|NDT.net - April 2002, Vol. 7 No.04|
Characterizing the mechanical properties of MEMS structures at a very early stage of manufacturing is a challenging task for quality assurance in this field. The paper describes a new solution that is based upon the vibration analysis of the microparts. The microvibrations have nm amplitudes and are detected by electronic speckle pattern interferometry (ESPI). A specific signal processing technique (moving phase reversal reference) has been applied to make the solution robust.Comprehensive numerical simulations provide the theoretical base for estimating the frequencies and mode shapes expected for perfect MEMS as well as for typical faults. The complete wafer ensemble was modeled to gain knowledge about best suited wafer clamping and about interactions between the microparts vibrating. A laboratory system for 4" wafer has been built, and extensive tests show that such key properties as e.g. the thickness of springs or membranes can be determined exactly by means of the hybride approach. Automated frequency scanning and corresponding digital image processing open the way to reliable and fast industrial systems for MEMS testing on wafer level.
Testing MEMS quality is realized by relating the resonant properties of a single element which
can be experimentally measured and its operating performance. Optical field methods guarantee
high efficiency and reliability for this task through their ability to yield resonant frequencies as
well as information about the vibration modes. To measure
are the main aspects for the choice of a well-suited measuring technique. Basically,
interferometry fullfil these requirements, its sensitivity allows the detection of vibration
amplitudes in the nanometer range. A comparison between classical interferometry and speckle
interferometry shows that measuring close to the process can be realized more convenient by the
speckle method. The following features are worth mentioning:
The testing concept is based upon the combination of experimental and computational methodologies. In addition to interferometry finite element simulations of the microsystems are performed both, for the single element and the wafer ensemble. The simulation step aimes at the prediction of the resulting behaviour of the micropart when defects occur. Previous investigations had shown that the testing process can be much more effective if simulation is combined with experiment in a hybride approach [1,2].
In a first step a CAD model is generated from the mask data set and the etching parameters by means of the SIMODE program . Then, the single element behaviour can be analysed by finite element simulation. Typical results obtained for three MEMS structures A (out-of-plane spring/mass system), B (membrane/mass system), and C (in-plane spring/mass system) are shown in Fig.1.
|Fig 1: First resonant mode for MEMS types A (left), B (middle), and C (right).|
|spring thickness [ľm]||1st natural frequ. [Hz]|
|Table 1: FE result for MEMS type A.|
The FE graphs illustrate the first mode for the case of perfect microparts. Beyond this, also the effect of imperfections can be studied in detail. As an example, table 1 shows the dependence of the first natural frequency upon variations in geometry, in particular upon spring thickness. The data are used for a polygon fit to establish a relation between the resonant frequency f and the spring or membrane thickness D, respectively:
|D = a + b.f + g.f2 + d.f3||(1)|
As the MEMS testing should be performed on wafer level the vibration behaviour of the complete disk has to be considered. The corresponding FE simulation aims at gaining knowledge about the interaction between the microparts and about the vibration modes of the whole structured disk. The CAD data sets of the single elements are the input data for the comprehensive modeling carried out by the I-DEAS program.
|Fig. 2: Finite element simulation result for the wafer ensemble, MEMS type B, vibration mode of wafer ensemble without (left) and with (right) vacuum clamping of the wafer.|
Up to 37.000 parabolic solid elements are needed for a realistic model. To optimize the fixture of the wafer on the testing stage, different boundary conditions have been investigated. Corresponding results are shown in Fig. 2: a pronounced disk vibration mode occurs if the wafer is not fixed. For successful MEMS testing, it is highly desireable to suppress such a global movement. This can be achieved by a circumferential vacuum clamping. As visible, the individual elements are vibrating while the disk is at rest.
Electronic Speckle Pattern Interferometry (ESPI) enables the measurement of in-plane and out-of- plane movements on engineering components with high sensitivity. Butters  introduced the method of time-average ESPI for vibration analysis. In the following years the application potential has been increased by a variety of developments in both, recording techniques and signal processing. At first, nanometer sensitivity was reached by sophisticated schemes of recording and modulation . In recent years, new developments of the interferometric set-up have shown that the object size successfully investigated can be scaled down to some ten microns [6,7].
|Fig 3: Laboratory set-up for wafer testing (left), in-plane and out-of-plane configurations (right).|
Fig. 3 illustrates the laboratory system built
at IWU. The configuration is designed for
testing of 4" wafers. The main part is a
fiber-optical speckle interferometer
equipped with an infrared laser diode and a
phase shifting unit [8,9]. Two modes of
operation can be chosen. The interferometer
is sensitive for in-plane movements if the
wafer is illuminated symmetrically from
two points, Fig. 3, above. In the other
configuration, one beam serves as a
reference wave so that out-of-plane
deformations are detected (Fig. 3, below). A
specific wafer mounting has been designed using a circumferential vacuum clamping to
guarantee defined boundary conditions and to suppress resonant modes of the whole disk.
Excitation of the single elements is realized by a computer controled piezo transducer or
loudspeaker via solid-state or acoustic waves, respectively. Concerning the signal processing,
there are a number of methods for the visualization of vibration modes by ESPI. The static
reference technique became most convenient when the electronic processing was substituted by
digital means  . The advantage is the high fringe contrast, however, the ESPI pattern does
also show any other rigid body movement disturbing the measuring signal. An example is given
in Fig. 4, left, where the vibration pattern is obviousely influenced by an additional tilt of the
wafer. Such misleading effects can be excluded by applying the moving phase reversal reference
. Fig. 5 illustrates the principle of this technique. The main idea is to use the modulation
capability of time-averaged speckle patterns as the measuring signal. This modulation, that
means the intensity change by phase reversal, is well developed in regions where the object does
not move, i.e. in the area of the vibration nodes. On the other hand, on vibrating parts of the
object, the speckle intensity varies with high frequency and is averaged out during a video frame
so that no modulation can be observed. In order to make the vibration mode visible, a phase
reversal is applied between every adjacent video frame. Taking moving differences
|A-B|, |B-C|, |C-D|, etc. produces a high intensity in areas of good modulation, i.e. on the nodes. In contrast, the vibrating zones, that do not show any modulation, appear dark. The example of Fig. 4 (right) demonstrates, that the moving reference is not longer sensitive for slow rigid body motions or deformations, it separates the vibration information and gives a clear to understand image.
Fig 4: Two realizations of time-average|
ESPI: static reference (left) and moving phase reversal reference (right).
Fig 5: Principle of moving phase reversal reference ESPI.
In the case of wafer testing, the ESPI signal is displayed on the system monitor at video rates so that resonant vibrations can be found by frequency scanning in the numerically pre-defined range. Typical fringe patterns for wafer testing are shown in Figs. 6 and 7. The advantage of the full-field-of-view technique is obvious: resonant vibrations of the disk as a whole can be reliably distinguished from the resonances of the single elements. Even different modes of the elements can be clearly seen. Amplitudes of 200 nm already produce maximum contrast so that the energy of excitation may be kept very small and the microparts are not subjected to dangerous loads.
|Fig 6: ESPI patterns of a MEMS type A wafer: whole disk vibration (left), first (middle) and second (right) mode of single elements.|
|Fig 7: ESPI patterns of first mode of single elements, type B- membrane/mass - (left) and type C - in-plane spring/mass - (right)|
Systematic tests have been carried out using the ESPI set-up described. Wafers with different thickness, variations in the fabrication process and local defects were prepared. For the three different types of MEMS a set of control parameters is chosen based upon the numerical analysis, for example 370-570 Hz and excitation voltage 15 mV for type A. Then, the frequency is scanned atuomatically with 1 Hz steps and the ESPI pattern is displayed for every frequency. All microparts can be observed simultaneousely and the resonances are identified by appropriate software. One frequency scan takes less than 1 minute and is sufficient for testing the whole wafer. Selected results obtained from a type A wafer will be shown below to highlight the capability of MEMS quality testing by the new approach. The result of such a test run is shown in Fig.8. A resonant frequency is assigned to each micropart. In the example, one of the elements did not at all vibrate in the frequency range of interest.
|Fig 8: 1st mode resonances across a wafer with microparts of type A.||Fig 9: Spring thickness for wafer in Fig. 8, ESPI result compared with destructive tactile measurements.|
Furthermore, it becomes visible in Fig.9 that the frequencies are systematically distributed across
the wafer. Two effects can be observed:
From a mechanical point of view, spring thickness is important for a quality assessment. Therefore, Equ. (1) is used to calculate D from the measured frequency for each single element. If, for example, the nominal thickness is 34 mm with a permissable variation of ą1 mm, a number of microparts are found out of tolerance and have to be refused. The graph in Fig. 9 shows the ESPI thickness results for all MEMS sites on the wafer. Additional tactile measurements which necessitate the wafer destruction have been performed for this wafer in order to verify the hybride ESPI / FEM values. The plot in Fig. 9 illustrates the very good agreement between the ESPI result and the corresponding tactile measured value for every single spring/mass structure on the wafer. The standard deviation for the difference is as small as s = 0.1 mm.
|Fig 10: SEM pictures of a part of MEMS type A, left: regular structure, right: spring with propagating crack.|
Finally, the micropart found non-vibrating during the ESPI test has been studied in detail by means of a scanning electron microscope (SEM). A closer look reveals that a crack is propagating across causing a completely different vibration behaviour of the damaged spring/mass system. Fig. 10 shows the SEM picture of the defect area in comparison with the view of a regular MEMS structure.
Putting together all details yields the final quality assessment. There are a number of microparts on the wafer that have to be sorted out because of variations in feature dimension and others are refused due to local defects. All other micro-mechanical parts are qualified to operate as expected. In the final testing sheet (Fig. 11) the MEMS on the wafer are marked by appropriate colors of quality.
|Fig 11: Final result of a ESPI test run: quality assessment for a MEMS type A wafer.|
The hybride approach of holographic non-destructive testing has been successfully further developed to contribute to the quality testing solution in MEMS fabrication. Numerical simulation proved to be valuable for both the design of the experimental set-up and the calculation of feature dimensions from the vibration behaviour. Advanced ESPI signal processing is introduced to receive reliable data suited for fully automatic evaluation. The frequency scan takes less than 1 minute and in the result, the resonant frequencies as well as spring or membrane thickness values are assigned to each of the microparts on the wafer. A quality assessment is made eliminating defect or out-of-tolerance parts from further manufacturing. The industrial application of the methodology developed is expected to increase the yield and to save costs in future MEMS manufacturing.
The work described was funded by the European Union and the State of Saxony under grant No. 5567/827 and 5386/827.
This Paper was presented at Fringe 2001 "The 4th International Workshop on Automatic Processing of Fringe Patterns" held in Bremen, Germany, 17-19 September 2001. Proceedings edited by Wolfgang Osten, BIAS, Germany. Please contact Wolfgang Osten for full set of proceedings at firstname.lastname@example.org.
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