Extension of inertial sensor circuits for detecting, calibrating and dynamically correcting extrusion

Abstract

The invention relates to a micromechanical inertial sensor and to a method for operating a micromechanical inertial sensor, comprising a sensor element movably arranged in a cavity and a detection device for detecting a transient measurement signal dependent on a deflection of the sensor element from an initial position in a detection direction, the detection device is used for detecting a small deflection of the sensor element parallel to the detection direction up to a geometric full deflection, also for causing a large mechanical deflection of the sensor element parallel to the detection direction in a test mode, and for this purpose has a first electrode structure arranged opposite the sensor element in the detection direction, a variable capacitance is formed between the sensor element and the first electrode structure and by means of an applied voltage, a gaseous medium is present in the cavity, which influences the movement of the sensor element, by means of which a deflection of the sensor element in the detection direction can be achieved, the influence of the gaseous medium in the region between the sensor element and the first electrode structure can be detected and stored by means of the transient measurement signal.

Description

TECHNICAL FIELD

[0001] The present application is based on a sensor system, for example a micromechanical inertial sensor, having a sensor element which is arranged moveably in a cavity, wherein the micromechanical inertial sensor has a detection device for detecting a transient measurement signal which is dependent on a deflection of the sensor element from an initial position in a probe direction, wherein the detection device is configured for detecting relatively small deflections of the sensor element parallel to the probe direction and geometrical full deflections, wherein the detection device is further configured for causing in a test mode a relatively large mechanical deflection of the sensor element parallel to the probe direction and for this has a first electrode structure, wherein the first electrode structure is arranged opposite the sensor element in the probe direction such that a variable capacitance is formed between the sensor element and the first electrode structure and by means of an applied voltage, wherein a gaseous medium is present in the cavity which influences the movement of the sensor element. The calibrated operation of such a system as a measurement system requires knowledge of the characteristic parameters of the contained electrical components (electrodes, electronic circuit, spring, mass) and the mechanisms which cause damping: for example the gas pressure in the sensor volume which causes friction and dissipation. BACKGROUND

[0002] Such micromechanical inertial sensors are typically operated in their functional and geometrical limits in order to achieve as efficient an operation as possible and a large measurement range. The functional design of the micromechanical inertial sensor is therefore set or conceived such that it can be used up to the physical limits of its functional manner. For example, applications or scenarios can be mentioned here in which relatively large deflections of the sensor element in the cavity are caused. Shock-type-applications are in particular typical (application) fields in which such relatively large deflections are (shockingly) produced.

[0003] The so-called pull-in effect, which is very important in this context, constitutes a severe limitation to the characterization options according to the prior art. The pull-in effect limits the static and dynamic small-signal characterization range of the sensor system to approximately 1 / 3 of the sensor actuation and the detectable measurement range. In shock-type scenarios, it is important that the micromechanical inertial sensor provides reliable data and that the risk of exceeding the physical limits, i.e. causing damage on or in the micromechanical inertial sensor, is reduced as far as possible. In direct test or characterization measurements, it is difficult to produce the comparatively large deflections of the sensor elements that occur in such shock-type scenarios, i.e. without causing damage. As a result, it is hardly possible to obtain data and information from direct test or characterization measurements. As an alternative, however, only indirect information or data is available, which cannot or only to a small extent be used purposefully for characterization purposes.

[0004] The disadvantage of all this is that comparatively few properties can be characterized for comparatively large deflections, in particular for a specific manufactured micromechanical inertial sensor. This is disadvantageous in particular in the automotive sector, since there are an increasing number of shock-type applications or scenarios there, so that it would be advantageous to characterize these comparatively large deflections directly.

[0005] The damping properties of the system are important for a correct sensor readout and its conversion into a correct sensor output value. In particular, the sensor properties depending on the applied signal frequency spectrum are largely dependent on the damping eigenvalues.

[0006] Not knowing the exact properties leads to a misinterpretation of the excitation to be measured or to a preventive limitation of the permissible use range of the sensor.

[0007] At present, the cognitive and characterization gap leads to the system not being usable in a range that is essentially calculable and thus calibratable, which often leads to a preventive limitation of the application specifications.

[0008] In addition, there is a relevance or need for the characterization of the cavity, in particular with regard to its hermetic encapsulation or sealing. If the hermetic encapsulation or sealing of the cavity has unsealed locations, the gaseous medium inside the cavity escapes and the pressure inside the cavity adapts to the external pressure. This has great disadvantages, since the gaseous medium or the pressure inside the cavity is matched very precisely to the functional way of the sensor, so that unsealed locations have a major impact on the functionality of the sensor. Therefore, it is necessary to check the hermetic encapsulation or sealing during the manufacturing process and afterwards during the operational process of the micromechanical inertial sensor in operation. Direct measurements in this respect are difficult to realize, so that an effective and efficient idea for a micromechanical inertial sensor for checking the hermetic encapsulation or sealing of the cavity is required. SUMMARY

[0009] Against this background, the task of the present application is to provide a micromechanical inertial sensor having a sensor element which is arranged movably in a cavity, which does not have the above-mentioned disadvantages, in particular due to its design.

[0010] The high load conditions (regarding the damping effect) which arise in actual operation should also be detectable in the characterization operation and over the life cycle by lifetime-retesting, in order to be able to calibrate the sensor output correctly in operation. The knowledge of this detectable property also enables preventive counter-regulation to avoid structural damage and extends the range of possible applications.

[0011] The apparatus and the instrument described here extend the ability to measure the damping behavior under "overpressure" conditions which are not accessible according to the prior art. This condition allows a more precise detection of even weak changes in the damping state and thus of the gas density and the gas-tightness of the components.

[0012] Advantageous configurations and extensions of the application can be gathered from the preferred embodiments and from the description with reference to the drawings.

[0013] According to an advantageous configuration of the application, the micromechanical inertial sensor is configured for detecting the influence of the gaseous medium in the region between the sensor element and the first electrode structure and / or in the region between the sensor element and the second electrode structure by means of a measurement signal when a static voltage which is higher than the pull-in voltage is applied. The detection of the measurement signal can take place using the electronic sensor readout mechanism which is normally used in normal operation. In normal operation, a reduced application bandwidth is usually used, which is usually achieved by downstream digital processing. For the test mode, sufficient bandwidth is required to detect the pulsed pull-in process. Therefore, an electronic front end with sufficient bandwidth is implemented for the signal recording. Typical values are 5 to 15 kHz to detect the details of the pull-in movement process.

[0014] According to an advantageous configuration of the application, the influence of the gaseous medium, in particular the damping effect, can be detected and stored in a further region within a damping structure, which is geometrically designed separately from the sensor element, the first electrode structure and / or the second electrode structure, wherein the damping structure is directly coupled to the movement state of the sensor element. In this case, too, a squeeze film is formed, which can be analyzed in a completely analogous manner by means of the apparatus described here.

[0015] According to an advantageous configuration of the application, a rectangular voltage with variable pulse height can be applied as an additional test signal to the readout signal. Such test signals with small voltage steps are common according to the prior art. However, the maximum value of the voltage is limited by the reference voltage of the ASIC technology used (stable bandgap voltage) to values below the typical snap-in voltage (more than 2 V). Beyond the prior art, the system is expanded in such a way that, in addition to the normal signal detection, such higher voltages (2 to 10 V, possibly higher) can be provided and applied by electronic circuitry.

[0016] According to an advantageous configuration of the application, a stop structure is provided between the sensor element and the first electrode structure and / or between the sensor element and the second electrode structure, wherein the sensor element can be deflected maximally to the positioning of the stop structure.

[0017] According to an advantageous configuration of the application, the micromechanical inertial sensor is configured for detecting the influence of a gaseous medium by triggering a large-scale motion process by applying a test voltage and recording it by means of the sensor readout principle. The influence of the damping medium is described by a model function inspired by physical theory. In the simple case, this can be modeled as the sum of a constant and a product of another constant multiplied by the fourth power of the deflection of the sensor element.

[0018] According to an advantageous configuration of the application, the micromechanical inertial sensor is configured for characterizing the influence of a gaseous medium based on the deflection of the sensor element and the measurement signal generated and stored by means of the sensor element by means of a compensation calculation, wherein the compensation calculation is based in particular on the time behavior or change process of the deflection and the time behavior of the stored motion process.

[0019] According to an advantageous configuration of the application, the sampling rate of the detection of the measurement signal is far above the range of the sensor eigenfrequency (kHz to 10 kHz) - for example in the range of 100 to 1000 kHz - so that the motion process to be characterized is not influenced by the applied readout mode.

[0020] According to an advantageous configuration of the application, the recording of the motion curve is supplemented by an additional memory. The write rate of the memory is typically at least in the range of 20 to 100 kHz in order to detect the signal frequencies required for evaluation at sufficiently high frequencies. The memory length is at least in the range of a few milliseconds in order to detect typical large signal processes (for example snap-in motion). In a variant of the method, the memory depth is much larger, for example in the range of 100 ms, in order to record a long sequence of signal transients of the same kind of excitation. The aim of this variant is to superimpose individual signals from the sequence, for example by means of averaging, in order to ensure a better signal-to-noise ratio.

[0021] A further subject-matter of the application is a method for operating a micromechanical inertial sensor having a sensor element movably arranged in a cavity.

[0022] For the method of operating a micromechanical inertial sensor having a sensor element movably arranged in a cavity, the advantages and configurations described in connection with the embodiments of the micromechanical inertial sensor having a sensor element movably arranged in a cavity according to the application can be applied.

[0023] Embodiments of the application are illustrated in the drawings and are described in detail in the following description. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 schematically showing a sensor element movably arranged in a cavity of a micromechanical inertial sensor according to an embodiment of the application in an initial position;

[0025] Figure 2 schematically showing a sensor element movably arranged in a cavity of a micromechanical inertial sensor according to an embodiment of the application substantially deflected from the initial position;

[0026] Figure 3 showing a modeling of the influence of a gaseous medium in the cavity depending on the deflection of the sensor element according to an embodiment of the application;

[0027] Figure 4a and b show the time course of the applied voltage and of the deflection of the sensor element, respectively, according to an embodiment of the application, for two damping media. DETAILED DESCRIPTION

[0028] The methods and instruments described here extend the ability to measure the damping characteristics under "overpressure" conditions, not reachable according to the prior art. This condition allows to detect even weak changes in the damping state, and hence in the gas density and in the hermeticity of the components, with greater precision.

[0029] The sensor basic principle is first explained below. Figure 1 It can be well explained as an overview of the following.

[0030] The inertial sensor has an inertial mass m in a spring-mass-damper system and an electronic evaluation circuit. In the simplest case, the dynamics in the sensor reference frame is described by the following Newtonian equation of motion:

[0031]

[0032] Normal sensor operation shall detect external accelerations a ext(t) and calibrated output. For this an electronic setup is used, but its influence on the measurement process must be negligible setup (U, t) ® 0.

[0033] In the detection of constant or slowly changing external accelerations (= quasi-static conditions: and thus In the "normal" operation of the sensor, at any time a static deflection is present, which is determined by the external acceleration according to the basic equation - equation 1, in which the external acceleration and the spring restoring force (Hooke's constant k) come to equilibrium:

[0034]

[0035] Thus, by detecting the deflection, in the case of known system parameters k and m, the acceleration can be calculated. The movable mass m of the system is connected to the electrode area, which usually forms a differential capacitor with other electrode elements of the system.

[0036] The measurement of the deflection x is achieved by means of electronic circuits, which measure the capacitance measurement quantities ΔC = C M-C1 -C M-C2 (*) or are measurable. These measurement quantities (ΔC* or ΔC / ∑C**) are proportional to the deflection x (for * approximately for small x « do; for ** even for larger deflections, although the capacitances themselves are non-linear quantities of the type

[0037] The theoretical working range extends across the entire deflection range of the mass 600 or CM - in Figure 1 from x = 0 (at the Figure 1 and Figure 2 is denoted by the reference 700 in

[0038] Further, the following describes a limitation of the characterization by the pull-in effect. The characterization of the sensor with regard to deflectability, restoring force, etc. is usually carried out by static electrical alternative excitation or time-dependent, for example periodic, electrical small-signal excitation, in order to detect the term F setup (U, t) in equation 1 around the static working point.

[0039] For this, first the working point is driven with a static voltage and by means of Equation 1 and the electrical force formula of the inter-plate capacitance results in:

[0040]

[0041] The analytical solution of this equation with respect to x can only be solved numerically in general and the solution only exists for a certain voltage size U determined by the spring strength and the capacitance geometry PI In the following, the maximum deflection achievable at this time is x PI .

[0042]

[0043] This means that almost 2 / 3 of the entire useful range (from (from Figure 1 indicated by reference 710) to the stop 106) cannot be reached by characterization experiments according to the prior art.

[0044] Furthermore, the following describes the Quetschfilm-Effekt. In particular in the large deflection region, narrow spatial gaps are formed in which the gas in the sensor atmosphere escapes more difficultly (see region 103' in Figure 2 This leads to an increased gas pressure in these regions, which results in an increased damping effect on the moving sensor mass 600 or CM and an additional spring-like restoring force.

[0045] The damping coefficient d = d(x) is therefore not constant in Equation 1, but has the characteristic d(x) that it increases significantly with increasing deflection x.

[0046] This very strongly influences the sensor characteristics - for example the sensitivity spectrum of the sensor with respect to the frequency and amplitude of the acceleration excitation. For example, the strong counter-pressure significantly reduces the sensitivity of the sensor to pulse cases.

[0047] However, these effects cannot be directly obtained with the characterization methods according to the prior art. Special laboratory characterization experiments on so-called vibration tables and centrifuge devices are known. However, such experiments are limited to a small number of components and the analysis depth is very strongly reduced due to the special setup and the lack of analysis options (fast transient storage). In other words, auxiliary experiments are known and are used, but their usefulness is small.

[0048] As previously mentioned, the deflection of sensor element 600 or CM can be achieved by applying static or pulsed acceleration. Only in the second case will an application-relevant squeeze film form, resulting in a significant change in sensor behavior. In the first case, static, continuous constant acceleration is easily achieved experimentally (the sensor has an adjustable rotational speed in a centrifuge, i.e., a constant centrifugal force), but it will not form the squeeze film of interest to the application.

[0049] However, by applying a voltage U(t), such as a step voltage whose final value exceeds the pull-in point (Pull-In-Punkt), the sensor can now be placed in a state similar to that of the application. This is in Figure 2 The text shows (550 or test:) In particular, the extrusion film to be characterized will form. Meanwhile, normal readout can be achieved via commonly used electrical wiring (530, 540, or U). ReadOut1 / 2 This process continues, allowing for the continued recording and evaluation of the movement of element 600 or CM.

[0050] Therefore, according to the present invention, the electronic evaluation circuit is equipped with an additional storage device for recording the obtained motion process, for example, when an additional test voltage (550 or test: U) is activated. ReadOut +U PI-Step It was recorded at that time.

[0051] In this case, the recorded motion process up to the stop element 106 is determined by Newton's equations of motion (differential) and can also be calculated:

[0052]

[0053] This equation corresponds to Equation 1 is given again here, with the force term (Kraftterm) of the electrical stimulation on the sensor electrodes explicitly added.

[0054]

[0055] Since the damping increases sharply when the extruded membrane scenario is reached, a position-dependent damping coefficient d(x) must be assumed in this describing equation, rather than the constant d in the small signal region.

[0056] The above differential equation Equation 5 can be solved numerically by integration (initial value problem, ODE integration) if the structural and dielectric parameters involved are known, such as the spring constant, the basic distance between the plate poles 730 or d0, the area A, the damping model d(x) related to x, and the time variation of the voltage U(t).

[0057] By comparing the recorded measurement curve and the solution of the differential equation parameterized with the model curve d(x), the form of the previously unknown damping characteristic can be determined by regression.

[0058] To this end, the evaluation circuit comprises an additional calculation unit, for example a microcontroller or a neural network, which can evaluate the recorded curve mathematically or with trained neuron coefficients. As with normal operation, normal readout operation (530, 540 or U ReadOut1 / 2 ) does not interfere with the dynamic test process.

[0059] Figure 1 A sensor element 101 arranged movably in a cavity 100 of a micromechanical inertial sensor is shown in a schematic view in an initial position 105 according to one configuration of the application. Along a detection direction 104, a second electrode structure 102' is arranged within the cavity 100 (from left to right), a sensor element 101 (in the initial position 105) suspended movably by a spring and a first electrode structure 102. Both the first electrode structure 102 and the second electrode structure 102' are arranged opposite the sensor element 101 along the detection direction 104, such that a variable capacitance is formed between the sensor element 101 and the first electrode structure 102 and another variable capacitance is formed between the sensor element 101 and the second electrode structure 102'. A gaseous medium is also contained in the cavity 100, which influences the movement of the sensor element 101. Furthermore, in the preferred configuration shown here, a stop structure 106 is arranged in a region 103 between the sensor element 101 and the first electrode structure 102 and the second electrode structure 102'. The sensor element 101 can therefore be deflected maximally to the positioning of the stop structure 106, or rather only to the positioning of the stop structure 106.

[0060] Furthermore, the micromechanical inertial sensor has a detection device for detecting a measurement signal which depends on the deflection of the sensor element 101 along the detection direction 104 to the left and right of the initial position 105 up to the positions 720 or x Max . To this end, electrical signals are applied by means of the contact pads 510 or P1, 520 or P2, 500 or PM, but these signals are not allowed to significantly influence the mechanical movement process. This is indicated in the schematic view in Figure 1 by the reference signs 530 and 540, the symbolic meaning of which is U ReadOut1 / 2 → ≈ 0.

[0061] The inertial sensor is generally designed symmetrically, so that accelerations in both directions can be detected by means of the sensor electrodes C2-CM-C1. For the sake of understanding the illustration, it is sufficient to consider only the elements on the right in Figure 1 and Figure 2 .

[0062] Furthermore, a higher voltage can also be applied via the contact pads in order to electrically pull the sensor element 101 towards the stop elements 106 on both sides for testing purposes. This is represented in Figure 2 by the reference 550 and its symbolic meaning "(test: )" for actuation to the right.

[0063] As already explained in the upper section on the prior art, with such voltages only the actuation of the sensor element 600 or CM up to the stop 106 can be achieved (typical voltages in the range of a few volts).

[0064] However, for testing purposes, the stable position can only be reached within a third of the rest distance 730 or d0. The region which can be reached stably in testing is marked in Figure 1 by the dashed line around the rest position on both sides. Beyond this range is the so-called pull-in region, in which no statically reachable equilibrium position exists.

[0065] When a voltage higher than the pull-in voltage is applied, the sensor moves with increased acceleration beyond the static region (710 or d0 / 3) and only stops at the stop element 106. Thus, according to the prior art, the main range beyond the 710 region or d0 / 3 region is not accessible for static testing and small-signal testing around the static operating point.

[0066] According to the application, the micromechanical inertial sensor is configured for, with the aid of Figure 2 the additional test voltage which is schematically drawn in, a comparatively large deflection of the sensor element 101 in the probe direction 104 can be achieved, so that the influence of the gaseous medium in the region 103 between the sensor element 101 and the first electrode structure 102 can be detected with the aid of the measurement signal. The normal readout voltage 530 or U Readout1 and 540 or U Readout2 In the so-called test run here, the voltages applied on the pads 510 or P1, 520 or P2, 500 or PM and thus also on the electrodes 610 or C1, 620 or C2, 600 or CM continue to be applied and the precise quantification of the sensor deflection is achieved as in the normal operation.

[0067] Figure 2 A sensor element 101 which is movably arranged in a cavity 100 of a micromechanical inertial sensor according to one configuration of the application is shown in a schematic view in deflection from an initial position 105 in a probe direction 104. The sensor element 101 is deflected by an applied electrical test voltage (compare Figure 2The reference mark in the image deflects relatively far from the initial position 105 toward the first electrode structure 102 (impactively) along the detection direction 104. This specifically produces a so-called pull-in effect. The movement of the sensor element 101 toward the first electrode structure 102 along the detection direction 104 is triggered by a generated electrical force, which acts between the sensor element 101 and the first electrode structure 102 due to an applied additional test voltage. This test voltage is higher than the structure-dependent voltage.

[0068] ( and Equation 4).

[0069] At voltage U PullIn In this case, the electrical force generated between the sensor element 101 and the first electrode structure 102 is balanced with the repulsive or restoring force of the coupling of the sensor element 101 within the micromechanical inertial sensor (e.g., achieved through a spring element). Due to this force balance, the sensor element establishes a new deflection position different from its initial position, below x. PullIn =d0 / 3.

[0070] The small deflection x achieved in this way can be determined experimentally, and can also be used... Equation 1 And the resulting implicit relations about x Numerical solution for position x in Equation 3.

[0071] This will not produce a relatively large deflection, or only a relatively small deflection of the sensor element 101.

[0072] However, if the test voltage U>U PullIn If the sensor element is deflected, the repulsive force of the spring 107 of the sensor element cannot balance the electrical force at any position, and the sensor element 101 will move towards the first electrode structure 102 in an impact manner.

[0073] This essentially results in a relatively large deflection. Region 103' suddenly narrows, and the gaseous medium located in region 103' (between sensor element 101 and first electrode structure 102) is impulsively compressed during this process. This impulsively compressed gaseous medium causes an additional braking or damping effect on sensor element 101 (therefore, sensor element 101 no longer accelerates unimpeded toward first electrode structure 102). This results in a temporary and significant delay in the movement of the sensor mass as it approaches stop element 106.

[0074] ​When the relatively rigid stop element 106 is reached, a prell behavior of the movable sensor mass 600 or CM can occur for a weakly damped gas medium, which is recognizable in the modeling as an oscillation of the curve 300. Figure 4b When there is stronger damping, in particular the formation of a squeeze film effect and a squeeze film repulsion, such an impact effect is strongly suppressed or not present, as shown by the curve 310 in Figure 4b .

[0075] In particular, the simulation of Figure 4b shows a delay in the movement behavior described above when the squeeze film effect is formed: the curve 300 is calculated under the assumption that there is no gas compression and no squeeze film effect.

[0076] The curve 310 is calculated using a realistic model of the squeeze film formation with regard to the damping coefficient d(x). Both curves of the fast impact-like temporal movement process are calculated by means of the Newtonian movement differential equation Equation 5 is calculated by means of numerical ODE initial value integration.

[0077] The movement processes shown take place in an impact-like manner, but their time range is in the range of a millisecond, which can be well and precisely detected by means of measurement technology.

[0078] On the basis of these measurable and calculable characteristics of the mapping, information or data can advantageously be generated about the gaseous medium in the cavity and about the relatively large deflection.

[0079] On the one hand, the characteristics of the relatively large deflection of the sensor element 101 itself can be effectively and efficiently acquired, and on the other hand the influence of the gaseous medium can be investigated. In particular, the fast impact-like movement process when suctioning is advantageous, since the increased damping d(x) due to the squeeze film formation is coupled with the high speed of the CM when the squeeze film is formed, by means of the multiplication in the movement differential equation Equation 5, so that this effect is particularly easy to observe in experiments.

[0080] In particular with respect to the influence of the gaseous medium (or by its absence), the hermetic sealing or sealing of the cavity can be analyzed. In the case of the presence of unsealed locations, in particular changes compared to previously generated information or data can be detected. In the case of changes or deviations from previous measurements of up to one order of magnitude, unsealed locations within the cavity can be particularly preferably located, indicating the presence of a defective hermetic sealing or sealing. Special structural defects, for example a breakage of the damping element in the case of an otherwise undamaged spring-mass and electrode structure, can also be identified by the special sensitivity of the squeeze film behavior of the damping element to the suction overload condition. Such defects cannot be identified by static tests or dynamic small-signal tests according to the prior art.

[0081] Figure 3 D L (x) is modeled depending on the deflection x (reference sign 204) of the sensor element 101 from the initial position 105. Therein the deflection x is given as a relative quantity with respect to the total deflection (700 or x = 0 to Figure 1 D L (x) is modeled by the sum of one constant D L0 and the product of another constant a times the fourth power of the deflection x of the sensor element 101. In particular, the modeling D L (x) is given by the following equation:

[0082] D L (x) = D L0 + a · x 4 Eq. 6

[0083] For small deflections x, in the model D L (x), the influence is essentially determined by the plateau 202. This essentially reflects the constant part D L (x) in the modeling D L0 , which is valid for small deflections, as long as the squeeze film effect is not added. For relatively large deflections x (reference sign 201), for example occurring in shock-like acceleration pulses in actual operation or in the case of the tests described here using the suction effect, the squeeze film effect becomes effective and a steep rise occurs (i.e. a large dissipative friction effect and a restoring action of the energy conservation). This can be mapped in the model by the influence of the fourth power of the deflection x and another constant a. This reflects the braking effect or damping effect of the gaseous medium on relatively large deflections. The empirical equation 6 is a simple and very well fitting modeling of the squeeze film damping effect to the experimental situation. In addition, more elaborate models, for example with more parameters, are also conceivable.

[0084] Furthermore, the deflection x of sensor element 101 is determined by modeling in Newton's equations of motion, according to which the acceleration of sensor element 101 (in the detection direction 104) is determined. It is proportional to the sum of three addends (force, effective acceleration of the force), where the first addend is proportional to the deflection x of sensor element 101 (in the detection direction 104) (Hooke's spring), and the second addend is proportional to the modeling D of the influence of the gaseous medium. L (x) and the velocity of sensor element 101 (in the detection direction 104) The product is proportional (Stokes' Law), and the third addend describes the force between the plate capacitor electrodes when the test voltage is applied. This is proportional to the square of the applied voltage U(t) multiplied by the initial position dist0 of the sensor element 101 (compare). Figure 1 and Figure 2 The reference mark 105 in the equation is proportional to the reciprocal of the square of the difference between the deflection x of the sensor element 101 (in the detection direction 104) and the reference mark 105 in the equation. Specifically, the modeling is given by the following equation:

[0085]

[0086] (corresponding to) Equation 5)

[0087] Where m is the first constant or the mass of the sensor element, k is the second constant or the effective spring constant of the sensor element 101 coupled within the micromechanical inertial sensor, and d(x) is the modeling term, which is related to the modeling of the influence of the gaseous medium. L The dielectric constant ε is proportional to d(x), and 1 / 2ε·A is used as the third constant term, or half of the product of the electrode area A and the dielectric constant ε. Modeling the effect of d(x) on the gaseous medium D L The direct proportional relationship between (x(t)) is derived from the following formula:

[0088]

[0089] Furthermore, a similar intention can be used to model energy-conserving (conservative) squeezing film action. To this end, the most direct approach is to modify accordingly. The Hooke's spring term in Equation 5, for example, can be extended if experimental evidence is available: -k·x → -(k+k′*x) n )·x. Such extensions and refinements are entirely consistent with the methods described here and do not require changes to the analysis process.

[0090] However, firstly, based on the fundamental principles of gas dynamics, it is reasonable to limit the main effect to the energy dissipation process (kinetic energy dissipated as heat), which proves the modeling based on Equation 6.

[0091] Figure 4aand b show the time course 810 of the applied voltage U(t) Figure 4a ) and the deflection x of the sensor element 101 for both damping media in the cavity Figure 4b , 300 low constant damping, no assumption of squeeze film formation, 310 sensor motion in case of a physically reasonable squeeze film formation, the damping increases with increasing deflection). To calculate the motion course in Figure 4a at t = 0, (the upper equation The test voltage U(t) in equation 5 is switched from zero to a value U(t) = const > U PullIn (reference 810) and remains constant.

[0092] where the time t (reference 400) is in milliseconds and the voltage U(t) (reference 800) is in volts. In Figure 4b , the time courses 300, 310 of the deflection x (reference 410) of the sensor element 101 with respect to the time t (reference 400) are plotted. Here the deflection x is in micrometers and the time t is in milliseconds. The time courses 300, 310 of the deflection x of the sensor element 101 can be divided into two regions 311 and 301. Within the region 311, the deflection x of the sensor element 101 represents a relatively small deflection. In this region 311, the influence D L (x) of the gaseous medium is mainly composed of the plateau 202 (i.e. the influence D L (x) is mainly composed of the constant D L0 described). Furthermore, the time courses 300 and 310 are essentially indistinguishable within this region 311. The region 301 represents a relatively large deflection of the sensor element 101. For the time courses 300, 310 of the deflection x, a difference occurs in this region 301. The influence D L (x) of the gaseous medium is modeled in this deflection region 301 by an expected realistic steep rise 201 for the time course 310 of the deflection x (i.e. by means of a large restoring action or braking effect and a damping effect), whereas for the time course 300 of the deflection x only the constant part D L0 (i.e. by means of the same damping effect as for small deflections) is modeled.

[0093] The two curves 300 and 310 represent extreme cases of the snap-in motion course:

[0094] curve 300: unrealistic assumption "no squeeze film formation"

[0095] Curve 310: Realistic movement course when forming squeeze film effect

[0096] Due to the difference in the characteristic course properties (presence / absence of bounce oscillations) and the assessable quantitative, the strength of the squeeze film effect can be determined from the experimental curve by comparison with the example curves 300 and 310.

[0097] During the experiment, for this purpose the experimental suction curve is recorded and with the aid of the description equation Equations 5 and 6, for a given sensor design calculate the model curve corresponding to the influence parameter a of the empirical equation 6. The parameter a assigned to the sensor ("squeeze film strength") can then be calculated by mathematical regression (optimal curve fitting).

[0098] Furthermore, the micromechanical inertial sensor is configured in particular such that based on the deflection x of the sensor element 101 and the measurement signal generated and stored with the aid of the sensor element 101, the influence of the gaseous medium can be characterized with the aid of a compensation calculation, in particular based on the temporal behavior or change course 300 of the deflection x in the region 310. Thus, in particular based on the compensation calculation and the comparison with the experimentally detected measurement signal or the data generated therefrom, the model quantity D L0 and the value of a can be derived. These data or information from the relatively large deflection of the sensor element 101 can advantageously be used for analyzing the relatively large deflection of the sensor element 101 itself within the cavity 100 and for checking the hermetic encapsulation or sealing of the cavity 100. In particular, these information or data can be compared with data or information generated earlier, in particular in a previous manufacturing step or in a previous operation of the micromechanical inertial sensor. For example, in particular when the information or data to be compared deviate by one order of magnitude, it can be determined that there is an unsealed location within the sealing or encapsulation of the cavity 100.

Claims

1. A micromechanical inertial sensor, said micromechanical inertial sensor having a sensor element (101) movably disposed in a cavity (100), in, The micromechanical inertial sensor has a detection device for detecting transient measurement signals, which depend on the deflection of the sensor element (101) along the detection direction (104) from its initial position (105). The detection device is configured to detect relatively small deflections and geometric total deflections of the sensor element (101) parallel to the detection direction (104). The detection device is further configured to induce a relatively large mechanical deflection of the sensor element (101) parallel to the detection direction (104) in a test mode, and for this purpose has a first electrode structure (102). The first electrode structure (102) is positioned opposite the sensor element (101) along the detection direction (104) such that a variable capacitance is formed between the sensor element (101) and the first electrode structure (102) and by means of the applied voltage. A gaseous medium is present in the cavity (100), and the gaseous medium affects the movement of the sensor element (101). The micromechanical inertial sensor is characterized in that it is configured such that the sensor element (101) can be deflected along the detection direction (104) by means of the voltage, so that the influence of the gaseous medium in the region (103, 103') between the sensor element (101) and the first electrode structure (102) can be detected and stored by means of the transient measurement signal.

2. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, The micromechanical inertial sensor is configured in such a way that... When a static voltage higher than the pull-in voltage is applied, the influence of the gaseous medium in the region (103, 103') between the sensor element (101) and the first electrode structure (102) and / or in the region between the sensor element (101) and the second electrode structure (102') is detected by means of the measurement signal.

3. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, In another region within the damping structure, the influence of the gaseous medium, particularly the damping effect, can be detected and stored. The damping structure is geometrically constructed separately from the sensor element (101), the first electrode structure (102), and / or the second electrode structure (102'). The damping structure is directly coupled to the motion state of the sensor element (101).

4. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, A rectangular voltage with a variable pulse height can be applied as an additional test signal to the readout signal.

5. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, A stop structure (106) is positioned between the sensor element (101) and the first electrode structure (102) and / or between the sensor element (101) and the second electrode structure (102'), wherein the sensor element (101) can be deflected to the location of the stop structure (106) at most.

6. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, The micromechanical inertial sensor is configured in such a way that... The influence of the gaseous medium can be detected by applying a test voltage to trigger a large-scale motion process and recording it using the sensor readout principle.

7. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, The micromechanical inertial sensor is configured in such a way that... Based on the deflection (300) of the sensor element (101) and the measurement signal generated and stored by means of the sensor element (101), the influence of the gaseous medium can be characterized by means of compensation calculation. The compensation calculation is specifically based on the temporal behavior or change process (301) of the deflection (300) and the temporal behavior of the stored motion process.

8. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, The sampling rate of the measured signal is located in a range much higher than the sensor’s inherent frequency, so that the motion process to be characterized is not affected by the applied readout mode.

9. The micromechanical inertial sensor according to any one of the preceding claims, characterized in that, The micromechanical inertial sensor is configured in such a way that... The recording of motion curves is supplemented by additional memory.

10. A method for operating a micromechanical inertial sensor, said micromechanical inertial sensor having a sensor element (101) movably disposed in a cavity (100), in, The micromechanical inertial sensor has a detection device for detecting a measurement signal, which depends on the deflection of the sensor element (101) from its initial position (105) along the detection direction (104). The detection device is capable of detecting relatively small to geometrically complete deflections of the sensor element (101) parallel to the detection direction (104). The detection device also has a relatively large mechanical deflection of the sensor element (101) parallel to the detection direction (104), which is caused by an additional static test voltage or rectangular voltage on the first electrode structure (102). The first electrode structure (102) is disposed opposite to the sensor element (101) along the detection direction (104), and a variable capacitance is formed between the sensor element (101) and the first electrode structure (102) by means of the applied voltage. A gaseous medium exists in the cavity (100), and the gaseous medium affects the movement of the sensor element (101). The feature is that a large deflection of the sensor element (101) along the detection direction (104) is achieved by means of a test voltage, and the influence of the gaseous medium in the region (103, 103') between the sensor element (101) and the first electrode structure (102) is detected by means of the measurement signal.

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