contactless inspection of planar electronic devices by capacitive coupling: development of a model...
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Sensors and Actuators A 172 (2011) 88– 97
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical
j ourna l h o me pa ge: www.elsev ier .com/ locate /sna
ontactless inspection of planar electronic devices by capacitive coupling:evelopment of a model describing the sensor signal and its impactn signal post-processing
. Koerdela,b,∗, F. Alatasa,c, A. Schicka, S.J. Rupitschb, R. Lerchb
Corporate Technology CT T DE HW2, Siemens AG, Munich, GermanyChair of Sensor Technology, Friedrich-Alexander-University Erlangen-Nuremberg, GermanyInstitute of Measurement Systems and Sensor Technology, Technische Universität München, Germany
r t i c l e i n f o
rticle history:vailable online 4 March 2011
eywords:lat panel display (FPD)
a b s t r a c t
With regard to a contactless inspection method for planar electronic devices, a model to derive thesignal of the employed sensors has been developed. The measurement technique is exclusively based oncapacitive coupling and, for instance, applied to the inspection of flat panel displays (FPDs) and printedelectronics. To analyze the sensor signals, to evaluate the sensor performance, and to advance signal
lanar electronic deviceontactless inspection systemapacitive couplingosition-dependent capacitanceonductor track configurationinite element (FE) simulation
post-processing, a model of the capacitive coupling is essential. Focussing on configurations of conductortracks arranged in parallel, the model approach is explained and illustrated in detail. Finite element(FE) simulations and measurements are used to derive the model parameters, to validate the modelapproach, and to evaluate the model performance. Possible applications to signal post-processing arediscussed. As an example, the model is used to reconstruct the voltages applied to individual tracks ofa configuration from the sensor signal. Furthermore, the model is extended to configurations of two-
ondu
onmatching grids dimensionally arranged c. Introduction
The inspection and characterization of planar electronic devices,uch as flat panel displays (FPDs), detector panels, and printedlectronics has become a major topic among the respective man-facturers. To stay competitive, they are looking for inspectionystems which are able to reduce the development time on the oneand and to increase the production yields on the other hand [1].bviously, this can only be achieved if a system allows for device
nspection as long as the fundamental electronic parts are stillccessible. In addition, the inspection should be conducted with-ut directly contacting any sensitive part of the devices to avoidamages [2,3].
Several contactless inspection methods meeting these require-ents have been developed in the past. Among them, optical
echniques like Fourier reconstruction and image processing [4–6]lay an important role. However, these methods suffer fromheir insensitivity to almost all electrical defects. In contrast,lectron-optical methods overcome this restriction and allow for
∗ Corresponding author at: Chair of Sensor Technology, Friedrich-Alexander-niversity Erlangen-Nuremberg, Paul-Gordan-Strasse 3/5, 91052 Erlangen, Bayern,ermany. Tel.: +49 9131 85 23139; fax: +49 9131 85 23133.
E-mail address: [email protected] (M. Koerdel).
924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2011.02.040
ctor tracks.© 2011 Elsevier B.V. All rights reserved.
the detection of nearly all typical defects [7–9]. With regard to anintegration into the production process, a drawback may be therestriction to high-vacuum environments [1]. Voltage imaging andoptical charge-sensing are further commonly used inspection tech-niques. Whereas charge-sensing makes use of the dependence ofthe refractive index on the charge density [10], voltage imagingtechniques rely on electro-optical effects of crystals (e.g., Pockelseffect) to sense the electric field originating from the conductiveparts of a device [11–14]. Concerning FPD inspection in particu-lar, several techniques are reported that cover all possible line andpixel defects by a separate contacting of each display line [15–17].Although these techniques can be applied to extract all thin-filmtransistor (TFT) parameters, a large number of contacts or evenadditional circuits attached to the display backplanes are required.
The contactless inspection technique underlying the model pre-sented in this paper, exploits the capacitive coupling between theconductive parts of the electronic devices and sophisticated sen-sors fabricated by thin-film technology. Currently, the sensors areemployed in an inspection system prototype, tested on liquid crys-tal display (LCD) backplanes and detector panels. To inspect a
device, the sensor is positioned in close proximity to the surfaceand moved along a predefined path across the device. During thisscan, the measured sensor signal is modulated by the position-dependent capacitance between the sensor electrodes and theconductive parts. In this way, possible structural and electrical
nd Actuators A 172 (2011) 88– 97 89
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efects can be resolved and an “image” of the geometrical andlectrical structure is obtained. In addition, the functionality ofhe electronic parts can be tested. The capacitance depends on theesign of the sensor chip, the distance between sensor electrodend the conductive parts (e.g., conductor tracks), and the arrange-ent of these parts.To analyze the sensor signal for a specific device beforehand and
o evaluate the sensor performance, a model of the capacitive cou-ling for arbitrary configurations of conductor tracks is essential.oreover, such a model can be used to define the maximum resolu-
ion that can be achieved for a specific track assembly, to determinehe crosstalk that can be expected in the sensor signal, and to studyarameter dependencies. Furthermore, it permits the developmentf signal post-processing procedures and may be used to evaluateifferent post-processing approaches.
The model presented in this paper is based on two mainssues. First, the position-dependent capacitance between the sen-or electrodes and the conductive parts of a device or conductorrack arrangement only depends on their configuration, whereaso dependence on the voltages applied to them (e.g., individualracks) exists [18]. Thus, by forcing appropriate voltage differencesetween the parts involved, it is possible to obtain the individual,osition-dependent capacitance to a specific part of an assemblyirectly from the influenced charge. The total position-dependentapacitance between the sensor electrodes and the assembly is thenbtained by adding the individual contributions, since the principlef superposition holds true [19]. Second, the design of the sensorhip as well as the measuring principle facilitates the developmentf a respective model. The sensor electrode and the surroundinghielding can be understood as a large and plane electrode, heldarallel to the conductive parts of the devices or assemblies. There-ore, the sensor signal can be derived from a model of the chargeistribution or the absolute value of the electric field strength athe electrode surface. Hence, the aim is to derive a model of theeld strength, whose parameters are exclusively determined byhe geometry of the conductive parts and the distance to the sensorlectrodes. The model illustrated within this paper can be appliedo arbitrary configurations of conductor tracks arranged in paral-el. In addition, the approach is transferable to configurations ofwo-dimensionally arranged tracks.
The paper is organized as follows: first, the model approach,he underlying measuring principle, and the finite element methodsed to simulate the sensor signal are explained. Subsequently, aunctional description of the model parameters, which is exclu-ively based on the geometry of the conductor track configurationsnd the distance to the sensor electrodes is derived. Next, theuperposition of the individual contributions to the total position-ependent capacitance is illustrated and the impact of the modeln signal post-processing is discussed. As an example, it is usedo reconstruct the voltages imposed on the individual tracks of aonfiguration from the sensor signal. Additionally, the extensibilityo configurations of two-dimensionally arranged tracks is demon-trated and the necessary modifications are determined.
. General conditions
This section is concerned with the measuring principle behindhe inspection method and the finite element simulations, whichre used to develop and validate the model approach.
.1. Inspection method
Fig. 1a shows a microscope image encompassing one sensorlectrode of the sensor chip. The circular sensor electrodes have
diameter of 50 �m and are separated from the lateral shielding
Fig. 1. (a) Microscope image of the sensor chip showing one sensor electrode andlateral shielding metallization. (b) Illustration of the measuring principle.
by a gap of about 5 �m. The shielding metallization extends to thefull size of the sensor chip (≈1 cm2) and covers the signal readoutconnection of the sensor electrodes.
An illustration of the measuring principle is shown in Fig. 1b.To inspect a device or a track configuration, AC voltages (e.g., Ua,Ub) are applied to the conductor tracks, e.g., the data and gate linesof a FPD. In the following, conductor track distances and widthsare denoted by dtrack and wtrack, respectively (Fig. 1b). The sensoris positioned at a fixed distance to the device surface dsen typicallyranging from 5 �m to 25 �m and moved along a predefined pathacross the device. During a scan, the displacement current
Idis = Csen,track · dUd
dt+ Ud · dCsen,track
dt(1)
as the actual sensor signal is recorded. Ud, dUd/dt, and Csen,trackdenote the voltage, the derivative of the voltage with respect totime t, and the position-dependent capacitance between sensorelectrode and track, respectively. Usually, the contribution due tothe time derivative of the capacitance dCsen,track/dt can be neglected,since the frequencies of the capacitance changes are much lowerthan the frequencies of the applied AC voltages. Csen,track modulatesthe displacement current and contains the information about thegeometrical and electrical device structure, such as possible struc-tural and electrical defects. Hence, the model describing the sensorsignal (see Section 3) is subject to the position-dependent capaci-tance. The sensor electrodes are forced to virtual ground potential
by an amplifier circuit, the lateral shielding is connected to groundpotential. In this way, influences on the sensor signal due to thecapacitance between the sensor electrodes and the shielding areavoided.
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.2. FE simulations
Finite element (FE) simulations of the sensor signal were con-ucted to analyze the performance of the inspection method withegard to sensor electrode and chip design, scan velocity, shieldingize, and sensor electrode distance dsen. The simulations corre-pond very well to measurements, see Fig. 6 and [20]. Concerninghe model, FE simulations were employed to determine the modelarameters and to validate the model results. The simulations areased on the nonmatching grid approach [21,22], which allows to
nclude the sensor movement as well as the synchronization withhe applied AC voltages. Moreover, this method drastically reduceshe simulation effort due to the flexibility of independent mesheneration, e.g., only two meshes have to be generated to simulate
complete scan of a device. Additionally, the meshes correspond-ng to sensor and device area can easily be interchanged if differentevice or sensor types are studied. The position-dependent capaci-ance between the sensor electrode and a device or an arrangementf conductor tracks is calculated from the charge at the sensorlectrode. The charge distribution is obtained from the simulationf the electric field distribution solving the Laplace equation [19]or constant voltages (Dirichlet boundary condition) imposed onhe conductive parts. For the simulations of the conductor trackrrangements discussed in this article, a track thickness of 0.5 �ms assumed.
. Model approach
Focussing on configurations of conductor tracks arranged in par-llel, the model approach is illustrated. Furthermore, the modelarameters are introduced and their meaning is discussed.
In order to derive the sensor signal, the position-dependentapacitance between the sensor electrode and the conductor tracksas to be modelled, see Eq. (1). The design of the sensor chip allows
or a two-step procedure, since it can be assumed that the sensorlectrode does not alter the electric field distribution as it crossesn arrangement of conductor tracks. First, the absolute value of theeld strength at the sensor chip surface E(x, y, z = dsen) originat-
ng from an individual conductor track is modelled. Secondly, theapacitance to the sensor electrode is calculated from the absolutealue of the field strength, which is directly proportional to theharge density �(x, y)sen surf at the chip surface
(x, y, z = dsen) = �(x, y)sensurf
ε0. (2)
relative permittivity of air equal to one is assumed, ε0 denoteshe permittivity of free space. The z-position is determined by theistance between the sensor chip and the conductor tracks (dsen).
The charge at the sensor electrode Qsen is formally given by [19]
sen = ε0
∫∂Vsen=Asen
E(x) · dA = ε0
∫Asen
E3(x, y, z = dsen) · dA. (3)
nly the z-component of the field strength E3 is involved, sincehe field always incidents perpendicular to sensor electrode andhip surface (equipotential surface). In general, the field strengthill show variations in x- and y-direction. However, for configu-
ations of conductor tracks arranged in parallel, field strength isonstant along the y-direction. Thus, it is possible to reduce Eq.
3) to a one-dimensional integration along the x-direction, if theifferential surface element is defined in the following mannerA = 2 ·√
r2sen − x2 · dx, (4)
uators A 172 (2011) 88– 97
rsen denotes the radius of the sensor electrode. The half circle func-tion (Eq. (4)) accounts for the circular sensor geometry and is in thefollowing referred to as sensor function f(x)sen,
f (x)sen =√
r2sen − x2. (5)
The variation of the sensor electrode area in y-direction can now beincorporated as a x-dependent factor that scales the integral underthe curve of the (one-dimensional) field strength E∗
3(x, z = dsen). Theposition-dependent charge at the sensor electrode Q (x0)sen is thengiven by
Q (x0)sen = 2ε0
∫ x0+rsen
x0−rsen
E∗3(x, z = dsen) · fsen(x − x0) dx
= 2ε0
∫ +∞
−∞E∗
3(x0 − x′, z = dsen) · f (x′)sen dx′, (6)
which corresponds to the convolution of the sensor function f(x)sen
and the absolute value of the field strength E∗3(x, z = dsen).
Now, the task is to find a simple approximation of the electricfield strength whose convolution with the sensor function agreeswell with the simulated and measured sensor signal and involves asfew as possible parameters. Moreover, the approximation shouldexclusively be based on the geometry of the conductor track config-urations (dtrack, wtrack) and the distance to the sensor electrode dsen.Following this approach, the sensor signal for arbitrary configura-tions of conductor tracks can easily be derived from the geometricalproperties only.
A sufficient approximation of the field strength may be deducedfrom the comparison to an ideal parallel plate capacitor. Assum-ing a track configuration with infinitely small track distances, thetracks and the sensor chip surface form the plates of such a capac-itor. By applying a voltage to one of the tracks (T1) and forcing allother tracks and the sensor chip surface to ground potential, theelectric field will almost completely be confined to the range ofT1 and the field strength at the sensor chip surface will be con-stant. Corresponding simulation results are shown in [20]. If thetrack distance is increased, the field can spread out into the areabetween the tracks. However, in the range of T1, the field strengthmay still be constant. Hence, the magnitude of the field strengthhas to decrease in a range defined by the borders of T1 and itsneighbouring tracks. As a first approximation, a linearly decreas-ing field strength may be assumed. Two parameters can already beextracted from these assumptions. First, the width of the constantpart of the field strength b in the range of T1, and, second, the cut-off position c of the linearly decreasing part of the field strength. Ofcourse, both parameters depend on the sensor distance dsen. As anexample, Fig. 2 shows the normalized modelled field strength
E∗3(x, z = dsen)norm = E∗
3(x, z = dsen)E∗
3(x, z = dsen)max(7)
at the sensor chip surface originating from one track of a con-figuration of conductor tracks arranged in parallel. A functionaldescription is shown in Section 4.1 (Eq. (11)). The field strengthis illustrated for sensor electrode distances of 5.5 �m, 15.5 �m, and25.5 �m. Track distances and widths of 25 �m and 50 �m are cho-sen, respectively. The comparison between simulation and modelresults (Eq. (6)) shows that one more parameter is necessary toachieve a sufficient agreement. Details about the determination ofthe model parameters are discussed in Section 4.1. The parameter
1/a (Fig. 2) describes the ratio between the values of the maximumfield strength of the constant and non-constant parts and accountsfor abrupt and non-linear variations of the field strength. For largersensor electrode distance, the influence of the parameter decreases(1/a ≈ 1), since the field strength varies more gently (Fig. 2).
M. Koerdel et al. / Sensors and Act
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ig. 2. Modelled electric field strength E∗3(x, z = dsen)norm at the sensor chip surface
riginating from the central track of a configuration and sensor function f(x)sen (notormalized). Track distances and widths are indicated by the grey bars. Curves areffset for clarity.
. Results and discussion
.1. Functional description of the model parameters
This paragraph treats the functional description of the modelarameters a, b, and c, in dependence of the geometry of therack configurations (dtrack, wtrack) and the distance to the sensorlectrode dsen. Distances of 5.5 �m, 15.5 �m, and 25.5 �m wereelected. The description is based on the analysis of simulationesults for various conductor track configurations. The excellentgreement between measurement and simulation is witnessed byhe results in [20] and Fig. 6 (Section 4.2). Thus, the FE simulationsan be regarded as reliable and flexible tool and be applied to theetermination of the model parameters without restricting accu-acy. The validity of the functional description is demonstrated byodelling the position-dependent capacitance for two configura-
ions not used for parameter extraction.The parameter values are derived as follows. First, the position-
ependent charge at the sensor electrode Q (x0)sim for variousonductor track configurations was determined from FE simu-ations. Within a simulation run, the charge is calculated byntegrating the electric field strength in the range of the sensorlectrode area Asen (Eq. (3)). To obtain the charge influenced byne track of a specific configuration, a voltage Uimp was imposedn the corresponding track, while all other tracks were forced toround potential (Dirichlet boundary conditions). In this way, thether tracks yield no contribution to the charge but their physicalresence shapes the electric field. The charge accumulated at theensor electrode was then divided by the imposed voltage to obtainhe position-dependent capacitance C(x0)sim
(x0)sim = Q (x0)sim
Uimp. (8)
ubsequently, the capacitance was normalized to the capacitancef an ideal parallel plate capacitor Cid showing plate sizes equal tohe sensor electrode area and a plate distance corresponding to theensor distance
id = ε0 · Asen
dsen(9)
(x0)simnorm= C(x0)sim
Cid. (10)
or track widths equal to or larger than the sensor electrode diam-ter (wtrack ≥ 50 �m), the capacitance of the ideal parallel plate
uators A 172 (2011) 88– 97 91
capacitor is the maximum capacitance that can be reached betweensensor electrode and tracks [20].
Second, the convolution integral (Eq. (6)) for the approx-imated field strength E∗
3(x, z = dsen)norm (Fig. 2) is calculated.E∗
3(x, z = dsen)norm is simply built from piecewise defined, linear andconstant functions incorporating the model parameters a, b, and cE∗
3(x, z = dsen)norm
= [� (x + c) − � (x + b/2)] · (x + c) + a · (−b/2 + c) · [� (x + b/2) − � (x)]a · [−b/2 + c]
. (11)
For the sake of simplicity only one half of E∗3(x, z = dsen)norm is
shown, � denotes the Heavyside step function. By using the nor-malized sensor function f (x)sennorm
f (x)sennorm= f (x)sen∫ +rsen
−rsenf (x)sen dx
. (12)
the convolution is normalized to the sensor area∫ +∞
−∞E∗
3(x0 − x, z = dsen)norm · f (x)sennormdx. (13)
Due to this normalization, Eq. (13) only equals one, if the con-stant part of the field strength shows a width equal to or largerthan the sensor electrode diameter �m (b ≥ 50 �m). Thus, position-dependent capacitances C(x0)simnorm
smaller than one can simply bemodelled by reducing the width of the constant part. Finally, theparameters a, b, and c are tuned in order to achieve a good agree-ment between the simulated position-dependent capacitance andEq. (13).
As can be seen from Fig. 2, the field strength at the sensor chipsurface originating from an individual track, is modelled to vanishin the range of the next neighbouring tracks. For a sensor electrodedistance of 5.5 �m it can be assumed to vanish at positions cor-responding to the corners of the adjacent tracks. With increasingdistance to the sensor electrode, the field strength extends furtherinto the area of the adjacent tracks leading to cut-off positions cin the range of these tracks. Fig. 3a shows the cut-off positions c′
(freed from track width) plotted over track distance dtrack.The analysis of the cut-off position for various track widths
shows that the extension of the field strength beyond the trackcorners (x-direction) is independent of track width wtrack. Hence,the cut-off positions can exclusively be described in dependence ofthe track distance dtrack. When the center of a given track is usedas reference point, half the width has to be added to obtain theactual cut-off positions (c = c′ + wtrack/2). The following functionsare obtained from linear regressions (Fig. 3a)
c5.5 = dtrack + wtrack
2(14)
c15.5 = 9.78 �m + 0.885 · dtrack + wtrack
2(15)
c25.5 = 17.59 �m + 0.821 · dtrack + wtrack
2. (16)
Except for a sensor distance of 5.5 �m, 1/a, which describesthe ratio between the maximum values of the constant and non-constant parts of the modelled field strength, is found to be afunction of track width and distance. For sensor distances of15.5 �m and 25.5 �m a reciprocal dependence on the track dis-tance dtrack is observed for a fixed track width wtrack. Therefore, theproduct of 1/a and track distance dtrack yields linear functions. Theoffset and/or the slope of these functions is found to be a functionof the track width. As an example, Fig. 3b shows the product of1/a and track distance plotted over track distance for a sensor dis-
tance of 15.5 �m. The following functions are obtained from linearregressions(1a
)5.5
= 1 + 0.011
�m· dtrack(�m) (17)
92 M. Koerdel et al. / Sensors and Actuators A 172 (2011) 88– 97
Fig. 3. (a) Cut-off positions c′ of modelled electric field strength at the sensor chipsurface (E∗
3(x, z = dsen)norm) for sensor distances of 5.5 �m, 15.5 �m, and 25.5 �m.(sm(
((
T
weas
rfitt
prcmdw
ct
Fig. 4. Comparison between model results (involving Eqs. (14)–(19)) and FE simula-
b) Intermediate step in the determination of a functional description of 1/a for aensor distance of 15.5 �m. The data points are gained from the comparison betweenodel (Eq. (13)) and FE simulation, the lines are obtained from linear regressionsleast squares).
1a
)15.5
= (7.46 − 0.135) · wtrack(�m)dtrack(�m)
+ 2.46 �mwtrack(�m)
+ 0.941 (18)
1a
)25.5
= (15.39 − 0.294) · wtrack(�m)dtrack(�m)
+ 0.98. (19)
he subscripts denote the respective sensor distance.Basically, there are no limitations for the track distances and
idths that can be modelled, however, the approximation of a lin-arly varying field strength (non-constant part) is only valid as longs the track distance dtrack is smaller than 50 �m (dtrack ≤ 50 �m),ee Section 4.2.
The influence of increasing sensor distances also enforces aeduction of the width of the constant part of the approximatedeld strength (b), see Fig. 2. For a distance of 5.5 �m it is assumedo be equal to the track width. For distances of 15.5 �m and 25.5 �mhe width is reduced to 70% and 50% of the track width, respectively.
Two track configurations not used to determine the modelarameters are chosen to illustrate the conformance of modelesults and FE simulations, see Fig. 4. From the geometry of theonfigurations (dtrack, wtrack), the parameters a and c were deter-ined from Eqs. (14)–(19). Track width wtrack and sensor distance
sen define the parameter b (see above). The obtained parametersere then plugged into E∗
3(x, z = dsen)norm (Eq. (11)).As a symmetric case, the position-dependent capacitance to the
entral track of a configuration with track distances of 35 �m andrack widths of 15 �m is shown (Fig. 4a). The results for an asym-
tions for sensor electrode distances of 5.5 �m, 15.5 �m, and 25.5 �m. (a) Symmetricconductor track configuration. (b) Asymmetric conductor track configuration. Trackwidths and distances are indicated by the grey bars. Curves are offset for clarity.
metric track configuration are illustrated in Fig. 4b. Track widthsare chosen to 35 �m, distances to 15 �m and 25 �m to the next leftand right track, respectively.
It should be noted, that the model provides absolute values forthe position-dependent capacitance. Multiplying the simulated ormodelled results by the capacitance of the corresponding ideal par-allel plate capacitor (Eq. (9)) yields the absolute position-dependentcapacitance.
4.2. Superposition for arbitrary conductor track configurations
In this paragraph, the superposition of contributions from indi-vidual tracks of a specific configuration to the total capacitance isillustrated. Additionally, the performance of the sensor currentlyused is characterized by the modulation depth obtained for sym-metric track configurations. The modulation depths gained fromthe FE simulations, a semi-empirical description based on thesesimulations and the model are compared and discussed.
The capacitance between the conductive parts of an assemblydoes not depend on the voltages applied to these parts [18]. Inorder to gain the individual capacitance between specific parts,the imposed voltages may be chosen as described in Section 4.1.
Concerning conductor track configurations, the individual contri-bution of each track can be added with respect to the track positionsto obtain the total position-dependent capacitance to the sensorelectrode (superposition principle [19,23,24]). Of course, this lin-
M. Koerdel et al. / Sensors and Actuators A 172 (2011) 88– 97 93
Fig. 5. Comparison between superposition of individual contributions obtainedfrom FE simulation/model (FE sim./model added) and simultaneous FE simulationsof complete configuration (sensor electrode distance 15.5 �m). Lower curves: samevtb
ettstl
rottttcvscOrscd
araHpyF((qbtcbps
sf
Fig. 6. Measurement compared to FE simulation and model. The inset shows theoverlay of the individual contributions of the modelled and simulated capacitance.Track widths and distances are indicated by the grey bars.
d (�m)
oltage applied to all tracks. Upper curves: 1.5 times higher voltage applied to cen-ral track of the configuration. Track widths and distances are indicated by the greyars. Curves are offset for clarity.
ar behaviour can only be assumed as long as at least the adjacentracks or conductive parts are physically included in the simula-ions. The voltages imposed on the individual tracks scale the sensorignal in accordance to Eq. (1). Thus, voltage variations among theracks can be accounted for by multiplying the modelled or simu-ated capacitance with the imposed voltage Uimp (Eq. (8)).
Fig. 5 shows the FE simulations for a complete track configu-ation (FE sim.) and the results obtained from the superpositionf the individual contributions (FE sim. added), if 10 V are appliedo all tracks (lower curves) and if 15 V are applied to the centralrack. As can be seen, the summation of the individual contribu-ions with respect to the track positions reproduces the results forhe simultaneous simulation of the whole configuration. Also, theontributions can be scaled, here by a factor of 1.5, to account foroltage variations. The deviation observed at the borders is under-tandable, since the simulation of the individual contribution wasonducted for the central track of a configuration of five tracks.bviously, the model (model added) also nicely reproduces the
esults obtained from the FE simulations. The overall capacitance islightly smaller, since the model is based on rigid cut-off positions
(Fig. 2), whereas the actual capacitance only vanishes for infiniteistances.
Fig. 6 shows a comparison between measurement, FE simulationnd model (individual contributions added) for a track configu-ation with track widths and distances of 50 �m. The very goodgreement between measurement and FE simulation is striking.owever, for this track configuration the model yields a peak-to-eak variation of about 5%, whereas simulation and measurementield a variation of about 15%. As mentioned in Section 4.1, theE simulations indicate that for track distances larger than 50 �mdtrack ≥ 50 �m) the approximation of linearly varying field strengthFig. 2) overestimates the capacitance and has to be replaced by auadratic approximation. The inset in Fig. 6 shows the comparisonetween the individual contributions to the capacitance. A devia-ion of about 5% can be observed, however, by adding the individualontributions with respect to track position, the deviation is dou-led. Hence, the functional description of the model parametersresented in Section 4.1 should not be used for track distances
ignificantly larger than 50 �m.To evaluate the model performance on the one hand and theensor performance on the other hand, the modulation depth MDor a broader range of symmetric conductor track configurations
Fig. 7. Modulation depth MD plotted over track distance for symmetric conduc-tor track arrangements (same voltage imposed on all tracks). The data points areobtained from FE simulations, the lines indicate the empirical description of themodulation depth (Eq. (21)). Sensor electrode distance 20.5 �m.
was studied. MD (in %) is defined by
MD =(
1 − Csen,trackmin
Csen,trackmax
)× 100. (20)
From the FE simulations it was possible to extract a semi-empiricaldescription of the modulation depth in dependence of the geome-try of the configurations and the distance to the sensor electrode.As can be seen from Fig. 7, the modulation depth decreases for trackwidths smaller than 50 �m but does not markedly change for largertrack widths. This can clearly be attributed to the sensor electrodediameter (50 �m). Moreover, in analogy to the sensor distance of20.5 �m (Fig. 7), the modulation depth increases almost linearlywith track distance up to about 75 �m and 150 �m for sensor dis-tances of 5.5 �m and 25.5 �m, respectively (not shown). For trackwidths smaller than 50 �m (wtrack ≤ 50 �m) only the offset B of therespective linear functions changes, the slope can be assumed tostay constant (Fig. 7). Based on these findings, the following func-tional description of the modulation depth MD can be obtainedfrom the analysis of the FE simulations
MD(dtrack, wtrack, dsen) = B(wtrack, dsen) + track
�m·
(1.1595 · exp
(−0.1086 · dsen(�m)
�m
)+ 0.3332
). (21)
94 M. Koerdel et al. / Sensors and Actuators A 172 (2011) 88– 97
Table 1Comparison of modulation depth MD in % (sensor dis. 15.5 �m).
wtrack (�m) dtrack (�m) Model Empirical FE sim.
50 50 5.3 14.4 14.950 40 4.4 8.9 9.950 25 2.4 0.7 3.950 10 0.7 0 0.550 5 1.4 0 0.1
25 50 4.8 11.1 11.225 40 4.5 5.6 6.525 25 3.0 0 1.325 10 2.1 0 025 5 0 0 0
10 50 4.6 6.0 6.310 40 3.0 0.5 2.2
W
d(attcEdutfdahf(damra%e
4
ptsvubdad
pd
Fig. 8. Fits of the modelled sensor signal (Eq. (23)) to FE simulations (sensor distance15.5 �m). The modelled signal incorporates scaling factors (s1–5) for the individual
10 25 0 0 010 10 0 0 010 5 0 0 0
ith
B(wtrack, dsen) = −13 + −0.0437 − 0.0025 · dsen(�m)/�mdsen(�m)/�m
·
(wtrack(�m)
�m− 50
)2
· dsen(�m)�m
. (22)
For track widths larger than 50 �m (wtrack ≥ 50 �m), the depen-ence on the track width vanishes and the offset stays constantmax. track width: 50 �m). As seen from Fig. 7, significant devi-tions between the values gained from the FE simulations andhe empirical description are only observed for small track dis-ances. Hence, a modulation transfer function [25,26] for the sensorurrently employed in the prototype system can be derived fromq. (21). Table 1 shows a comparison between the modulationepth MD obtained from the model, Eq. (21), and the FE sim-lations (sensor distance 15.5 �m). The comparison reveals thathe model provides a better description of the modulation depthor small track distances but shows strong deviations for largeristances. However, these deviations are inherent to the modelpproach, as discussed before. As one great benefit, the modelolds the possibility to obtain the maximum modulation depth
or arbitrary track configurations from the modelled field strengthE∗
3(x, z = dsen)norm). Thus, the performance for different sensorsesigns can be evaluated as long as the lateral shielding is notltered. It is found that the sensor currently used reduces theaximum modulation depth by about 1% for the first five configu-
ations of Table 1, about 5% for the second five configurations, andbout 16% for the last five configurations (differences of absolute-values!). This reduction clearly correlates with the ratio of sensorlectrode size to track width.
.3. Application to signal post-processing
This paragraph deals with the impact of the model on signalost-processing. A method, to reconstruct the voltages appliedo individual tracks of a configuration from the measured sensorignal is discussed. The approach is illustrated by retrieving theoltages imposed on individual tracks of an arbitrary track config-ration from the simulated sensor signal. This method can, e.g.,e employed to check the functionality of electronic devices byetecting deviations between specified and actually received volt-
ges. In addition, further applications to signal post-processing areiscussed.Besides the detection of structural defects, such as missingarts and lateral contractions also the functionality of an electronicevice has to be tested during an inspection cycle. One aspect of
contributions of the tracks. Lower curves: same voltage applied to all tracks. Uppercurves: 1.5 times higher voltage applied to central track and 1.25 higher voltageapplied to track right of center. Track widths and distances are indicated by the greybars. Curves are offset for clarity.
a functionality test may be the divergence between the appliedand actually received voltage. As seen from Fig. 4, the amplitudeof the sensor signal depends on the capacitance between sensorelectrode and tracks. Additionally, the amplitude depends on thevoltages applied to the tracks, see Fig. 5. Since the measured sensorsignal is given by the product of position-dependent capacitanceand track voltage (Eq. (1)), additional information is necessary toretrieve the received track voltages from the measured signal, if acomplex track configuration is present. The geometrical propertiesof the devices are usually well known. As discussed in Section 4.1,the model parameters are exclusively determined by the geome-try of the track configurations. Hence, the individual capacitanceto each track of a configuration can be gained from the model.Based on this capacitance, the individual contribution to the sen-sor signal is obtained from the multiplication with the track voltage(Section 4.2). Therefore, the amplitudes of the applied voltages caninterpreted as (unknown) scaling factors si for the individual con-tributions E∗
3(x0 − x, z = dsen)normi. Extending the model approach
discussed in Section 4.1 by incorporating these scaling factors
si ·∫ +∞
−∞E∗
3(x0 − x, z = dsen)normi· fsen(x)norm dx (23)
and summing over the individual contributions with respect totrack position, a prototype sensor signal is obtained. This signal canbe fitted (method of least squares) to the measured or simulatedsensor signal in order to gain the values of each factor. The valuescan then be compared to the specified voltages in order to revealany deviations.
Fig. 8 shows FE simulations of the sensor signal for a more com-plex track configuration. The lower curve illustrates the signal fora voltage of 10 V imposed to all tracks. The upper curve shows thesimulation for the same track configuration but a voltage of 15 Vimposed to the central track and a voltage of 12.5 V imposed to thetrack right of center. As can be seen, the variations in the signalamplitudes of the individual tracks would render it impossible todetermine the applied voltages from the simulated or measuredsignal alone. However, by incorporating scaling factors (s1–5) forthe individual contributions of the tracks, a fit of the prototype sen-
sor signal to the simulation results yields a common voltage for thelower curve. For the upper curve a voltage about 1.5 times higher forthe central track and 1.25 times higher for the track right of centeris obtained from the fit. The individual scaling factors are recapit-
M. Koerdel et al. / Sensors and Actuators A 172 (2011) 88– 97 95
Table 2Scaling factors (fit of model to simulated sensor signal).
ukaacbsTt
twrtttcoctd
4c
rcfiii
psrTb
Q
w
f
Hd
dtT5(msiest
Fig. 9. Illustration of the studied conductor track grids. Modelled and simulatedresults are compared at the positions indicated by the dashed lines.
Table 3Studied conductor track grids, dtrack and wtrack in �m.
Grid wtrackx dtrackx wtracky dtracky
#1 50 50 50 50#2 50 50 50 25#3 50 50 50 10
values of the constant and non-constant parts of the field strengthenters the model as one parameter. Hence, compared to config-urations of tracks arranged in parallel only two (left and right)additional parameters have to be introduced to account for the
Voltage (V) s1 s2 s3 s4 s5
All 10 1.005 0.990 1.034 1.003 1.03315, 12.5 1.004 0.998 1.531 1.253 1.034
lated in Table 2. Since the absolute values of the capacitance arenown, see Section 4.1, the absolute values of the extracted volt-ges can also be determined. In this sense, the method allows forn accurate extraction of the actually received track voltages, basi-ally, based on the geometry of a given track configuration. It shoulde noted that the modelled sensor signal, which is fitted to theimulations, rests on the parameters obtained from Eqs. (14)–(19).hus, an even better approximation can be achieved by adjustinghe model parameters with respect to a specific track configuration.
In addition to the reconstruction of track voltages just discussed,he model can be applied to signal post-processing in several otherays. Concerning defect inspection it can, for instance, be used to
ecover device defects in the measured signals. For this purpose,he measured signals can be divided by the modelled signals orhe modelled signal can be subtracted from the measurement. Fur-hermore, the reduction of the modulation depth resulting from theonvolution with the sensor function may be reversed by inverser Wiener filtering [27,28]. Another important information, whichan be gained from the model is the crosstalk of adjacent trackshat has to be expected in the sensor signal. If required, the sensoristance may be adjusted to reach a defined crosstalk level.
.4. Extension to two-dimensionally arranged conductor trackonfigurations
In this section, the extension of the model to configurations ofectangular, two-dimensionally arranged conductor tracks is dis-ussed. As in the case of tracks arranged in parallel, the aim is tond a sufficient approximation of the electric field strength involv-
ng as few as possible parameters. Additionally, the influence ofntersections has to be included into the model.
In contrast to configurations of conductor tracks arranged inarallel, for two-dimensionally arranged tracks, the electric fieldtrength E varies in x- and y-direction (see Section 3). Hence, theeduction to a one-dimensional convolution (Eq. (6)) is not possible.he position-dependent charge at the sensor electrode is describedy
(x0, y0)sen
= ε0
∫ +∞
−∞
∫ +∞
−∞E3(x0 − x, y0 − y, z = dsen) · f (x, y)sen dx dy, (24)
ith
(x, y)sen = � (r2sen − x2 − y2). (25)
ere, � denotes the Heavyside step function, thus, f(x, y)sen justefines the range for the integration over the electric field strength.
To study the field strength for configurations of two-imensionally arranged tracks, rectangular, symmetric conductorrack grids (Fig. 9) were investigated by means of FE simulations.he simulations were conducted for sensor electrode distances of.5 �m, 15.5 �m and 25.5 �m. A vertical track distance of 0.5 �misolation layer) and a track thickness of 0.5 �m are assumed. The
odelled and simulated sensor signals were compared at three
pecific positions along the individual conductor tracks of the grids:n the middle between to horizontal tracks (i), at the intersectiondge (ii) and in the middle of the intersection (iii). Table 3 lists thetudied grid configurations. Analogue to configurations of conduc-or tracks arranged in parallel (Section 4.1), all tracks but one were#4 50 25 50 50#5 50 10 50 50#6 50 25 50 25
forced to ground potential (Dirichlet boundary condition) to obtainthe individual contribution of a track.
To allow for an unambiguous interpretation of the results, thetrack width was limited to 50 �m. The analysis of the FE simula-tion shows that the field strength between two horizontal tracks(arranged in x-direction) and in the area of the intersection can bemodelled independently. Whereas in the intersection area a linearapproximation is still sufficient, a quadratic variation of the fieldstrength has to be modelled in the area between two horizontaltracks (x-direction). The field strength modelled for an overlyingtrack (arranged in y-direction) of grid #1 is shown in Fig. 10. Theconstant part of the modelled field strength has to be reduced inproportion to the sensor distance, analogously to tracks arrangedin parallel (Section 4.1). Again, the ratio between the maximum
Fig. 10. Modelled field strength at the sensor chip surface for an overlying track ofgrid #1. Sensor distance 15.5 �m. Two intersections of horizontal tracks (arrangedin x-direction) are shown.
96 M. Koerdel et al. / Sensors and Act
FtC
dfihrsFrtotttst
dtdfsHcatdcioat
itfiamTs
5
tas
[
[
[
[
ig. 11. FE simulations for grid #2. The capacitance for three different sensor posi-ions (y-direction) for sensor distances of 5.5 �m, 15.5 �m and 25.5 �m is shown.urves are offset for clarity.
ifferent extensions of the electric field strength. One importantnding is the strong dependence of the field strength between twoorizontal tracks on the track distance in y-direction dtracky . Theeduction of the track distance shrinks the extension of the fieldtrength in the area between the intersections. Thus, as shown inig. 11, an almost homogeneous field strength along the y-directionesults for all sensor distances, when the distance of the horizontalracks becomes smaller than about 25 �m. Due to the restrictionf the field strength, the same parameters can be used to modelhe field strength for grid #2 and grid #6. In contrast, the dis-ance between the vertical tracks dtrackx has a weaker influence onhe extension of the electric field strength. However, for distancesmaller than 10 �m again a nearly constant field strength along theracks can be observed (grid #5).
So far, the results discussed apply to the overlying tracks of theifferent grid configurations. The influence of the intersections onhe subjacent tracks is discussed next. Due to the small verticalistance between the tracks (0.5 �m), the field strength originatingrom the subjacent track will not yield a contribution to the fieldtrength at the sensor chip surface in the area of the intersection.owever, the field strength originating from the track areas notovered by the overlying track will extend into the intersectionrea. FE simulations conducted for grid #1 and grid #6 show thathe contribution due to this extension can be neglected for a sensoristance of 5.5 �m. For the larger sensor distances the extensionan be modelled by a linear or quadratic decrease starting at thentersection edge. In consequence, compared to the configurationsf tracks arranged in parallel again only two additional parametersre necessary to describe the electric field strength originating fromhe subjacent tracks.
Based on these results, the development of a model describ-ng more complex configurations of two-dimensionally arrangedracks seems reasonable. A thorough investigation for grid con-gurations of various geometries is necessary to evaluate thepproach. From this investigation a functional description of theodel parameters based on the grid geometry has to be derived.
hereby, the effort can be reduced drastically by assuming a con-tant field strength along the overlying tracks.
. Conclusion
The inspection of planar electronic devices by means of capaci-ive coupling emerges as a completely new and versatile techniquemong the existing inspection methods. Based on the design ofensors employed in an inspection system prototype, a model
[
[
uators A 172 (2011) 88– 97
describing the sensor signal has been derived with the help offinite element (FE) simulations. Involving only three parame-ters, an approximation of the absolute value of the electric fieldstrength at the sensor chip surface leads to a model of the position-dependent sensor signal for arbitrary configurations of conductortracks arranged in parallel. Moreover, a functional description ofthese parameters exclusively determined by the geometry of theconfigurations and the sensor distance is obtained. The deviationsbetween the model results and the corresponding FE simulationsstay around 5%.
For each individual track of a specific configuration, the modelyields the contribution to the sensor signal, which is determined bythe position-dependent capacitance between the sensor electrodesand the conductor tracks. Hence, the sensor signal for arbitrarytrack configurations (total capacitance) can be obtained by sum-ming the individual contributions with respect to track position.Since the voltages applied to the tracks only scale the contribu-tion to the sensor signal, voltage variations among the tracks canalso be modelled by multiplying individual position-dependentcapacitances and corresponding voltages. With regard to signalpost-processing this allows for the reconstruction of the receivedtrack voltages from the measured sensor signal. Furthermore, themodel can be applied to recover device defects, to restore the max-imum modulation depths (i.e., enhance the contrast) as well as toevaluate the performance of different sensor designs.
The study of two-dimensionally arranged track configurationshows that an extension of the model approach is possible byincluding only two additional parameters for the overlying and sub-jacent tracks, respectively. Moreover, small track distances allowfor the approximation of a homogeneous field strength along theextension of the overlying tracks, in return reducing the necessaryparameters.
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iographies
artin Koerdel was born in Kassel (Germany) in 1982. He is currently pursuing hish.D. degree at the Friedrich-Alexander-University of Erlangen-Nuremberg in theepartment of Sensor Technology, working in close cooperation with the Corpo-
ate Technology Division at the Siemens AG in Munich (CT T DE HW2). He receivedis M.S. degree in Physics from the State University of New York at Albany in006 and his Diploma degree in Physics (Dipl. Phys.) from the Julius-Maximilians-niversity of Wuerzburg in 2008. His research is concerned with the inspection oflanar electronic devices by capacitive coupling including the development of neweasurement techniques and the application of finite element methods.
atih Alatas was born in Munich in 1981. Currently, he is pursuing his Ph.D. degreet the Technische Universität München in the Institute of Measurement Systemsnd Sensor Technology, working in close cooperation with the Corporate Technol-gy Division at Siemens AG in Munich (CT T DE HW2). He received his Diplomaegree (Dipl.-Ing.(FH)) in Electrical Engineering and Information Technology from
uators A 172 (2011) 88– 97 97
the Munich University of Applied Sciences in 2006 and his M.S. degree in ElectricalEngineering and Information Technology from the Technische Universität Münchenin 2008. His research is focussed on the structural and functional inspection of pla-nar electronics involving the evaluation of new measurement methods and dataprocessing.
Anton Schick was born in Guenzburg (Germany) in 1955. He received his Diplomaand Ph.D. degree in Physics from the Technische Universität München in 1983 and1988, respectively, and is inventor of over thirty granted patents. Currently, he isa principal research scientist at the Corporate Technology Division at the SiemensAG in Munich (CT T DE HW2). Previously, he was the director of the developmentunit of Optical Solutions at Siemens I DT EA with more than thirty direct reports. Hisresearch group developed an extremely fast confocal 3D measurement techniquethat the Siemens EA business unit was commercializing. Anton Schick has more thantwenty years of experience in the field of optical technologies, and regards the fieldas multidisciplinary; a view which has allowed deep insights into optical design,electro-optic systems and laser technology.
Stefan J. Rupitsch was born in Kitzbuehel (Austria) in 1978. He received hisDiploma and Ph.D. degrees in Mechatronics from the Johannes Kepler University,Linz, Austria, in 2004 and 2008, respectively. In 2004, Dr. Rupitsch was a juniorresearcher at the Linz Center of Mechatronics. From 2005 to 2008, he was with theInstitute for Measurement Technology, Johannes Kepler University, Linz. In 2009,he received the Award of the Austrian Society of Measurement and AutomationTechnology for his Ph.D. thesis. Currently, he is a postdoctoral researcher at theFriedrich-Alexander-University Erlangen-Nuremberg (Chair of Sensor Technology),Germany. His research interests include electromechanical transducers, simulation-based material characterization, digital signal and image processing as well asnon-contacting measurements.
Reinhard Lerch was born in Lauterbach (Germany) in 1953. He received the M.S.degree in 1977 and the Ph.D. degree in 1980 in Electrical Engineering from theTechnical University of Darmstadt, Germany. From 1977 to 1981, he was engagedin the development of a new type of audio transducer based on piezoelectric poly-mer foils at the Institute of Electroacoustics at the University of Darmstadt. From1981 to 1991, he was employed at the Research Center of Siemens AG in Erlangen,Germany, where he was responsible for the implementation of new computer toolssupporting the design and development of piezoelectric transducers. Dr. Lerch is theauthor of more than 200 papers in the field of electromechanical sensors and actu-ators, transducers, acoustics, and signal processing. In 1982, he received the Awardof the German Nachrichtentechnische Gesellschaft for his work on piezopolymermicrophones. In 1990, he was honoured with the Outstanding Paper Award of theIEEE-UFFC Society and in 1991, he was the recipient of the German Philipp-ReisAward. From 1991 to 1999, he had a full professorship for Mechatronics at the Uni-versity of Linz, Austria. Since 1999 he is the head of the Chair of Sensor Technology at
the Friedrich-Alexander-University of Erlangen-Nuremberg, Germany. His currentresearch is directed toward establishing a computer-aided design environment forelectromechanical sensors and actuators, especially piezoelectric ultrasound trans-ducers and microacoustic components. Future areas of research are piezoelectricand magnetic sensors in thin film technology. In 2009, he was honoured with theDistinguished Service Award of the IEEE-UFFC Society.