No Physical Stimulus Testing and Calibration for MEMS Accelerometer

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 23, NO. 4, AUGUST 2014 811

No Physical Stimulus Testing and Calibrationfor MEMS Accelerometer

Tehmoor Dar, Member, IEEE, Krithivasan Suryanarayanan, and Aaron Geisberger

Abstract— Conventional MEMS devices require physical stim-ulus for calibration and test. This is not only time consuming butalso uses expensive equipment. In this paper, it is presented thatan accelerometer can be tested and calibrated with no physicalstimulus; this is achieved by using electrostatic forces applied attransducer test plates to excite the proof mass. It is demonstratedthat gain parameters required to calibrate the device can beestimated using an extended Kalman filter algorithm providedan accurate physical system model is developed as a functionof critical silicon process parameters. Our methodology is notonly time efficient, but cost effective as well. This methodologymay be applied to most silicon processes used for MEMS inertialsensors. [2013-0010]

Index Terms— No physical stimulus test, MEMS shaker-lesstest, electrostatic trim test, no mechanical stimulus MEMScalibration, process modeling.

I. INTRODUCTION

MEMS TESTING and calibration contribute significantlytowards the total cost of a typical system. Testing and

calibrating have always been a challenge to engineers sinceMEMS sensors typically need to be tested across multipleenergy domains; hence comprehensive knowledge may berequired from electrical properties to mechanical and chemicalproperties. MEMS devices are required to be tested at severalstages before they are packaged and shipped to customers.Typically, wafer level devices are probed electrically to iden-tify faulty behavior before packaging to save time and material,but it is still necessary to introduce it to extreme conditionslike physical motion, temperature, pressure, etc., at final testto physically calibrate and test the device. These essentialtests significantly enhance the device cost and manufacturersare looking for new state of the art testing technologies, aswell as also focused on developing their own indigenous testcapabilities to reduce the manufacturing time and overhead.

The MEMS industry is still nascent as compared to moreconventional large scale mechanical or electrical industries.Therefore, it leaves room for improvement to the existing stan-dards in testing and calibration methods for MEMS devices.Due to uncertainty in process variation and characterizationof the material used in MEMS devices, it is difficult to test

Manuscript received January 7, 2013; revised August 27, 2013; acceptedNovember 16, 2013. Date of publication January 9, 2014; date of currentversion July 29, 2014. Subject Editor H. Fujita.

The authors are with the Sensor Solution Division, Freescale Semicon-ductor Inc., Tempe, AZ 85283 USA (e-mail: [email protected];[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2013.2294562

the devices with repeatable accuracy [1]. Nonlinear dynamicproperties such as spring stiffness, damping coefficient andmover mass along with material properties such as Young’sModulus and residual stress make it complicated to definestand alone calibration and testing methods. Clark et al. [2]discussed the inability to control process variation and micro-scale properties in MEMS that lead to the development ofnon-standard testing methods. Vacuum chambers to reducedamping, FEA based analysis for mechanical design and scan-ning electron microscopy (SEM) are few such methods thatfall under the category of these non-standard testing methods[1], [3], [4]. These methods rely on some un-establishedMEMS dynamics and material properties which make themless accurate. For example, the SEM can be used to locate thestructure failure but it cannot be used to measure preciselythe various beam characteristics. The National Institute ofStandard and Technologies has recently introduced varioustesting standards for beam length and residual stress [5], [6].

High performance MEMS sensors are used in multipleapplications ranging from military equipment to commercialproducts. We see their use in every day electronics prod-ucts (cell phone, gaming device, etc.) to life saving medicaldevices. These MEMS sense physical motion like acceleration,force, pressure, etc., and convert them into electrical signalswhich get further processed by the Application Specific Inte-grated Circuits (ASIC). Design engineers have had modestsuccess predicting static and dynamic behavior of MEMSdevices using commercially available design tools [7], [8].Recently the research focus has shifted to establishing self cal-ibration and auto testing processes for sensors. MEMS designengineers see Built-in Self Test (BIST) as a quick remedialmeasure to establish the reliability of MEMS devices whichis critical for success of any product. This test can check thefunction and operational-ability of the device [9]–[11]. Duringthis BIST a bias voltage is applied to electrodes, producingelectrostatic force between the capacitor plates and resultingin the motion of the proof mass [12], [13]. This motion isassumed to be equivalent to an acceleration experienced bythe sensor [14] and has been suggested as a means to calibratea device [13], [15]. However, such BIST techniques have theirown limitations with detection or correction of manufacturingand process defects.

In general, test equipment is expensive since it is designedto provide physical stimulus for a particular MEMS sensor.It is therefore desired to establish a test methodology that notonly has low cost benefit but is time efficient as well. Thetests should not just establish pass/fail criteria but calibrate

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812 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 23, NO. 4, AUGUST 2014

and trim the device. Li demonstrated the design of a selfcalibrated MEMS inertial sensor by measuring the geometricaldifference between fabrication and layout [16]. The authorselectrically probed the wafer and used it to calculate othersystem parameters such as force, mass, stiffness, etc. Thesesystem parameters were used to develop a self calibration sen-sor algorithm. Similarly, Rocha developed electro-mechanicalcalibration for MEMS [8]. He developed experiment basedanalytical model to simulate external acceleration by com-puting electrostatic forces based on process induced varia-tion. Clark also discussed techniques for measuring variousMEMS geometric and dynamic properties [2]. However, mostresearchers stopped short of demonstrating the success of theirmethodology against various silicon processes adopted by theindustry in recent years.

The proposed methodology in this paper is intended toreplace the physical acceleration with electrostatic forces. Thismodel based methodology using the Extended Kalman Filterwill help in evaluating the linearity and sensitivity of the devicewithout using any state of the art equipment thus reducingcapital cost requirements. The No-Physical Stimulus (NPS)approach, as we call it, will help in calibrating and testing thedevices ranging from low-G to high-G developed using varioussilicon design processes. The two significant developments inthis paper are the use of a pseudo random signal to capturethe low and high frequency dynamics of the system, and thedevelopment and verification of a physically based nonlinearmodel that correlates input signal to the device output. Thiscorrelation is developed using statistical process variation andwell controlled design techniques.

II. SYSTEM MODEL AND PROCESS

The NPS calibration for an inertial sensor begins by devel-oping a comprehensive accelerometer model. Each accelerom-eter has a mass, damping coefficient and spring constant,responsible for converting acceleration into displacement andthus creating a delta change in output capacitance. Using elec-trostatic forces for calibration requires dynamic data becauseboth mass and damping can impart forces only through accel-eration and velocity respectively. This dynamic data can beprocessed by a statistical algorithm in an approach known assystem identification.

The concept of the statistical approach is to take the inputand output data from devices to solve for the best parameterestimate of a model that represents the device. The goalin this paper is to excite an accelerometer transducer usingthe self-test actuator with some known input voltages anduse the capacitance output through the ASIC signal chainto determine a set of unknown parameters. In many casessimple polynomials can be used to approximate a system,which results in a straight forward least squares estimation.The situation is more complicated in the transducer applicationsince the proof mass position cannot be directly measured; it isan unknown state within the nonlinear system. This makes theExtended Kalman Filter an ideal approach to provide both stateand parameter estimations of a nonlinear system as shown inFig. 1. In order to formulate the mathematical representation

Fig. 1. A system identification block diagram showing how both the testsignals and system output are used in the estimation algorithm.

for this approach, a comprehensive dynamic model of theaccelerometer is developed, cased and verified against silicondata.

A. HARMEMS Process

High resolution inertial sensors show enhanced perfor-mance using high aspect ratio microstructures due to theirincreased mass and improved lateral capacitive sensingdensity [17]. High Aspect Ratio Micro-Electro MechanicalSystems (HARMEMS) is Freescale’s proven technology fornext generation inertial sensors (airbag sensing systems, etc.).HARMEMS technology is designed to provide over-dampedmechanical response with an excellent signal-to-noise ratiothat enhances sensors offset performance [18].

The HARMEMS process has been used by Freescale Semi-conductor Inc. (FSL) to manufacture low-g to high-g inertialsensing devices, see Fig. 5. An SOI (Silicon on Insulator)wafer with specific buried oxide and device layer thicknessform the starting substrate. The device layer is then etchedto form the proof mass and fixed electrodes. A sequence ofPSG (Phosphosilicate glass) depositions fill the device layeretch and enable a layer of polysilicon to be deposited andpatterned over the structure to complete electrical contacts.

The lateral single axis HARMEMS device is selected as atest case for this NPS study. The process specific advantage isthe use of single crystal silicon which provides reasonable jus-tification for setting a constant Young’s Modulus. In additionthe process design rules limit design geometry and make forconsistent etch loss within the localized transducer area. Thisetch loss effects both sides of a designed structure and thereduction in total dimension is referred to here as the criticaldimension (C D). The layer thickness (T hk) is also assumedconstant over the local device area. With these fundamentalsin place, an analytical model that incorporates most dynamiceffects has been verified with a statistically significant set ofsilicon data. The casing procedure indicates two mechanicalprocess parameters that may be shifted within the model toencompass the population of measured data, these are thestructural silicon etch C D and T hk.

B. Pseudo Random Input

A pseudo random binary noise signal was used as an inputto the self-test electrode. The designed random signal resultsin achieving the optimal solution by avoiding the prematureconvergence of the algorithm to local minima. This random

DAR et al.: NO PHYSICAL STIMULUS TESTING AND CALIBRATION FOR MEMS ACCELEROMETER 813

Fig. 2. Pseudo random input noise sequence applied to the selftest electrodes.The positive and negative electrodes are switched between high bias and zeroin order to introduce significant acceleration to the proof mass.

Fig. 3. Force contribution comparison between different minimum timeintervals of the pulsed voltage excitation.

signal is generated from a constant voltage applied to eitherthe positive or negative electrode. The waveform generationwas divided such that only one electrode is powered at onetime, as shown in Fig. 2.

To evaluate the effectiveness of the input signal it is impor-tant that the dynamic output contains contributions from thethree significant lumped parameters within the system model;mass, stiffness and damping coefficient. To evaluate this, atest input waveform was generated and applied to the systemmodel. The model was enhanced to output the force contri-butions from these three system parameters (Fm, Fb and Fk).Although each are tied to the process parameters, the modelanalysis does indicate that electrostatic forces and stiffness aremore highly correlated to the CD, whereas the mass is highlycorrelated to the Thk. Fig. 3 displays these forces over 2mswith a 4 V amplitude pulse waveform. The pulses were spacedat a minimum of 0.2ms. From Fig. 3 the contribution from theparameters are Fm = 0.91%, Fb = 24.58% and Fk = 74.51%.These force contributions are important to verify that thedynamic output signal has enough content from each of thelumped parameters which in turn improves the convergence

Fig. 4. Depiction of a typical mass-spring system with parallel platecapacitors forming the motion transducer. Capacitors C1 and C2 changedifferentially with proof mass motion.

and accuracy of the filter algorithm. As the time intervalis reduced the part has higher acceleration and velocity andtherefore sees increased percent contributions from the inertiaand damping effects. Reducing the minimum time intervalfrom 0.2ms to 0.075ms, as shown in Fig. 3, sees a change incontribution to Fm = 3.95%, Fb = 42.42% and Fk = 53.64%.

C. Mass Spring Model

A typical MEMS accelerometer can be modeled as a 2ndorder spring mass damper system. A schematic representationis shown in Fig. 4 and mathematically it can be represented as:

mx + bx + kx = �Ft , (1)

where m is the proof mass (moveable plate), k is springconstant, b is system damping factor, and Ft are the totalforces due to acceleration and electrostatics. The gaps betweenthe two fixed and moveable plate represent the two variablecapacitors of the system. The moveable plate is assumed to bein the middle unless there is an offset from package stresses.The change in capacitance resulting from change in gap dueto physical acceleration can be mathematically represented as

C1 = εA

d − x(2)

C2 = εA

d + x(3)

This shows the transduction method is nonlinear over largerproof mass displacements, and this must be captured for accu-rate performance in certain applications. The electrostatic forcebetween parallel plates is represented mathematically as [19],

F1 = 1

2ε

V 21

(d − x)2 A (4)

F2 = 1

2ε

V 22

(d + x)2 A, (5)


Fig. 5. Image showing the HARMEMS process and highlighting featuresthat make up the lumped parameter model of the system.

where V1 and V2 are the applied voltages to the plates, ε is thedielectric constant, A is the overlap area between moveableand fixed plates and d is the gap between the plates. x maybe a small displacement as a result of motion of mass m. Thedifference between C1 and C2 i.e �C can be written as

�C = 2εAx

d2 − x2 (6)

The relationship between device output �C and accelerationa is defined as sensitivity. Mathematically it can berepresented as

S = �C/a

= �C

(F2 − F1 + mx + bx + kx) /m(7)

Equation 7, demonstrates the nonlinear nature of the sensingelement. It can be noted that under static acceleration,x = x = 0, and with no voltage, the sensitivity isprimarily dependent on system parameters like mass mand stiffness k, overlap area A, and gap d . As discussed insection II-A, with careful design these lumped elementparameters can be successfully made into a function ofprocess parameters such as CD and Thk. In order to developa robust approach the model must account for cases wherex is not small and the capacitance transfer function becomesnonlinear. With this in mind, a comprehensive model wasdeveloped as a function of these process parameters and othergeometric parameters such as the proof mass perimeter, springquantity, beam length, etc., highlighted in Figs. 5 and 6.Equation 8 shows the proof mass of the system in terms ofprocess and other geometric parameters. Similar approachescan be used to develop relationships between other lumpedelements and process parameters.

m = Ma(T hk) + Mb(C D)(T hk) + Mc(T hk)2 (8)

where the parameter Ma is in kg/um and is calculated fromthe product of drawn proof mass area and silicon density. Theparameter Mb is in kg/um2 and is a product of half the drawnproof mass perimeter and density. Finally, Mc is in kg/um2

and is a product of half the perimeter, the density, and thesymmetric high aspect ratio sidewall angle calculated inradians.

Fig. 6. Detailed model view showing two fixed electrodes surrounded by theproof mass. This depiction helps illustrate how design and process parametersare used to calculate the lumped element model.

Fig. 7. Block diagram of the sigma delta modulator.

A model image of the single axis transducer is shown inFig. 5, indicating the design features that are relevant for thelumped parameter model. The design geometry is applied toconnect the process variation to the system model parameters.Once this model structure is assembled the proposed method-ology uses the extended Kalman filter to estimate unknownprocess parameters, which in turn are used in calculating thesystem parameters such as m, k, A, d , etc. Once estimates arefound, the model can be used to calibrate and test the device.

D. Modulator and SINC Filter

Multiple methods are employed in a device to convert itsanalog signal to digital. In this case, a second order sigma-deltamodulator as shown in Fig. 7 is used, followed by a SINC filterto attenuate high frequency noise from the modulator. Withoutgoing into details of this Analog to Digital conversion, whichis beyond the scope of this paper, the output recorded from thisdevice is represented mathematically by a transfer function asin equation 9

H (z) = 1

2Cdac(9)

where Cdac is feedback reference capacitor represented inFarads.

It is very critical to capture and analyze the signal from adevice that carries all the attributes of process and physicalacceleration, this means achieving a high sample rate whichis at least an order of magnitude higher than the mechanicalbandwidth of the transducer. In addition, ASIC signal chainfilters must not eliminate the transient and steady state contentof the signal. Thus, while capturing the intended signal, anylow pass filter is bypassed. The output from the device isexpressed by the equation 10

Dout = �C

2Cdac.2N (10)


where N is the number of bits used to represent the deviceoutput in counts.

III. EXTENDED KALMAN FILTER

EKF is not only robust but also quite flexible in terms ofthe extent to which its design requires a specific model. InEKF, the process governed by a nonlinear stochastic equationis given by,

xk = f (xk−1, uk−1, wk−1) (11)

zk = h(xk, vk), (12)

where xk−1 is the state, uk−1 is the known input vector, andf (., ., .) is the nonlinear state transition function that mapsthe previous state and the current control input to the currentstate. In Equation 12, zk is the observation made at time tk andh(., .) is the nonlinear observation model mapping the currentstate to the observation. Random variables wk and vk representthe uncorrelated process and measurement noise respectively.These random variables are considered independent and arezero-mean Gaussian white noise with respective covariancematrices Q and R.

The second order accelerometer model is a typical multipleinput to single output system (MISO). It is represented in statespace as

X = X (2)

X = − k

mX (1) − b

mX (2) + Fes

m, (13)

In matrix form this is written as,[X1X2

]=

[0 1

− km − b

m

] [X1X2

]+

[01m

]Fes , (14)

It is pertinent to mention here that all state space parametersare function of CD, Thk, and other geometric parameters asdiscussed earlier. The variables to estimate are,⎡

⎢⎢⎣X1V

C DT hk

⎤⎥⎥⎦ =

⎡⎢⎢⎣

X1X2X3X4

⎤⎥⎥⎦, (15)

where X1 is the mass displacement, V is the mass velocity.The time derivative of equation 15 can be written as,

[X

] =

⎡⎢⎢⎣

X1X2X3X4

⎤⎥⎥⎦ =

⎡⎢⎢⎣

X2X200

⎤⎥⎥⎦, (16)

Equation 16 results in differential equations required to besolved using EKF algorithm. The state space model in discreteform is represented as,

X = Xk+1 − Xk

T, (17)

where T is the required sampling rate. The initial conditionsfor the displacement and velocity are assumed to be zero,whereas the initial condition for CD and Thk are assumedto be closer to a process nominal value. The measurable statevariable is the capacitance output converted using the circuit

Fig. 8. Operation flow of the Extended Kalman Filter.

transfer function in 10. The observation model required forEKF is represented by equation 12.

The state space model developed in equation 16 is alsochecked for observability using lie derivative and the matrixwas found to be of full rank. The flow diagram for the imple-mentation of the EKF algorithm is shown in Fig. 8. At thebeginning of the algorithm the initial values of estimatedstate vector Xk−1, error covariance Pk−1, process noise wk−1and measurement noise vk−1 were set accordingly. Kalmangain K at time stage k was calculated using the equation asfollows,

Kk = Pk|k−1 H Tk

(Hk Pk|k−1 H T

k + Rk

)−1(18)

where Hk is the Jacobian matrix of partial derivative ofh(., .) with respect to state variables. Subsequent steps in thealgorithm were to measure the values of uk and to calculate thelinearization matrix f (xk−1, uk−1, wk−1). After linearization,the estimated value of Xk and error covariance matrix Pk werecalculated. Finally, the state estimate xk , and error covariancePk were updated using equation as follows,

Pk = (I − Kk Hk) Pk, (19)

where I is the identity matrix. Steps were repeated fork = k + 1. The detailed explanation and implementation ofthe EKF algorithm can be found in several text books andreference papers [20]–[24].

IV. SIMULATION MODEL AND VERIFICATION STUDIES

The electrostatic voltage input waveforms were setup to runsimulations using the VerilogA (Vlog) model. No accelerationwas applied to the model in the identification procedure.Output from the model included the differential sense capac-itance value between left and right capacitor plates, and theproof mass motion was saved from the model for reference.In this case, the parasitic capacitance values were not relevantsince only a change in the capacitances is passed as inputto the identification procedure. Fig. 9 shows the differentialcapacitance output from the model that results from the voltageinput as discussed in Section II-B. Data from the model wasloaded into Matlab and processed to represent the device


Fig. 9. Capacitance output from the VerilogA model using nominal processparameters and the random input voltage sequence.

Fig. 10. Estimated process parameters using simulated model data. Thisshows the convergence of the process CD (top) and Thickness (bottom).

signal chain. First, some representative noise was added tothe differential capacitance output at each time point. Thiscapacitance was then used in equation 10 to estimate thedevice output. The input voltage moves the proof mass to about50% of full scale and no noise was added to the input sincethe same controlled input voltage is used in the estimationalgorithm as discussed in section III.

The simulation data from equation 10 was used as a test caseto generate input for the EKF algorithm parameter estimation.This is ideal since the estimated parameters can be comparedto actual parameters that were used to generate model data.In addition, the proof mass motion is known in this case andcan be compared to the estimated state variable for guidance.

The estimated results using EKF algorithm is shown inFig. 10. The two parameters, CD and Thk, can be seenconverging to expected values. These values were verifiedagainst the Vlog model discussed earlier using the establishedprocess corners, with room temperature assumed. Fig. 11shows as the process parameters converge the error in the proof

Fig. 11. The proof mass displacement from simulated data and comparedto the estimated state from the filter algorithm.

Fig. 12. Block diagram of the proposed test flow for the NPS calibrationprocedure.

mass displacement between Vlog model and EKF algorithmbecomes negligible.

The model updated with the estimated parameters cannow be used to calculate linear and nonlinear compensa-tion parameters. With all unknowns estimated in the model,acceleration input can be modeled to determine the change incapacitance output. These values were generated at severalpoints over the desired range of acceleration and used togenerate a polynomial equation for the device compensation.Effectively this technique can generate nonlinear compensationcodes for calibration.

V. EXPERIMENTAL RESULTS AND DISCUSSION

The test flow adopted to capture data output from packageddevices and used to estimate the state variables is shown inFig. 12. Input voltage to the algorithm is the pseudo randomsignal discussed earlier in section II-B. Devices from differentlots were electrostatically stimulated to provide data for theEKF algorithm which is then tuned heuristically for accurateresults.

The observed device output and estimated device outputusing equation 10 is shown in Fig. 13. The accurate conver-gence of the data can be observed after a few iterations. After10ms the error between the observed and estimated deviceoutput is negligible for the selected pseudo random input,thus based on our verification studies in section IV it can bestated that the estimated device output accurately captured theintended contributions from mass, stiffness, and system damp-ing. It can be noted in Fig. 14 that the two estimated processvariables, namely CD and Thk, converged to a value whichis within the defined process variation window. As discussed


Fig. 13. Estimated and observed device output in counts, showing how thefilter tracks the measured response.

Fig. 14. Plot showing convergence of the estimated process parameters usingexperimental data.

Fig. 15. NPS trimmed sensitivity vs untrimmed sensitivity of devices.

earlier, the model updated with estimated parameters can nowbe used to estimate the linear and nonlinear gain parametersfor device compensation. As verification, the above estimatedcompensation parameters are compared with those calculatedfrom physically accelerated devices using a mechanical tester.

For devices under study, the sensitivity is targeted at 291 cts/g±4%. Fig. 15 shows the sensitivity comparison between NPStrimmed devices and untrimmed devices and it can be observedthat all the NPS trimmed devices fall within ±2.5% of thetargeted sensitivity.

VI. CONCLUSION

The output from an electrostatically stimulatedaccelerometer in conjunction with an accurate system model,reduced to a set of unknown process parameters, can be usedto compensate and test the device. It is important to designa pseudo random signal in such a way that it can capturethe dynamics of the system, especially the contributions frommass, stiffness and damping. The device output based onestimated differential capacitance can be used in a statisticalalgorithm such as EKF to estimate the process parameters.These estimated parameters can be used to calculate the essen-tial parameters required to calibrate the device with nonlinearbehavior. Results have demonstrated that this NPS techniquecan be used to calibrate and test devices with comparableaccuracies achieved by physical acceleration. This approachmay alleviate the need for dedicated physical tests systems.

Future directions include employing the NPS technique forother sensors such as Gyroscope and Pressure sensors. Thismethodology is also being analyzed to conduct estimations atwafer level to eliminate faulty wafers at early stage to improvefinal yield at packaged level.

ACKNOWLEDGMENT

The authors would like to thank the design enablement teamfor validating the model. Also, we would like to thank the testand validation team for help with experimental setup and datacollection.

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Tehmoor Dar (M’10) received the M.S. and Ph.D.degrees from the University of Texas, Austin, TX,USA, in 2005 and 2010, respectively.

He joined the Freescale Semiconductor Inc. in2010, where he is currently a System Archi-tecture and Design Engineer. His previous workincludes vehicle-terrain parameter estimation forrobotic tracked vehicles. His current research inter-ests include developing a no-physical stimuli basedtesting and calibration system for accelerometer,gyroscope, and pressure sensors.

Krithivasan Suryanarayanan received the M.S.degree from Wayne State University, Detroit,MI, USA, in 2007.

He has been with Freescale Semiconductor Inc.since 2008 as a Systems and Modeling Engineer. Hisinterests include developing system level models foranalyzing device performance over process corners,performing Verilog-AMS simulations for noise andtiming analyses, and verification of compensationalgorithms for device calibration.

Aaron Geisberger received the B.A.Sc and M.A.Scdegrees in mechanical engineering from the Univer-sity of Waterloo, ON, Canada, in 1998 and 2000,respectively.

He was with Zyvex Corporation from 2001 to2006 as a research engineer working on the design,modeling, and simulation of microsystems. He iscurrently a sensor design engineer with FreescaleSemiconductor Inc. working on the design of gyro-scopes and high accuracy accelerometer design thatenables no-physical stimulus based calibration. He

has authored or coauthored ten scientific publications including a bookchapter, and has been awarded fourteen patents as an inventor or coinventor.

Documents

No Physical Stimulus Testing and Calibration for MEMS Accelerometer