Abstract:
Various embodiments of the invention provide for stiction testing in MEMS devices, such as accelerometers. In certain embodiments, testing is accomplished by a high voltage smart circuit that enables an analog front-end circuit to accurately read the position of a movable proof-mass relative to a biased electrode in order to allow the detection of both contact and release conditions. Testing allows to detect actual or potential stiction failures and to reject defective parts in a Final Test stage of a manufacturing process where no other contributors to stiction issue can occur, thereby, minimizing stiction failure risks and extending the reliability of MEMS devices.

Description:
CROSS REFERENCE TO RELATED PATENT APPLICATIONS 
       [0001]    The present application claims priority to U.S. Provisional Application Ser. No. 61/887,880, titled “Systems and Methods to Determine Stiction Failures in MEMS Devices,” filed on Oct. 7, 2013 by Giorgio Massimiliano Membretti, Roberto Casiraghi, and Igino Padovani, which application is hereby incorporated herein by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    A. Technical Field 
         [0003]    The present invention relates to integrated micromechanical systems and, more particularly, to systems, devices, and methods of reducing stiction failures in Micro Electro Mechanical System (MEMS) sensors. 
         [0004]    B. Background of the Invention 
         [0005]    Stiction phenomena are well-known problems in MEMS type devices with movable parts. Stiction effects typically occur between two surfaces when an external force deflects a movable part in a manner so as to cause its surface to come in physical contact and adhere to the surface of an adjacent stationary part. 
         [0006]    Sensor type MEMS devices are particularly vulnerable to stiction, which may occur intermittently during regular use of the device or during the manufacturing process. Stiction adversely affects device performance and may be caused by a variety of forces including capillary forces caused by the presence of moisture and van der Waals forces caused by surface contamination, such as polishing residuals that may fluctuate depending on surface preparation processes. 
         [0007]    For example, in a MEMS accelerometer sensor, an external disturbance such as a mechanical shock may deflect a suspended proof-mass in a manner so as to cause a portion of its surface to contact and adhere to an adjacent wafer substrate surface. When the total adhesion force between the two surfaces is higher than the mechanical restoring force inherent to the proof-mass, stiction occurs and temporarily immobilizes the proof-mass and prevents it from recovering its original position even after the external disturbance ceases to act on the sensor. This prevents the accelerometer from producing an accurate acceleration signal, until the stiction force is overcome, for example, by a sufficiently large counteracting force. 
         [0008]    Since stiction causes the proof-mass to adhere to the substrate, the two parts are no longer separated from each other, blocking the movement of the proof mass and, in some cases, also causing a short circuit event that destroys the electric field between the two surfaces. Therefore, the sensor can no longer measure capacitive changes to derive an acceleration value during the time the stiction condition is present, which affects both device reliability and performance. 
         [0009]    Some prior art approaches allow to improve stiction robustness of a MEMS device, for example, by increasing material stiffness and, thus, the mechanical restoring force in order to aid releasing the adhered parts of the device. Other approaches seek to improve surface conditions during the fabrication process in order to minimize stiction. However, such improvements result from design tradeoffs that come at the cost of reduced device performance, increased device size, and/or increased cost of manufacturing. What is needed are tools for MEMS designers to overcome the above-described limitations without increasing device size or sacrificing device performance. 
       SUMMARY OF THE INVENTION 
       [0010]    The disclosed systems and methods increase reliability of MEMS devices by allowing to detect and screen out from a production batch units that suffer from actual stiction or are prone to stiction effects, for example, resulting from surface contamination during the manufacturing process. Detection involves performing a stress test that aids in identifying existing or expected stiction failures. 
         [0011]    In certain embodiments, a high voltage smart circuit allows to select between a regular acceleration reading mode and a stiction test mode of operation using a stress test apparatus. The stress test apparatus comprises dedicated circuitry configured to selectively apply a voltage to a fixed electrode to generate an electrostatic force that attracts a movable proof-mass within the MEMS device in a manner so as to cause contact between the movable mass and a stationary part. In one embodiment, the dedicated circuitry comprises an external high voltage source configured to apply a high voltage to one or more fixed electrodes to induce the contact. The dedicated circuitry protects the main front-end from overvoltage stress when the sensor is coupled to the high voltage source. 
         [0012]    In one embodiment, the stress test comprises directly or indirectly determining a capacitance value between the movable part and a fixed electrode, e.g., from a position of the movable part in relation to the fixed electrode. Once the voltage is removed, information about existing or future stiction events, including the causes and the severity of the stiction can be obtained. In some embodiments, the voltage is removed gradually to generate a hysteresis curve from which additional information may be obtained that allows for characterization and in-depth analysis of a particular stiction effect. 
         [0013]    Certain features and advantages of the present invention have been generally described here; however, additional features, advantages, and embodiments presented herein will be apparent to one of ordinary skill in the art in view of the drawings, specification, and claims hereof. Accordingly, it should be understood that the scope of the invention is not limited by the particular embodiments disclosed in this summary section. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]    Reference will be made to embodiments of the invention, examples of which may be illustrated in the accompanying figures. These figures are intended to be illustrative, not limiting. Although the invention is generally described in the context of these embodiments, it should be understood that this is not intended to limit the scope of the invention to these particular embodiments. 
           [0015]    FIG. (“FIG.”)  1 A shows a block diagram of a prior art MEMS sensor front-end readout circuit. 
           [0016]      FIG. 2  shows a prior art MEMS sensor for differential readout. 
           [0017]      FIG. 3A  shows a general mechanical model representing MEMS sensor in  FIG. 2 . 
           [0018]      FIG. 3B  shows a general electrical equivalent circuit representation of the MEMS sensor shown in  FIG. 3A . 
           [0019]      FIG. 4  illustrates an exemplary block diagram of a testing system to detect stiction failures in a MEMS sensor, according to various embodiments of the invention. 
           [0020]      FIG. 5  depicts the testing system of  FIG. 4  utilizing a high voltage control circuit, according to various embodiments of the invention. 
           [0021]      FIG. 6  depicts aspects of the testing system during stiction test mode, according to various embodiments of the invention. 
           [0022]      FIG. 7A  illustrates an exemplary procedure for performing a stiction test according to various embodiments of the invention. 
           [0023]      FIG. 7B  illustrates an exemplary C/V curve for characterizing MEMS structures according to various embodiments of the invention. 
           [0024]      FIG. 8  is a flowchart of an illustrative process to determine stiction failures in MEMS devices in accordance with various embodiments of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0025]    In the following description, for the purpose of explanation, specific details are set forth in order to provide an understanding of the invention. It will be apparent, however, to one skilled in the art that the invention can be practiced without these details. One skilled in the art will recognize that embodiments of the present invention, described below, may be performed in a variety of ways and using a variety of means. Those skilled in the art will also recognize that additional modifications, applications, and embodiments are within the scope thereof, as are additional fields in which the invention may provide utility. Accordingly, the embodiments described below are illustrative of specific embodiments of the invention and are meant to avoid obscuring the invention. 
         [0026]    Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, characteristic, or function described in connection with the embodiment is included in at least one embodiment of the invention. The appearance of the phrase “in one embodiment,” “in an embodiment,” or the like in various places in the specification are not necessarily referring to the same embodiment. 
         [0027]    Furthermore, connections between components or between method steps in the figures are not restricted to connections that are affected directly. Instead, connections illustrated in the figures between components or method steps may be modified or otherwise changed through the addition thereto of intermediary components or method steps, without departing from the teachings of the present invention. In this document mass and seismic mass are used interchangeably. 
         [0028]      FIG. 1  shows a block diagram of a prior art MEMS sensor front-end readout circuit  100 . Circuit  100  comprises voltage stimulus generator  102 , MEMS sensor  106 , and front-end amplifier  110 . Voltage stimulus generator  102  is coupled to MEMS sensor  106 , which outputs differential sense signal  120 ,  122  to low-noise main front-end amplifier  110 . In this example, MEMS sensor  106  is an accelerometer sensor configured to read out the position of a proof-mass (not shown) and, in response, output voltage V OUT    130 . 
         [0029]    In operation, voltage stimulus generator  102  provides a voltage stimulus to electrodes (not shown) within sensor  106  to determine variations in differential capacitance  108 ,  118 . MEMS sensor  106  generates differential output signal  120 ,  122  in response to receiving acceleration information from the sensor electrodes. Front-end amplifier  110  amplifies signal  120 ,  122  to generate output signal V OUT    130 . 
         [0030]      FIG. 2  shows a prior art MEMS sensor for differential readout. MEMS sensor  200  comprises movable proof-mass  202 , sensing electrode  208 ,  218  and stopper electrode  210 ,  220 . Movable mass  202  typically is a seismic proof-mass that is anchored to a substrate on which MEMS sensor  200  is constructed. The anchor suspends seismic mass  202  and separates it from the substrate (not shown). Mass  202  is configured to pivot around center  206 . The solid line indicates an initial position prior to the application of an electrostatic force. 
         [0031]    Upon application of a bias voltage to sensing electrode  208 ,  218 , movable mass  202  rotates clockwise or counterclockwise due to an electrostatic force. If the voltage is applied to electrode 1  208 , movable mass  202  will rotate counterclockwise from its initial position, such that the left end is rotated towards stopper electrode  210 , as indicated by dotted line  204 . Conversely, if a voltage is applied to electrode 2  218 , movable mass  202  will rotate clockwise towards stopper electrode  220 . Stationary stopper electrode  210 ,  220  serves as a contact surface that stops the rotational movement of mass  202  when the movement of sensor MEMS  200  becomes too large, for example, during phases of very high acceleration due to heavy oscillation or mechanical shock. 
         [0032]    Once sensor electrodes  208 ,  218  are biased, electrostatic forces due to the charge on the plates of the capacitive electrodes add to the total force applied to proof-mass  202 . The net electrostatic force F e1  can be expressed by equation: 
         [0000]        F   EL   =a   X ( V   E1+   −V   M ) 2   −a   −X ( V   E2−   −V   M ) 2    
         [0000]    where V E1+  and V E2−  are bias voltages; and V M  is the stimulus applied to mass  202 , and coefficients a x  and a −x  are proportionality factors that depend on the particular geometry of sensor  200 , e.g., the gap between proof-mass  202  and sensor electrodes  208 ,  218 . 
         [0033]    Ideally, the sum of the electrostatic forces applied to electrodes  208 ,  218  are balanced, such that the net force of the mechanical system cancels out. As a result, the application of the bias voltage should not cause any additional forces on the proof mass that possibly create perturbations and negatively impact the readout voltage V OUT . 
         [0034]    During a stiction condition, the contact force between movable mass  202  and the surface of stopper  210  will be larger than a restoring force of movable mass  202 , such that movable mass  202  will not be able to return to its nominal position, until the restoring force exceeds the stiction force in response to, for example, a subsequent shock that releases the two surfaces. 
         [0035]    Existing approaches to minimize the occurrence of stiction events include increasing restoring force of proof-mass  202  in order to counteract stiction forces. Typically, the restoring force is proportional to the stiffness of the material of movable mass  202 . Since material stiffness, in turn, is a function of the elasticity of both material and geometry, designing and fabricating seismic mass  202  with an appropriate stiffness can increase the restoring force. However, one drawback of this approach results from the fact that a stiffer seismic mass  202  adversely affects sensitivity of the signal to be measured due to reduced deflection of the material thereby limiting the sensitivity of the accelerometer. 
         [0036]    One approach to minimize stiction involves optimizations at the system design level, e.g., the minimizing of electrostatic forces during normal operation while the accelerometer is being read out. Another approach to minimize stiction forces between electrodes targets manufacturing processes and surface conditioning. For example, in order to decrease the contact area between two surfaces that have a tendency adhere to each other, the surface roughness of, e.g., stopper  210 ,  220  and movable mass  202 , is increased in order to reduce adhesion forces between the layers of material. In this context, anti-stiction materials can be used in the fabrication process in order to decrease the likelihood of stiction events. However, such process solutions are cost intensive and typically do not lend themselves to mass production for high volume markets. 
         [0037]    Therefore, it would be desirable to have systems and methods that allow to detect and screen out defective sensors and anomalous process lots that are prone to suffer from stiction failures. 
         [0038]      FIG. 3A  shows a general mechanical model representing MEMS sensor in  FIG. 2 . Sensor  300  is an inertial MEMS accelerometer sensor. The mechanical model represents a harmonic resonator having a natural resonant frequency. The resonator comprises proof-mass  202 , spring  304 , and damping element  306 . As shown in  FIG. 3A , proof-mass  202  is connected to a parallel configuration of spring  304  and damping element  306 . The parallel configuration is anchored to substrate  308 . Proof-mass  202  is characterized by mass m, spring  304  is characterized by spring constant k, and damping element  306  is characterized by damping coefficient b. 
         [0039]    Displacement  312  is characterized by a movement in position, x, of proof-mass  202  resulting from inertial acceleration force Fin(t)  310  acting on proof-mass  202 . Displacement  312  can be capacitively measured and converted into a measured acceleration value. In addition to gravity, the sum of acceleration force, spring force F k , and damping force F b  determine the total time-varying force F(t)  310  that acts on proof-mass  202 . Force F(t)  310  is related to displacement  312  of proof-mass  202  in the mechanical model of sensor  300  through the following second order differential equation: 
         [0000]        F ( t )= m{umlaut over (x)}+b{dot over (x)}+kx    
         [0000]    which can be solved by numerical analysis. 
         [0040]      FIG. 3B  shows a general electrical equivalent circuit representation  350  of the MEMS sensor shown in  FIG. 3A . The electrical model comprises a pair of parallel variable capacitors  108 ,  118  that are typically coupled between movable mass  302 , which has an inertial resistance to acceleration, and a sensing circuit (not shown) coupled to capacitors  108 ,  118 . The variation of the differential capacitance of capacitors  108 ,  118  is related to the movement of movable mass  302 . 
         [0041]      FIG. 4  illustrates an exemplary block diagram of a testing system to detect stiction failures in a MEMS sensor, according to various embodiments of the invention. System  400  comprises voltage stimulus generator  102 , MEMS sensor  106 , auxiliary front-end circuit  404 , high-voltage smart circuit  412 , forcing driver  440 , and main front-end amplifier  410 . Both forcing driver  440  and main front-end amplifier  410  are selectively coupled to MEMS sensor  106 . Similarly, voltage stimulus generator  102  and auxiliary front-end circuit  404  are selectively coupled to MEMS sensor  106  via high-voltage smart circuit  412 . MEMS sensor  106  may be a capacitive MEMS accelerometer sensor similar to  FIG. 1  and comprises movable proof-mass M  202 , which is capacitively coupled to fixed electrodes  208 ,  218  forming a capacitive bridge that is configured to read out the position of movable mass  202  and output differential output signal  120 ,  122 . 
         [0042]    In one embodiment, in regular acceleration reading mode, voltage stimulus generator  102  and main analog front-end amplifier circuit  410  are coupled to MEMS sensor  106 , while auxiliary front-end circuit  404  and forcing driver  440  are decoupled from MEMS sensor  106 . In this embodiment, voltage stimulus generator  102  provides voltage stimulus  105  that is applied to movable mass  202  of sensor  106 . Electrodes  208 ,  218  are coupled to main front-end amplifier circuit  410 , which determine variations in the capacitance of sensor electrodes  208 ,  218 . The capacitive imbalance between movable mass  414  and electrodes  208 ,  218  generates differential readout signal  120 ,  122  that is output by the capacitive bridge. Main front-end amplifier circuit  410  is a low-noise analog amplifier that receives signal  120 ,  122  and amplifies it to generate output signal V OUT    130  from which an acceleration value can be extracted. 
         [0043]    During operation in stiction test mode, both auxiliary front-end circuit  404  and forcing driver  440  are coupled to MEMS sensor  106 , while voltage stimulus generator  102  and main front-end amplifier circuit  410  are decoupled from to MEMS sensor  106 . In one embodiment, forcing driver  440  alternately applies a relatively high voltage to electrodes  208 ,  218  to generate an electrostatic force that selectively rotates movable mass  202  closer to one of the two fixed electrodes  208 ,  218 . Forcing driver  440  may be implemented as an external high voltage source that employs an algorithm to gradually increase and decrease the bias voltage. 
         [0044]    In this example, auxiliary front-end circuit  404  is coupled to movable mass  202  to detect a distance between movable mass  202  and each of electrode  208 ,  218 , for example, by selectively sensing the absolute capacitance value between movable mass  202  and the respective electrode  208 ,  218 . The capacitance value, which, by definition, is a function of geometry, is representative of the relative position between movable mass  202  and the respective electrode  208 ,  218 . In one embodiment, the obtained capacitance value is used to determine whether contact has occurred between moving and stationary parts. 
         [0045]    Switching between modes of operation is accomplished by high voltage smart circuit  412 . During stiction test mode, forcing driver  440  applies a relatively high voltage (e.g., &gt;5V) to electrode  208 ,  218  that provides an electrostatic force to sensor  106  in order to cause contact between movable mass  202  and one of electrode  208 ,  218 . However, such a high voltage range is generally not tolerated by analog main front-end  410 , which is typically designed as a low voltage (e.g., &lt;2V) circuit. As will be further explained with respect to  FIG. 5 , the operation of voltage smart circuit  412  protects main front-end circuit  410  from overvoltage stress. 
         [0046]    One of ordinary skill in the art will appreciate that any known method be used to approximate a change in capacitance. For example, instead of a voltage, a current or a charge may be used from which variations in capacitance may be determined. 
         [0047]      FIG. 5  depicts the testing system of  FIG. 4  utilizing a high voltage control circuit, according to various embodiments of the invention. For clarity, components similar to those shown in  FIG. 4  are labeled in the same manner. For purposes of brevity, a description or their function is not repeated here. 
         [0048]    High-voltage control circuit  412  of testing system  500  comprises MEMS sensor  106 , transmission gates T1  520  and T2  522 , logic circuit  540 , charge pump  542 , and transistor  550 ,  552 . In this example, transistors M1  550  and M2  552  are implemented as MOSFETs. Transmission gate T1  520  is coupled between voltage stimulus generator  102  and MEMS sensor  106 . Transmission gate T2  522  is coupled to auxiliary front-end circuit  404  and to MEMS sensor  106 . Logic circuit  540  is coupled between transmission gates  520 ,  522  and charge pump  542 . In example in  FIG. 5 , testing system  500  comprises selector  544  that selects which of charge pump  542  or external high voltage source  546  polarizes forcing driver  440 . Transmission gates T1  520  and T2  522  enable the selective coupling and decoupling of movable mass  202  to voltage stimulus generator  102  and auxiliary front-end circuit  404 , respectively. Logic circuit  540  controls the connections between MEMS sensor  106  and the interfacing electronics. Charge pump  542  controls transistors M1  550  and M2  552 . 
         [0049]    In normal acceleration reading mode, control circuit  412  controls charge pump  542  to turn on transistors M1  550  and M2  552 . This allows acceleration signal  120 ,  122  to be forwarded to the input terminals of main front-end circuit  410 . Conversely, in stiction test mode, transistor  550 ,  552  is switched off to protect the inputs of main front-end from the high voltage generated by forcing driver  440 . Transistor  550 ,  552  is designed such that in its off state it can withstand the relatively higher voltage impressed by forcing driver  440 . Charge pump  542  is designed to operate high voltage transistors M1  550  and M2  552 , which require a higher gate voltage (&gt;2V) to be switched on when compared to the low voltage transistors used in existing front-end interface designs, which are driven by power supply voltages below 2 V. One advantage of utilizing an external high-voltage circuit  546  to bias forcing driver  440  when operating in stiction test mode is that if the test is performed, for example, only once during the final stages of the manufacturing process, control circuit  412  can be designed with less components and, thus, more cost efficient. 
         [0050]    In detail,  FIG. 6  depicts aspects of the testing system during stiction test mode, according to various embodiments of the invention. System  600  comprises MEMS sensor  106  that is coupled between auxiliary front-end circuit  404  and forcing driver  440 . Movable mass  202  within sensor  106  is coupled to electrode  208 ,  218  through capacitance C1  108  and C2  118 . 
         [0051]    In operation, forcing driver  440  is controlled to apply a bias voltage to one of electrodes  208 ,  218 , while no voltage or a zero voltage is applied to both the other electrode and movable mass  202 . In example in  FIG. 6 , forcing driver  440  applies a voltage, V E1 , to electrode E1  208  while the terminal of electrode E2  218  is grounded. It is noted that while V E1  is applied to electrode E1  208  instead of grounding electrode E2  218 , a second voltage, V E2 , may be applied to electrode E2  218 , whereby V E2  is equal to and opposite in magnitude to a stimulus voltage V M  that is applied to movable mass  202 . 
         [0052]    Referring to  FIG. 2 , a bias voltage applied to electrode E1  208  will generate an electrostatic force between movable mass  202  and electrode E1  208  that causes movable mass  202  to rotate counterclockwise. The applied voltage, which is proportional to the square root of the electrostatic force, attracts the two parts, and given a sufficiently high bias voltage, movable mass  202  will rotate until it contacts stationary stopper electrode  210  (labeled STP1 in  FIG. 2 ). Therefore, unlike during regular operation where an equal bias voltage is applied to both electrodes in order to generate a force balance, the objective in this embodiment is not to balance the electrostatic forces. As a result, the equation previously mentioned with respect to  FIG. 2  that describes the net electrostatic force F e1  simplifies to the following expression: 
         [0000]        F   EL   =a   x ( V   E1+ ) 2    
         [0000]    wherein V E1+  is the bias voltage applied to electrode E1  208 . Likewise, when a bias voltage is applied to electrode E2  218 , the electrostatic force between movable mass  202  and electrode E2  218  will cause movable mass  202  to rotate clockwise. In this scenario, the net electrostatic force F e1  can be expressed by: 
         [0000]        F   EL   =−a   −x ( V   E2− ) 2    
         [0053]    Once the bias voltage, i.e., the electrostatic force is removed, it is possible to determine whether the contact surfaces are prone to stiction by examining the response of structure  200 . If, for example, moveable mass  202  remains in contact with stopper electrode 1  210  after the electrostatic force has been disengaged, for example, due to strong Van der Waals forces between the surfaces caused by process residuals on the surface of stopper electrode 1  210 , sensor  200  would be deemed to have a potential stiction issue. Conversely, if moveable mass  202  recovers its initial position after the removal of the electrostatic force, it may be concluded that sensor  200  is not likely to be prone to stiction. 
         [0054]    In one embodiment, the position of moveable mass  202  is determined via a dedicated capacitive sensing. Returning to  FIG. 6 , auxiliary front-end circuit  404  alternately detects the capacitance value between proof-mass  202  and electrode E1  208  and between proof-mass  202  and electrode E2  218  to detect the position of movable mass  202  during stiction test mode. 
         [0055]    Auxiliary front-end circuit  404  may comprise an ordinary charge sensing amplifier with a feedback capacitor that transforms the capacitance into a voltage signal. However, this is not intended as a limitation. A person of ordinary skill in the art will appreciate that any method of capacitive sensing may be used to determine the position of movable mass  202  in order to determine the presence of a stiction condition. 
         [0056]      FIG. 7A  illustrates an exemplary procedure for performing a stiction test according to various embodiments of the invention. As shown in  FIG. 7A , electrode E1 is selected for stiction testing. First, voltage V E1    702  is applied to the selected electrode via a voltage source, e.g., the forcing driver shown in  FIG. 6 . The voltage source gradually increases voltage V E1    702  in discrete steps  706 , such that at each step a capacitance value can be measured, for example, by using the auxiliary front-end circuit shown in  FIG. 6  to measure a second voltage that is proportional to the capacitance value. The magnitude of voltage  702  required to rotate the movable mass is a function of the design of the spring-mass system. For example, higher material stiffness of the movable mass will require a higher voltage  702  and electrostatic force to generate a rotation. 
         [0057]    As shown in  FIG. 7B , once an increase in bias voltage V E1    702  no longer leads to further increases in measured capacitance C1  752 , this indicates that a maximum or final capacitance value  752  is reached. At this point, the voltage source may be controlled to gradually decrease voltage V E1    702  in discrete steps, while the measurement circuit continues to measure capacitance C1  752 . Due to adhesion effects between the two surfaces, however, the relationship between bias voltage V E1    702  applied to the selected electrode and the measured capacitance value C1  752  may not reversible, but rather result in a hysteresis effect as voltage V E1    702  is decreased. 
         [0058]    A shown in  FIG. 7B , the reverse path of C/V curve  750  may exhibit a hysteresis resulting from surface forces that continue to act on the two parts and keep them in contact until voltage V E1    702  is sufficiently lowered, such that the parts can overcome the surface forces and separate, thereby, decreasing capacitance C1  752 . 
         [0059]    From hysteresis curve  750 , a control logic may then determine that an adhesion effect is present between the movable mass and the stopper electrode as a result of the contact and the surface forces. The movable mass is not immediately released, since the surface forces continue to keep the two parts in contact, until voltage V E1    702  and, thus, the electrostatic force is sufficiently lowered to a level below contact voltage  710  that allows for a separation of the parts. 
         [0060]    In a scenario where the surface forces cannot be overcome, such that measured capacitance C1  752  remains at a high saturation value  760  in response to decreasing bias voltage V E1    702 , control logic may deduce that a stiction condition is present, i.e., that stiction prevents the movable mass from regaining its original position despite a significant reduction in voltage V E1    702  (e.g., 0 V) and electrostatic force. 
         [0061]    In this manner, method  700  allows to generate C/V curves  750  for each electrode of each MEMS sensor within a batch of sensors. From the C-V curve and the hysteresis between the increasing and decreasing voltage curves, a given MEMS structure may be directly or indirectly characterized in terms of sensitivity and tendency to suffer from stiction in operation. Stiction testing may also be used to measure and analyze the entire C-V curve, for example, in order to establish failure criteria that may reach from benign to catastrophic, or to characterize surface conditions, material quality, particle count, geometry, and the like. As a result, a sensor under test may be rejected as failing to meet predetermined specifications. 
         [0062]    In one embodiment, e.g., in order to decrease testing time, instead of generating a complete C/V curve  750 , a sufficiently high bias voltage V E1    702  is applied to each electrode under test so as to force a contact between the stopper electrode and the movable mass. Then, upon removal of voltage V E1    702 , the auxiliary analog front-end circuit can determine whether capacitance C1  752  has changed sufficiently so that it can be concluded whether stiction has, in fact, occurred. 
         [0063]    In one embodiment, hysteresis curve  750  is used to predict reliability. The determination of a stiction condition in combination with electrostatic forces that emulate a real application environment in which the MEMS sensor experiences the stiction condition, for example, as a consequence of a strong acceleration or a shock that causes the movable proof-mass to contact and adhere to one of the stopper electrodes allows not only for the detection of zero life time stiction failures, but also for the detection parts that are prone to suffering from stiction failures. 
         [0064]      FIG. 8  is a flowchart of an illustrative process to determine stiction failures in MEMS devices in accordance with various embodiments of the invention. The process  800  to determine stiction failures starts at step  802  when a stimulus signal generator is decoupled from a MEMS device. 
         [0065]    At step  804 , a first front-end circuit is decoupled from the MEMS device. 
         [0066]    At step  806 , a voltage source is connected to the MEMS device. 
         [0067]    At step  808 , a bias voltage is applied to the MEMS device, for example, via a second front-end circuit. 
         [0068]    At step  810 , a capacitance relating to the MEMS device is determined, for example, by determining a distance between a movable and a stationary part within the MEMS device. 
         [0069]    At step  812 , the voltage source is disconnected. 
         [0070]    At step  814 , a change in the capacitance value is detected to determine existing or potential stiction failures in the MEMS device. 
         [0071]    It will be appreciated by those skilled in the art that fewer or additional steps may be incorporated with the steps illustrated herein without departing from the scope of the invention. No particular order is implied by the arrangement of blocks within the flowchart or the description herein. 
         [0072]    It will be further appreciated that the preceding examples and embodiments are exemplary and are for the purposes of clarity and understanding and not limiting to the scope of the present invention. It is intended that all permutations, enhancements, equivalents, combinations, and improvements thereto that are apparent to those skilled in the art, upon a reading of the specification and a study of the drawings, are included within the scope of the present invention. It is therefore intended that the claims include all such modifications, permutations, and equivalents as fall within the true spirit and scope of the present invention.