Extension of a circuit for inertial sensors for the detection, calibration and dynamic correction of squeeze film damping and restoring effects in high-load operation

Abstract

A micromechanical inertial sensor and a method for operating a micromechanical inertial sensor with a sensor element movably arranged in a cavity are proposed, wherein the micromechanical inertial sensor has a detection device for detecting a transient measurement signal as a function of a deflection of the sensor element along a detection direction from a starting position, wherein the detection device is configured to detect comparatively small up to geometric full deflections of the sensor element parallel to the detection direction, wherein the detection device is further configured to cause a comparatively 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, wherein the first electrode structure is arranged along the detection direction opposite the sensor element such thatthat a variable capacitance is formed between the sensor element and the first electrode structure by means of an applied electrical voltage, wherein a gaseous medium is located in the cavity which influences movements of the sensor element, characterized in that the micromechanical inertial sensor is configured such that the deflection of the sensor element along the detection direction can be realized by means of the electrical voltage in such a way that an influence of the gaseous medium in a region between the sensor element and the first electrode structure can be detected and stored by means of the transient measurement signal.

Description

State of the art

[0001] The invention is based on a sensor system, e.g. a micromechanical inertial sensor according to the preamble of claim 1. The calibrated operation of such systems as a measuring system requires knowledge of the characteristics of the included electrical components (electrodes, electronic circuitry, springs, masses) and also of the damping-causing mechanisms: e.g. gas pressures in sensor volume causing friction and dissipation.

[0002] Such micromechanical inertial sensors are often operated to their physical and geometric limits to achieve the most efficient operation and a large measuring range. Accordingly, the functional design of these sensors is such that they can be used right up to their physical limits. For example, this applies to applications and scenarios that cause a comparatively large displacement of the sensor element within the cavity. Shock-type applications, in particular, are typical fields where such a large displacement is generated (shock-like).

[0003] The so-called pull-in effect, which is very important in this context, represents a significant limitation of characterization options according to the current state of the art. The pull-in effect limits the range of static and dynamic small-signal characterization of sensor systems to approximately one-third of the sensor actuation range and thus also of the measurable range. In shock-type scenarios, it is crucial that the micromechanical inertial sensor delivers reliable data and that the risk of exceeding its physical limits (i.e., causing damage to or within the micromechanical inertial sensor) is minimized. Comparatively large deflections of the sensor element, such as those that occur in such a shock-type scenario, are difficult to generate (i.e., without causing damage) during direct test or characterization measurements. Therefore, data and information from direct test or characterization measurements are often only available after the fact.Characterization measurements are scarce. Alternatively, only indirect information or data is available, which cannot be used specifically for characterization purposes, or only to a limited extent.

[0004] All of this has the disadvantage that relatively few properties can be characterized for comparatively large deflections, especially for a specific manufactured micromechanical inertial sensor. This is particularly disadvantageous in the automotive sector, where shock-type applications and scenarios are increasingly common, and a direct characterization of these comparatively large deflections would therefore be advantageous.

[0005] The system's damping characteristics are crucial for accurate sensor readout and conversion into a correct sensor output value. In particular, the sensor characteristics as a function of the frequency spectrum of the incoming signal are strongly dependent on the damping parameters.

[0006] Lack of knowledge of the exact properties leads to misinterpretation of the stimulus to be measured or, preventively, to a limitation of the permissible application range of the sensor.

[0007] The knowledge and characterization gap currently means that the systems cannot be used up to the fundamentally calculable and therefore calibratable range, which usually leads to a preventive restriction of the application specification.

[0008] Furthermore, characterizing the cavity, particularly its hermetic seal, is also relevant and necessary. If a leak occurs within the cavity's hermetic seal, the gaseous medium inside escapes, and the pressure within the cavity adjusts to the external pressure. This has the significant disadvantage that the gaseous medium and pressure within the cavity are precisely calibrated to the sensor's operation, and therefore a leak represents a major disruption to the sensor's functionality. Consequently, it is essential to verify the hermetic seal both during manufacturing and after commissioning the micromechanical inertial sensor.Direct measurements in this regard are difficult to carry out, therefore there is a need for an effective and efficient design of a micromechanical inertial sensor to check the hermetic sealing of the cavity. Disclosure of the invention

[0009] Against this background, the task is to provide a micromechanical inertial sensor with a sensor element movably arranged in a cavity, which does not have the aforementioned disadvantages, especially due to its design.

[0010] The high-load conditions arising during real-world operation, with regard to damping effects, should also be detectable during characterization runs and throughout the life cycle via lifetime retesting, so that correct calibration of the sensor output can be performed during operation. Knowledge of these detectable properties also enables preventive countermeasures to avoid structural damage and an expansion of the specifiable application range.

[0011] The device and instrumental extension described here enable measurements of damping properties under an "overpressure" condition not yet accessible according to the prior art. This condition allows for a far more precise detection of even slight changes in the damping state and thus in the gas density and the hermetic tightness of the components.

[0012] Advantageous embodiments and further developments of the invention can be found in the dependent claims and the description with reference to the drawings.

[0013] According to an advantageous embodiment of the invention, the micromechanical inertial sensor is configured such that, when a static voltage above a pull-in voltage is applied, the influence of the gaseous medium in the area between the sensor element and the first electrode structure and / or in the area between the sensor element and a second electrode structure is detected using the measurement signal. The measurement signal can be acquired using the usual electronic sensor readout mechanisms, as in normal operation. In normal operation, reduced application bandwidths are typical, usually achieved through downstream digital processing. For the test mode, sufficient bandwidth is necessary to detect the pulse-like pull-in processes. Therefore, a sufficiently broadband electronic front end is implemented for signal recording.Typical values ​​are 5 to 15 kHz to capture the details of the pull motion sequence.

[0014] According to an advantageous embodiment of the invention, the influence of the gaseous medium, in particular a damping effect, can be detected and stored in a further area within damping structures, wherein the damping structures are geometrically separate from the sensor element, the first electrode structure, and / or the second electrode structure, and wherein the damping structures are directly coupled to a state of motion of the sensor element. In this case as well, a squish film formation occurs, which can be analyzed entirely analogously by the device described here.

[0015] According to an advantageous embodiment of the invention, rectangular voltages with variable pulse height can be applied as an additional test signal to the readout signal. In the prior art, such test signals with small voltage swings are common. However, the maximum voltage is limited to values ​​below typical pull-in voltages (greater than 2V) by the reference voltages (stabilized bandgap voltages) of the ASIC technology used. Going beyond the prior art, the system is extended to allow such higher voltages (2 to 10V, possibly higher) to be provided and applied by the electronic circuit in addition to the normal signal acquisition.

[0016] According to an advantageous embodiment of the invention, it is provided that stop structures are positioned 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 up to the positioning of the stop structures.

[0017] According to an advantageous embodiment of the invention, the micromechanical inertial sensor is configured such that the influence of the gaseous medium can be detected by applying a test voltage to trigger large-scale movements and recording them using the sensor readout principle. The influence of the damping medium is described by a model function motivated by physical theory. In a simple case, this can be modeled as the sum of a constant and the product of another constant and the fourth power of a displacement of the sensor element.

[0018] According to an advantageous embodiment of the invention, the micromechanical inertial sensor is configured in such a way that the influence of the gaseous medium can be characterized by means of a compensation calculation based on the deflection of the sensor element and the measurement signal generated and stored by means of the sensor element, wherein the compensation calculation is carried out in particular on the basis of the temporal behavior or course of the deflection and the temporal behavior of the stored motion sequence.

[0019] According to an advantageous embodiment of the invention, it is provided that a sampling rate with which the measurement signal is acquired lies in a range far above the sensor's natural frequencies (kHz to 10 kHz) - i.e., for example, in the range of 100 to 1000 kHz - so that the motion sequence to be characterized is not influenced by the imposed readout pattern.

[0020] According to an advantageous embodiment of the invention, the recording of the motion curves is supplemented by an additional memory. The write rate of the memory is typically at least in the range of 20 to 100 kHz to capture the necessary signal frequencies for evaluation at a sufficiently high frequency. The memory length is at least in the range of a few milliseconds to capture typical large-signal waveforms (e.g., pull-in movements). In a variant of the method, the memory depth is considerably greater, e.g., in the range of 100 ms, to record a long sequence of similarly actuated signal transients. The purpose of this variant is to superimpose the individual signals of the sequence, e.g., with averaging, and thus ensure a better signal-to-noise ratio.

[0021] Another object of the invention is a method for operating a micromechanical inertial sensor with a sensor element movably arranged in a cavity according to the dependent method claim.

[0022] The advantages and features described in connection with the embodiments of the micromechanical inertial sensor according to the invention with a sensor element movably arranged in a cavity can be applied to the method for operating a micromechanical inertial sensor with a sensor element movably arranged in a cavity.

[0023] Exemplary embodiments of the present invention are shown in the drawings and explained in more detail in the following description. Brief description of the drawings: Fig.Figure 1 shows a schematic representation of a sensor element movably arranged in a cavity of a micromechanical inertial sensor in a starting position according to an embodiment of the present invention. Fig. Figure 2 shows a schematic representation of a sensor element movably arranged in a cavity of a micromechanical inertial sensor, strongly deflected from a starting position according to an embodiment of the present invention. Fig. Figure 3 shows a model of the influence of a gaseous medium located in the cavity, depending on a deflection of the sensor element according to an embodiment of the present invention. Fig. Figures 4a and b show time courses of an applied electrical voltage and time courses of a deflection of a sensor element according to an embodiment of the present invention for two embodiments of the damping medium. Embodiments of the invention:

[0024] The method and instrumental extension described here enable measurements of damping properties under an "overpressure" condition not yet accessible according to the state of the art. This condition allows for a far more precise detection of even slight changes in the damping state and thus in the gas density and the hermetic tightness of the components.

[0025] The basic sensor principle will be explained first. The illustration Fig. Figure 1 can be used very well to illustrate the following summary. Inertial sensors have an inertial mass m in a spring-mass-damping system and an electronic evaluation circuit. The dynamics in the sensor's reference frame are described in the simplest case by the following Newtonian equation of motion: m⋅x¨+k⋅x+d(x)⋅x˙=−m⋅aext(t)+Fsetup(U,t)

[0026] Normal sensor operation is intended to detect external acceleration. ext (t) acquire and output a calibrated value. For this purpose, an electronic circuit (setup) is used, which, however, must only have a negligible influence on the measurement process (F). setup (U, t) → 0).

[0027] Normal operation consists of detecting constant or slowly varying external accelerations (= quasi-static conditions): aext=aextc,x˙≈0 and consequently also ẍ ≈ 0), the sensor assumes a static deflection at any given time, which is determined by the external acceleration according to the fundamental equation EQ. 1, where external acceleration and spring return (Hook's constant k) are in equilibrium: aextc=−k / m⋅x

[0028] By measuring the displacement, the acceleration can be calculated if the system parameters k and m are known. The moving mass m of the system is connected to electrode surfaces, which, together with other electrode elements of the system, typically form differential capacitors.

[0029] The displacement x is measured using electronic circuits, the capacitance measurement parameters ΔC = C M-C1 - C M-C2 (*) or ΔC / ∑C=(CM−C1−CM−C2)(CM−C1+CM−C2) to make them measurable. These measured quantities (ΔC* or ΔC / ΣC**) are proportional to the displacement x (approximately for small x << d0 in the case of * and also for larger displacements in the case of **, although the capacitances themselves are non-linear quantities of the type C(x)=ε⋅Ad0∓x represent.

[0030] The theoretical operating range extends over the entire deflection range of the mass 600 or CM - in Fig. 1 of x=0 (in the Fig. 1 and Fig.2 (shown with reference numeral 700) up to the stop points 106 almost to the counter electrode 610 or C1 (or 620 or C2), i.e., almost over the entire rest distance 730 or d0.

[0031] The following section describes the limitations of the characterization due to the pull-in effect. The characterization of the sensor with respect to deflection, restoring forces, and the like is generally performed using static electrical equivalent stimuli or time-dependent, e.g., periodic, small-signal electrical stimuli for dynamic characterization around static operating points using the term F. setup (U, t) in m x+k x + d(x) ẋ = -m a ext (t) + F setup (U, t) EQ. 1 through the sensor electronics or a test setup.

[0032] To do this, one first approaches operating points with static stresses (↔ ẍ = 0, ẋ = 0) and it follows that m·x+k · x + d(x) · ẋ = m + a ext (t) + F setup(U, t) EQ. 1 and the formula for electrical forces between plate capacitances F(U)=12ε⋅A(d0−x)2⋅U2: k⋅x=12ε⋅A(d0−x)2⋅U2

[0033] Solving this equation for x is only possible numerically in the general case, and a solution is only obtained up to a certain voltage value U given by the spring strength and capacitance geometry. PI with a maximum deflection x that can then be achieved PI . UPI=427⋅kε⋅A⋅d03 and xPI=13d0

[0034] This means that almost 2 / 3 of the total usable area (of xPI=13d0 (in Fig. 1 (represented by reference numeral 710) to the stops 106) cannot be achieved according to the state of the art by characterization experiments.

[0035] Furthermore, the squeeze-film effect is described below. Particularly in areas of large deflections, narrow spatial gaps form, from which the gas of the sensor atmosphere can escape less easily (see Zone 103' in [reference]). Fig. 2) This gives rise to an increase in gas pressure in these zones and thus an increased damping effect on the moving sensor mass 600 or CM and also additional spring-like restoring forces.

[0036] The damping coefficient d = d(x) in m x + k x + d(x) ẋ = -m a ext (t) + F setup (U, t) EQ. 1 is therefore not constant, but has a very strong increasing characteristic d(x) with increasing displacement x.

[0037] This strongly influences the sensor characteristics – for example, the sensor's sensitivity spectrum across the frequency and amplitude of the acceleration stimulus. The strong back pressure, for instance, significantly reduces the sensor's sensitivity to pulse situations.

[0038] However, these effects are not directly accessible using state-of-the-art characterization methods. Specialized laboratory characterization experiments using shaker and centrifuge setups are known. However, such experiments are limited to a small number of components, and the depth of analysis is severely reduced due to the specific setup and the lack of analytical options (fast transient storage). In other words, auxiliary experiments are known and used, but their usefulness is limited.

[0039] The deflection of the 600 or CM sensor element can be achieved, as previously described, by applied static or pulsed accelerations. However, only in the latter case does the application-relevant squash film form, leading to significant changes in the sensor's behavior. The first case, static, constant acceleration, is readily achievable experimentally (sensor in a centrifuge with adjustable rotational speed, i.e., constant centrifugal force), but the squash film of interest for the application does not form.

[0040] By applying a voltage waveform U(t), e.g., a stage with a final value that overcomes the pull-in point, the sensor can now be brought into states similar to those in the application situation. This is in Fig. 2 shown (550 or test: U ReadOut + U PI-Step (>U PI)_┌). In particular, the squeeze film to be characterized forms. At the same time, the normal readout process can be carried out using the usual electrical circuitry (530, 540 or U). ReadOut1 / 2 ) continue so that the movement of element 600 or CM can continue to be recorded and evaluated.

[0041] According to the invention, the electronic evaluation circuit is equipped with an additional storage device for the resulting sequence of movements, which, for example, activates the additional test voltage (550 or test: U). ReadOut + U PI-Step ) is recorded.

[0042] In this case, the recorded motion sequence up to the stop elements 106 is determined and also calculable by Newton's equation of motion (differential): m⋅x¨=−k⋅x−d(x)⋅x+12ε⋅A˙(d0−x)2⋅U(t)2

[0043] This corresponds to m x + k x + d(x) · ẋ = -m · a ext (t) + F setup(U, t) EQ. 1 is reproduced here again and explicitly modified by the force term F(U(t), x) = 12ε⋅A(d0−x)2⋅U(t)2 the electrical stimulation via the sensor electrodes.

[0044] Because of the sharply increasing attenuation when reaching the squeeze-film scenario, a location-dependent attenuation coefficient d(x) must also be assumed in this descriptive equation instead of the constant d of the small-signal range.

[0045] The differential equation above m⋅x¨=−k⋅x−d(x)⋅x+12ε⋅A˙(d0−x)2⋅U(t)2 EQ. 5 can be solved numerically by integration (initial value problem, ODE integration) if one knows the involved structural and media quantities spring constant, plate base spacing 730 or d0, area A and the x-dependent damping model d(x) and the time history of the electrical voltage U(t).

[0046] By comparing the recorded measurement curve and the differential equation solution parameterized with a model curve d(x), the shape of the previously unknown damping characteristic can be determined by regression. For this purpose, the evaluation circuit is equipped with an additional processing unit (e.g., a microcontroller or a neural network) which can evaluate the recorded curve using mathematical methods or a trained neuron coefficient. As in normal operation, the normal readout operation (530, 540, or U) interferes with this process. ReadOut1 / 2 ) the dynamic test process.

[0047] Fig.Figure 1 shows a schematic representation of a sensor element 101 movably arranged in a cavity 100 of a micromechanical inertial sensor in a starting position 105 according to an embodiment of the present invention. Along a detection direction 104, within the cavity 100 (from left to right) a second electrode structure 102', the sensor element 101 movably suspended on a spring in the starting position 105, and a first electrode structure 102 are arranged. 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'.Cavity 100 also contains a gaseous medium which influences the movement of the sensor element 101. Furthermore, in this preferred embodiment shown, stop structures 106 are positioned in the area 103 between the sensor element 101 and the first electrode structures 102 and 102'. The sensor element 101 can thus be deflected only up to the position of the stop structures 106.

[0048] Furthermore, the micromechanical inertial sensor has a detection device for detecting a measurement signal as a function of the deflection of the sensor element 101 along the detection direction 104 from the initial position 105 on both sides up to positions 720 and x, respectively. Max on.

[0049] For this purpose, electrical signals are applied via contact pads 510 or P1, 520 or P2, 500 or PM, which, however, must not noticeably influence the mechanical movement process. This is shown in the sketch. Fig. 1 by reference symbols 530 and 540 with the symbolic meaning U ReadOut1 / 2 →≈ 0 indicated. Inertial sensors Furthermore In the The If According to the invention

[0050] Fig. Figure 2 shows a schematic representation of a sensor element 101 movably arranged in a cavity 100 of a micromechanical inertial sensor, deflected from a starting position 105 along the detection direction 104 according to an embodiment of the present invention. The sensor element 101 is deflected parallel to the detection direction 104 by means of the applied electrical test voltage (compare the reference numerals in Figure 2). Fig.2) is deflected relatively far from the initial position 105 in the direction of the first electrode structure 102 (shock-like). In detail, this results in a so-called pull-in effect. The movement of the sensor element 101, along the detection direction 104 towards the first electrode structure 102, is triggered by an electrical force that acts between the sensor element 101 and the first electrode structure 102 due to the applied additional test voltage. This voltage is higher than the structure-related voltage. UPulln(UPI=427⋅kε⋅A⋅d03 and xPI=13d0 EQ. 4). In the case of a voltage U Pullln ​If a force equilibrium is achieved between the generated electrical force between the sensor element 101 and the first electrode structure 102, and in particular the repulsive or restoring force of a coupling of the sensor element 101 within the micromechanical inertial sensor, for example by means of a spring element, a new deflected position of the sensor element below X arises due to the force equilibrium, which differs from the initial position. Pullln = d0 / 3 in.

[0051] The resulting small displacement x can be determined experimentally and also with m·x+k · ẋ + d(x) · ẋ = -m · a ext (t) + F setup (U, t) EQ. 1 (↔ ẍ = 0, ẋ = 0) and the resulting implicit relation in x EQ. 3 k⋅x=12ε⋅A(d0−x)2⋅U2 Solve numerically for position x.

[0052] This essentially results in no comparatively large deflection or only a comparatively small deflection of the sensor element 101. This happens Herein At the

[0053] In particular, the simulation of Fig. 4b the above-described delay in the movement behavior when squish film effects form: Curve 300 is calculated under the assumption that no gas compression and squish film effect form.

[0054] Curve 310, on the other hand, is calculated using a realistic model for the formation of the compression film with respect to the damping coefficient d(x). Both curves for the rapid, shock-like temporal motion sequence are calculated using Newton's differential equation of motion. m⋅x=−k⋅x−d(x)⋅x+12ε⋅A(d0−x)2⋅U(t)2 EQ. 5 calculated by numerical ODE initial value integration.

[0055] The movement shown occurs abruptly, but can be measured accurately and precisely within a time span of one millisecond.

[0056] Based on these measurable and computationally representable characteristics, it is advantageous to generate information or data about the gaseous medium in the cavity and also about the comparatively large deflection.

[0057] Firstly, characteristics for the comparatively large deflection of the sensor element 101 itself can be determined effectively and efficiently, and secondly, the influence of the gaseous medium can be investigated. The rapid, shock-like motion during the pull-in is particularly advantageous, as the coupling of increased damping d(x) due to the squish film formation and the high velocity ẋ of CM during squish film formation results in the effect described by multiplication (-d(x) · ẋ) in the motion differential equation. m⋅x=−k⋅x−d(x)⋅x+12ε⋅A˙(d0−x)2⋅U(t)2 EQ. 5 makes it particularly easy to observe in the experiment.

[0058] The hermetic seal of the cavity can be analyzed, particularly with regard to the influence of the gaseous medium (or its absence). In the case of a leak, a change compared to previously generated information or data can be detected. Changes or deviations from previous measurements of up to an order of magnitude are particularly likely to identify a leak within the cavity and thus reveal a faulty hermetic seal. Specific structural defects, such as the breakage of damping elements with an otherwise undamaged spring-mass and electrode structure, can also be detected by the exceptional sensitivity of the pull-in overload condition to the compression film properties of the damping elements. Such defects cannot currently be detected by static or dynamic small-signal tests according to the state of the art.

[0059] Fig. Figure 3 shows a model of the influence of the gaseous medium D L (x) (reference numeral 205), which is located in cavity 100, as a function of a deflection x (reference numeral 204) of the sensor element 101 from the initial position 105. Where the deflection x is a relative measure to the achievable total deflection (700 or x=0 up to the stop element 106 in Fig. 1) is specified. The influence of the gaseous medium D L (x) is replaced by a sum of a constant D L0 and modeled as a product of another constant a with the fourth power of the deflection x of the sensor element 101.

[0060] In detail, the model D L (x) also through DL(x)=DL0+a⋅x4

[0061] For small deflections x, in the model D L (x) the influence is essentially determined by a plateau 202. This essentially reflects the constant proportion DL0 in the modeling D L(x) is effective for small displacements as long as no increase occurs due to squeeze-film effects. For comparatively large displacements x (reference symbol 201), such as those resulting from shock-like acceleration pulses in real-world operation or from the test situation described here using the pull-in effect, squeeze-film effects become effective, resulting in a steep increase (i.e., large dissipative friction effects and also an energetically conservative restoring effect). This can be modeled by the influence of the fourth power of the displacement x and the other constant a. This reflects the braking or damping effect of the gaseous medium for comparatively large displacements. The empirical equation EQ.6 is a simple model of the squeeze-film damping effect that already corresponds very well to the experimental situation. More refined models are also available, e.g.Models with additional parameters are conceivable.

[0062] Furthermore, the displacement x of the sensor element 101 is determined in Newton's equation of motion by means of a model according to which an acceleration ẍ of the sensor element 101 (in the detection direction 104) is proportional to a sum of three summands (forces, force-effective accelerations), where a first summand is directly proportional to the displacement x of the sensor element 101 (in the detection direction 104) (Hooke's spring), where a second summand is directly proportional to the product of the modeled influence of the gaseous medium D L(x) and a velocity x of the sensor element 101 (in the detection direction 104) is (Stokes' law), where a third term describes the force acting between the electrodes of the plate capacitor when the test voltage is applied. This is directly proportional to the product of the square of a modeled applied electrical voltage U(t) and the inverse of the square of a difference between the initial position dist0 (compare reference numeral 105 in Fig. 1 and Fig. 2) of the sensor element 101 and the deflection x of the sensor element 101 (in the detection direction 104). In detail, the modeling results from m⋅x¨=−k⋅x−d(x)⋅x˙+12ε⋅A(dist0−x)2⋅(U(t))2(corresponds to m⋅x=−k⋅x−d(x)⋅x+12ε⋅A˙(d0−x)2⋅U(t)2) with m as the first constant or mass of the sensor element, k as the second constant or an effective spring constant of the coupling of the sensor element 101 within the micromechanical inertial sensor, d(x) as a model which is directly proportional to the model of the influence of the gaseous medium D L (x) is, and 12ε⋅A as the third constant term, or half the product of the electrode area A and the electric field constant ε. The directly proportional relationship between d(x) and the modeling of the influence of the gaseous medium D L (x(t)) results from DL(x(t))=d(x(t))2km.

[0063] Furthermore, with a similar intention, one can also model an energetically conservative (energy-conserving) compression film effect. For this, the most obvious approach would be to use Hooke's spring term in m⋅x=−k⋅x−d(x)⋅x+12ε⋅A˙(d0−x)2⋅U(t)2 Correct EQ. 5 accordingly, e.g.: -k · x → -(k+k'*x n )·x can be extended if experimental evidence emerges. Such extensions and refinements are fully consistent with the method described here and do not require any change to the analytical procedure.

[0064] Initially, however, due to the gas dynamics principles, it is plausible to limit ourselves to an energetically dissipative process (kinetic energy is dissipated into heat) as the largely dominant effect, which justifies a modeling according to EQ. 6.

[0065] Fig. Figures 4a and b show a time course 810 of the applied electrical voltage U(t) ( Fig. 4a) and time courses 300, 310 of the deflection x of the sensor element 101 for two characteristics of the damping medium within the cavity ( Fig. 4b, Fig.300 ≙ low constant damping without assumption of squish film formation, 310 ≙ sensor movement with increasing damping and higher deflection due to the physically plausible squish film formation). For calculating the motion sequences in Fig. 4a at t=0 the test voltage U(t) (in the equation above) m⋅x=−k⋅x−d(x)⋅x+12ε⋅A˙(d0−x)2⋅U(t)2 EQ. 5) from zero to a value U(t) = const > U PullIn (Reference symbol 810) is switched on and held constant. Where the time t (reference symbol 400) is given in milliseconds and the voltage U(t) in volts (reference symbol 800). In Fig.Figure 4b shows the respective time profiles 300 and 310 of the deflections x of sensor element 101 (reference 410) plotted against time t (reference 400). The deflections x are given in micrometers and the time t in milliseconds. The time profiles 300 and 310 of the deflection x of sensor element 101 can be divided into two regions 311 and 301. Within region 311, the deflections x of sensor element 101 represent comparatively small deflections. In this region 311, the influence of the gaseous medium D is modeled. L (x) essentially from plateau 202 (i.e. the influence of the gaseous medium D L (x) is essentially given by the constant D L0(described). Furthermore, the time profiles 300 and 310 within this area 311 do not differ essentially. Area 301 represents comparatively large deflections of the sensor element 101. For the time profiles 300, 310 of the deflection x, a difference arises in this area 301. The influence of the gaseous medium D L (x) in this deflection range 301 for the time course 310 of the deflection x by means of realistically expected steep rise 201 (i.e. by means of a large restoring effect or braking and damping effects) and for the time course 300 of the deflection x exclusively taking into account the constant component D L0 (also modeled using the same damping effect as for small deflections).

[0066] The • Curve 300: unrealistic assumption of “no squeeze film formation” • Curve 310: realistic motion sequence when squish film effects are formed

[0067] Since the two curves differ in characteristic course properties (occurrence / absence of rebound oscillations) and in quantitatively evaluable ways, the strength of the squeezing film effect can be determined from experimental curves by comparison with the exemplary curves 300 and 310.

[0068] In the experimental procedure, the experimental pull-in curve will be plotted and analyzed using the descriptive equations. m⋅x=−k⋅x−d(x)⋅x+12ε⋅A˙(d0−x)2⋅U(t)2 Calculate model curves for EQ.5 and EQ.6 for the given sensor design according to the influence parameter a of the empirical EQ.6. The parameter a (the "squeeze film thickness") assigned to the sensor can then be calculated using mathematical regression (optimal curve fit).

[0069] Furthermore, the micromechanical inertial sensor is configured such that the influence of the gaseous medium can be characterized by means of a least-squares adjustment based on the displacement x of the sensor element 101 and the measurement signal generated by the sensor element 101, wherein the least-squares adjustment is performed in particular on the basis of the temporal behavior or course 300 of the displacement x in the region 310. Thus, in particular, a value for the model quantities D can be determined based on the least-squares adjustment and the comparison with the experimentally acquired measurement signal or the data generated therefrom. L0and derive from this. This data or information, derived from the comparatively large size of the sensor element 101, can be advantageously used to analyze the comparatively large deflections of the sensor element 101 within the cavity 100 itself, as well as to examine the hermetic sealing of the cavity 100. In particular, this information or data can be compared with older data or information, especially those generated in earlier manufacturing steps or during previous operations of the micromechanical inertial sensor. For example, a leak within the sealing of the cavity 100 can be detected if the information or data being compared deviates by an order of magnitude.

Claims

[1] Micromechanical inertial sensor with a sensor element (101) movably arranged in a cavity (100), wherein the micromechanical inertial sensor has a detection device for detecting a transient measurement signal as a function of a deflection of the sensor element (101) along a detection direction (104) from a starting position (105), wherein the detection device for detecting comparatively small deflections and geometric full deflections of the sensor element (101) is configured parallel to the detection direction (104), wherein the detection device is further configured to cause a comparatively large mechanical deflection of the sensor element (101) parallel to the detection direction (104) in a test mode and has a first electrode structure (102) for this purpose, wherein the first electrode structure (102) is arranged along the detection direction (104) opposite the sensor element (101) such that a variable capacitance is formed between the sensor element (101) and the first electrode structure (102) and by means of an applied electrical voltage, wherein a gaseous medium is located in the cavity (100) which influences movements of the sensor element (101), characterized by , that the micromechanical inertial sensor is configured such that the deflection of the sensor element (101) along the detection direction (104) can be realized by means of the electrical voltage in such a way that an influence of the gaseous medium in a region (103, 103') between the sensor element (101) and the first electrode structure (102) can be detected and stored using the transient measurement signal. [2] Micromechanical inertial sensor according to any of the preceding claims, characterized by, that the micromechanical inertial sensor is configured such that when a static voltage above a pull-in voltage is applied, the influence of the gaseous medium in the area (103, 103') between the sensor element (101) and the first electrode structure (102) and / or in the area between the sensor element (101) and a second electrode structure (102') is detected using the measurement signal. [3] Micromechanical inertial sensor according to any of the preceding claims, characterized by , that the influence of the gaseous medium, in particular a damping effect, can be detected and stored in a further area within damping structures, wherein the damping structures are geometrically separate from the sensor element (101), the first electrode structure (102) and / or the second electrode structure (102'), wherein the damping structures are directly coupled to a state of motion of the sensor element (101). [4] Micromechanical inertial sensor according to any of the preceding claims, characterized by , that rectangular voltages of variable pulse height can be applied as an additional test signal to the readout signal. [5] Micromechanical inertial sensor according to any of the preceding claims, characterized by , that stop structures (106) are 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 a maximum extent up to the positioning of the stop structures (106). [6] Micromechanical inertial sensor according to any of the preceding claims, characterized by , 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 large-scale movements and recording them using the sensor readout principle. [7] Micromechanical inertial sensor according to any of the preceding claims, characterized by , that the micromechanical inertial sensor is configured such that the influence of the gaseous medium can be characterized by means of a least squares calculation 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 adjustment calculation is based in particular on the temporal behavior or course (301) of the deflection (300) and the temporal behavior of a stored motion sequence. [8] Micromechanical inertial sensor according to any of the preceding claims, characterized by that a sampling rate at which the measurement signal is acquired lies in a range far above sensor natural frequencies, so that the motion sequence to be characterized is not influenced by the imposed readout pattern [9] Micromechanical inertial sensor according to any of the preceding claims, characterized by , that the micromechanical inertial sensor is configured in such a way that the recording of the motion curves is supplemented by an additional memory. [10] Method for operating a micromechanical inertial sensor with a sensor element (101) movably arranged in a cavity (100), wherein the micromechanical inertial sensor has a detection device for detecting a measurement signal as a function of a deflection of the sensor element (101) along a detection direction (104) from a starting position (105), the detection device can detect comparatively small deflections up to the geometric full deflection of the sensor element (101) parallel to the detection direction (104), wherein the detection device further comprises a comparatively large mechanical deflection of the sensor element (101) parallel to the detection direction (104) caused by an additional static test voltage or a rectangular voltage via a first electrode structure (102), wherein the first electrode structure (102) is arranged opposite 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 an applied electrical voltage, wherein a gaseous medium is located in the cavity (100) which influences movements of the sensor element (101), characterized by, that a large deflection of the sensor element (101) along the detection direction (104) is achieved by means of a test voltage and an influence of the gaseous medium in a region (103, 103') between the sensor element (101) and the first electrode structure (102) is detected using the measurement signal.

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