TECHNICAL FIELD

The present invention refers to the field of electronics. In greater detail, the present invention concerns a system and a relative method for testing the operation of Micro Electro-Mechanical Systems or MEMS type accelerometers.

BACKGROUND

Micro Electro-Mechanical Systems or MEMS type sensors are widely used in various sectors from consumer electronics to the aerospace applications, thanks to their extremely small size and low energy consumption, while ensuring a reliable transduction of physical parameters into electrical signals.

In particular, the accelerometers in MEMS technology are widely used in portable devices - such as smartphones, tablets, wearables, etc. -, in game interfaces - such as gamepads -, in the realization of IMU - acronym for Inertial Measurement Unit - in robotics, in medical and industrial applications.

However, the micrometric and nanometric sizes of the components of the MEMS accelerometers involve a particular statistical variability of the salient parameters inherent to the manufacturing process.

Consequently, a fundamental aspect of the MEMS accelerometer manufacturing cycle is the verification or test of the operation of the components, aimed to verify that these devices operate correctly.

In the prior art tests are carried out that comprise testing the MEMS accelerometers at the end of manufacturing by connecting them electrically to a test rig, stimulating them by means of a mechanical vibration at a known frequency, and evaluating the signals supplied in output by the MEMS accelerometers. In particular, the electrical signal generated by the MEMS accelerator is analysed to verify that it corresponds to an expected signal which is a function of the vibration frequency used. For example, CN 111679099, US 2022/113333 and US 2007/073502 disclose systems for testing accelerometers known in the art.

The Applicant has observed that the test systems and procedures for MEMS accelerometers known in the art are particularly complex and costly to implement. In particular, complex electromechanical systems are required to perform the electrical connection of each accelerometer to the test apparatus.

In addition, the Applicant has found that the test systems and procedures known in the art have a limited capacity, at most do not allow to provide a classification of the MEMS accelerometers tested based on the accuracy achieved in the detection of an acceleration/vibration.

Finally, the Applicant has noted that the known test systems and procedures do not allow to limit the energy consumption of the manufacturing plant and the production of waste associated with the manufacturing of malfunctioning MEMS accelerometers. PURPOSES AND SUMMARY OF THE INVENTION

Aim of the present invention is to overcome the drawbacks of the prior art.

In particular, an aim of the present invention is to provide a system and a method for testing MEMS accelerometers capable of testing the operation of a MEMS accelerometerorof a plurality of MEMS accelerometers in a fast and reliable manner.

A further aim of the present invention is to propose a system and a method for testing MEMS accelerometers capable of testing the operation of the MEMS accelerometers indirectly, i.e. without the need to electrically connect one or more accelerometers under test to an electronic circuit.

A further aim of the present invention is to present a system and a method for testing MEMS accelerometers which allows to avoid encapsulation of defective MEMS accelerometers in a respective package.

These and other aims of the present invention are achieved by a system incorporating the features of the accompanying claims, which form an integral part of the present description.

According to a first aspect, the present invention is directed to a system for testing a MEMS accelerometer in a wafer of semiconductor material.

The system comprises a vibrator module configured to transmit a vibration to the wafer such as to impose a vibration at a desired vibration frequency to the MEMS accelerometer, a lamp configured to illuminate a wafer portion comprising the MEMS accelerometer to be tested, a camera configured to acquire a plurality of images in sequence of the wafer portion comprising the MEMS accelerometer to be tested, and a control module.

The control module is advantageously configured to determine a trend as a function of time of the vibrations of a moveable element of the MEMS accelerometer, due to the vibration imposed by the vibrator module, based on a variation in brightness in the plurality of acquired images or, at least, in a portion thereof, and calculate an indicative value of the reliability of the MEMS accelerometer starting from the trend as a function of time of the vibrations of the moveable element of the MEMS accelerometer.

Preferably, the detection of the brightness variations of the MEMS accelerometer is limited, i.e. corresponds to the moveable portion(s) of the MEMS accelerometer.

The system according to the present invention allows to evaluate the goodness of MEMS accelerometers at the wafer level, i.e. before dividing them into individual elements. In this way, the defective MEMS accelerometers are identified before the connection and encapsulation phases, thus allowing to eliminate waste in terms of manufacturing time and consumption of materials linked at least to the wiring and encapsulation of the defective MEMS accelerometers in a corresponding package.

In addition, the test system is much simpler and more compact than known test equipment, but at the same time it provides an accurate and precise evaluation of the MEMS accelerometers. In particular, the verification system makes it possible to reliably identify defective MEMS accelerometers and also makes it possible to effectively evaluate a degree of precision of each tested MEMS accelerometer based on this indicative value.

In one embodiment, the indicative value of the reliability of the MEMS accelerometer calculated by the control module is a resonator quality factor, simply referred to as a quality factor in the following, associated with the moveable portion of the MEMS accelerometer stressed to vibrate at the resonance frequency of the moveable portion of the MEMS accelerometer.

Calculating the quality factor of the moveable portion of the MEMS acceleration, for example a cantilever arm, allows the characteristics of the MEMS to be precisely and reliably determined.

In one embodiment, the camera is positioned with a point of view inclined both to the surface of the wafer and to the direction of incidence of the light beam which illuminates said at least a portion of the surface of the wafer.

Preferably, a focal axis of the camera and a main direction of the lamp intersect at the surface portion of the wafer and delimit an angle comprised between 10° and 60°, preferably comprised between 15° and 45°, more preferably equal to 30°.

The Applicant has observed that it is possible to determine an inclined shooting angle of the wafer and therefore of the accelerometers, such as to allow to identify in a simple and effective way the variations in brightness and, consequently, the movements of the moveable parts of a MEMS under test.

In one embodiment, the system further comprises a receiving module adapted to receive said wafer. This receiving module comprises a grooved plate adapted to support the wafer. Advantageously the grooved plate comprises a plurality of grooves arranged so as to allow a vibration of the wafer.

Thanks to this solution, the wafer vibrates at the frequency imposed by the vibrations transmitted by the vibrator module without undergoing substantial drifts and/or local damping due to contact with the grooved plate.

Preferably, although in a non-limiting way, the grooved plate is interposed between the vibrator module, and the lamp and the camera.

In one embodiment, the vibrator module is adapted to generate a sound wave directed towards the wafer, said sound wave being adjustable to impose vibration of the moveable portion of the MEMS accelerometer at a desired frequency.

A different aspect of the present invention is directed to a method fortesting a MEMS accelerometer in a wafer of semiconductor material.

The method comprises illuminating at least a portion of a surface of the wafer comprising the MEMS accelerometer to be under test, vibrating the wafer at a predetermined frequency, acquiring a sequence of images of the accelerometer, reconstructing a trend of the vibrations MEMS accelerometer as a function of time based on the variations in brightness in the acquired images of the MEMS accelerometer, and calculating an indicative value of the reliability of the MEMS accelerometer based on the trend of the vibrations of the MEMS accelerometer. In one embodiment, the method further comprises vibrating the wafer at an average resonance frequency of the MEMS accelerometers comprised in the wafer, acquiring an initial sequence of images of the accelerometer, reconstructing a trend of the vibrations of the MEMS as a function of time based on the variations in brightness in the acquired images of the MEMS accelerometer, estimating the resonance frequency of the MEMS accelerometer under test. I n this case, the step of vibrating the wafer at a predetermined frequency comprises vibrating the wafer at the resonance frequency estimated for the MEMS accelerometer under test.

In one embodiment, the step of estimating the resonance frequency of the MEMS accelerometer under test comprises performing a fast Fourier transform of the trend of the vibrations of the MEMS accelerometer as a function of time, and identifying the estimated resonance frequency of the MEMS accelerator under test as the frequency with greatest amplitude, possibly excluding the average resonance frequency of the MEMS accelerometers.

In one embodiment, the step of acquiring an initial sequence of images of the accelerometer provides that each of said images is acquired with a point of view inclined both to the surface of the wafer and to the direction of incidence of the light beam which illuminates said at least a portion of the surface of the wafer.

The method according to the embodiments of the present invention allows to obtain advantages corresponding to those provided by the various embodiments of the system that have been set forth above.

Furthermore, in one embodiment, the step of calculating an indicative value of the reliability of the MEMS accelerometer comprises calculating a quality factor of the MEMS accelerometer by means of an algorithm of the Filter Diagonalization Method (FDM) type to which the trend of the vibrations of the MEMS accelerometer as a function of time is supplied in input.

The Applicant has found that this algorithm, employed in the art for spectral analysis applications and in nuclear magnetic resonance applications, can be used to calculate in a simple, precise and accurate way a quality factor of the MEMS accelerometers starting from a simple sequence of images thereof.

In one embodiment, the method comprises calculating a plurality of oscillation modes by means of the FDM algorithm, wherein said plurality of oscillation modes refer to frequencies comprised in a frequency interval centred on said predetermined frequency. Among the calculated oscillation modes, the oscillation mode having the greatest amplitude and preferably associated with the minor error is therefore selected. Finally, the quality factor of the MEMS accelerometer is determined based on the selected oscillation mode.

Preferably, each oscillation mode is calculated by the FDM algorithm in the form: where A is the oscillation amplitude, / is the imaginary unit (V^l), t is the time, fR is the resonance frequency, <p is the phase - also called “phase shift” - and dec is the exponential decay constant of the oscillations. In this case, the quality factor of the tested MEMS accelerometer is advantageously calculated as:

Thanks to this embodiment of the method it is possible to calculate the quality factor in an extremely precise and reliable way. This allows not only to discriminate among functioning MEMS accelerometers, but also to subdivide each of the MEMS accelerometers tested by degree of precision. This in turn enables supplying MEMS accelerometers with the precision required for each specific application.

Moreover, through the oscillation mode it is possible to calculate in a particularly precise way the resonance frequency of the MEMS accelerometer, thus allowing a better processing of the signals produced by it.

Further features and advantages of the present invention will be clearer from the description of the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described below with reference to some examples, provided for explanatory and non-limiting purposes, and illustrated in the accompanying drawings. These drawings illustrate different aspects and embodiments of the present invention and reference numerals illustrating structures, components, materials and/or similar elements in different drawings are indicated by similar reference numerals, where appropriate.

Figure 1 qualitatively illustrates a system for testing MEMS accelerometer according to an embodiment of the present invention;

Figure 2A is a schematic view of a wafer of semiconductor material, in which a plurality of MEMS accelerometers that can be tested by means of the system of Figure 1 are formed;

Figure 2B is a schematic sectional side view of a MEMS accelerator with cantilever arm tested by the system comprised in the wafer of Figure 2A;

Figures 3A-3C are schematic sectional side views of three different embodiments of a support module of the system of Figure 1 ;

Figure 4 is a flowchart of a procedure for testing MEMS accelerometers according to an embodiment of the present invention;

Figure 5A is a qualitative graph of the vibrations of a tested accelerometer as a function of time;

Figures 5B and 5C are enlargements of the graph of Figure 5A in a forced vibration phase and a damping phase, respectively, and

Figure 6 is a schematic view of a graphical interface displayed through a user interface of the system of Figure 1 .

DETAILED DESCRIPTION OF THE INVENTION

While the invention is susceptible to various modifications and alternative constructions, certain preferred embodiments are shown in the drawings and are described hereinbelow in detail. It must in any case be understood that there is no intention to limit the invention to the specific embodiment illustrated, but, on the contrary, the invention intends covering all the modifications, alternative and equivalent constructions that fall within the scope of the invention as defined in the claims.

The use of “for example”, “etc.”, “or” indicates non-exclusive alternatives without limitation, unless otherwise indicated. The use of “includes” or “comprises” means respectively “includes, but not limited to”, and “comprises, but not limited to”, unless otherwise indicated.

With reference to Figure 1 , a system fortesting MEMS accelerometers according to an embodiment of the present invention, referred to as system 1 hereinafter for brevity's sake, is configured to perform the test of one or more MEMS accelerometers comprised in the wafer W of semiconductor material.

As known in the art, the wafer W - of which Figure 2A is a schematic view - is a disk of semiconductor material with two substantially circular main surfaces separated by a side wall with a size much smaller than the radius of the main surfaces. The wafer W comprises a plurality of electronic devices, in this case MEMS accelerometers, made inside the wafer W through known techniques and not described here for brevity’s sake. The MEMS accelerometers are arranged one next to the other in rows I and columns J (where 1 < i < I and 1 < j < J). The MEMS accelerometers are subsequently separated into a corresponding plurality of chips, which are then encapsulated in a respective package (not illustrated), and electrically connected to one or more electrical terminals of the package in order to allow an electrical connection with other electronic devices.

In the following, the case where the MEMS accelerometers are of the cantilever type, of which Figure 2A is a schematic side sectional view, will be considered in a non-limiting manner. A generic MEMS accelerometer Ai comprises an arm B provided with a counterweight C inside a cavity H. The vibrations of the arm B are converted into an electrical signal by means of a suitable transducer T, for example a piezoresistor, and used to determine the acceleration to which the MEMS accelerometer Ai j is subjected. An example of this type of MEMS accelerometer is described in Y. Wu, J. Wang, X. Zhang, C. Zhang, and G. Ding, “Modeling of a bistable MEMS mechanism with torsion/cantilever beams,” 2010 IEEE 5th International Conference on Nano/Micro Engineered and Molecular Systems, 2010, pages 153-156.

In the example considered in Figure 1 , the system 1 comprises an optical module 10, a vibrator module 20, a receiving module 30, a positioning module 40, a control module 50 and an interface module 60.

The optical module 10 comprises a lamp 11 , for example comprising one or more illumination LEDs, and a high acquisition frequency camera 12, for example with a maximum image acquisition frequency - that is, of frames per second - comprised between 60,000 fps and 100,000 fps. In one embodiment, an EoSens® 3CL Full CL MC3010 camera manufactured by Mikrotron is used.

Furthermore, the optical module 10 comprises a movement and positioning assembly 13 movable on three axes x, y, z. Such an assembly allows the optical module 10 to be moved to illuminate and frame a desired portion of a wafer W to be tested and to position the optical module 10 at a desired distance from the wafer W - allowing a focus of the camera 12 to be adjusted.

The vibrator module 20 is configured to transmit vibrations to the wafer to be tested. Preferably, the vibrator module 20 is configured to generate acoustic waves at one or more desired frequencies. To this end, the vibrator module 20 comprises a magnet 21 , for example toroidal, which is closed above by a first (upper) metal plate 22 and is closed below by a second (lower) metal plate 23, moreover the second metal plate comprises a pillar 23a that fits in the hole 21 a delimited by the magnet 21 . The first plate 22 comprises an opening coaxial to the hole 21a. In the present description, the terms “upper” and “lower” are referred to a direction parallel to the axis z. A moveable coil 24 is arranged between the pillar 23a and the first plate 22, which is surmounted by a cover 25 and held in place by a membrane or “spider” 26 in turn coupled to the walls 27 of the vibrator module 20. In particular, the moveable coil 24 is movable along a direction parallel to the axis z. In other words, the vibrator module 20 substantially comprises a magnetodynamic loudspeaker without a diaphragm or “cone”.

The wafer receiving module 30 is superimposed on the vibrator module 20, preferably, although in a non-limiting way, spaced therefrom. The receiving module 30 comprises a support plane configured to receive the wafer W to be tested, holding it in place while it is brought to vibrate by means of the vibrator module. For example, the receiving module 30 comprises a grooved plate 31 , preferably disc-shaped, with a larger surface or substantially corresponding to one of the main extension surfaces of the W to be tested. The grooved plate 31 comprises one or more grooves arranged so as to receive the wafer W and allow modes of vibration of the wafer W along a direction parallel to the main surfaces of the wafer W - examples of grooved plate are shown in side section in Figure 3A where a plate 31 provided with a single groove 31 a is illustrated, for example adapted to receive the wafer W with a diameter of 200 mm, in Figure 3B where a plate 31 provided with a pair of grooves 31 a and 31 b is illustrated, for example adapted to receive the wafer W with a diameter of 200mm and 150mm, respectively, and in Figure 3C where a plate 31 provided with two grooves 31a and 31 b, and an opening 31c at the bottom, is shown. Preferably, although in a nonlimiting way, the receiving module 30 comprises a vibration sensor 33, for example one or more piezoelectric sensors or strain gauges, configured to provide a representative signal in a vibration to which the grooved plate 31 is subjected and, therefore, the wafer W arranged thereon.

The wafer positioning module 40 comprises adapted to collect the wafer W from a storage or entry point (not illustrated) of the wafer W and position it on the receiving module 30. For example, the positioning module 40 comprises a robotic arm provided with tools suitable for manipulating the wafer W without damaging it.

The control module 50 comprises a processing unit 51 - in its turn comprising one or more processors, microprocessors, microcontrollers, ASICs, FPGAs, DSPs or the like -, a memory unit 52 - comprising one or more non-volatile and volatile memory elements configured to store data, preferably in binary format -, and one or more input/output interfaces 53 through which it is connected to the remaining modules of the system 1 to exchange data therewith and coordinate the operation of the remaining modules 10 - 60. The interface module 60 comprises one or more input/output elements for providing information and/or receiving instructions from a user.

Finally, the system comprises one or more ancillary modules (not illustrated) which are necessary for the operation of the system 1 and per se known in the art and not described here for simplicity’s sake. An example of such ancillary modules is a power circuitry configured to adapt voltage and current levels and distribute electrical energy to each one of the aforementioned modules 10 - 60.

In the embodiments of the present invention, the lamp 11 is configured to illuminate a portion WA of wafer W (as shown in Figure 2A) to be tested positioned on the grooved plate 31 of the receiving module 30. At the same time the camera 12 is oriented to frame the portion WA of the wafer W illuminated by the lamp 11 so that the axis of the focal f of the camera 12 and a direction / of the light beam which illuminates the wafer portion WA form an angle a selected so that the light reflected towards the camera 12 by the cantilever arm B assumes relative maximum and minimum intensity values substantially at the relative maximum and minimum amplitude in each oscillation period, when the cantilever arm B oscillates in response to a mechanical stress. Preferably, the selected angle a also ensures that the variation in intensity between the maximum intensity value and the minimum intensity value (and vice versa) occurs as linearly as possible.

In the embodiment considered, the angle a is comprised between 10° and 60°, preferably an angle a comprised between 15° and 45°, for example an angle a substantially equal to 30° (schematically illustrated in Figure 1).

The system 1 is configured to perform a procedure 100 - of which Figure 4 is a flowchart - which allows one or more MEMS accelerometers Ai,j comprised in the Wafer W to be tested.

The procedure 100 provides that the positioning module 40 collects the wafer W to be tested from a collection point (not illustrated) and places it on the receiving module (step 101).

Preferably, the positioning module 40 and the optical module 10 are operated to perform a subprocedure of alignment of the wafer W (step 103). In detail, the wafer W is arranged so that the rows and columns of the MEMS accelerometers Ai,j are aligned along two predetermined directions, for example the axis x and the axis y illustrated in Figure 1 , or it is verified that one or more reference elements of the wafer -for example symbols printed or engraved on the visible surface of the wafer W or on the perimeter edge of the Wafer - are in respective predetermined positions. To this end, the camera 12 of the optical module 10 acquires an image of the wafer W or a portion thereof, the control module 50 analyses the image supplied by the optical module 10 and verifies whether the wafer W is positioned as desired and, if not, the positioning module 40 is operated to change the positioning of the wafer W in the receiving module and the sub-procedure is reiterated until the wafer W is in the desired position. Preferably, during this alignment phase, the camera 12 operates acquiring images of the wafer W with a reduced frequency, for example comprised between 2000 fps and 10,000 fps, for example equal to 5000 fps, even more preferably framing an area comprising the entire wafer W or a substantial portion thereof, for example comprised between 30% and 60% of the wafer W.

The optical module 10 is positioned at a portion WA of wafer W comprising a MEMS accelerometer Aij to be under test (step 105). To this end, the control module 50 stores a table containing an expected position, for example in terms of coordinates i,j, of each MEMS accelerometer Ai comprised in the wafer W correctly oriented by the previous step. For example, the optical module 10 is positioned at - i.e., substantially on the vertical of - a first MEMS accelerometer Ai,i formed in the wafer W and then moves to an adjacent MEMS accelerometer Ai, 2 or MEMS A2,I along a row or column, respectively.

Preferably, the optical module 10 is positioned so that the lamp 11 is in a position substantially perpendicular to the portion WA, so as to illuminate said portion WA with a light beam perpendicular to the visible surface of the wafer W - in other words the light beam is substantially parallel to the axis z illustrated in Figure 1.

The lamp 11 then illuminates the portion WA of the wafer W comprising the MEMS accelerometer Aij to be under test (step 107).

The vibrator module 20 generates an acoustic wave such as to vibrate the wafer W with a frequency corresponding to a nominal average resonance frequency fw of the MEMS accelerometers comprised in the wafer W arranged on the receiving module 30 for a first time interval Ati (step 109). In general, the specific characteristics of the acoustic wave - e.g. frequency, amplitude and duration - depend on the material and on the geometry of the wafer W to be tested and can be defined empirically at an early stage of testing. In one embodiment, in order to vibrate silicon wafers of 150 mm or 20 mm, the generated acoustic waveform is a sinusoid with oscillation frequency around 6 kHz with duration of about 5 ms, preferably, the waveform has an increasing amplitude value from an initially null value to the maximum amplitude value equal to about 20 dB. Preferably, the time interval Ati has a duration such that the cantilever arm B of the MEMS accelerometer Aij under test reaches and maintains a stable oscillation substantially completely comprised in a plane parallel to the axis z - that is, without triggering flexing effects other than bending, for example torsion. The exact duration of the first time interval Ati depends on the number and on the arrangement of the MEMS accelerometers Aij in the wafer W. For example, the duration of the first time interval Ati is determined empirically, for example during a calibration phase at the end of the production of the system 1 or at the beginning of the test of a new batch of wafers, preferably using a first wafer W of the batch to perform the calibration of the time interval Ati .

While the wafer W vibrates, the camera 12 acquires a first sequence of images S1 (step 111). Preferably, the images of the sequence S1 are acquired with a much greater frequency than the average resonance frequency fw, for example the image acquisition frequency measured in frames per second, or fps, is comprised between 3 and 20 times, for example equal to 10 times, the average resonance frequency f/v. For example, in this case the camera 12 operates by acquiring images of the wafer W with a high frequency, preferably equal to or greater than 60,000 fps, even more preferably framing only the MEMS accelerometer Aij under test.

In one embodiment, the images are acquired in greyscale with N levels (e.g., N = 255 or 128).

The first sequence of images Si is processed by the control module 50 to calculate an estimated resonance frequency fs of the MEMS accelerometer Aij under test (step 113). For example, the control module 50 performs a pattern matching algorithm, i.e. of recognition of a shape or contour designed to identify the cantilever arm B of the MEMS accelerometer Ai,j portrayed in the images of the sequence of images Si .

For each image of the sequence Si , the control module 50 is configured to identify the cantilever arm B of the MEMS accelerometer Ai (sub-step 113A) and determine a representative value of the angle of inclination of the cantilever arm of the MEMS accelerometer Ai in each image of the sequence Si based on the grey level of the image portion depicting the cantilever arm B (sub-step 113B).

The set of the values extracted from the grey values associated with the cantilever arm B portrayed in the sequence of images Si composes a signal Xi - illustrated qualitatively in Figure 5A and in detail in Figure 5B - corresponding to the oscillation speed of the cantilever arm B of the MEMS accelerometer j as a function of time.

The control module 50 then performs a fast Fourier transform or FFT of the signal thus obtained (sub-step 113C). The fast Fourier transform comprises two greater amplitude frequencies: the average resonance frequency fw and an estimated resonance frequency fs of the MEMS accelerometer Aij under test, i.e. a frequency value close to, at most corresponding to, the actual resonance frequency of the MEMS accelerometer Aij under test. The control module 50 excludes the average resonance frequency f/v (sub-step 113D) and then identifies the estimated resonance frequency fs as the frequency associated with the remaining greatest amplitude value remaining in the FFT (sub-step 113E).

Once the estimated resonance frequency fs of the MEMS accelerometer Aij under test has been identified, the vibrator module 20 is adjusted to emit an acoustic wave such as to vibrate the wafer W at the estimated resonance frequency fs of the MEMS accelerometer Aij under test for a second time interval At? (step 115). Preferably, the second time interval At? has a duration in the order of milliseconds, more generally sufficient to cause the MEMS accelerometer Aij to vibrate at the estimated resonance frequency fs.

The camera 12 acquires a second sequence of images S? (step 117). Analogously to what described above with respect to step 111, the images of the sequence S1 are preferably acquired with a much greater frequency than the estimated resonance frequency fs. In the embodiments of the present invention the second sequence S? is acquired for a period of time comprising the second time interval At? and a damping time interval At? of the vibration of the cantilever arm B of the MEMS accelerometer Aij following the second time interval At? - i.e., the second sequence of images comprises images of the MEMS accelerometer Aij, under test, from when the vibration is imposed to the estimated resonance frequency fs to when the vibration of the cantilever arm of the MEMS accelerometer j is cancelled.

The second sequence of images S? is processed by the control module 50 to calculate a quality factor Q of the MEMS accelerometer Aij under test (step 119).

For each image of the second sequence of images S?, the control module 50 is configured to identify the cantilever arm B of the MEMS accelerometer Aij (sub-step 119A) and determine a representative value of the angle of inclination of the cantilever arm of the MEMS accelerometer Aij based on the grey level of the image portion depicting said cantilever arm (sub-step 119B). The set of the values extracted from the second sequence of images S2 composes a signal X2 - illustrated qualitatively in Figure 5A and in detail in Figure 5C - corresponding to the oscillation speed of the cantilever arm B of the MEMS accelerometer Ai as a function of time from the beginning of the vibration to its damping. The control module 50 processes the signal extracted from the images of the second sequence S2 by means of an algorithm of the Filter Diagonalization Method type - FDM - so as to calculate an oscillation mode m(t) of the MEMS accelerometer Aij (step 119C).

In one embodiment, the FDM algorithm used is based on the teachings contained in V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals", J. Chem. Phys., vol. 107, no. 17, pages 6756-6769 (Nov. 1 1997), in “Erratum: “Harmonic inversion of time signals and its applications’"’, ibid, vol. 109, no. 10, page 4128 (Sep. 8 1998), and in Michael R. Wall, Daniel Neuhauser “Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short-time segment of a signal. I. Theory and application to a quantum-dynamics modef’, J. Chem. Phys. 102, 8011 -8022 (1995), incorporated herein for reference.

The FDM algorithm defines an interval of considered frequencies comprising the estimated resonance frequency fs - and calculates one or more oscillation modes extracted from the data supplied in input - i.e. the signal X2 obtained by processing the second sequence of images. The frequency interval is equal to a band comprised between 2KHz and 3KHz, e.g. equal to 2.5KHz. Preferably, although not in a limiting way, the frequency interval is centred on the estimated resonance frequency fs. For example, in the case considered above of an oscillation frequency around 6 KHz, the considered frequency interval is comprised between 4.5 Hz and 7 KHz.

Each oscillation mode m(t) is calculated by the FDM algorithm in the form: where A is the oscillation amplitude, / is the imaginary unit (V^l), t is the time, fR is the resonance frequency, rp is the phase - also called “phase shift” - and dec is the exponential decay constant of the oscillations - also called the oscillation “lifetime”.

In addition, for each oscillation mode m(t) an error err, is also calculated, i.e. an estimate of the relative error associated with the frequency. The error err is a figure of merit that provides an indication of the reliability of the oscillation mode estimate. For example, the error err is calculated according to the formula 2.19 defined in the already mentioned Michael R. Wall, Daniel Neuhauser “Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short-time segment of a signal. I. Theory and application to a quantum-dynamics modef’, J. Chem. Phys. 102, 8011-8022 (1995).

In the embodiment considered, the FDM algorithm is configured to select - i.e. to supply in output - the oscillation mode m(t) having the greatest amplitude A with positive value and the minor error err. The control module 50 is configured to calculate the quality factor Q (step 119D) based on the selected oscillation mode m(t). In the example considered, the quality factor Q of the MEMS accelerometer Aj under test is calculated according to the following formula:

Q = — dec ■ ( '2) '

Preferably, the control module 50 supplies in output the resonance frequency tn calculated starting from the oscillation mode m(t) as it provides a more accurate estimate of the effective resonance frequency of the MEMS accelerometer Ai,j since it is not affected by non-idealities due to the sampling resolution of the FFT (step 119E).

Optionally, one or more of the following parameters of the MEMS accelerometer Ai,j can be supplied in output in addition to the quality factor Q: the decay constant dec, the maximum oscillation amplitude in absolute value |A|, the phase and the error err (step 119F).

In the embodiment considered, the control module 50 stores the quality factor Q and, preferably at least the resonance frequency fR, together with an identifier code of the MEMS accelerometer Ai under test and, preferably, an identification code of the wafer W comprising the MEMS accelerometer Aj (step 121).

The test result is made available to an operator through the user interface 60 (step 123). In one embodiment, it is envisaged to display a screen 61 of the user interface 60 - schematically illustrated in Figure 6 - a graphical representation 62 of the wafer W in which the MEMS accelerometers under test, the MEMS accelerometers not under test, are identified. Preferably, it is envisaged to identify the MEMS accelerometers with a quality value Q higher than a minimum value - i.e. MEMS accelerometers suitable for use (symbol A/ in Figure 6) -, with quality factor Q lower than a minimum value - i.e. MEMS accelerometers not suitable for use (symbol X in Figure 6) and/or with quality factor Q comprised in a predetermined interval - e.g. MEMS accelerometers with standard performance or with above-average performance (as schematically illustrated in Figure 6). In one embodiment, the MEMS accelerometers are represented on the user interface 60 with a different colouring and/or symbol according to the value of the corresponding quality factor Q. Still, through the user interface 60 the operator may retrieve one or more detailed information 63 on a single MEMS accelerometer or on a set of selected MEMS accelerometers. For example, the detailed information comprises one or more of the following information: the calculated quality factor Q, the calculated resonance frequency f , the average resonance frequency f/v, the estimated resonance frequency fs, the exponential decay constant dec of the oscillations, the maximum oscillation amplitude A - preferably in absolute value -, the phase rp, and the relative error err.

The control module 50 verifies whether there is at least one other MEMS accelerometer of the wafer W under test (decision step 125). For example, the control module verifies whether there is an untested MEMS accelerometer A+i, j or Aj+i adjacent to the newly tested MEMS accelerometer Aij.

In the affirmative case (output branch Y of step 125) it positions the optical module so as to test a new MEMS accelerometer bringing the execution of the procedure 100 back to step 105 described above. Otherwise, if all the MEMS accelerometers of the wafer W have been tested (output branch N of step 125) the procedure 100 ends, preferably with the control module 50 providing an indication of completion of the test through the user interface 60 (step 127).

However, it is clear that the above examples must not be interpreted in a limiting sense and the invention thus conceived is susceptible of numerous modifications and variations.

For example, in alternative embodiments, the receiving module may comprise actuating means that allow the Wafer arranged thereon to be oriented in a desired manner.

Still, nothing prevents the use of an appropriately trained machine learning algorithm to recognize the moveable element of the MEMS accelerometer in the acquired images.

In alternative embodiments (not illustrated), the system is configured to evaluate the quality of two or more MEMS accelerometers in parallel, where such accelerometers occupy adjacent positions in the wafer, are illuminated simultaneously by the lamp and are captured in a same sequence of images. In this case it is possible to acquire the first sequence of images for the two or more MEMS accelerometers framed and to estimate the resonance frequencies of each MEMS accelerometer by means of a respective FFT. Subsequently, the quality factor Q and the final resonance frequency fp are determined for each MEMS accelerometer individually. In this way, it is possible to reduce the number of shifts of the optical module and of stresses to the average frequency of the wafer as a function of the number of MEMS that can be framed simultaneously.

Although the embodiment described above refers to a system for testing MEMS accelerometers with cantilever arm, alternative embodiments (not illustrated) comprise a system for testing MEMS accelerometers of different type, i.e. with a different moveable element. For example, an embodiment of the present invention (not illustrated) is configured to test MEMS accelerometers with a comb structure - comprising two structures having a comb shape with teeth spaced apart from each other. In this case, the control module is configured to reconstruct the trend of the relative movement of the teeth of the two combs over time as a function of the variations in brightness detected in the images acquired by the camera and evaluate the quality of the accelerometer based on this information. In general, the procedure and the system described above reconstruct and analyse the trend as a function of time of the vibrations of a moveable element of the MEMS accelerometer to be tested.

As will be apparent to the person skilled in the art, one or more steps of the procedure described above may be performed in parallel with each other - such as the steps relating to the presentation of information on the MEMS accelerometers through the user interface and the positioning and test of a MEMS accelerometer - or in a different order from the one presented above - for example, the information may be presented only after testing all MEMS accelerometers of a wafer. Similarly, one or more optional steps can be added or removed from one or more of the procedures described above.

In one embodiment, the method may comprise subjecting to test a small group of MEMS accelerometers comprised in a wafer, for example a predetermined group of MEMS accelerometers or a number of randomly selected MEMS accelerometers.

In one embodiment, the method may comprise adjusting a resolution of the acquired images as a function of the phase in which they are executed and/or as a function of the acquisition frequency. For example, the resolution may be higher during the wafer alignment phase, whereas it may be reduced when the acquisitions of the first sequence and of the second sequence of images are performed.

In one embodiment, the system is connected to a control system of a plant for producing electronic devices and is configured to transfer one or more information obtained from the test of the MEMS accelerometers where it can be used to divide the MEMS accelerometers based on the corresponding value of the quality factor determined during the test phase.

Naturally, all the details can be replaced with other technically-equivalent elements.

For example, nothing prevents the receiving module from comprising adjustable retaining elements, rather than fixed grooves, in order to adjust the sizes of the plate to the sizes of the wafer. In other words, the receiving module may comprise a chuck adapted to hold a wafer to be tested in place. In conclusion, the materials used, as well as the shapes and contingent dimensions of the devices, apparatuses and terminals mentioned above, may be any according to the specific implementation needs without thereby departing from the scope of protection of the following claims.