A hybrid 2D/3D inspection concept with smart routing optimisation for high throughput, high dynamic range and traceable critical dimension metrology

2D machine vision is a very mature technology [12] and many off the shelf systems are available. Here we have chosen to implement a state-of-the-art 2D machine vision system comprising of a line-scan camera (8160 px  ×  1 px, 80 kHz line rate) equipped with a telecentric imaging system (180 mm width of view, i.e. approximately 22 µm in sample space per pixel). Telecentric optics provide a constant magnification image of an object, making calibration and linking of coordinate systems in the hybrid sensor more straightforward. Position referencing encoder-or reference interferometer-based triggering can be used to enable line-wise assembly of a high-resolution 2D image during an acquisition in the case of R2R and S2S, respectively. By default, an isotropic image is acquired but anisotropic sampling strategies are feasible. The high camera line-rate permits sub-pixel motion blur for substrate velocities up to 1.7 m s⁻¹, subject to sufficient illumination intensity. Various illumination options are possible including bright- and dark-field illumination from an LED source impinging on the sample directly or via a large plate beam-splitter (see figure 5); further optimisation using spectral and polarisation filters is possible with this setup.

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The data acquired from the 2D module is first used to detect features/defects and create a listing of all points of interest (POI) for potential local 3D measurement. To detect features we employ various edge detection [13] and cross-correlation methods in combination with a priori print design information. This information is then used for registration in a model-based defect detection algorithm [5] that compares optical response of the product with a modelled optical response. Data from this model-based method is then used to assign each POI a process-relevant score indicating the inspection desirability attached to the defect. This score is linked to the defect's specific functional significance that is derived from proprietary process-specific information obtained by functional correlation studies that may be performed both offline prior to manufacture, and online in a continuous training process, correlating data from functional acceptance tests and any through-life metrology with the inspection data obtained and stored by this system.

Items that may appear to be effectively planar within a high-resolution 3D sensor's field of view (FoV) often have a significant macroscale form. For thin objects, such as a PV wafer, this is dominated by deformation due to fixturing and self-weight, and may not necessarily be predicted from a design (see a solid 3D workpiece). This can result in vertical displacements beyond the axial working range of a typical 3D sensor.

As exemplified in the case of the PV wafer example, to obtain an appropriate level of optical signal to measure both the highly-reflective silver electrodes and the highly-photoabsorbing active surface, the acquisition parameters of the sensor must be adjusted. Reactive auto-adjustment methods are available on some commercial 3D sensors but have a finite response time and are best suited to stepping between extended regions of fixed reflectivity since potentially important data from regions of the intensity step change may not be measured. Reactive methods are also inappropriate for the measurement of small, sparse features with a vastly different optical response to their surroundings.

Therefore, to enable the use of 3D sensors with finite axial (vertical) working range and limited dynamic sensing range, we suggest that the initial 2D feature detection is supplemented by coarse form measurement and intensity mapping. In this way, when a 3D sensor arrives at the 2D location of a feature of interest, the sensor may be vertically pre-aligned with acquisition parameters preconfigured for optimum intensity gain/exposure (sensing technology dependent). Such a system could then be considered as HDR in both a dimensional (defect size/throughput ratio) and an optical sense (high-to-low reflectivity ratio). This proactive compensation technique may be also adapted for other optical systems, such as photo-electronic property mappers [8] or point scatterometry systems [14], or as a complementary feedback route for laser machining processes [15].

Coarse form measurement is achieved using a chromatic confocal point sensor [16] (Precitec Chrocodile-E, 3 mm working range). To acquire a full form measurement the sample may be moved in a raster pattern under the confocal probe, with location dependent triggering supplied from the position referencing system. Faster 3D optical scanner techniques such as laser triangulation sensors [17, 18] would enable faster uniform measurement of an extended area as would be required in the case of R2R, but one or more point probes may provide a cost-effective alternative when used with intelligent sampling strategies linked to a priori defect models and feature design information [19, 20].

Localised high-resolution surface topography measurement is acquired using a STIL MPLS180 Nanoview line sensor, also employing the chromatic confocal principle. This line sensor may be considered as an array of 180 parallel optical profilometers on a 7.4 µm pitch. The line sensor has a line-rate of 1.8 kHz, corresponding to about 13 mm s⁻¹ throughput for an isotropic sampling grid. Exposure time and LED intensity may be adjusted to suit specific measurement requirements. As with the other sensors triggering is provided by a position referencing system.

The coarse form measuring point sensor is positioned ahead of the local surface topography measuring line sensor. The sensors are attached to a 50 mm travel vertical stage for vertical pre-alignment (Thorlabs LNR50SE, see figure 6).

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Successful implementation of the hybrid 2D/3D measurement strategy requires efficient pruning of potential 3D measurement targets or POIs based on ranking of process-relevant POI scores, combined with hardware-appropriate trajectory planning. We call this iterative process of POI pruning and route-planning 'smart route optimisation' since the initial ranking of POIs may radically change based on their location, proximity and the parameters of the dynamic inspection system. In this section, we describe a general method to optimise the inspection of a pre-existing ranked list of scored POIs with the 3D sensor, while under different realistic scenarios.

We suggest that the typical goal of measurement route optimisation is to maximise the 'thoroughness' of the inspection, whilst respecting defined budgets of time or energy. The precise meaning of 'thoroughness' would be context specific, and linked to the inspected process itself; a very simple example would be the total count of unique POIs visited. Further constraints must also be applied to the optimisation to account for finite variation of motion system parameters, ranges of travel, and so on. In particular, the dynamics of this inspection process mean that small changes in the initial conditions of the sensor can introduce large changes in the final optimised route for a given set of targets. Furthermore, for inspection of continuously moving substrates in a R2R process, it becomes impossible to inspect multiple non-overlapping POIs aligned transversely across the substrate with a single sensor on a single transverse motion stage. In this case, smart routing optimisation can easily be extended to take in to account multiple sequential sensors down a production line in order to approach 100% inspection of relevant defects.

General routing algorithms such as the travelling salesman problem (TSP) provide a basis for computing the order of visits to the set of POIs as nodes; node separations would be calculated in terms of required time or energy expenditure. By also assigning a proportionate reward for the successful visit to a given node, it is possible to attempt to increase the total reward or score by pruning low-value, high-cost nodes from the route. The basis for the smart routing algorithms developed for this work is the Mathworks TSP example [21, 22]. Major changes implemented in our new algorithm are summarised in order of importance in the remainder of this section. Standard TSP terminology such as 'city' and 'trip' are used figuratively in the explanation.

2.3.1. Cost function to minimise.

2.3.2. New constraints for measurement speed boundary condition.

In order to generate areal surface topography maps from the 3D line scan measurements with data arranged on an easy to process nominally orthogonal grid of points, velocity boundary conditions are applied to ensure that the line sensor arrives at the start of the local 3D measurement associated with a given node (a) at the required measurement speed and (b) from a direction parallel or anti-parallel to the required scan direction (see figure 7); that is, moving with fixed speed either up or down the scan axes, and stationary in the step axis. This has the advantage of reducing acceleration-induced errors. For the purposes of the optimisation, each POI is now represented by two co-located nodes, representing the parallel and anti-parallel measurement direction options, respectively. A new inequality constraint is added for each such co-located pair of nodes to allow a visit to, at most, one node of each co-located pair in the solution. To enable automated pruning of POIs, inequality constraints are used, in place of the equality constraints in the original algorithm that enforced exactly one visit to every POI.

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2.3.3. Calculation of trip resources.

2.3.4. Miscellaneous data cleansing.

2.3.5. Simplifications for the R2R method.

The simulation platform supports a number of methods for samples support and fixturing, via a common tilt-adjustable base (see figure 9). A vacuum chuck is used to fix thin flexible or semi-rigid items into a well-defined measurement plane, reducing out-of-plane surface tracking and improving collision avoidance reliability. Repeatable in-plane alignment and position referencing was implemented using universal fixturing principles reported previously [23]. Use of a common fixturing system simplifies and speeds up fusion or comparison of measurement data from multiple instruments within a defined workflow, and is consistent with the 5S methodology, one component of lean manufacturing [24]. Samples with well-defined geometry and sufficient later stiffness, such as amorphous-silicon PV wafers, may be repeatably installed using only a side fence, realised here using precision steel rules. For routine or significant one-off measurements campaigns of features on flexible, easily deformed films, extracted film pieces with poor edge definition may be semi-permanently attached to identical thin, stiff square substrates, for handling as for a PV wafer. We also implemented a more pragmatic approach to universal fixturing to promote wider adoption, using a system of interchangeable plates available from Thorlabs (MLSP series). Finally, with the vacuum chuck removed, there is a volume available to mount small non-planar parts or calibration artefacts on an appropriate translation/rotation adjustment stack.

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The internal stage encoders are supplemented by external (reference) laser displacement interferometry where required (Zygo ZMI 2001 series; see figure 10(a)). FPGA-based control of a custom backplane, developed for the NPL Areal Instrument [25], optionally enables mutually- and externally-synchronised multi-axis spatial triggering. To partially mitigate the Abbe error associated with the vertical offset of the inspection plane, the reference interferometer measurement-arm retroreflectors are attached directly to the underside of the sample holder tip/tilt thrust plate, the uppermost fixed component in the sample stack. Beam paths are directed directly under the centre of the vacuum chuck. Stage motion is limited to a single axis whilst reference interferometry is used, to avoid the requirement for costly and bulky plane mirror blocks typically required to directly measure two-axis motion of an object [25]. Alternatively, motion of the two stacked drives may be done separately, as in figure 10(b).

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We previously reported [26] an example application, in which the reference interferometer provided an independent estimated position of a grating-instrumented film, for the testing of a sub-micrometre accuracy substrate tracking metrology for precision R2R processes. This example also demonstrated the secondary function of the simulation platform as an instrument development host.

Automation and control software implementation consists of several semi-autonomous actors distributed over two PCs (basis: NI LabVIEW). Each actor manages one item of hardware via the supplier's API. A coordinator module interacts with each actor to carry out scripted tasks, monitor progress and collect returned data. The distributed architecture reduces the resource load on each machine, thereby relaxing the PC specifications required; the architecture also permits additional support for other temporary sensors hosted by the demonstrator. Repetitive low-level handshaking and triggering, such as move completion signalling, is done directly between actors. Appropriate metadata is automatically stored with measurement data, for traceability and to simplify documentation and reporting. Alignment is planned toward one or more standardised metadata formats such X3P [27], SDF [28] or QIF [29].

Calibration of the line-scan camera sensor consists of (a) traceable characterisation of the image scale along the pixel line; (b) measurement of, and optional correction for, undesirable tilt or roll of the camera FoV; and (c) estimation of the final effective lateral resolution for a stationary object. To guard against malfunction of the stage or triggering timing, the lateral scale in the scanned direction of an assembled 2D image is also verified.

The adjustment and calibration procedure makes use of an ISO 12233-consistent camera calibration artefact (CCA) developed specifically for line-scan cameras and reported separately [30]. In brief, the CCA (shown in figure 11) consists of a 120 mm  ×  20 mm feature field designed to enable, without motion, estimation of absolute XY location and roll about Z, as well as the MTF of the line-scan camera. Additional features on the CCA assist the operator with coarse initial alignment. Using this method, the mean pixel spacing of the camera was estimated to be 21.84 µm  ±  0.03 µm. Roll about Z results in a shear distortion on an assembled 2D image.

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The chromatic confocal point sensor (the probing system) and the XY stage (the lateral scanning system) combine to form an areal surface texture measurement instrument, whose metrological characteristics may be calibrated according to ISO 25178-602 [31]. For the areal instrument incorporating the line sensor, the step axis of the lateral scanning system is assembled from a series of Y-aligned line acquisitions arranged along Y; that is, every 180 steps along the step axis are measured simultaneously as the 180 channels of the line sensor. Stitching is done using only the stage encoders, not from overlaps in measurement data.

Metrological characteristics to be calibrated for each sensor as a measuring instrument include amplification coefficients for the X, Y and Z scales; flatness; static and dynamic noise; and some measure of spatial resolution such as the width limit for full transmission of an application-matched height [31]. For brevity, we present here the in situ calibration and verification procedures that differ from the general methods to calibrate metrological characteristics discussed elsewhere [32–34].

The XY stage encoders, which measure the relative motion of each sensor over the sample, are calibrated by comparison to the reference interferometer. This calibration provides the lateral amplification coefficients for the two 3D sensors, if combined with a traceable description of the relative spatial relationship between the line sensor's 180 parallel measurement points. This relative spatial relationship is determined by comparison to the XY stage encoders and the line sensor's internal axial (Z) scale. The line sensor's internal scale using PGR features at a number of positions within the working range of the sensor.

A discussion of the chromatic confocal line sensor's inter-channel spatial relationship follows; for clarity, analysis is presented for a single wavelength corresponding to the centre of the probing system's working range. As summarised in figure 12, the nominal positions of the points are distributed with a uniform spacing $s$ along a mean centreline, which may be slightly rotated from the Y-axis (by ${{\theta}_{x}}$, ${{\theta}_{z}}$). These rotations are deliberately minimised during installation and are assumed to be small, such that small-angle approximations may be applied. Successive line acquisitions remain centred on the Y-axis, so that the small rotation from the Y axis forms a saw-tooth pattern in the residuals. The true centre of each focal spot is then further displaced from the mean centreline. The true position X_j of the centre of the working range of the $j$th point in the set is then given by

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\boldsymbol{X}}_{\boldsymbol{j}}}=\left(\begin{array}{@{}cccccccccccccccccccc@{}} {{x}_{j}} \nonumber \\ {{y}_{j}} \nonumber \\ {{z}_{j}} \end{array} \right)=&\left(\begin{array}{@{}cccccccccccccccccccc@{}} {{x}_{0}} \nonumber \\ {{y}_{0}} \nonumber \\ {{z}_{0}} \end{array} \right)+s\left(\,j-\frac{n-1}{2} \right)\left(\begin{array}{@{}cccccccccccccccccccc@{}} {{\theta}_{z}} \nonumber \\ 1 \nonumber \\ {{\theta}_{x}} \end{array} \right) \nonumber \\ &+\left(\begin{array}{@{}cccccccccccccccccccc@{}} \delta {{x}_{j}} \nonumber \\ \delta {{y}_{j}} \nonumber \\ \delta {{z}_{j}} \end{array} \right),1\leqslant j\leqslant n\nonumber \end{align} \tag{ 1 }$$

where $\left\{{{x}_{0}},{{y}_{0}},{{z}_{0}} \right\}$ is the global position of the midpoint of the mean centreline, $n$ is the number of points (i.e. 180), the term in $s$ represents the mean centreline and $\left\{\delta {{x}_{j}},\delta {{y}_{j}},\delta {{z}_{j}} \right\}$ represents the pointwise residuals to the mean centreline. In terms of global topography measurement error, the mean centreline describes with respect to the Y-axis the mean sampling interval in Y (i.e. $s$), as well as any roll (${{\theta}_{z}}$) or tilt (${{\theta}_{x}}$) misalignment. Similarly, $~\left\{\delta {{x}_{j}},\delta {{y}_{j}},\delta {{z}_{j}} \right\}$ can be subtracted from subsequent data corrections; $\left\{\delta {{z}_{j}} \right\}$ is effectively the flatness deviation of the line sensor. Where line sensor data is expected to be patched together in Y, sensor Y steps are programmed in exact multiples of $s$ to simplify data fusion.

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By moving the global reference point from the centre to the start of the measurement, $\left(x_{0}^{*},y_{0}^{*},z_{0}^{*} \right)$, (1) can be simplified to a constant term, a $j$-dependent centreline term, and the point-wise residuals:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\boldsymbol{X}}_{\boldsymbol{j}}}=\left(\begin{array}{@{}cccccccccccccccccccc@{}} {{x}_{j}} \nonumber \\ {{y}_{j}} \nonumber \\ {{z}_{j}} \end{array} \right)=\left(\begin{array}{@{}cccccccccccccccccccc@{}} x_{0}^{*} \nonumber \\ y_{0}^{*} \nonumber \\ z_{0}^{*} \end{array} \right)+sj\left(\begin{array}{@{}cccccccccccccccccccc@{}} {{\theta}_{z}} \nonumber \\ 1 \nonumber \\ {{\theta}_{x}} \end{array} \right)+\left(\begin{array}{@{}cccccccccccccccccccc@{}} \delta {{x}_{j}} \nonumber \\ \delta {{y}_{j}} \nonumber \\ \delta {{z}_{j}} \end{array} \right),1\leqslant j\leqslant n.\nonumber \end{align} \tag{ 2 }$$

To quantify the unknown parameters, a position estimate $\left\{{{x}_{j}},{{y}_{j}},{{z}_{j}} \right\}$ is obtained for each point in $j$, and nonlinear least-squares line fits applied to the position estimates. Position estimates were obtained experimentally using the following procedure, which required only a single step height calibration feature. An NPL Areal Standard artefact [35] was mounted onto a tilt-adjustment stack with the vacuum chuck removed (see section 2.1), so that the Areal Standard top surface was a few millimetres above the main sample table. The Areal Standard was adjusted to reduce tilt such that the complete chip remained within the 100 µm working range of the line sensor. To estimate ${{y}_{j}}$ and ${{z}_{j}}$, the lateral scanning system was configured to scan along the Y-axis (the conventional step axis, that is, nominally collinear with the point array, see also figure 13). The sampling interval in Y was set to be much smaller than the nominal value of the Y sampling interval, i.e. $s$ (1 µm and 7.45 µm, respectively). The measurement location was centred on a 2 µm depth PGR feature (a step height standard, see [36]), and scan length set to greater than the sum of sensor line width (1.35 mm) and three widths of the PGR feature (grand total 1.67 mm). Thus, each of the 180 channels measured a profile containing the PGR feature and the adjacent regions required for an ISO 5436-1:2000-compliant step height calculation [37]. This was repeated ten times. Values for ${{z}_{j}}$ were taken as the mean Z over all repeats of all points in the three flat step height calculation regions used for the $j$th point step height. Each value for ${{y}_{j}}$ was taken as the centre of mass in Y of the $j$th point step height. A non-linear least-squares line fit to the set of $\{{{z}_{j}}\}$ and $\{{{y}_{j}}\}$ yielded estimates for $\{{{\theta}_{x}},\delta {{z}_{j}}\}$ and $\{s,\delta {{y}_{j}}\}$, respectively by equation (2). To estimate ${{x}_{j}}$, the lateral scanning system was then configured for a conventional areal measurement with sampling intervals of 1 µm and $s$ in X and Y, respectively. The measurement was centred on the 2 µm PGR feature as before, with a measurement size of three times the PGR feature X dimension (total 600 µm) in the X direction and at least $ns$ in the Y direction. This configuration ensures that at least one set of n collinear profiles across the PGR feature can be extracted comprising one from each channel of the line sensor. These collinear profiles nominally describe the same physical line across the feature; apparent differences can be attributed to relative misalignment of points. Each value for ${{x}_{j}}$ was taken as the centre of mass in X of the step height from the $j$th profile. A nonlinear least-squares line fit to the set of $\{{{x}_{j}}\}$ yielded estimates for $\{{{\theta}_{z}},\delta {{x}_{j}}\}$ by equation (2). Note that this method avoids the need to provide a well-formed, perfectly Y-aligned step feature as wide as the line sensor, but at the expense of an $n$-fold increase in measurement time. Further, if the PGR feature height is well matched to the user's measurement task, the measurement data above can also be exploited to verify the scales of the complete XYZ motion system.

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Typical methods used to estimate the spatial resolution of a topography measuring instrument involve 3D Siemens stars or linear gratings [34]. Rotated reflectivity edges are used to estimate the spatial frequency response of a conventional camera [30]. Noting the implementation constraints on in situ calibration of industrial metrology, we supplemented the conventional method with an approach using the tilted edge of the 2 µm PGR feature (see figure 13). The edge quality and profile of the PGR feature was first measured using a reference instrument, to qualify the assumption that any two parallel profiles across the feature edge are equivalent. Then, an areal measurement of the tilted edge could be used to construct a super-sampled profile of the edge response of the confocal sensor under calibration. The edge response function can be converted to a modulation transfer function (MTF), an indication of the sensor spatial resolution for features of 2 µm height. This compromise method can be applied to detect changes in sensor resolution during in-process use.