Method and apparatus for identifying dynamic parameters of a MEMS device, and a MEMS device

Abstract

The present invention provides a method for determining at least one dynamic parameter of a MEMS device, the MEMS device having at least one moving part, the at least one dynamic parameter describing a dynamic characteristic of the at least one moving part. A test signal is applied to the MEMS device, the test signal having at least one static excitation having a constant amplitude, and a response signal of the MEMS device to the test signal is detected. The at least one static parameter of the MEMS device is determined by evaluating the response signal with respect to the at least one static excitation using a model of at least the moving part of the MEMS device, the at least one static parameter describing a geometrical and / or structural characteristic of the at least one moving part. The at least one dynamic parameter of the MEMS device is calculated based on the determined at least one static parameter.

Description

Technical Field

[0001] The present invention relates to a method and apparatus for identifying dynamic parameters of a microelectromechanical (MEMS) device. Further, the present invention relates to a MEMS device.

Background Art

[0002] MEMS systems can be used to measure acceleration, rotational speed, magnetic field, pressure, etc. An exemplary pressure sensor device is known from German Patent Invention No. 102014200512. Such a system can be composed of mechanical or electronic components that can be dynamically excited, particularly periodically. The frequency characteristics of these components are one of the most important device characteristics. For example, a PT2 system can be characterized by a resonance frequency f 0 and a damping constant d or Lehr damping rate DL.

[0003] Since these are dynamic characteristics, they are usually determined by dynamic tests. For example, a sine wave or more generally a periodic test signal can be applied to the device, and the response of the device can be identified by the amplitude or phase at two or more frequency test points. As another method for determining dynamic characteristics, recording and analyzing the turn-on or turn-off transient state may be performed, and the dynamic characteristics can be extracted by regression or fitting simultaneously.

[0004] These methods are prone to errors because of high time resolution (i.e., short averaging time). Further, highly overdamped systems are difficult to evaluate because they do not exhibit meaningful frequency characteristics. In particular, overdamped systems are difficult to dynamically excite.

[0005] Furthermore, when strong excitation stimuli are required, these excitations may change the natural frequency and damping value due to the feedback mechanism of the test device on the sensor structure. For example, the stiffness of the spring element may decrease.

[0006] A further problem is that frequency and attenuation are mathematically insufficiently conditioned with respect to each other, especially in critical situations (such as overdamping). Therefore, in noisy test data, the extraction of these parameters is difficult.

[0007] By introducing special equipment and using laboratory test equipment, for example, by applying a large stimulus to a precisely prepared chip, the measurement results can be improved. However, this is almost impossible under more general production or field conditions using already integrated components. Similarly, calibration steps for self-regulating modules have so far been almost impossible to implement.

Prior Art Documents

Patent Documents

[0008]

Patent Document 1

Summary of the Invention

Means for Solving the Problem

[0009] The present invention provides a method and apparatus for identifying dynamic parameters of a MEMS device, and a MEMS device having the features of the independent claims. Preferred embodiments are the subject matter of each of the dependent claims.

[0010] According to a first aspect, the present invention relates to a method for identifying at least one dynamic parameter of a MEMS device, the MEMS device having at least one movable component, and the at least one dynamic parameter describing the dynamic characteristics of the at least one movable component. A test signal is applied to the MEMS device, the test signal having at least one static excitation with a constant amplitude, and a response signal of the MEMS device to the test signal is detected. At least one static parameter of the MEMS device is identified by evaluating the response signal with respect to the at least one static excitation using a model of at least the movable component of the MEMS device, and the at least one static parameter describes the geometric and / or structural characteristics of the at least one movable component. At least one dynamic parameter of the MEMS device is calculated using the identified at least one static parameter.

[0011] According to a second aspect, the present invention relates to an apparatus for identifying at least one dynamic parameter of a MEMS device, the MEMS device having at least one movable component, and the at least one dynamic parameter describing the dynamic characteristics of the at least one movable component. The apparatus includes a test device configured to apply a test signal to the MEMS device, the test signal having at least one static excitation with a constant amplitude, and the test device is further configured to receive a response signal of the MEMS device to the test signal. The MEMS device further includes an evaluation device configured to identify at least one static parameter of the MEMS device by evaluating the response signal with respect to the at least one static excitation using a model of at least the movable component of the MEMS device, the at least one static parameter describing the geometric and / or structural characteristics of the at least one movable component. The evaluation device is further configured to calculate at least one dynamic parameter of the MEMS device based on the identified at least one static parameter.

[0012] According to a third aspect, the present invention relates to a MEMS device comprising at least one movable part and a device according to the invention for identifying at least one dynamic parameter of the MEMS device.

[0013] According to the present invention, within the framework of a selected model, the dynamic behavior of the MEMS device can be completely determined. At this time, since at least one dynamic parameter is determined by a non-dynamic method, the determination of the dynamic characteristics is very much simplified experimentally and instrumentally.

[0014] This simplification is made possible by compensatorily obtaining the corresponding complex and effective mathematical model of at least the movable parts of the MEMS device. The present invention is particularly advantageous for overdamped systems with limited excitability and poor dynamic signal-to-noise ratio. Furthermore, the present invention is also suitable for highly integrated components with restricted access to high-frequency (HF) analysis. Such high integration can be expected for future sensor devices, for example, where ASIC (application-specific integrated circuit) readout electronics can be directly integrated. As a result, it is not possible to access the MEMS device itself and characterize the dynamic parameters.

[0015] Therefore, the present invention enables very accurate characterization of the dynamic characteristics even when the components are highly integrated. The burden of integrating the corresponding extensive HF analysis resources on the silicon substrate of the readout electronics can be avoided.

[0016] Since static measurements are usually performed after manufacturing, no additional time consumption occurs. Preferably, the measurement can be performed in only a few milliseconds. This method is particularly suitable for performing dynamic high-level characterization of autonomous edge devices. By splitting the dynamic characterization into a simpler static characterization and a dynamic supplementary characterization, the burden of device integration is significantly reduced. Compensating means such as arithmetic units and memories are very low-cost and possible because microcontrollers and digital signal processors are available and are already included in current MEMS devices.

[0017] For implementation, only additional functions for simplified static operation, such as a test voltage, etc., are required, and most of these are usually standard equipment. Recording and preparation of static signals can usually be performed by the signal processing of an existing ASIC circuit.

[0018] Since most of the complexity is covered by static measurements and model equations, only a limited measurement infrastructure is required for performing dynamic partial measurements. According to one embodiment, a FIFO (First In First Out) memory is provided for recording a one-time short-time transient state.

[0019] In particular, it is possible to calculate important performance characteristics of the MEMS device through geometric characteristics. For example, the spring constant can be specified by the beam formula, and the mass can be specified based on the volume and density. Using the spring constant and the mass, the resonance frequency can be specified. By knowing geometric sizes such as the length and height of structural elements, or the amount of electrical doping, it becomes possible to calculate performance quantities such as bandwidth and power consumption.

[0020] According to a further embodiment of a method for specifying at least one dynamic parameter of a MEMS device, the test signal has a plurality of static excitations with a constant amplitude, and at least one further dynamic parameter of the MEMS device is further specified by evaluating a response signal regarding the transient behavior between two static excitations. However, the dynamic measurement values may be reduced by evaluation based on static tests and models.

[0021] According to a further embodiment of a method for specifying at least one dynamic parameter of a MEMS device, the calculation of at least one dynamic parameter includes the steps of specifying the mass of the movable parts of the MEMS device, specifying the spring constant of the movable parts of the MEMS device, and calculating the natural frequency of the movable parts as a dynamic parameter of the MEMS device based on the mass and the spring constant. Here, the natural frequency depends only on the mass and the spring constant.

[0022] According to a further embodiment of a method for identifying at least one dynamic parameter of a MEMS device, a model of at least the movable parts of the MEMS device includes a discretized structural mechanics description, in particular a finite element model.

[0023] According to a further embodiment of a method for identifying at least one dynamic parameter of a MEMS device, the identification of at least one static parameter is performed using at least one force equilibrium equation. This force equilibrium equation describes the conditions of static behavior.

[0024] According to a further embodiment of a method for identifying at least one dynamic parameter of a MEMS device, at least one static parameter includes geometric structural characteristics of the movable parts of the MEMS device, in particular the structural width of the movable parts of the MEMS device and / or the structural height of the movable parts of the MEMS device.

[0025] According to a further embodiment of a method for identifying at least one dynamic parameter of a MEMS device, at least one further dynamic parameter includes the damping coefficient of the movable parts of the MEMS device.

[0026] According to a further embodiment of a method for identifying at least one dynamic parameter of a MEMS device, the movable parts are modeled as a PT2 system, i.e., a spring-mass-damping system, and at least one dynamic parameter includes the resonance frequency of the movable parts and / or the damping ratio of the movable parts. The PT2 system is set by these two dynamic parameters.

[0027] For example, the resonance frequency of a movable part can be determined separately from pure static excitation. The advantage here is that static experiments are much less affected by noise and errors compared to dynamic tests. Subsequently, for further dynamic parameters, such as the second dynamic parameter in the case of a PT2 description, i.e., the attenuation in this case, since the relevant dynamic variables are determined in advance by precise static tests and remain fixed in the actual dynamic characteristic experiment, they can be separated and accurately determined using a model-based dynamic characteristic evaluation technique. In particular, it is particularly advantageous when the quantities to be determined in the dynamic characteristic experiment (such as in an overdamped system) have insufficient mutual conditioning.

[0028] This approach avoids the insufficient mathematical conditioning of the two frequency parameters, and the noisy and sensitive dynamic test data are only used to determine a small group of dynamic characteristic parameters that can be better managed.

[0029] However, the present invention is not limited to PT2 systems. Therefore, the model of at least one movable part of the MEMS device may include corrections beyond a simple PT2 description, i.e., more complex dynamic descriptions.

[0030] According to a further embodiment of the method for identifying at least one dynamic parameter of the MEMS device, drift detection, impermeability detection, etc. can be performed based on the identified dynamic parameters. In particular, since the hardware requirements are simple, the test procedure can be executed on a self-regulating device by a microcontroller on-site.

[0031] According to a further embodiment of the apparatus for identifying at least one dynamic parameter of a MEMS device, the test signal has a plurality of static excitations with a constant amplitude, and the evaluation apparatus is further configured to identify at least one further dynamic parameter of the MEMS device by evaluating a response signal regarding the transient behavior between two static excitations. If a plurality of excitation levels are available, the error in determining at least one parameter can be reduced, or the amount of available information can be increased to determine further design parameters.

[0032] Further advantages, features and details of the present invention will become apparent from the following description which details various embodiments with reference to the drawings.

Brief Description of the Drawings

[0033]

Figure 1

Figure 2

Figure 3

Figure 4

[0034] The numbering of the method steps is for ease of viewing and is not generally intended to imply a specific time series order. In particular, a plurality of method steps may be executed simultaneously.

Modes for Carrying Out the Invention

[0035] FIG. 1 is a schematic block diagram of a MEMS device 1 comprising a device 2 for identifying at least one dynamic parameter of the MEMS device 1. The MEMS device 1 includes one or more movable components 3 such as a vibrating element (such as a micromirror) or a deflectable and vibratable electrode. The MEMS device 1 may be a pressure sensor, a density sensor, an acceleration sensor, a rotational speed sensor, etc. The at least one dynamic parameter characterizes the dynamic characteristics of at least one movable component. The dynamic parameter may include, for example, the natural frequency of the movable component 3 of the MEMS device 1.

[0036] The device 2 for identifying at least one dynamic parameter of the MEMS device 1 includes a test device 21 that generates a test signal and applies it to the MEMS device 1. The test signal may have, for example, a stepped waveform. The test signal has at least one static excitation with a constant amplitude. For example, when the waveform is stepped, each step corresponds to a static excitation. The test device 21 is further configured to receive a response signal of the MEMS device 1 to the test signal, and this response signal depends on the displacement of the movable component 3.

[0037] Furthermore, the MEMS device 1 includes an evaluation device 22 including an arithmetic device such as a microprocessor or a microcontroller. The evaluation device 22 is configured to identify at least one static parameter of the MEMS device 1 by evaluating a response signal regarding at least one static excitation. At this time, the evaluation device 22 uses a model that models the MEMS device 1, or at least a model that models the movable component 3 of the MEMS device 1. The model may be, for example, a finite element model, a system of differential equations, or a machine learning model.

[0038] The at least one static parameter relates to the geometric and / or structural characteristics of at least one movable component 3. In particular, the static parameter may include the structural width of the movable component 3 of the MEMS device 1 and / or the structural height of the movable component 3 of the MEMS device 1.

[0039] The evaluation device 22 is further configured to calculate at least one dynamic parameter of the MEMS device 1 based on the at least one identified static parameter. FIG. 2 shows an exemplary test signal for application to the MEMS device 1 as a function of time t. The test signal can represent, for example, excitation by a voltage or an acceleration stimulus. At this time, the test signal has a stepped waveform. Between each step, the movable part 3 is excited with a constant amplitude A. The amplitudes A of different steps are preferably different. In particular, sub-signals having amplitudes A of different signs can be applied. Optionally, the MEMS device 1 may be tested for at least some steps in different spatial directions, that is, static excitation may be applied with a constant amplitude A.

[0040] The measured values by the constant excitation in the step correspond to a static experiment to be evaluated to determine at least one statically determined dynamic parameter. The time-dependent measurement points during the transition from one static level to the next may be used in a second step to calculate at least one additional dynamic parameter.

[0041] FIG. 3 is an exemplary flowchart for explaining the determination of the dynamic parameters of the MEMS device 1. A test signal X_in is applied to the MEMS device 1, and this signal X_in is triangular in the first time zone and rectangular in the second time zone, that is, it has a static excitation with a constant amplitude. The transient behavior of the movable part 3 is identified by the triangular signal (or the transition range between rectangular signals), so that the remaining dynamic parameters can be determined.

[0042] The model 200 provides a description of the dynamic system, that is, the following equations.

[0043]

Equation

[0044] Here, \(F_{ext}\) represents an external force (such as gravity), \(Y\) represents the system state, and \(f\) represents a function dependent on the system. The inherent structural parameters \(s_1,\cdots,s_n\) of the MEMS device 1 can be determined by a plurality of static measurements. For example, a force equilibrium equation dependent on the structural parameters may be used through the model equation or model description \(f\) of the MEMS device 1. Here, the static behavior corresponds to the following conditions.

[0045]

Number

[0046] From this equation, at least some of the structural parameters \(s_1,\cdots,s_n\) can be determined. Therefore, the information content lacking for determining dynamic variables from static parameters is provided by adding the design equations of the movable parts, that is, by using the model. For example, the spring constant of a bending beam can be specified from the geometric dimensions using the formulas of structural mechanics.

[0047] The static structural characteristics can be specified by static tests, for example, by the thickness of the movable parts, by evaluating the static force equilibrium equation, or by the mass value obtained by testing the free geometric setting range.

[0048] According to the design equations, for a PT2 system, the spring constants and mass values of the sub-components can be calculated from, for example, geometric or structural data, and the variables derived therefrom can also be calculated. For example, the resonance frequency \(f_0\) is derived from the following known relationship.

[0049]

Number

[0050] The resonance frequency \(f_0\) is a dynamic variable, while the spring constant \(k\) and mass \(m\) can be specified by static measurements. If the resonance frequency f0 is known, further dynamic parameters (such as the attenuation rate D_L) may be identified by dynamic regression. For this purpose, the parameter sets Pl, P2,..., P3 shown in FIG. 3 are investigated until the calculated waveform corresponds as well as possible to the measured waveform Y_out. Thereby, the solution parameter set 201 is determined.

[0051] In an overdamped system, the resonance frequency f0 and the attenuation rate D_L, which are two free parameters, have insufficient mathematical relationships. However, the resonance frequency f0 is known from static measurements and design equations. Therefore, it is possible to calculate the insufficient mathematical conditioning of these two parameters. If the resonance frequency f0 is known, only the attenuation rate D_L is determined from dynamic measurements. Thereby, the two parameters are provided with excellent accuracy.

[0052] This approach is not limited to simple PT2 dynamic characteristics, but can also be extended to more complex dynamic characteristic systems. Ideally, all relevant parameters can be identified by static measurements. Thereafter, a plurality of other performance parameters and calibration parameters of the MEMS device 1, for example, the offset, sensitivity, linearity, etc. of the components and systems of the MEMS device 1 can be derived from the design equations.

[0053] Generally, N independent static measurement quantities without errors can be identified, from which up to N structural parameters of the movable part 3 can be determined. Each measurement quantity corresponds to a determination relationship, that is, a mathematical formula. Usually, the measurement is affected by the noise of the test data. Therefore, the accuracy decreases when determining the structural quantity to be calculated. The calculation error can be reduced by increasing the number of test values to M > N. Mathematically, this corresponds to an overdetermined equation system in which the optimal solution can be determined by regression.

[0054] FIG. 4 is a flowchart of a method for identifying at least one dynamic parameter of the MEMS device 1. The MEMS device 1 has at least one movable part 3. In particular, it may be the above-described MEMS device 1. The at least one dynamic parameter describes the dynamic characteristics of the at least one movable part 3.

[0055] In a first method step S1, a test signal having a predetermined shape is applied to the MEMS device, and the test signal has at least one static excitation with a constant amplitude. The test signal has at least one static excitation with a constant amplitude. The test signal may have a plurality of stages. A response signal of the MEMS device 1 to the test signal is detected.

[0056] In a second method step S2, at least one static parameter of the MEMS device 1 is identified by evaluating a response signal regarding at least one static excitation using a model of at least the movable part 3 of the MEMS device 1.

[0057] At least one dynamic parameter of the MEMS device is calculated in a third method step S3 based on the identified at least one static parameter. In a further method step S4, at least one further dynamic parameter of the MEMS device 1 can be further identified by evaluating a response signal regarding the transient behavior between two static excitations.

[0058] For example, as described above, the spring constant of the movable part 3 of the MEMS device 1 may be determined, and then, based on the mass and the spring constant, the natural frequency of the movable part 3 may be calculated as a dynamic parameter of the MEMS device 1.

Claims

1. A method for determining at least one dynamic parameter of a MEMS device (1), the MEMS device (1) having at least one moving part (3), the at least one dynamic parameter describing a dynamic characteristic of the at least one moving part (3), the method comprising: - applying (S1) a test signal to the MEMS device (1), the test signal having at least one static excitation of constant amplitude, and detecting a response signal of the MEMS device (1) to the test signal; - determining (S2) at least one static parameter of said MEMS device (1) by evaluating said response signal for said at least one static excitation using a model of at least said moving part (3) of said MEMS device (1), said at least one static parameter describing geometrical and / or structural properties of said at least one moving part (3); - calculating (S3) said at least one dynamic parameter of said MEMS device (1) on the basis of said determined at least one static parameter; A method comprising:

2. 2. The method of claim 1, wherein the test signal comprises a plurality of static excitations having constant amplitude, and wherein at least one further dynamic parameter of the MEMS device (1) is further identified by evaluating the response signal for a transient behavior between two static excitations.

3. The method according to claim 2 , wherein the at least one further dynamic parameter comprises a damping factor of the movable part (3) of the MEMS device (1).

4. 2. The method of claim 1, wherein the calculation of the at least one dynamic parameter comprises the steps of: determining a mass of the movable part (3) of the MEMS device (1); determining a spring constant of the movable part (3) of the MEMS device (1); and calculating a natural frequency of the movable part (3) as a dynamic parameter of the MEMS device (1) based on the mass and the spring constant.

5. The method of claim 1 , wherein the model of at least the moving part (3) of the MEMS device (1) comprises a refined structural mechanics description.

6. The method of claim 1 , wherein the determination of the at least one static parameter is performed using at least one force balance equation.

7. The method of claim 1 , wherein the at least one static parameter comprises a geometrical construction characteristic of the movable part (3) of the MEMS device (1).

8. A device (2) for determining at least one dynamic parameter of a MEMS device (1), the MEMS device (1) having at least one moving part (3), the at least one dynamic parameter describing a dynamic characteristic of the at least one moving part (3), the device (2) comprising: a test device (21) configured to apply a test signal to the MEMS device (1), the test signal having at least one static excitation of constant amplitude, the test device (21) further configured to receive a response signal of the MEMS device (1) to the test signal; an evaluation device (22) configured to determine at least one static parameter of the MEMS device (1) by evaluating the response signal for the at least one static excitation using a model of the at least one moving part (3) of the MEMS device (1), the at least one static parameter describing geometrical and / or structural properties of the at least one moving part (3), the evaluation device (22) being further configured to calculate the at least one dynamic parameter of the MEMS device (1) on the basis of the determined at least one static parameter; An apparatus (2).

9. The apparatus (2) of claim 8, wherein the test signal has a plurality of static excitations having a constant amplitude, and the evaluation device (22) is further configured to identify at least one further dynamic parameter of the MEMS device (1) by evaluating the response signal for transient behavior between two static excitations.

10. A MEMS device (1) comprising at least one moving part (3) and a device (2) as claimed in claim 8.

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