Patent Application
20150177272
The present application relates to microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS).
Microelectromechanical systems (MEMS) are commonly fabricated on silicon (Si) or silicon-on-insulator (SOI) wafers, much as standard integrated circuits are. However, MEMS devices include moving parts on the wafers as well as electrical components. Examples of MEMS devices include gyroscopes, accelerometers, and microphones. MEMS devices can also include actuators that move to apply force on an object. Examples include microrobotic manipulators. However, when a MEMS device is fabricated, the dimensions of the structures fabricated often do not match the dimensions specified in the layout. This can result from, e.g., under- or over-etching.
Reference is made to the following:
Reference is also made to the following:
Reference is also made to the following:
Reference is also made to the following:
The discussion above is merely provided for general background information and is not intended to be used as an aid in determining the scope of the claimed subject matter.
According to an aspect, there is provided a method of measuring displacement of a movable mass in a microelectromechanical system (MEMS), the method comprising:
According to another aspect, there is provided a method of measuring properties of an atomic force microscope (AFM) having a cantilever and a deflection sensor, the method comprising:
According to another aspect, there is provided a microelectromechanical-systems (MEMS) device, comprising:
According to another aspect, there is provided a motion-measuring device, comprising:
According to another aspect, there is provided a temperature sensor, comprising:
This brief description is intended only to provide a brief overview of subject matter disclosed herein according to one or more illustrative embodiments, and does not serve as a guide to interpreting the claims or to define or limit the scope of the invention, which is defined only by the appended claims. This brief description is provided to introduce an illustrative selection of concepts in a simplified form that are further described below in the detailed description. This brief description is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. The claimed subject matter is not limited to implementations that solve any or all disadvantages noted in the background.
The above and other objects, features, and advantages of the present invention will become more apparent when taken in conjunction with the following description and drawings wherein identical reference numerals have been used, where possible, to designate identical features that are common to the figures, and wherein:
The attached drawings are for purposes of illustration and are not necessarily to scale.
Reference is also made to the following, the disclosure of each of which is incorporated herein by reference:
Symbols for various quantities (e.g., Agap) are used herein. Throughout this disclosure, italic and non-italic variants of each of these symbols (e.g., “Δgap” and “Δgap”) are equivalent.
Various aspects relate to calibrating an atomic force microscope (AFM) with self-calibratable micro-electro-mechanical system (MEMS). Various arrangements for calibration of an atomic force microscope (AFM) using Micro-Electro-Mechanical Systems (MEMS) are disclosed herein. Some methods herein use a self-calibratable MEMS technology to traceably measure AFM cantilever stiffness and displacement. The calibration of displacement includes measuring the change in optical sensor voltage per change in displacement, or optical level sensitivity (OLS), and the calibration of stiffness along with displacement yields an accurate measurement of force. Calibrating the AFM is useful because the AFM has been a useful tool for nanotechnologists for over two decades, yet the accuracy of the AFM has been largely unknown. Previous efforts to calibrate the AFM, such as a thermal vibration method, an added weight method, and a layout geometry method, are about 10% uncertain. As a consequence, such AFM measurements yield about 1 significant digit of accuracy. Various aspects herein advantageously use a MEMS device, with traceably-calibrated force, stiffness, and displacement, as a sensor to calibrate the displacement reading and cantilever stiffness of the AFM. Various methods and devices described herein are practical, easy to use, and suitable for fabrication in a standard silicon on insulator (SOI) process. In the present disclosure, use of a general MEMS design is described and associated accuracy, sensitivity, and uncertainty analyses are presented.
Due to the specific capabilities of the AFM, the field of nanotechnology has seen extraordinary growth. The AFM is used to apply and sense forces or displacements to better understand phenomena at the nanoscale, which is a key building block scale of matter.
The AFM includes a cantilevered stylus for probing matter. Displacement is sensed by reflecting a beam of light off the cantilever onto a photodiode that detects the position of the light beam. Measurement of force is found by multiplying this deflection by the cantilever stiffness. The problem is that finding an accurate and practical way of calibrating the AFM cantilever stiffness and its displacement has been difficult. Several common methods used to calibrate AFM are described below.
In an AFM calibration method that requires the accurate knowledge of cantilever geometry and material properties, due to process variations, such properties should be measured; however, there has not been an accurate and practical means for such measurements.
In a calibration method that exploits thermally-induced vibration of the AFM cantilever, the accurate measurement of cantilever temperature and displacement are required; however, there has not been an accurate and practical means for such measurements.
A mixed method depends on geometry and dynamics.
A traceable method uses a series of uniform cantilevers calibrated by an electrostatic force balance method as calibration references for AFM cantilever stiffness. However, the method is impractical and therefore difficult for widespread use.
The optical level sensitivity (OLS) of the AFM is the ratio of the change in photodiode voltage to the change in displacement. This calibration is in some embodiments done by pressing the cantilever tip onto a non-deformable surface. It is assumed that a particular displacement can be prescribed by a piezoelectric positioning stage; however, calibrating the accuracy and precision of this positioning stage is difficult and impractical.
To address the above problems of inaccuracy, imprecision, and impracticality, the AFM's stiffness and displacement are calibrated by using the self-calibratable MEMS according to various aspects herein. This self-calibration is referred to herein as electro micro metrology (EMM), and is advantageously capable of extracting accurate and precise mechanical properties in terms of electronic measurands. Microfabrication of the MEMS micro-device can be done using a standard foundry process such as SOIMUMPs. Once the force, displacement, and stiffness of the MEMS are accurately calibrated, the micro-device can be used to calibrate the AFM by measuring its stiffness and deflection.
Various terms used herein are given in Table 1, below.
Electro micro metrology (EMM) is an accurate, precise, and practical method for extracting effective mechanical measurements of MEMS. Various methods of EMM use two unequal gaps to determine the difference in gap geometry between layout and fabrication (since MEMS devices change from layout to fabrication). These gap stops establish a means of equating a well-defined distance in terms of change in capacitance.
Using differential capacitive sensing, e.g., of sensing combs 140, measurements at zero-state and upon closing gap 111 and gap 112 by applying enough actuation voltage may be expressed as:
where define Δgap=gap1−gap1,layout, and parasitics cancel. Similarly, closing the second gap yields
The unknowns are eliminated by taking the ratio
which allows accurately measured change in gap stop from layout to fabrication as:
Once ΔC1 and Δgap are measured, the comb drive displacement is calibrated. The comb drive constant Ψ can be determined as:
where Ψ is the quantity 4 Nβεh/g expressed in the previous section. That is, Ψ is the ratio of the change in capacitance to traverse a gap-stop distance to that distance. This ratio is applies to any intermediate displacement x≦gap1 and corresponding change in capacitance ΔC. The displacement may be computed as:
Comb drive force can next be calibrated. Electrostatic force is defined as
When applied to comb drives within their large linear operating range, the partial derivatives in (7) can be replaced by differences,
where the measured comb drive constant from (5) has been substituted. It is useful to note that the force in (8) accounts for fringing fields and accommodates some non-ideal asymmetric geometries in the comb drive due to process variations.
System stiffness can then be calibrated. From measurements of comb drive displacement and force, system stiffness is defined as their ratio as
which is able to account for large linear deflections. That is, the quantity V2/AC in (9) is nearly constant for small deflections, but is expected to increase for large deflections.
Uncertainties accompany all measurements, yet reporting uncertainties with measurements are noticeably lacking in micro and nanoscale peer reviewed literature. Their absence is usually due to difficult or impractical metrological methods.
One method for measuring uncertainties is done by taking a multitude of measurements and computing the standard deviation in measurement from the computed average. As the number of measurements increase, the smaller the standard deviation becomes. If taking a large number of measurements is impractical, a more efficient method of measuring uncertainties due to a single measurement can be used as follows.
With respect to the above analyses, electrical uncertainties in the measured capacitance δC and voltage δV produce corresponding mechanical uncertainties in displacement δx, force δF, and stiffness δk. To determine such uncertainties, all quantities of capacitance and voltage can be rewritten in the above analyses as ΔC→ΔC+δC and ΔV→ΔV+δV. The first order terms of their multivariate Taylor expansions can then be identified as the mechanical uncertainties. For instance, the uncertainty in displacement δx of a single measurement is the first order term of the Taylor expansion of (6) about δC. As a result,
where the parenthetical coefficient of δC is the sensitivity ∂Δx/∂δC. Similarly, the uncertainties can be found in force δF and stiffness δk as
where the parenthetical coefficients of δC and δV are the respective sensitivities.
AFM calibration can be performed with a MEMS device such as that shown in
In various aspects of AFM calibration, the calibrated MEMS 100 can be used as an accurate and practical way to calibrate an AFM. Since the device is calibrated for in-plane operation, the sidewall of the device is used as the line of action. By placing the MEMS chip carrying sensor 100 vertically underneath the AFM cantilever stylus 211, the chip can be probed with the AFM. The AFM displacement and stiffness can be calibrated by relating the interaction displacement and force measurements of the MEMS sensor 100 against corresponding AFM output readings.
The AFM cantilever displacement can be calibrated as follows in various aspects. AFM cantilever 210 is configured to press vertically downward upon the calibrated MEMS. This action will result in an initial deflection in the flexures and comb drive of the MEMS, and a corresponding deflection of the cantilever and its beam of light of the AFM.
From this initial state, the reading of the photodiode voltage Uinitial is noted, and a voltage V is applied to the MEMS comb drive 120 (
where Δx=ΔxAFM in (13) because the AFM base and MEMS substrate are fixed with respect to each other. It should be noted that AFM base or MEMS substrate is not fixed during the initial engagement as the two devices are brought into contact by a piezoelectric stage or other mechanism. For arbitrary AU, calibrated measurements of AFM cantilever displacements may be determined by
ΔxAFM=Θ−1ΔU. (14)
The uncertainty in AFM displacement or stiffness may be determined by either of the two methods mentioned in Section 2.5.
The AFM cantilever stiffness can be calibrated, e.g., as follows. Given a measurement of AFM cantilever displacement (14) from an initial photodiode reading of initial U to a final reading of final U, the AFM cantilever stiffness can be measured as
where Δx and k of the MEMS are measured by (6) and (9). Here Δx≠ΔxAFM, unlike in (13), because the AFM base and MEMS substrate are moving with respect to each other during this interaction. In (15), the AFM and MEMS interaction forces are static equilibrium, and are equal and opposite, kΔx=kAFMΔXAFM.
Various aspects of self-calibratable MEMS described herein advantageously permit calibration of an AFM cantilever displacement and stiffness. A MEMS sensor design and a method of application are described. Measurement uncertainties using the method are identifiable and are easily determined. Measurement accuracy is achieved by eliminating unknowns and implementing accurate measurements of force, displacement, and stiffness.
Various aspects relate to a gravimeter on a chip. In the present disclosure an arrangement of a novel gravimeter on a chip is disclosed. A gravimeter is a device used to measure gravity or changes in gravity. There are several kinds of conventional gravimeters: pendulum, free falling body, and spring gravimeters. They are all large, expensive, delicate, and require an external reference for calibration. One novel aspect of the gravimeter of the present disclosure was its micro-scaled size which increases portability, robustness, and lowers it costs; and its ability to self-calibrate on chip, which increases its autonomy. Gravimeters are often used in geophysical applications such as measuring gravitational fields for navigation, oil exploration, gravity gradiometry, earthquake detection, and possible earthquake prediction. Precisions of such gravimetry can require measurement uncertainties on the order of 20 μGal (1 Gal=0.01 m/s2). Various aspects described in the present disclosure provide self-calibration methods of micro electromechanical systems (MEMS) gravimeters capable of achieving accuracy and precision needed for use as a gravimeter or sub-micro-G accelerometer. For practical reasons, various aspects of MEMS designs described herein adhere to design constraints of a standard silicon on insulator (SOI) foundry process.
A gravimeter is a device used to measure gravity or changes in gravity. They are often referred to absolute and relative gravimeters respectively. Gravimeters have found application in geophysical and metrological areas such in navigation, oil exploration, gravity gradiometry, earthquake detection, and possible earthquake prediction. Measurement resolution that is often required in the above geophysical applications to resolve spatial gravity variations is ˜20 μGal=20×10−8 m/s2. However, the time rate of gravitational change for many crustal deformation processes is on the order of 1 μGal per year. Gravimetry is also used in a number of metrological measurements such as the calibrations of load cell for mechanical force standards. Desirable attributes for gravimeters are smaller size, lower cost, increased robustness, and increased resolution. Decreasing their size increases their portability. Lowering their costs allows a larger number of them to be deployed simultaneously for finer spatial resolution. Improving their robustness to changes in temperature, age, and handling improves their reliability or repeatability. And improved accuracy and resolution increase confidence in measurement.
Various gravimeters are disclosed here that can be about a 100 times smaller (meter-size to centimeter-size) than prior gravimeters, 1000 times lower in cost ($500 k-$100 k to ˜$50), just as accurate and precise, and advantageously adapted to self-calibrate at any desired moment. Micro-fabrication reduces the size and costs of such a device by being able to batch fabricate a multitude of microscale devices simultaneously. The self-calibration feature allows the devices to recalibrate after experiencing harsh environmental changes or long-term dormancy.
Various aspects of self-calibration described herein related to change from layout to fabrication. Electro micro metrology (EMM) is an accurate, precise, and practical method for extracting effective mechanical measurements of MEMS. A method of EMM begins by using two unequal gaps to determine the difference in gap geometry between layout and fabrication. These gap stops establish a means of equating a well-defined distance in terms of change in capacitance.
Using differential capacitive sensing, measurements at zero-state and upon closing gap 511 and gap 512 by applying enough actuation, voltage may be expressed as:
ΔC1=−4Nβεh(gap1,layout+Δgap)/g, (16)
defining Δgap≡gap1−gap1,layout; parasitics cancel in the difference. Similarly, closing the second gap yields
ΔC2=4Nβεh(ngap1,layout+Δgap)/g. (17)
The unknowns are eliminated by taking the ratio of (16) to (17) and solve for the measurement of the change in gap-stop from layout-to-fabrication as
Δgap=−gap1,layout(nΔC1+ΔC2)/(ΔC1+ΔC2). (18)
Displacement, stiffness, and mass can then be calibrated.
Once ΔC1 and Δgap are measured, the comb drive is calibrated. The comb drive constant is measured as
Ψ≡ΔC1/(gap1,layout+Δgap)=ΔC1/gap1, (19)
where Ψ is the quantity 4Nβεh/g expressed above.
Regarding displacement, Ψ is the ratio of the change in capacitance to traverse a gap-stop distance to that distance. This ratio can be applied to any intermediate displacement x≦gap1 and a corresponding change in capacitance ΔC. The displacement can be measured based on
Ψ≡ΔC1/gap1=ΔC/ΔxΔx=Ψ−1ΔC. (20)
Regarding electrostatic force, when applied to comb drives within their large linear operating range, partial derivatives in the electrostatic-force equation can be replaced by differences. The electrostatic force is measured as
F≡½V2∂C/∂x=½V2ΔC/Δx=½V2Ψ. (21)
where the measured comb drive constant from (19) has been substituted. The force in (21) accounts for fringing fields and accommodates some non-ideal asymmetric geometries in the comb drive due to process variations.
Regarding stiffness, from measurements of displacement and force, system stiffness is defined as their ratio as
k≡F/Δx=0.5Ψ2V2/ΔC (21B)
which is able to account for large nonlinear deflections. The quantity V2/AC in (21B) is nearly constant for small deflections, but is expected to increase for large deflections.
Mass. From measurements of stiffness from (21B) and resonance ω0, system mass can be measured as
m=k/ω
0
2, (22)
where ω0 is not the displacement resonance that is affected by damping, but the velocity resonance that is independent of damping and equal to the undamped displacement frequency.
One method for measuring uncertainties is done by taking a multitude of measurements and computing the standard deviation in measurement from the computed average. As the number of measurements increase, the smaller the standard deviation becomes. If taking a large number of measurements is impractical, a more efficient method of measuring uncertainties due to a single measurement can be used which is described below.
With respect to the above analyses, electrical uncertainties in the measured capacitance δC and voltage δV produce corresponding mechanical uncertainties in displacement δx, force δF, mass δm, and stiffness δk. To determine such uncertainties, all quantities of capacitance can be rewritten and voltage in the above analyses as ΔC→ΔC+δC and ΔV→ΔV+δV. The first order terms of their multivariate Taylor expansions as the mechanical uncertainties can then be identified. The uncertainties in displacement, force, stiffness, and mass are:
Performance predictions of a gravimeter on a chip are now discussed. The EMM results above can be used as a design factor in predicting the desired resolution of a MEMS gravimeter. That is, the necessary uncertainties in capacitance, voltage, and frequency can be identified to know the precision in the device's measurement of gravitational acceleration. Flexure length can then be parameterized. Other parameters such as mass, number of comb fingers, finger overlap, flexure width, layer thickness, etc., can also affect precision. In an example, the following parameters can be chosen: 1000 comb fingers total, 2 μm gap between each finger, 2 μm flexure width, 3500 μm-squared proof mass, and single crystal silicon material.
Regarding design issues, besides the abovementioned parameters, other issues that can be considered are the sizes of the gap-stops, the range of gravitational forces, and the comb drive levitation effect.
Gravitational acceleration acting on one of the MEMS gravimeter designs, according to the present disclosure, is identified in
For the type of EMM analysis presented above, the translation of the comb drive remains in-plane. Comb drive levitation can cause a slight out-of-plane deflection. Such levitation is produced when there is an asymmetric distribution of surface charge about the comb fingers. This is usually due to the close proximity of the underlying substrate. In various aspects, a backside etch is implement underneath comb drives to reduce this levitation effect.
Results. To determine the uncertainty in measurement of the MEMS gravimeter, measurements are expressed as follows. Nominal measurement of gravitational acceleration is g=kx/m. Uncertainty in measurement yields
g+δg=(k+δk)(x+δx)/(m+δm). (26B)
Substituting uncertainties (23), (25), (26), a multivariate Taylor yields
which shows that the resolution of the gravitational acceleration depends on the uncertainties of δC and δω.
In an example of (27), typical measurement values are used for the following quantities: stiffness k=4Ehw3/L3 based on flexure length L that is used to sweep below, mass m=density×volume, x=mg/k, ΔC based on x, and ω0 from (22). As previously mentioned a 1-20 μGal resolution is desirable. By constraining (27) such that δg=1 μGal, a simulation can be performed. In
Various aspects of a gravimeter arrangement on a chip are described above. A test case is described above according to which uncertainties in electrical measurands are used to achieve the desired uncertainty in gravitational acceleration. The uncertainty due to voltage and capacitance can be eliminated. This leaves the uncertainty in frequency, which can be on the order of micro-Hertz.
Various aspects described herein relate to a self-calibratable inertial measurement unit. Various methods described herein permit an inertial measurement unit (IMU) to self-calibrate. Self-calibration of IMU can be useful for: sensing accuracy, reducing manufacturing costs, recalibration upon harsh environmental changes, recalibration after long-term dormancy, and reduced dependence on global positioning systems. Various aspects described herein, unlike prior schemes, offer post-packaged calibration of displacement, force, system stiffness, and system mass. An IMU according to various aspects includes three pairs of accelerometer-gyroscope systems located within the xy-, xz-, and yz-planes of the system. Each pair of sensors oscillates 90 degrees out of phase for continuous sensing during turning points of the oscillation where velocity goes to zero. An example of self-calibration of a prototype system is discussed below, as are results of modeling IMU accuracy and uncertainty through sensitivity analysis. Various aspects relate to a self-calibratable gyroscope, a self-calibratable accelerometer, or an IMU system configuration.
IMUs (inertial measurement units) are portable devices that are able to measure their translational and rotational displacements and velocities in space. Translational motion is usually measured with accelerometers, and rotational motion is usually measured with gyroscopes. IMUs are used in military and civil applications, where position and orientation information is needed [A1]. Advancements in micro electro mechanical system (MEMS) technology have made it possible to fabricate inexpensive accelerometers and gyroscopes, which have been adopted into many applications where traditionally inertial sensors have been too costly or too large [A2].
IMU accuracy, cost, and size are often critical factors in determining their use. Due to various sources of initial errors and accumulation of errors, an IMU is often recalibrated with the aid of global position systems. Calibration of IMU is important for overall system performance, but such calibration can be 30% to 40% of manufacturing costs [A3-A5].
Conventionally, the calibration of an IMU has been done using a mechanical platform, where the platform subjects the IMU to controlled translations and rotations [A6]. At various states, the output signals from the accelerometers and gyroscopes are observed and correlated with the prescribed inputs. However, this methodology is only as accurate at the mechanical platform, and this method treats the IMU as a black box, where the IMU's system masses, comb drive forces, displacements, stiffnesses, and other quantities that are useful for a mathematical description of its motion remain unknown.
One problem for the traditional calibration scheme is that the signal outputs are often scalar, yet are determined by several unknown factors that can produce results that are not unique. That is, two more different conditions may yield the same output signal. Without knowing the physical quantities within the IMU's equation of motion, then reliable predictions, clearly identifiable improvements, and a more complete understanding of what is precisely being sensed remain uncertain. Moreover, a more complete understanding of such physical quantities can facilitate recalibration after long-term dormancy or after harsh environmental changes, such as with temperature. For example, variations in temperature can affect the geometry or stress of the sensor or its packaging. Various aspects herein include electronically-probed self-calibration technology which can be an integral part of a packaged IMU (see, e.g., controller 1186,
Regarding Self-Calibration of a MEMS IMU, Electro micro metrology (EMM) is an accurate, precise, and practical method for extracting effective mechanical measurements of MEMS [A7]. It works by leveraging the strong and sensitive coupling between microscale mechanics and electronics through fundamental electromechanical relationships. What results are expressions that relate fabricated mechanical properties in terms of electrical measurands.
In addition to the set of self-calibratable MEMS gyroscope and accelerometer shown in
where N is the number of comb fingers, L is the initial finger overlap, h is the layer thickness, g is the gap between comb fingers, β is the capacitance correction factor, ε is the permittivity of the medium, Δgap=gap1−gap1,layout is the uncertainty from layout to fabrication, a is the relative error (or mismatch) that accounts for non-identical process variations between the two gaps, C+P and C−P are the unknown parasitic capacitances. By taking the ratio of (1) and (2), all unknowns except Δgap are removed. Δgap can be written as:
where the fabricated gap is now measurable as gap1=gap1,layout+Δgap; a may be ignored if mismatch is insignificant.
A comb drive constant of the given device is defined as the ratio between the gap and the change in capacitance required to traverse the gap. That is:
where the comb drive can also be associated with the relation Ψ=4Nβεh/g in (28).
Regarding displacement, the ratio of capacitance to gap distance in (31) applies to any intermediate change in capacitance ΔC and displacement Δx<gap, since comb drives are linear between capacitance and displacement. Displacement can thus be determined using:
Electrostatic force often expressed as
For comb drives that traverse laterally within their linear operating range, the partial derivative can be replaced by a difference, which is the comb drive constant from (31). Thus:
It is important to note that the force in (34) accounts for fringing fields and accommodates some non ideal asymmetric geometry in the comb drive due to process variations.
From measurements of displacement and force, system stiffness can be expressed as:
which becomes nonlinear for large deflections.
From measurements of stiffness and resonance frequency ω0, system mass can be measured as
where ω0 is either the velocity resonance if damping is present, or displacement resonance if the system is in vacuum.
From (31)-(36), it can be seen that comb drive constant plays an important role in the process of self calibration. From (31) it can be seen that the accuracy of comb drive constant depends on Δgap and ΔC1. At the same time, (30) indicates that Δgap and ΔC1 are correlated. To see the relationship clearly, an expression is derived for sensitivity and uncertainty in measurement of gap in (30) by a Taylor expansion.
The uncertainty of measuring capacitance is included into (30) by replacing instances of ΔC with ΔC±√{square root over (2)}|δC|. That is, ±√{square root over (2)}δC is the perturbation that results from adding independent random uncertainties in quadrature:
where O(δCinitial)=O(δCfinal). Substituting (37) into (38), its first order multivariate Taylor expansion about δC and σ is
where the first term on the right-hand side of (38) is Δgap, and the other terms represent δgap. The multiplicands in curly brackets are respectively the sensitivity in gap uncertainty to capacitance uncertainty, and the sensitivity in gap uncertainty to mismatch. discussed further below.
The self-calibratable IMU in various aspects includes three pairs of accelerometer-gyroscope systems, respectively located within the xy-, xz-, and yz-planes of the IMU. Each oscillatory system includes a neighboring copy that operates 90 degrees out of phase to counter lost information due to the turning points of proof-mass oscillation where velocity is goes to zero.
Considering the proportional relationship between Coriolis force and velocity, small velocities may result in an inability to resolvable Coriolis forces near the turning points of oscillation. While one proof-mass is slowing down, the other is speeding up, to that sensing the Coriolis force is maximal at all times. This configuration permits not only characterizing the mechanical quantities of the system, but also various noninertial forces, e.g., translational, centrifugal, Coriolis, or transverse forces.
An aspect of a method described herein was applied to an accelerometer with asymmetric gaps. Various aspects of methods described herein are applicable to vibratory gyroscopes.
Controller 1186 can provide control signals to voltage source 1130 to operate actuators 1140. Controller 1186 can also receive capacitance measurements from capacitance chip 1114 or another capacitance meter. Controller 1186 can use the capacitance measurements to perform various computations described herein, e.g., to compute Ψ, displacement, comb-drive force, stiffness, and mass. Controller 1186, and other data processing devices described herein (e.g., data processing system 5210,
In the tested self-calibratable accelerometer, parameters included left and right gaps of 2 μm and 4 μm, finger overlap of 11 μm, number of sense fingers is 90, finger width is 3 μm, and finger gap is 3 μm. At zero and gap-closed states, 300 capacitive measurements are taken with the AD7746 (5 msec each) that yields nominal capacitances, and a standard deviation of 21 aF. ADI specifies a resolution of 4 aF [A11].
Using (38), assuming σ=0, measurements of ΔC1 and ΔC2 were taken and it was determined that Δgap=0.150±0.001 μm. Optical and electron microscopy measurements on design 1100 were performed by refining measurement bars using monitor pixilation software. By using an experimenter's best guess at locating sidewall edges, gaps were estimated to be Δgapoptical=0.1±0.2 μm and Δgapelectron=0.19±0.07 μm. Results using EMM as described herein were within the range of results of optical and scanning electron microscopy (SEM) [A10].
Then from (31), the comb drive constant can be obtained. Then the self calibration scheme can be implemented as follows:
1) Displacement: Δx=ΔC/Ψ
2) Comb drive force: F=ΨV2/2
3) Stiffness: k=(Ψ2V2)/(2ΔC)
4) Mass: m=k/ω02
The uncertainties for measurements of displacement, comb drive force, system stiffness, and system mass can be obtained by performing a first order multivariate Taylor expansion as done in (38). That is, in (38) the sensitivity to capacitance error δC is on the order of 108 m/F, and the sensitivity to mismatch a is on the order of 10−7 m for the tested design. Per (38), the sensitivity to capacitance also depends on design parameters.
Described herein are various methods to permit IMUs to self-calibrate. Various aspects include applying enough voltage to close two unequal gaps and measuring the resulting changes in capacitances. Through this measurement, geometrical difference between layout and fabrication can be obtained. Upon the determination of fabricated gap, displacement, comb drive force, and stiffness can be determined. By measuring velocity resonance, mass can also be determined.
An IMU configuration according to various aspects includes three pairs of accelerometer-gyroscope systems located within the xy-, xz-, and yz-planes, respectively. The sensors in each pair of sensors oscillate 90 degrees out of phase with each other. This advantageously helps to counter lost information due to the turning points of proof-mass oscillation where velocity goes to zero.
Various aspects described herein relate to a self-calibratable microelectromechanical systems absolute temperature sensor. A self-calibratable MEMS absolute temperature sensor according to various aspects can provide accurate and precise measurements over a large range of temperatures.
Due to the high accuracy and precision required for some experiments and devices, such as studies involving fundamental laws or sensor drift due to thermal expansion, accurate temperature sensing is necessary. Conventional temperature sensors require factory calibration, which significantly increases the cost of manufacture. Using the equipartition theorem, nanotechnologists have long determined the stiffness of their atomic force microscope (AFM) cantilevers by measuring temperature and the cantilever's displacement. Various aspects described herein measure MEMS stiffness and displacement and determine temperature using those measurements. Various methods for accurately and precisely measuring nonlinear stiffness and expected displacement are described herein, as is an expression for quantifying the uncertainty in measuring temperature. Various nomenclature is described in Table 4.
Due to the temperature sensor's abundance of applications in personal computers, automobiles, and medical equipment [B1], for monitoring and controlling temperature they account for 75-80% of the worldwide sensor market [B2]. The types of techniques for measuring temperature include thermoelectricity, temperature dependent variation of the resistance of electrical conductors, fluorescence, and spectral characteristics [B3]. The most important performance metric of a temperature sensor is reproducibility in measurement. This metric is hard to achieve due to the limitations in calibrating procedures. Typically, a standard called International Temperature Scale (ITS) [B4] is followed to calibrate temperature sensors. This scale defines standards for calibrating temperature measurements ranging from 0K to 1300K, which is subdivided into multiple overlapping ranges. For applications within the temperature range of 13.8033K to 1234.93K, the standard is to calibrate against defined fixed points. Depending on the type of measurement these points can be triple-point, melting point, or freezing point of different materials that are accurately known. The limitation with these calibration standards is that the procedures are difficult, making their recalibration or batch calibration impractical.
The thermal method, based on the equipartition theorem, is commonly used to measure the stiffness of atomic force microscope (AFM) cantilevers [B5]. In the thermal method, the expected potential energy due to thermal disturbances is equated to the thermal energy in a particular degree of freedom by
½ky2
=½kBT. (39)
where k is the stiffness of the AFM cantilever, <y2> is the expected or mean square displacement, kB is Boltzmann's constant (1.38×10−23 NmK−1), and T is absolute temperature in Kelvin. By measuring cantilever displacement and temperature, the stiffness can be determined. Due to the uncertainty in measuring displacement and temperature of the AFM cantilever, the uncertainty in measuring cantilever stiffness is about 5-10% [B6]. The problem with measuring displacement in the AFM is due to the difficulty in finding an accurate relationship between the voltage readout of the AFM's photodiode and the true vertical displacement of the cantilever. And the problem with measuring the temperature of the AFM cantilever is that it is not known if the thermometer that is nearby the cantilever is the same temperature as the AFM cantilever that is being measured. There are also decoupled mechanical vibrations between the mechanical support of the cantilever and the mechanical support of the photodiode that add to the uncertainty.
Herein is described a MEMS temperature sensor that is self-calibratable and provides accurate and precise temperature measurements over a large temperature range. Various methods herein include measuring the change in capacitance to close two asymmetric gaps to accurately determine displacement, comb drive force, and system stiffness. By substituting the MEMS stiffness and mean square displacement into the equipartition theorem, the temperature and its uncertainty is measured.
If a system can be described by classical statistical mechanics in equilibrium at absolute temperature T, then every independent quadratic term in its energy has a mean value equal to kBT/2 [B5, B9-B11]. The equipartition theorem applied to cantilever potential energy [B11] gives (39). The equipartition theorem has been extensively used in the area of nanoscale metrology.
Hutter, in [B5], showed the use of this theorem for measuring the stiffness of individual cantilevers and tips used in AFM. In [B5] he states that for a spring constant of 0.05 N/m, thermal fluctuations will be of the order of 0.3 nm at room temperature which are relatively small deflections, so an AFM cantilever can be approximated to a simple harmonic oscillator. Hutter measured the root mean square fluctuations of a freely moving cantilever with a sampling frequency higher than its resonant frequency in order to estimate the spring constant. He computes the integral of power spectrum which is equal to the mean square of fluctuations in the time series data [B7]. The spring constant then is k=kBT/P, where P is the area of the power spectrum of the thermal fluctuations alone.
Stark in [B8] calculated the thermal noise of an AFM V-shaped cantilever by means of finite element analysis. He showed that the stiffness can be calculated from equipartition theorem.
Butt in [B9] showed the use of equipartition theorem for calculating thermal noise of a rectangular cantilever. Levy in [B10] applied Butt's method to a V-shaped cantilever. Jayich in [B11] showed that thermomechanical noise temperature could be determined by measuring the mean square displacement of the cantilever's free end.
Herein are described the dependence of displacement amplitude on temperature and stiffness; some applications of the equipartition theorem; methods for accurately and precisely measuring MEMS displacement and stiffness; and details of measuring MEMS temperature.
Regarding dependence of displacement amplitude on stiffness and temperature, the dependence of amplitude on stiffness and temperature can be characterized. For a device vibrating sinusoidally, the expected or mean square displacement is
y
2
=y
rms
2=½A2. (40)
where yrms is the root mean square of its displacement and A is its amplitude of motion. Substituting (40) into (39) gives an amplitude of
A=√{square root over (2kBT/k)}. (41)
By differentiating (40) with respect to stiffness and temperature, the sensitivities of amplitude with stiffness and temperature are determined to be:
dA/dk=(−½k)√{square root over (2kBT/k)}, and (42)
dA/dT=(½)√{square root over (2kB/kT)}. (43)
Regarding displacement and stiffness, described herein is a self-calibratable measurement technology for measurement of stiffness and displacement using electrical measurands [B12-B14]. Various methods herein involve applying the steps described below to a MEMS structure.
In step 2030, comb drive force is determined as
F=½V2∂C/∂x=½V2ψ. (46)
The system stiffness is k≡F/Δy. Using expressions of displacement (45) and force (46), in step 1940, the nonlinear stiffness is determined as
k=½ψ2V2/ΔC. (47)
Regarding MEMS temperature sensing, an exemplary method herein for measuring temperature using MEMS involves solving the equipartition theorem (39) for absolute temperature by substituting the measured displacement using (45) and stiffness using (47). The root mean value of displacement used for (39) is
where displacements can be dynamically measured using a transimpedance amplifier, as illustrated in
Referring back to
T=k
y
2
/k
B. (49)
Regarding mean and standard deviation, each measurement of temperature taken is based on the expected displacement, which is an averaging process. Therefore, each measurement of temperature is actually from a sampling of a distribution of average temperatures, assuming the true temperature is not changing. It is well-known that the mean of the mean measurement of temperatures quickly converges to the true temperature, regardless of the distribution type, according to the Central Limit Theorem. Once the standard of the temperature distribution is measured,
then the sample standard deviation of the of the mean of means is
Regarding uncertainty, uncertainty in temperature can be found by the first order terms of a multivariate Taylor expansion about the uncertainties in capacitance δC and voltage δV. These uncertainties can be practically found by determining the order of the decimal place of the largest flickering digit on a capacitance or voltage meter. The standard deviation and uncertainty in temperature, respectively, are:
where T from (39) is a function of capacitance and voltage due to displacement (45) and stiffness (47).
By substituting (40) and (47) into (49), temperature T can be determined as:
Differentiating (53) with respect to change in capacitance ΔC and voltage V yields uncertainty in temperature (54) as:
For a test case, a finite element analysis software package called COMSOL [B15] was used to model the mechanical and electrical physics. As discussed above, when closing 2 unequal gaps, the change in capacitance is measured. By substituting these values in (54) the uncertainty in measuring temperature can be predicted.
Regarding the comb drive constant, to increase precision through convergence analysis using a maximal number of elements, the comb drive constant can be modeled separately from mechanical properties of the structure. Assuming that each comb drive finger can be modeled identically, a single comb finger section can be modeled as shown in
To determine stiffness, using 34000 elements, a simulated comb drive voltage of 50V was applied and the corresponding change in capacitance was determined via simulation to be ΔC=1.04×10−14 F. Substituting these values into (47), the stiffness of the structure shown in
Regarding amplitude, corresponding to the stiffness of 0.38197 N/m, from
Regarding uncertainty, substituting k=0.38197 N/m, A=1.4742×10−10 m, kB=1.38×10−23NmK−1, V=50V, ΔC=1.04×10−14F, δV=1×10−6 V, δC=1×10−18F into (54), the sensitivities are
|∂T/∂ΔC|=2.89×1016K/F
and
|∂T/∂V|=12.04K/V.
The uncertainty in the measurement of T due to the uncertainty in capacitance is |∂T/∂ΔC|δC=0.029 K, and the uncertainty in the measurement of T due to the uncertainty in voltage is |∂T/∂ΔC|δV=1.2×10−5 K. The total uncertainty is 0.029K at T=300K. The uncertainties for capacitance and voltage used here are the typical precision specifications of capacitance meters from ANALOG DEVICES INC. and voltage sources from KEITHLEY INSTRUMENTS. From the magnitude of the sensitivities in this test case, it can be seen that the uncertainty in temperature is weakly sensitive to the uncertainty in voltage, yet strongly sensitive to the uncertainty in capacitance. Fortunately, zeptofarad O(10−24) capacitance resolution is possible, which would appear to reduce the uncertainty in temperature due to capacitance by another three orders of magnitude. In addition, as shown in (54), the sensitivities depend on design parameters such as stiffness and gap size.
Various aspects described herein include methods for measuring the MEMS temperature based on electronic probing. Various aspects use devices with comb drives. Various aspects permit temperature sensing using post-packaged MEMS that can self-calibrate. Various aspects include measuring the change in capacitance to close two asymmetric gaps. Measurements of the gaps are used to determine geometry, displacement, comb drive force, and includes stiffness. By substituting the accurate and precise measurements of stiffness and mean square displacement into the equipartition theorem, accurate and precise measurements of absolute temperature are determined. Expressions for the measurement of mean, standard deviation, and uncertainty of absolute temperature were discussed above.
Various aspects relate to an Electrostatic Force-Feedback Arrangement for Reducing Thermally-Induced Vibration of Microelectromechanical Systems. Electrostatic force-feedback is used to counter thermally-induced structural vibrations in micro electro mechanical systems (MEMS). Noise, coming from many different sources, often negatively affects the performance of N/MEMS by decreasing the precision for sensors and position controllers. As dimensions become small, mechanical stiffness decreases and the amplitude due to temperature increases, thereby making thermal vibrations become more significant. Thermal noise is most often regarded as the ultimate limit of sensor precision. This limit in precision impedes progress in discovery, the development of standards, and the development of novel NEMS devices. Hence, practical methods to reduce thermal noise are greatly needed. Prior methods to reduce thermal vibration include cooling and increasing flexure stiffness. However, the cooling increases the overall size of the system as well as operating power. And increasing the flexure stiffness can come at the cost of reduced performance. Electrostatic position feedback has been used in accelerometers and gyroscopes to protect against shock and improve performance. Various aspects described herein advantageously use such techniques to reduce vibration from noise by using velocity controlled force-feedback. Described herein are analytical models with parasitics that are verified through simulation. Using transient analysis, the vibrational effects of white thermal noise upon a MEMS can be determined. Greatly reduced vibration can be achieved due to the inclusion of a simple electrostatic feedback system.
The ultimate lower limit of most sensing performance has previously been set by noise in micro-machined devices. There are numerous sources of noise that affect performance. However, after noise from electronics has been reduced and after extraneous electromagnetic fields have been shielded, thermal noise is one of the most significant sources of noise that remain. Mechanical vibration due to this thermal noise has often been called the ultimate limit. Described herein is a method to reduce such vibrations in MEMS.
Gabrielson [C1] presented an analysis of the mechanical-thermal vibrations, or thermal noise, in MEMS. At the fundamental level, thermal noise is understood to result from the random paths and collisions of particles described by Brownian motion. From quantum statistical mechanics, the expected potential energy of a given node equals the thermal energy in a particular degree of freedom of a structure, yielding
½kx2
=½kBT (55)
where k is the stiffness in the degree of freedom, kB is Boltzmann's constant, T is the temperature, and x2 is the mean of the square of the displacement amplitude. Equivalently, thermal noise can be described by Nyquist's Relation as a fluctuating force
F=√{square root over (4kBTD)} (56)
where D is the mechanical resistance or damping [C1]. From either (55) or (56) it is clear that there will be some expected amplitude of fluctuation or vibration, x, of a mechanical structure for all temperatures. This vibration is what is referred to as thermal noise here. Leland [C2] extended the mechanical-thermal noise analysis for a MEMS gyroscope. Vig and Kim [C3] provide an analysis of thermal noise in MEMS resonators.
The problem of thermal noise is significant in atomic force microscopy (AFM), where the AFM's probe consists of a cantilever that is subject to the vibrations caused by thermal noise. Reference [C4] demonstrates the calculation, yielding results similar to equations (55) and (56), of thermal noise specifically for AFM. Using an example from [C5], given a microstructure at T=306K with a stiffness of k=0.06 N/m, then its expected amplitude of vibration would be about 0.3 nm, which is about the length of ˜1 to 3 atoms. Such vibration is often not suitable for molecular scale manipulation. With such uncertainty in displacement, and uncertainty in the measurement of AFM stiffness from 10-40%, then AFM force is uncertain by as much as <F>=k<X>˜10-100 pN. Gittes and Schmidt [C6] predict smaller vibrations of ˜0.4 pN from thermal vibrations, but acknowledge that true values will be much larger based on AFM tip and surface geometries. Regardless, these uncertainties limit the ability to resolve hydrogen bonds in DNA or measure protein unfolding dynamics [C7], as examples.
To move beyond this thermal noise limit, according to various aspects herein, electrostatic force-feedback control is used to reduce the amplitude of mechanical vibrations due to thermal noise. Boser and Howe [C8] discuss the use of position controlled electrostatic force-feedback in MEMS to improve sensor performance. Their approach uses position controlled feedback to increase device stability and extend bandwidth. The extended bandwidth is important because they propose minimizing thermal noise by design of high-Q structures with optimized resonant frequency, and therefore small useable bandwidth. Thus, Boser and Howe propose position controlled feedback as a means of extending the useful bandwidth and address thermal noise with improved mechanical design, which is still thermal noise limited. In contrast, methods herein use velocity controlled electrostatic force-feedback to directly limit thermal vibrations of MEMS structures.
There are numerous examples of the use of feedback in MEMS. Dong et al. in [C9] describe the use of force feedback with a MEMS accelerometer in order to lower the noise floor. However, the feedback is used to improve linearity, bandwidth, and dynamic range. That scheme uses digital feedback (discrete pulses) to reduce the electrical and quantization noise, taking the mechanical noise as the limiting case. In contrast, methods herein use feedback to reduce the thermal (limiting component of mechanical) noise. Similar to [C9], Jiang et al. in [C10] extended the use of digital force-feedback to a MEMS gyroscope in order to lower the noise floor down to the thermal noise limit. This scheme considers mechanical-thermal noise as the limiting factor and the feedback design only addresses electrical noise and sampling errors, while ignoring thermal noise. Handtmann et al. in [C11] describe the use of position controlled digital force-feedback with a MEMS inertial sensor to enhance the sensitivity and stability be using electrostatic capacitive sensor and actuator pairs to sense a displacement and feedback force pulses for position re-zeroing. This scheme also addresses other types of noise and leaves mechanical-thermal noise as the limit. In the prior art the feedback is used to improve performance above the thermal noise limit and is addressing other problems besides thermal noise (linearity, bandwidth, stability, etc.).
Gittes and Schmidt in [C6] discuss the use of feedback for force zeroing in AFM. They present two typical methods of feedback in a theoretical discussion about the thermal noise limits. The first type of feedback common to AFM is the position-clamp experiment where the probe tip is held stationary by using the position of the probe tip as the feedback signal to control the motion of the cantilever anchor. The result is feedback which varies the strain on the cantilever but keeps the probe tip stationary. The second type of feedback common to AFM is the force-clamp experiment where the motion of the anchor is controlled by the feedback signal in order to keep the probe strain constant. Thus, the probe tip moves with the cantilever while maintaining a constant force on the measured surface. In either case, the feedback is a part of the measurement apparatus and is not intended to address thermal vibrations. Rather, Gittes and Schmidt describe thermal noise as the source of uncertainty within the feedback system.
Huber et al. in [C12] presented the use of position based feedback control of a tunable MEMS mirror for laser bandwidth narrowing. Their approach specifically addresses thermal vibrations with a feedback system based on wavelength. Brownian motion causes the MEMS mirror to vibrate, resulting in laser wavelength blurring. Using an etalon and a difference amplifier, the resulting wavelength is compared to an expected value and the difference is used as the feedback signal. The authors were able to demonstrated reduced linewidth from 1050 to 400 MHz, a reduction of 62%. Although their system was successful, it used static position based feedback control. In contrast, methods and systems described herein use velocity controlled feedback, which does not depend on specific position, but rather uses velocity to reduce vibrations directly. At the macroscale, feedback to reduce thermal vibrations has been demonstrated. Friswell et al. in [C13] use piezoelectric sensors and actuators to feedback a damping signal for thermal vibrations in a 0.5 m aluminum beam. They use the aluminum beam as a purely experimental example to demonstrate the effects of feedback damping on thermal vibrations. They are able to demonstrate greatly reduced settling times for thermal excitations with vibrations on the order of 0.1 mm.
Regardless of the feedback applied to MEMS, an actuating mechanism is required. Two of the most common actuation methods are piezoelectric actuators and electrostatic comb drives. Wlodkowski et al. in [C14] present the design of a low noise piezoelectric accelerometer and Levinzon in [C15] derives the thermal noise expressions for piezoelectric accelerometers, looking at both the mechanical and electric thermal noise. The piezoelectric phenomenon can be applied to reducing inherent vibrations. Herein are described various aspects using electrostatic comb drive actuators, which are a common actuation mechanism in MEMS. One of the primary challenges of using MEMS to detect and provide corrective forces for vibrations induced by thermal noise is the extremely small size of the displacements. In order to provide velocity controlled feedback which reduces random thermal vibration amplitudes from nanometers to angstroms or below, the MEMS sensor and feedback electronics should rapidly sense motion and instantaneously feedback an opposing electrostatic force to counter the motion using preferably analog circuitry.
Herein are described the components of an exemplary circuit that senses vibrational proof mass motion in MEMS comb drives, and then applies electrostatic feedback forces that counter such motion using another set of comb drives; simulations of each system component that exemplify their roles; simulations of an integrated system including the feedback circuit and a MEMS structure that is subject to white noise disturbances; and simulations of the motion of the MEMS before and after activating the feedback circuit in the face of noise sources.
Various aspects herein include a force feedback damping circuit. This circuit produces an electrostatic feedback force to oppose noise-induced motion. The feedback force is proportional to velocity to emulate the well-known viscous damping force on the proof mass. Electronics are used to emulate largely-damped mechanical system dynamics that are able to reduce the noise-induced motion.
The comb drive 2620 on the right hand side (RHS) in
A circuit attached to the RHS comb drive 2620 will sense this change in capacitance and produce a proportional voltage signal through a trans-impedance amplifier 2650. This signal is further processed through different parts of the circuit (see
The proof mass of the comb drive 2601 vibrates, due to white noise sources, at its mechanical resonance frequency of ωm2πfm. This thermal vibration causes the MEMS capacitance to vary as a function of time as
where N is the number of comb drive fingers, ε is the permittivity of the medium, h is the layer thickness, g is the gap between comb fingers, L0 is the overlap of comb fingers and) xmax is the maximum deflection amplitude due to noise. In relation to (55), <x2> and xmax are related by
To sense this noise-induced mechanical motion through the change in capacitance, a current signal (IC) is passed through the position-dependent capacitor. This input signal is a sinusoid of frequency ω which is much higher than ωm as to not further excite the mechanical motion. The frequency ω is tunable and provided by the input voltage source 2625 (Vin) (
V
in
=V
ac sin(ωt) (60)
The current signal IC is passed through the capacitor which is then converted to a voltage signal and amplified through an inverting amplifier, as shown in
The current IC through the capacitor is modulated by both amplitude and phase due to the time varying nature of the capacitance. The output signal Vout can be expressed as
Here, A1 is the overall gain of the circuit in
Using the first assumption, equation (63) can be reduced to:
Further, the considered device here exhibits capacitance in the picofarad range, while the change in capacitance due to thermal vibration is several magnitudes smaller. Hence the cubic term can be neglected, resulting in a linear dependency:
A
2(t)≈ωC(t). (66)
Again, the first assumption yields 1/(ωR1C(t)) as a large value which indicates θ(t)≈−π/2. Since the change in capacitance is relatively small, there is negligible change in this angle. Moreover, the second approximation ensures that the rate change of cot is much higher than θ(t). Thus the output voltage Vout can be linearized as
V
out
≈ωA
1
V
ac
C(t)cos(ωt) (67)
The process to retrieve the time varying nature of the capacitance is simple amplitude demodulation. The output voltage is multiplied by a demodulating signal Vac cos(ωt) which is derived by passing the input signal Vin through a differentiator 2665 (
A multiplier 2870 is used to multiply Vac cos(ωt) with Vout. The multiplier circuit can be envisioned with op-amps as reported in [C16]. The output of the multiplier is given by
V
m=½ωAVac2C(t)+½ωAVac2C(t)cos(2ωt). (68)
The output of the multiplier contains a term directly proportional to the capacitance which is varying at a relatively low frequency (˜30 kHz) and high frequency component, which can be eliminated by a 6th order Butterworth filter as shown in
The output of the filter is directly proportional to the capacitance of the comb drive:
V
f
≈ωAV
ac
2
C(t). (69)
If this signal is passed through another differentiator shown in
The first step of filtering does not eliminate the noise (high frequency component) altogether. Thus the differentiator may make this reminiscent noise prominent. Thus the signal can be further filtered to reduce noise using a low-order low-pass butter worth filter as shown in
The filtered output of the differentiator is passed through both non-inverting and inverting zero-crossing detectors (see
When the capacitance is decreasing, the differentiator output becomes negative (i.e., negative slope) which causes VZC1 to be equal to −Vsat and VZC2 to be equal to +Vsat. Thus the Q2 transistor is driven to cut-off while tuning on the Q1 transistor. Thus the Vin signal is provided as the feedback signal Vfeedback. Here, |Vsat| is the saturation voltage of the op-amp.
The increase in capacitance indicates that the proof mass 2601 is moving towards the right due to an increase in comb finger overlap. Similarly, the decrease in the capacitance indicates that the proof mass 2601 is moving towards the left due to a decreasing comb finger overlap. The differentiator 2665 output senses these movements as a positive slope or a negative slope respectively, and generates square wave signals using the zero-crossing detectors 2675 to control the conditional circuit 2680 (all
Still referring to
A simulation was performed to test the force feedback system shown in
This output of the multiplier is passed through the 6th order low-pass Butterworth filter with roll-off of −140 dB/dec, as mentioned in
It can be observed that the output of the filter stabilizes after ˜30 μs. The direction of change in capacitance is determined with a differentiator which gives either a positive or negative voltage depending on whether the voltage is increasing or decreasing respectively. The output signal from the differentiator can be noisy due to the noises left after filtering, as shown in
This signal can be filtered using a filter of same cut-off frequency (fC=0.35 MHz). The filtered output is shown in
This signal is then fed to the two zero-crossing detectors described above. These two zero-crossing detectors produce square wave signals of same frequency at which the capacitance is varying. These square wave signals are shown in
The feedback signal from the conditional circuit is shown in
This feedback signal is applied to the left comb drive to create an electrostatic feedback force. When the proof mass of the device moves to the left, the net electrostatic force is ˜0 N, because the output of the conditional circuit is Vin, so both plates of actuator 2640 (
Herein are described various aspects of an electrostatic force feedback circuit that can advantageously reduce the passive vibrations of MEMS that are due to parasitic disturbances such as thermal noise. Models and simulations of various integrated circuit components with a MEMS structure comprising of a pair of comb drives and folded flexure supports are described above. Various circuits herein sense motion with one comb drive and apply feedback forces with the other comb drive. The feedback force can be proportional to the velocity of the MEMS proof mass, such that the feedback force is similar to viscous damping common to simple mechanical systems. Simulation results demonstrate that the noise-induced amplitude in the MEMS device can be greatly reduced by applying electrostatic viscous force feedback. Various parameters can be adjusted to provide various strengths of under-, critical-, and overdamping.
Various aspects relate to methods and arrangements for measuring Young's modulus by electronic probing. Herein are described accurate and precise methods for measuring the Young's modulus of MEMS with comb drives by electronic probing of capacitance. The electronic measurement can be performed off-chip for quality control or on-chip after packaging for self-calibration. Young's modulus is an important material property that affects the static or dynamic performance of MEMS. Electrically-probed measurements of Young's modulus may also be useful for industrial scale automation. Conventional methods for measuring Young's modulus include analyzing stress-strain curves, which is typically destructive, or include analyzing a large array of test structures of varying dimensions, which requires a large amount of chip real estate. Methods herein measure Young's modulus by uniquely eliminating unknowns and extracting the fabricated geometry, displacement, comb drive force, and stiffness. Since Young's modulus is related to geometry and stiffness that can be determined using electronic measurands, Young's modulus can be expressed as a function of electronic measurands. Also described herein are results of a simulation using a method herein to predict the Young's modulus of a computer model. The computer model is treated as an experiment by using only on its electronic measurands. Simulation results show good agreement in predicting the exactly known Young's modulus in a computer model within 0.1%.
Young's modulus is one of the most important material properties that determine the performance of many micro electro mechanical systems (MEMS). There have been many methods developed for measuring the Young's modulus of MEMS. For example, Marshall in [D1] suggests the use of laser Doppler vibrometer for measuring the resonance frequency of an array of micromachined cantilevers to determine Young's modulus. This method requires the use of laboratory equipment, and requires the estimation of local density and geometry which can introduce significant error. The uncertainty of this method is reported to be about 3%. In [D2], Yan et al. uses a MEMS test to estimate Young's modulus using electronic probing. Yan's method requires the estimates of many unknowns, including parasitic capacitance, gap spacing, beam width, beam length, residual stress, permittivity, layer thickness, fillets, and displacement, which can introduce significant error in the measurement of Young's modulus. As a last example, in [D3], Fok et al. used an indentation method for measuring Young's modulus. That is, an indention force is applied causing surface deformation. The size of the deformed area is used to estimate Young's modulus, with unreported uncertainty. Various methods herein advantageously eliminate unknowns, and the uncertainty in measurement is quantifiable with just a single measurement. Various methods herein use electronic probing.
Presently, there is no ASTM standard for measuring micro-scale Young's modulus. This difficulty in developing a standard has to do with various methods not agreeing with each other and the difficulty in tracing the micro-scale measurement to an accepted macro-scale standard.
The need for an efficient and practical method for measuring the Young's modulus is critical due to process variation and the dependence of MEMS performance on Young's modulus.
In addition to variations in material properties, upon fabrication there are also variations in geometry that can significantly affect performance. In [D5], Zhang did some work to show the high sensitivity between geometry and performance. It was found that a small change in geometry could lead to a large change from the predicted performance.
Various methods described herein predict the Young's modulus by including the presence of tapered beams to nearly eliminate the effect of fillets, and uses the measurement of stiffness to determine the Young's modulus. A herein-described analytical model for determining the stiffness and Young's modulus closely matches finite element analysis.
Herein are described a comparison of the effect of fillets due to fabrication upon beams with and without tapered ends; an analytical expression for the tapered beam which nearly eliminates the presence of fillets and can be used to obtain the Young's modulus; various methods of electro micro metrology (EMM) for measuring stiffness; and a simulated experiment to verify herein-described methods to extract Young's modulus.
Regarding filleted versus tapered beams, one problem with determining the Young's modulus of a flexure is the presence of fillets that appear at the locations of acute vertices. See
For example,
Simulations were done using finite element analysis using COMSOL [D6] with a high mesh refinement of over 32000 linear quadratic elements and over 130,000 degrees of freedom.
It is clear that fillets have a significant effect on the static and dynamics performance of MEMS. The analyst's problem is that it is difficult to predict what the radius of curvature will be for any one fabrication. To address this problem, various aspects described herein reduce the effect of fillets on flexures using tapered beam sections between the beam and anchor. Since a tapered beam has large obtuse angles, instead of sharp acute angles, any fillet that forms during fabrication should have a smaller effect on static and dynamic performances.
Tapering a flexure at the ends can thus reduce the significance of fillets. A curved tapering (i.e., tapered sections with curved sidewalls) that has a radius of curvature that is larger than what would be expected from any fabricated fillet can substantially reduce the filleting effect from fabrication. Below are described tapered sections with straight sidewalls.
Below is described an analytical model and an exemplary method for predicting the Young's modulus. The analytical equation for finding the stiffness of a tapered element is developed as shown in
The relation that can be used for predicting the Young's modulus is
k
measured
=k
model (71)
where kmodel is the stiffness from an analytical model and kmeasured is the stiffness from an experiment such as herein-described methods of electro micro metrology (EMM) [D12]. An analytical model for the net stiffness is developed by using the matrix condensation [D7] technique to combine a tapered beam's stiffness matrix to a straight beam's stiffness matrix. The analytical model for the tapered beam is developed by using a method of virtual work [D8-D9]. “Virtual work” refers to applications of various techniques known in the physics art.
As shown in
By Maxwell's Theorem of Reciprocal Displacements [D10] the flexibility matrix is symmetric and since f12=f21=0 and f13=f31=0 it is necessary to find only f11, f22, f33, and f23. For the tapered component shown in
To find the flexibility coefficient, f11, a unit real load is placed at degree of freedom 1 in the natural system. This gives N(x)=1. A virtual load placed at degree of freedom 1 in the natural system gives n(x)=1. By using the method of virtual work for axial displacements, f11 is computed as:
To find f22, a unit real load placed at degree of freedom 2 in the natural system gives the moment of M(x)=x/L−1. Placing a unit virtual load at degree of freedom 2 in the natural system gives the moment of m(x)=x/L−1. By using the virtual method for flexural displacements the flexibility coefficient is calculated to be
To find f33, a unit real load placed at degree of freedom 3 in the natural system gives the moment of M(x)=x/L. Placing a unit virtual load at degree of freedom 3 in the natural system gives the moment of m(x)=x/L. By using the virtual method for flexural displacements the flexibility coefficient is calculated to be
To find f23, a unit real load placed at degree of freedom 3 in the natural system gives the moment of M(x)=x/L. Placing a unit virtual load at degree of freedom 2 in the natural system gives the moment of m(x)=x/L−1. By using the virtual method for flexural displacements the flexibility coefficient is calculated to be
The above equations can be substituted into the flexibility matrix. The transformation matrix F from the natural to the complete degrees of freedom is [D9]
The stiffness matrix for the tapered beam is
Similarly, using the method of virtual work for a straight beam of length l and a moment of area I=hw13/12, Kbeam is:
where A=w1h is the cross-sectional area of the straight beam and c=EI/l3.
Combining the tapered (79) and straight (80) stiffnesses into a single flexure, the net flexure stiffness is:
and where the right boundary of the flexure is anchored at the location where the width is w2, whereby eliminating the rows and columns of the anchored boundary node.
Considering a vertically applied force located at the right free end of the flexure,
the stiffness seen by the vertical displacement at the point of application of the force is
Using the parameters of the filleted test case shown in
(83) is then used to determine the Young's modulus of a fabricated device. That is, the fabricated stiffness is measured using EMM, then that stiffness is modeled using (83) without the Young's modulus since it is the unknown. The true Young's modulus is thus:
Regarding stiffness measurement using Electro Micro Metrology, below is described a theoretical basis for a measurement of system stiffness using electro micro metrology [D11-D12]. AN exemplary method involves applying the following steps to states of a structure such as the one shown in
In subsequent step 4940, a displacement of the comb drive is measured using the relation in (85) as
y=ΔC/Ψ. (86)
In step 4950, the comb drive force is computed as
F≡½V2∂C/∂x=½V2Ψ. (87)
In step 4960, stiffness is computed. The system stiffness is defined as k≡F/Δy. Using the expressions of displacement (86) and force (87), nonlinear stiffness can be computed as
A simulated experiment (SE) was performed. This was done because some experimental measurement methods for Young's modulus have unknown accuracy and an uncertainty larger than numerical error. In SE, measurements of capacitance are emulated, because capacitance would be one type of measurement that is available in a true experiment. As discussed above, by measuring the capacitance required to close 2 unequal gaps, system stiffness (88) of the structure under test can be obtained.
Regarding comb drive constant, to improve precision through convergence analysis through finite element mesh refinement using a maximal number of elements, the comb drive constant was modeled separately from mechanical properties of the structure. By assuming that each comb drive finger can be modeled identically in their totality, a single comb finger section can be modeled as shown in
Regarding stiffness, using 34000 mechanical elements, a simulated comb drive force was applied using a voltage of 50V and the corresponding change in capacitance was simulated (see
k
measured=22.907N/m. (89)
By substituting (89) into (84), the measured Young's modulus was determined to be Emeasured=160.18 GPa. The true Young's modulus (i.e., the Young's modulus provided as input to the FEA model) is exactly Etrue=160 GPa. So the SE prediction of Young's modulus has a relative error of 0.11%.
Material properties and geometries as fabricated are often significantly different than what was predicted from simulation and layout geometry. One of the geometric changes is the formation of fillets, which have a radius of curvature that is difficult to predict, and the fillets can have a significant effect on stiffness. Another property that changes is Young's modulus, which is difficult to measure due to non-accurate measurements of stiffness. Various methods and systems described herein substantially reduce the effect of fillets by using tapered beams. Various methods and systems described herein permit accurate, precise, and practical measurement of Young's modulus by measuring stiffness. An exemplary method was tested using a simulated experiment and showed agreement with true values of Young's modulus to within 0.11%.
In view of the foregoing, various aspects measure differential capacitance. A technical effect is to permit determination of mechanical properties of MEMS structures, which can in turn permit determination of, e.g., temperature, orientation, or motion of the MEMS device.
Throughout this description, some aspects are described in terms that would ordinarily be implemented as software programs. Those skilled in the art will readily recognize that the equivalent of such software can also be constructed in hardware (hard-wired or programmable), firmware, or micro-code. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, or micro-code), or an embodiment combining software and hardware aspects. Software, hardware, and combinations can all generally be referred to herein as a “service,” “circuit,” “circuitry,” “module,” or “system.” Various aspects can be embodied as systems, methods, or computer program products. Because data manipulation algorithms and systems are well known, the present description is directed in particular to algorithms and systems forming part of, or cooperating more directly with, systems and methods described herein. Other aspects of such algorithms and systems, and hardware or software for producing and otherwise processing signals or data involved therewith, not specifically shown or described herein, are selected from such systems, algorithms, components, and elements known in the art. Given the systems and methods as described herein, software not specifically shown, suggested, or described herein that is useful for implementation of any aspect is conventional and within the ordinary skill in such arts.
The data processing system 5410 includes one or more data processor(s) that implement processes of various aspects described herein. A “data processor” is a device for automatically operating on data and can include a central processing unit (CPU), a desktop computer, a laptop computer, a mainframe computer, a personal digital assistant, a digital camera, a cellular phone, a smartphone, or any other device for processing data, managing data, or handling data, whether implemented with electrical, magnetic, optical, biological components, or otherwise.
The phrase “communicatively connected” includes any type of connection, wired or wireless, between devices, data processors, or programs in which data can be communicated. Subsystems such as peripheral system 5420, user interface system 5430, and data storage system 5440 are shown separately from the data processing system 5410 but can be stored completely or partially within the data processing system 5410.
The data storage system 5440 includes or is communicatively connected with one or more tangible non-transitory computer-readable storage medium(s) configured to store information, including the information needed to execute processes according to various aspects. A “tangible non-transitory computer-readable storage medium” as used herein refers to any non-transitory device or article of manufacture that participates in storing instructions which may be provided to processor 1186 or another data processing system 5410 for execution. Such a non-transitory medium can be non-volatile or volatile. Examples of non-volatile media include floppy disks, flexible disks, or other portable computer diskettes, hard disks, magnetic tape or other magnetic media, Compact Discs and compact-disc read-only memory (CD-ROM), DVDs, BLU-RAY disks, HD-DVD disks, other optical storage media, Flash memories, read-only memories (ROM), and erasable programmable read-only memories (EPROM or EEPROM). Examples of volatile media include dynamic memory, such as registers and random access memories (RAM). Storage media can store data electronically, magnetically, optically, chemically, mechanically, or otherwise, and can include electronic, magnetic, optical, electromagnetic, infrared, or semiconductor components.
Aspects of the present invention can take the form of a computer program product embodied in one or more tangible non-transitory computer readable medium(s) having computer readable program code embodied thereon. Such medium(s) can be manufactured as is conventional for such articles, e.g., by pressing a CD-ROM. The program embodied in the medium(s) includes computer program instructions that can direct data processing system 5410 to perform a particular series of operational steps when loaded, thereby implementing functions or acts specified herein.
In an example, data storage system 5440 includes code memory 5441, e.g., a random-access memory, and disk 5443, e.g., a tangible computer-readable rotational storage device such as a hard drive. Computer program instructions are read into code memory 5441 from disk 5443, or a wireless, wired, optical fiber, or other connection. Data processing system 5410 then executes one or more sequences of the computer program instructions loaded into code memory 5441, as a result performing process steps described herein. In this way, data processing system 5410 carries out a computer implemented process. For example, blocks of the flowchart illustrations or block diagrams herein, and combinations of those, can be implemented by computer program instructions. Code memory 5441 can also store data, or not: data processing system 5410 can include Harvard-architecture components, modified-Harvard-architecture components, or Von-Neumann-architecture components.
Computer program code can be written in any combination of one or more programming languages, e.g., JAVA, Smalltalk, C++, C, or an appropriate assembly language. Program code to carry out methods described herein can execute entirely on a single data processing system 5410 or on multiple communicatively-connected data processing systems 5410. For example, code can execute wholly or partly on a user's computer and wholly or partly on a remote computer or server. The server can be connected to the user's computer through network 5450.
The peripheral system 5420 can include one or more devices configured to provide digital content records to the data processing system 5410. For example, the peripheral system 5420 can include digital still cameras, digital video cameras, cellular phones, or other data processors. The data processing system 5410, upon receipt of digital content records from a device in the peripheral system 5420, can store such digital content records in the data storage system 5440.
The user interface system 5430 can include a mouse, a keyboard, another computer (connected, e.g., via a network or a null-modem cable), or any device or combination of devices from which data is input to the data processing system 5410. In this regard, although the peripheral system 5420 is shown separately from the user interface system 5430, the peripheral system 5420 can be included as part of the user interface system 5430.
The user interface system 5430 also can include a display device, a processor-accessible memory, or any device or combination of devices to which data is output by the data processing system 5410. In this regard, if the user interface system 5430 includes a processor-accessible memory, such memory can be part of the data storage system 5440 even though the user interface system 5430 and the data storage system 5440 are shown separately in
In various aspects, data processing system 5410 includes communication interface 5415 that is coupled via network link 5416 to network 5450. For example, communication interface 5415 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 5415 can be a network card to provide a data communication connection to a compatible local-area network (LAN), e.g., an Ethernet LAN, or wide-area network (WAN). Wireless links, e.g., WiFi or GSM, can also be used. Communication interface 5415 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information across network link 5416 to network 5450. Network link 5416 can be connected to network 5450 via a switch, gateway, hub, router, or other networking device.
Network link 5416 can provide data communication through one or more networks to other data devices. For example, network link 5416 can provide a connection through a local network to a host computer or to data equipment operated by an Internet Service Provider (ISP).
Data processing system 5410 can send messages and receive data, including program code, through network 5450, network link 5416 and communication interface 5415. For example, a server can store requested code for an application program (e.g., a JAVA applet) on a tangible non-volatile computer-readable storage medium to which it is connected. The server can retrieve the code from the medium and transmit it through the Internet, thence a local ISP, thence a local network, thence communication interface 5415. The received code can be executed by data processing system 5410 as it is received, or stored in data storage system 5440 for later execution.
In step 5510, the movable mass 101 is moved into a first position in which the movable mass is substantially in stationary contact with a first displacement-stopping surface.
In subsequent step 5515, using a controller, a first difference between the respective capacitances of two spaced-apart sensing capacitors 120 is automatically measured while the movable mass is in the first position. Each of the two sensing capacitors includes a respective first plate attached to and movable with the movable mass and a respective second plate substantially fixed in position (e.g.,
In step 5520, the movable mass is moved into a second position in which the movable mass is substantially in stationary contact with a second displacement-stopping surface spaced apart from the first displacement-stopping surface.
In subsequent step 5525, using the controller, a second difference between the respective capacitances is automatically measured while the movable mass is in the second position.
In step 5530, the movable mass is moved into a reference position in which the movable mass is substantially spaced apart from the first and the second displacement-stopping surfaces. A first distance between the first position and the reference position is different from a second distance between the second position and the reference position (e.g., gap1 vs. gap2).
In subsequent step 5535, using the controller, a third difference between the respective capacitances is automatically measured while the movable mass is in the reference position.
In step 5540, using the controller, a drive constant is automatically computed using the measured first difference (e.g., ΔC1), the measured second difference (e.g., ΔC2), the measured third difference (e.g., ΔC0), and first and second selected layout distances corresponding to the first and second positions, respectively (gap1,layout and gap1,layout). In some aspects, the computing-drive-constant step 5540 includes, using the controller, automatically computing the following:
In subsequent step 5545, using the controller, a drive signal is automatically applied to an actuator 140 to move the movable mass into a test position.
In subsequent step 5550, using the controller, a fourth difference between the respective capacitances is automatically measured while the movable mass is in the test position.
In subsequent step 5555, using the controller, the displacement of the movable mass in the test position is automatically determined using the computed drive constant and the measured fourth difference.
In various aspects, step 5555 is followed by step 5560. In step 5560, using the controller, a force is computed using the computed drive constant and the applied drive signal.
In step 5565, using the controller, a stiffness is determined using the computed drive constant, the applied drive signal, and the measured fourth difference.
In step 5570, a resonant frequency of the movable mass is measured.
In step 5575, using the controller, a value for the mass of the movable mass 101 is determined using the computed stiffness and the measured resonant frequency.
In step 5610, using a controller, differential capacitances of two capacitors having respective first plates attached to and movable with a movable mass are measured. The capacitances are measured at a reference position of a movable mass and at first and second characterization positions of the movable mass spaced apart from the reference position along a displacement axis by respective, different first and second distances.
In step 5615, using the controller, a drive constant is automatically computed using the measured differential capacitances and first and second selected layout distances corresponding to the first and second characterization positions, respectively.
In step 5620, using an AFM cantilever, force is applied on the movable mass along the displacement axis in a first direction so that the movable mass moves to a first test position.
In subsequent step 5625, while the movable mass is in the first test position, a first test deflection of the AFM cantilever is measured using the deflection sensor. A first test differential capacitance of the two capacitors is also measured.
In step 5630, a drive signal is applied to an actuator to move the movable mass along the displacement axis opposite the first direction to a second test position.
In step 5635, while the movable mass is in the second test position, a second test deflection of the AFM cantilever is measured using the deflection sensor. A second test differential capacitance of the two capacitors is also measured.
In step 5640, an optical-level sensitivity is automatically computed using the drive constant, the first and second test deflections, and the first and second test differential capacitances.
In various aspects, step 5640 is followed by step 5645. In step 5645, a selected drive voltage is applied to the actuator.
In step 5650, while applying the drive voltage, using the AFM cantilever, force is applied on the movable mass along the displacement axis. Successive third and fourth deflections of the AFM cantilever and successive third and fourth test differential capacitances are contemporaneously measured using the deflection sensor.
In step 5655, a stiffness of the movable mass is automatically computed using the selected drive voltage and the third and fourth test differential capacitances, and the drive constant.
In step 5660, a stiffness of the AFM cantilever is automatically computed using the computed stiffness of the movable mass, the third and fourth deflections of the AFM cantilever, the third and fourth test differential capacitances, and the drive constant.
Referring back to
Two spaced-apart sensing capacitors 120 each includes a respective first plate attached to and movable with the movable mass (one set of fingers) and a respective second plate 121 substantially fixed in position (the other set of fingers, e.g., mounted to substrate 105). Respective capacitances of the sensing capacitors vary as the movable mass 101 moves along the displacement axis 199.
Movable mass 101 can include an applicator 130 forming an end of the movable mass 101 along the displacement axis 199.
One or more displacement stopper(s) are arranged to form a first displacement-stopping surface and a second displacement-stopping surface. In this example, anchor 151 is the single displacement stopper and the displacement-stopping surfaces are the top and bottom edges of anchor 151, i.e., the faces of anchor 151 normal to displacement axis 199. The first and second displacement-stopping surfaces limit travel of the movable mass 101 in respective, opposite directions along the displacement axis 199 to respective first and second distances away from the reference position, wherein the first distance is different from the second distance (gap1,layout≠gap2,layout).
Referring to
The actuation system can include a plurality of comb drives 1140 and corresponding voltage sources 1130.
First and second accelerometers 5741, 5742 are located within the XY plane, each accelerometer including a respective actuator and a respective sensor (
First and second gyroscopes 5781, 5782 are located within the XY plane, each gyroscope including a respective actuator and a respective sensor (see
Actuation source 5710 is adapted to drive the first accelerometer and the second accelerometer 90 degrees out of phase with each other, and adapted to drive the first gyroscope and the second gyroscope 90 degrees out of phase with each other. Controller 5786 is adapted to receive data from the respective sensors of the accelerometers and the gyroscopes and determine a translational, centrifugal, Coriolis, or transverse force acting on the motion-measuring device. Other accelerometers and gyroscopes are shown in the XY, XZ, and YZ planes.
In various aspects, each accelerometer and each gyroscope includes a respective movable mass. The actuation source 5710 is further adapted to selectively translate the respective movable masses along respective displacement axes with reference to respective reference positions. Each accelerometer and each gyroscope further includes a respective set of two spaced-apart sensing capacitors 120, each including a respective first plate attached to and movable with the respective movable mass and a respective second plate substantially fixed in position, wherein respective capacitances of the sensing capacitors vary as the respective movable mass moves along the respective displacement axis; and a respective set of one or more displacement stopper(s) (e.g., anchor 151) arranged to form a respective first displacement-stopping surface and a respective second displacement-stopping surface, wherein the respective first and second displacement-stopping surfaces limit travel of the respective movable mass in respective, opposite directions along the respective displacement axis to respective first and second distances away from the respective reference position, wherein each respective first distance is different from the respective second distance.
Further details of controllers such as controller 5786 are described in U.S. Publication No. 20100192266 by Clark, incorporated herein by reference. The controller may be fabricated on the same chip as the MEMS device. The MEMS device can be controlled by a computer which may be on the same chip or separate from the chip of the primary device. The computer may be any type of computer or processor, e.g., as discussed above. As discussed herein, EMM techniques can be used to extract mechanical properties of the MEMS device as functions of electronic measurands. These properties may be geometric, dynamic, material or other properties. Therefore, an electronic measurand sensor is provided to measure the desired electrical measurand on the test structure. For instance, an electronic measurand sensor may measure capacitance, voltage, frequency, or the like. The electronic measurand sensor may be on the same chip with the MEMS device. In other embodiments, electronic measurand sensor may be separate from the chip of the MEMS device.
Referring back to
One or more displacement stopper(s) (next to gap 2111, 2112) are arranged to form a first displacement-stopping surface and a second displacement-stopping surface, wherein the first and second displacement-stopping surfaces limit travel of the movable mass in respective, opposite directions along the displacement axis to respective first and second distances away from the reference position, wherein the first distance is different from the second distance, and wherein the actuation system is further adapted to selectively permit the movable mass to vibrate along the displacement axis (“vibration due to T”) within bounds defined by the first and second displacement-stopping surfaces.
A differential-capacitance sensor (
As shown, each first and second plate can include a respective comb. The actuation system can includes voltage source (not shown) adapted to selectively apply voltage to the second plates to exert pulling forces on the respective first plates.
In the example shown, the first plate of a selected one of the sensing capacitors 2120 (RHS) is electrically connected to the movable mass 2102. The displacement-sensing unit includes voltage source 2119 electrically connected to the movable mass 2101 and adapted to provide an excitation signal, so that a first current passes through the selected one of the sensing capacitors 2120; and a transimpedance amplifier 2130 electrically connected to the second plate of the selected one of the sensing capacitors 2120 and adapted to provide the displacement signal corresponding to the first current.
The excitation signal can include a DC component and an AC component.
A second current can pass through the non-selected one of the sensing capacitors 2120 (LHS). The differential-capacitance sensor can include a second transimpedance amplifier (not shown) electrically connected to the second plate of the non-selected one of the sensing capacitors (2120, LHS) and adapted to provide a second displacement signal corresponding to the second current; and a device for receiving the displacement signal from the transimpedance amplifier and computing the differential capacitance using the displacement signal and the second displacement signal.
The invention is inclusive of combinations of the aspects described herein. References to “a particular aspect” and the like refer to features that are present in at least one aspect of the invention. Separate references to “an aspect” or “particular aspects” or the like do not necessarily refer to the same aspect or aspects; however, such aspects are not mutually exclusive, unless so indicated or as are readily apparent to one of skill in the art. The use of singular or plural in referring to “method” or “methods” and the like is not limiting. The word “or” is used in this disclosure in a non-exclusive sense, unless otherwise explicitly noted.
The invention has been described in detail with particular reference to certain preferred aspects thereof, but it will be understood that variations, combinations, and modifications can be effected by a person of ordinary skill in the art within the spirit and scope of the invention.
This application is a nonprovisional application of, and claims priority to, U.S. Provisional Patent Applications Nos. 61/659,179, filed Jun. 13, 2012; 61/723,927, filed Nov. 8, 2012; 61/724,325, filed Nov. 9, 2012; 61/724,400, filed Nov. 9, 2012; 61/724,482, filed Nov. 9, 2012; and 61/659,068, filed Jun. 13, 2012, the entirety of each of which is incorporated herein by reference.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2013/043595 | 5/31/2013 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 61659179 | Jun 2012 | US | |
| 61659068 | Jun 2012 | US | |
| 61723927 | Nov 2012 | US | |
| 61724325 | Nov 2012 | US | |
| 61724400 | Nov 2012 | US | |
| 61724482 | Nov 2012 | US |
