platform. tt Approximate representation: The average pressure on the side of the platform is derived from the pressure p at the bottom edge of the platform. u Approximate representation; the surface pressure F on the central protrusion sa equal to the pressure p at the center of the upper bottom surface of the platform. tt The product of the area of ​​the upper base and the pressure p at the bottom edge of the platform u The product of the surface area of ​​the platform and its projected area on the plane.

[0056] Furthermore, in step S11, when the central protrusion is a column, the average pressure on the top surface of the column is equal to the pressure p at the center of the top surface of the column. ct Approximate representation; the surface pressure F on the central protrusion sa equal to the pressure p at the center of the top base of the column ct The product of the area of ​​the top surface of the column and the area of ​​the top surface of the column.

[0057] When the protrusion is a pyramid, frustum, or prism with a base side length of l, the protruding structure can be approximated as a cone, frustum, or cylinder with the same base area and a base radius of r.

[0058] Pressure p at the apex of the cone ct The pressure p at the center of the upper bottom surface of the platform tt And the central pressure p on the top surface of the columnbt All can be calculated using a unified expression, which is:

[0059] in, The ratio of the protrusion height H to the initial spacing h of the flat plate; The ratio of the equivalent upper base radius r1 to the long side L of the plate; when At this time, p = p ct ; At this time, p = p tt or p = p bt .

[0060] Example 1:

[0061] like Figure 1 As shown, the present invention provides a MEMS device with a micro-bump structure. The MEMS device includes two parallel plates that can move relative to each other in the vertical direction. One of the two parallel plates is a square fixed plate 2 and the other is a square movable plate 1. The inner surface of the fixed plate is provided with an array of protrusion structures 3. The type of protrusion structure is a frustum. The array of protrusion structures 3 includes a central protrusion located on the inner surface of the fixed plate or the inner surface of the movable plate.

[0062] When vertical vibration occurs, when the movable plate 1 is displaced to the maximum displacement point (i.e., the movable plate 5 at the maximum displacement point), the fluid medium between the two inner surfaces flows outward and inward along the air film 4 between the two inner surfaces due to the compression and suction effects. At this time, the inner surface of the fixed plate 2 and the frustum will be subjected to the force of the fluid medium in the vertical direction. This force is the pressure film damping force F. d .

[0063] In this invention, the frustum structures are arranged in an array on a fixed plate, as shown below. Figure 2 As shown, the central frustum 6 is located at the center of the fixed plate 2; when the number of frustums needs to be changed, the number of frustums should be increased or decreased around the central frustum, such as... Figure 3 As shown.

[0064] The specific process of calculating the pressure damping of a MEMS device with a micro-bump structure is described below:

[0065] The movable plate 1 moves at a speed of v, the fixed plate 2 has a side length of L, the air film thickness between the two planes is h, the viscosity coefficient of the fluid medium in the air film is μ, the side length of the top surface of the truncated pyramid is l1, the side length of the bottom surface of the truncated pyramid is l2, the height of the truncated pyramid is H, and the number of truncated pyramids is n.

[0066] like Figure 2The bottom face of the frustum is equivalent to a circle of the same area (7), and the bottom face of the frustum is equivalent to a circle of the same area (8). The radius of the equivalent top face is... Equivalent lower base radius The radius of the top base and the height of the frustum are normalized. The normalized radius of the top base is: The normalized height of the frustum is

[0067] When the fixed plate 2 contains a single frustum, the calculation method for the pressure damping force on the frustum is as follows:

[0068] When the number of frustums is 1, the pressure damping force F on a single frustum portion is... sa The pressure p at the center of the bottom surface of the frustum tt With the base area S of the frustum 11 The product of the product and the pressure p at the bottom edge of the frustum u The projected area S of the lateral surface of the frustum on the flat plate 12 The product of F is obtained; sa It has the following expression:

[0069] F sa =p tt S 11 +p u S 12

[0070] Pressure p at the center of the bottom surface of the frustum tt It can be obtained from the following expression:

[0071]

[0072] Where p0 is the pressure value at the center of the plate under the pressure film damping effect when there are no protrusions:

[0073]

[0074] The pressure pu at the bottom edge of the frustum can be obtained by the following expression:

[0075]

[0076] When there are n frustums, the damping force on the central frustum is calculated as follows:

[0077] When the number of frustums is n, the pressure damping force F on the frustum located at the center is... a It can be obtained from the following expression:

[0078]

[0079] in, This is the ratio of the equivalent upper base radius r1 to the equivalent lower base radius r2. S1 is the ratio of the height H of the frustum to the equivalent lower base radius r2; Sn is the sum of the lower base areas of the n frustums, and S1 is the lower base area of ​​a single frustum.

[0080] When there are n frustums, the pressure damping increment ΔF generated by the central frustum is... n The calculation method is as follows:

[0081] When the plate does not contain any protrusions, due to the pressure film damping effect, the pressure film damping force on the square region with a side length of l2 at the center of the plate (the region where the original central frustum is located) can be obtained by the following formula:

[0082]

[0083] For a flat plate containing n frustums, the pressure damping increment ΔF generated by the central single frustum is... n It can be obtained from the following formula:

[0084] ΔF n =F a -F b

[0085] The total pressure film damping coefficient of a plate containing n frustums is calculated as follows:

[0086] When the flat plate does not contain any protrusions, the planar pressure damping force F p It can be obtained from the following formula:

[0087]

[0088] ΔF n Approximating the average increase in membrane damping generated by each frustum, the membrane damping force Fd on a plate containing n frustums can be obtained by the following formula:

[0089] Fd=Fp+nΔFn

[0090] Dividing Fd by the velocity v of the moving plate yields the total pressure film damping coefficient of the plate containing n frustums.

[0091] Figure 4 This is a comparison chart between the pressure film damping coefficient of MEMS devices with different numbers of frustum microstructures calculated using the calculation method of this invention, and the calculation results using Fluent numerical simulation software, when specific parameter values ​​are assigned to this embodiment. The specific parameter values ​​used are: fixed plate side length of 2mm, plate gap of 0.1mm, frustum height of 0.035mm, upper surface side length of the frustum of 0.03mm, lower surface side length of the frustum of 0.08mm, and number of frustums ranging from 9 to 361.

[0092] This invention has been described through embodiments. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of this invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this invention should still be covered by the claims of this invention.

[0093] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for calculating the pressure damping of a MEMS device with a micro-bump structure, characterized in that: The MEMS device includes two parallel plates that can move relative to each other in the vertical direction. One of the parallel plates is a fixed plate, and the other is a movable plate. The inner surface of either the fixed or movable plate is provided with an array of protrusions, including a central protrusion located at the center of the inner surface of either the fixed or movable plate. The method includes the following steps: S1. When two parallel flat plates move relative to each other in the vertical direction, calculate the surface pressure F exerted on the central protrusion. a ; S2. When neither the inner surface of the fixed plate nor the inner surface of the movable plate contains any protrusions, and the two parallel plates move relative to each other in the vertical direction, calculate the surface pressure F exerted on the area occupied by the original central protrusion. b ; S3, Apply the surface pressure F obtained in step S1 a The surface pressure F obtained in step S2 b Subtracting the two values ​​yields the incremental pressure damping force ΔF generated by the central protrusion on the overall MEMS device; this incremental pressure damping force ΔF is used to approximately represent the incremental pressure damping force generated by each of the other protruding structures. S4. Multiply the pressure film damping force increment ΔF obtained in step S3 by the total number N of protrusions in the MEMS device to obtain the total pressure film damping increment ΔF generated by all protrusions. n ; S5. Calculate the pressure damping force F of the MEMS device without any protrusions. p ; S6: Calculate the total pressure film damping increment ΔF obtained in step S4. n The pressure damping force F calculated in step S5 p Adding them together, we obtain the pressure damping force F of the MEMS device with an arbitrary number of protrusions. d The damping force F of the pressure membrane d Dividing by the relative velocity v of the two plates yields the pressure damping coefficient C of the MEMS device with micro-bumps. d .

2. The method for calculating the pressure damping of a MEMS device with a micro-bump structure according to claim 1, characterized in that: The pressure damping force F of the MEMS device without any protrusions as described in step S5 p The expression is: Where μ represents the airflow viscosity coefficient, L represents the length of the plate, ω represents the width of the plate, and h represents the initial distance between the moving plate and the motion plate.

3. The method for calculating the pressure damping of a MEMS device with a micro-bump structure according to claim 2, characterized in that: The type of protrusion structure can be any one of cone, frustum, and column; protrusion structures distributed in the same array are of the same type.

4. The method for calculating the pressure damping of a MEMS device with a micro-bump structure according to claim 3, characterized in that: In step S1, the surface pressure F on the calculation center protrusion a The specific process includes the following steps: S11: Calculate the surface pressure F on the central protrusion when the inner surface of the fixed plate or the inner surface of the movable plate contains only the central protrusion. sa ; S12: When the inner surface of a fixed plate or the inner surface of a movable plate contains an array of protrusions, the surface pressure F of the central protrusion is defined. a Divide by the surface pressure F on the central protrusion obtained in step S11 sa For the normalized center convex surface pressure S13: When calculating the total projected area S of the array of protrusions on the inner surface of a fixed plate or a movable plate, where the inner surface contains an array of protrusions. n Calculate the inner surface area S of the flat plate containing the array of protrusions. p The total projected area S n Divide by the inner surface area S p The normalized projected area of ​​the array of protrusions on the plane is obtained. S14: Create normalized center convex surface pressure Normalized projected area of ​​the array protrusion structure on the plane The linear expression is used to calculate the surface pressure F on the central protrusion. a The linear expression is: in, This represents the ratio of the height H of the protruding structure to the initial spacing h of the flat plate; This represents the ratio of the equivalent upper base radius r1 to the equivalent lower base radius r2 of the protruding structure. This represents the ratio of the bulge height H to the equivalent lower base radius r2.

5. The method for calculating the pressure damping of a MEMS device with a micro-bump structure according to claim 4, characterized in that: In step S11, when the central protrusion is a cone, the surface pressure F on the central protrusion is... sa The calculation method is as follows: The surface pressure of a single cone is divided into two parts: the surface pressure in the region of rapid pressure change and the surface pressure in the region of stable pressure. The region below two-thirds of the cone height is defined as the stable pressure region, and the average surface pressure in this part is determined by the pressure p at the bottom of the cone. u An approximation is that the surface pressure in the pressure stabilization region is equal to the pressure p at the bottom of the cone. u The product of the area projected onto the plane where the pressure stability region lies; the region located above two-thirds of the cone's height is defined as the region of rapid pressure change, and the pressure at the cone's apex is p. ct The pressure at two-thirds of the height of the cone is approximately equal to the pressure p at the base of the cone. u , Adding the pressure in the region of rapid pressure change to the pressure in the region of stable pressure yields the surface pressure F of the cone-shaped structure containing a single cone plane. sa F sa The expression is:

6. The method for calculating the pressure damping of a MEMS device with a micro-bump structure according to claim 4, characterized in that: In step S11, when the central protrusion is a platform, the surface pressure F on the central protrusion is... sa equal to the pressure p at the center of the upper bottom surface of the platform. tt The product of the area of ​​the upper base and the pressure p at the bottom edge of the platform u The product of the surface area of ​​the platform and its projected area in the plane; Its expression is: F sa =πr1 2 p tt -πr1 2 p u +πr2 2 p u ; Where r1 represents the equivalent radius of the upper bottom surface of the platform, and r2 represents the equivalent radius of the lower bottom surface of the platform; 7. The method for calculating the pressure damping of a MEMS device with a micro-bump structure according to claim 4, characterized in that: In step S11, when the central protrusion is a cylinder, the surface pressure F on the central protrusion is... sa equal to the pressure p at the center of the top base of the column bt The product of the area of ​​the top base of the column; Its expression is: F sa =πr2 2 p bt Where r2 represents the equivalent radius of the cylinder.

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