Overlay accuracy fundamentals Daniel Kandel, Vladimir Levinski, Noam Sapiens, Guy Cohen, Eran Amit, Dana Klein, Irina Vakshtein KLA-Tencor Corporation, 1 Halavyan Street, Migdal Haemek 23100, Israel ABSTRACT Currently, the performance of overlay metrology is evaluated mainly based on random error contributions such as precision and TIS variability. With the expected shrinkage of the overlay metrology budget to < 0.5nm, it becomes crucial to include also systematic error contributions which affect the accuracy of the metrology. Here we discuss fundamental aspects of overlay accuracy and a methodology to improve accuracy significantly. We identify overlay mark imperfections and their interaction with the metrology technology, as the main source of overlay inaccuracy. The most important type of mark imperfection is mark asymmetry. Overlay mark asymmetry leads to a geometrical ambiguity in the definition of overlay, which can be ~1nm or less. It is shown theoretically and in simulations that the metrology may enhance the effect of overlay mark asymmetry significantly and lead to metrology inaccuracy ~10nm, much larger than the geometrical ambiguity. The analysis is carried out for two different overlay metrology technologies: Imaging overlay and DBO (1st order diffraction based overlay). It is demonstrated that the sensitivity of DBO to overlay mark asymmetry is larger than the sensitivity of imaging overlay. Finally, we show that a recently developed measurement quality metric serves as a valuable tool for improving overlay metrology accuracy. Simulation results demonstrate that the accuracy of imaging overlay can be improved significantly by recipe setup optimized using the quality metric. We conclude that imaging overlay metrology, complemented by appropriate use of measurement quality metric, results in optimal overlay accuracy. Keywords: Overlay Accuracy, Measurement Quality Metric.
1.
OVERLAY MARK IMPERFECTIONS, OVERLAY AMBIGUITY AND ACCURACY
The standard evaluation of the capability of an overlay metrology tool relies mostly on a Total Measurement Uncertainty (TMU), which includes effects of precision, TIS variability and tool matching. Overlay control requirements of future nodes lead to the very tight requirement of TMU < 0.5nm. It is known, however, that small TMU does not guarantee that the overlay metrology budget is met, because some metrology errors are not taken into account in the TMU. The most important additional errors are associated with process (litho, etch, CMP, etc.) induced overlay mark imperfections and their interaction with the metrology technology, which may lead to inaccurate overlay measurement. Such inaccuracy may be reflected, for example, in bias between after develop and after etch measurements, difference between measurements carried out with different wavelengths or different focus positions of the metrology tool. In extreme cases, the resulting inaccuracy can be much larger than 1nm, and can consume the whole overlay control budget. In this work we explain the origin of overlay mark related inaccuracy, and show that a measurement quality metric developed by KLA-Tencor is a valuable tool to address this problem. We show that using this quality metric it is possible to eliminate outlier measurements and to select a recipe setup which enables an accurate overlay metrology. We start by realizing that in overlay metrology we measure the distance between the centers of symmetry of features of the overlay mark, printed in different layers. Such a methodology leads to accurate well defined overlay only if each feature of the overlay mark is symmetric to reflection. Unfortunately, a variety of process effects generate asymmetric features. This asymmetry can have a random nature, where no specific wafer level signature is observed, or a systematic nature where overlay correctibles are affected directly.
Metrology, Inspection, and Process Control for Microlithography XXVI, edited by Alexander Starikov, Proc. of SPIE Vol. 8324, 832417 路 漏 2012 SPIE 路 CCC code: 0277-786X/12/$18 路 doi: 10.1117/12.916369
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Overlay ambiguity
Resist α BARC
90°
Other layers 80° 80°
Process layer
Figure 1. An illustration of an overlay mark imperfection. The resist feature has two different side wall angles and is therefore asymmetric. The value of the overlay between the resist and process layers is ambiguous. The magnitude of the ambiguity is shown in red. Figure 1 illustrates such an imperfect overlay mark. In this case, the process layer structure is symmetric, while the resist structure is not. The right side wall angle of this structure is equal to 90°, while the left side wall angle differs by a few degrees. Therefore, the process layer structure has a well defined center of symmetry, whereas the resist structure does not. As a result, this overlay mark does not correspond to a well defined overlay. For example, the overlay defined with respect to the top of the resist structure is different from the overlay defined with respect to its bottom. Thus, this overlay mark leads to an ambiguity in the value of the overlay. This geometrical ambiguity is shown in red in Figure 1.
Overlay mark asymmetry
Measurement technology
Overlay ambiguity
Enhanced signal asymmetry
Overlay inaccuracy
Figure 2. A chart which explains that overlay mark asymmetry leads to a geometrical overlay ambiguity. If the metrology technology has a high sensitivity to mark asymmetry, it may lead to an enhanced asymmetry in the measured signal and generate overlay measurement inaccuracy.
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A good, process compatible design of the overlay mark should give rise to a relatively small overlay ambiguity of the order of 1nm or less. However, such a good design does not guarantee an accurate overlay value as measured by the overlay tool. The reason for this is that the metrology technology may have a particularly high sensitivity to overlay mark asymmetry. If this is the case, the deviation of the measurement from the true overlay value may be larger than the geometrical ambiguity discussed above. Overlay inaccuracy can be as large as 10nm, due to enhancement of the geometrical ambiguity by the metrology technology. The mechanism responsible for this enhancement is explained and demonstrated in simulations in the next section. The notions of overlay ambiguity and inaccuracy are summarized graphically in the chart of Figure 2, where an asymmetry of the overlay mark induces a geometrical ambiguity in the value of the overlay. High sensitivity of the metrology technology to such asymmetry leads to an enhanced asymmetry in the measured signal, which in turn generates significant overlay inaccuracy.
2.
OVERLAY MARK ASYMMETRY AND OVERLAY ACCURACY: SIMULATIONS AND THEORY
In this section, we demonstrate by simulations that overlay ambiguity induced by overlay mark asymmetry indeed leads to inaccuracy of overlay metrology, which may be significantly larger than the geometrical ambiguity. We also give a theoretical explanation of this phenomenon for two different overlay metrology technologies: Imaging overlay and diffraction based first order overlay metrology (DBO).
Optical architecture parameters
RCWA
Optics simulator
“Measured” signal
Overlay algorithms
“Measured” overlay
Wafer Jones matrices
Stack info
Figure 3. An illustration of the building blocks of the overlay accuracy simulator and their inter-relations. The simulator consists of an optics simulator complemented by a Maxwell equation solver, to take into account the detailed effects of the overlay mark. The simulations have been carried out using a simulator developed in house. As shown in Figure 3, the simulator consists of three major components: A Maxwell equation solver, an optics simulator and an overlay calculation algorithm. The optics simulator propagates the electric field from the light source through the illuminator to the wafer. Scattering from the overlay mark on the wafer is simulated with a RCWA engine. The optics simulator then propagates the scattered field through the collection optics to the detector. The simulated overlay is calculated from the simulated detector signal using the appropriate overlay algorithms. We have carried out simulations of the type described above for several combinations of stacks, overlay metrology technologies and overlay mark designs. Typical results of overlay accuracy are shown in Figure 4, for a Poly/STI stack. The asymmetry in all the simulated overlay marks corresponds to geometrical overlay ambiguity of 1.2nm, as marked by the red line in the figure. The results for imaging overlay (shown in blue) are for box-in-box overlay marks with a variety of color filters. DBO (first order diffraction based overlay) results are shown in orange (grating-over-grating overlay mark of period 600nm) and green (grating-over-grating overlay mark of period 800nm). It is evident from these results that overlay inaccuracy can exceed the geometrical overlay ambiguity by more than 2x for imaging overlay and more than 10x for DBO. These results also indicate that the inaccuracy is sensitive to overlay mark design and to the metrology wavelength.
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20 Overlay inaccuracy [nm]
18
Geometrical ambiguity
16 14 12 10 8 6 4 2 0 500nm 550nm 600nm 650nm 700nm 532nm 673nm 532nm 673nm Imaging
DBO, P=600nm DBO, P = 800nm
Figure 4. Results of simulations of overlay inaccuracy induced by overlay mark asymmetry in a Poly/STI stack after develop. The simulations correspond to a geometrical overlay ambiguity of 1.2nm (marked in red). We now proceed with a theory which explains the observations made based on simulations. The theoretical calculations are carried out separately for imaging overlay and DBO. For simplicity, we assume that asymmetry of the overlay mark exists only in one of the layers and that the relevant structure of the mark is periodic with period P. Similar results can be obtained for the cases where asymmetry exists in both layers and the target is non-periodic. For imaging overlay, the part of the image which corresponds to the layer with asymmetry can be written as
Image ∝ a 0 e
iφ0
+ a +1e
i φ +1
⋅e
2πi ( x −OVL ) P
+ a −1e
iφ−1
⋅e
−
2πi ( x −OVL ) P
2
+K ,
Where a 0 , a +1 , a +1 , K correspond to the amplitudes of the different diffracted orders of the electric field, and
φ 0 , φ +1 , φ +1 ,K correspond to the phases. The assumption of a symmetric signal can be expressed as a + n = a − n and φ + n = φ −n for every n.
Since the phases of the electric field determine the geometrical center of the signal, the breakdown of phase symmetry corresponds to a geometrical overlay ambiguity. Breakdown of symmetry of the amplitudes ( a + n ≠ a − n ) leads to inaccuracy, which may exceed the geometrical ambiguity significantly. For example, when most of the error comes from the first diffracted order, one can show that the overlay inaccuracy, Δ, takes the form
Δ≈
P 2π
⎛ φ − φ −1 a − a −1 ⎞ ⎟⎟ , ⋅ ⎜⎜ +1 + α ⋅ +1 + 2 a a +1 −1 ⎠ ⎝
Where α depends on material parameters, wavelength, etc. The first term in this expression is the geometrical ambiguity, which for a good overlay mark design is expected to be smaller than 1nm. The second term is the additional inaccuracy representing the sensitivity of the metrology technology to overlay mark asymmetry. For some material
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parameters, α can take values as large as 10, and then the second term gives rise to a large inaccuracy. This is seen in Figure 4 in blue for the cases where the inaccuracy is larger than the ambiguity marked by the red line. For DBO (first order diffraction based overlay), the overlay mark consists of gating-over-grating structures, one of which is symmetric and the other asymmetric according to our simplifying assumption above. Overlay is extracted from a signal calculated as the difference between the +1st diffracted order and the -1st diffracted order. This differential signal can be written as
Signal ∝ a 0, +1e
iφ0 , +1
+ a +1,0 e
iφ +1, 0
⋅e
2πi (OVL + offset ) P
2
+ K − a 0, −1e
iφ0 , −1
+ a −1, 0 e
iφ−1, 0
⋅e
−
2πi (OVL + offset ) P
2
+K ,
Where a n , m is the amplitude of the (n+m)th diffracted order from the grating-over-grating mark, which consists of the nth diffracted order from the asymmetric grating and the mth diffracted order from the symmetric grating. As with imaging, when most of the error comes from the first diffracted order from the asymmetric grating, the inaccuracy, Δ, takes the form
Δ≈
P 2π
⎛ φ +1, 0 − φ −1, 0 a +1, 0 − a −1, 0 ⋅ ⎜⎜ +α ⋅ 2 a +1,0 + a −1,0 ⎝
⎞ ⎟, ⎟ ⎠
Where α depends on material parameters, wavelength, etc. Here, too, the first term corresponds to the geometrical ambiguity which is expected to be smaller than 1nm for a well designed overlay mark. The second term is responsible for the inaccuracy beyond the ambiguity. As is seen in Figure 4, this term can be larger than 10nm. The results in Figure 4 also indicate that DBO is more sensitive to overlay mark asymmetry than imaging overlay. This can be attributed to the fact that in imaging overlay the signal is averaged over a broader range of wavelengths and angles. Since different wavelengths and angles give rise to different inaccuracy, the averaging reduces the inaccuracy in the statistical sense. 3.
MEASUREMENT QUALITY METRIC AND ITS USES
Measured Signal Overlay algorithm 1
Overlay estimate 1
Overlay algorithm 2
Overlay estimate 2
Overlay algorithm 3
Overlay estimate 3
Quality metric Based on distribution of overlay values from different algorithms
Figure 5. An illustration of the concept of measurement quality metric. Several algorithms are used with the same measured signal to evaluate the overlay. All the algorithms are guaranteed to give the same overlay estimate if the signal is perfectly symmetric. If the signal is not symmetric each algorithm gives a somewhat different value. The quality metric is related to the width of the distribution of these overlay values.
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According to the results of the previous section, the magnitude of overlay inaccuracy can be a few nanometers and thus these errors may consume the whole overlay control budget for advanced nodes. It is therefore essential to reduce such inaccuracy to the sub-nanometer level to enable adequate overlay control. Here we show that this can be done for imaging overlay by using a measurement quality metric. Our concept of a quality metric is defined in general terms in Figure 5. Generally, imaging overlay is based on finding the center of symmetry of portions of an image of the overlay mark. This can be done using a variety of algorithms, all of which are guaranteed to give the exact center of symmetry of a symmetric signal. If, however, the signal is not symmetric, different algorithms may give different estimates of the approximate center of symmetry. Our definition of the quality metric includes a class of algorithms, which give a distribution of overlay values for each measured signal. The quality metric is a function of the width of this distribution. It vanishes for a perfectly symmetric signal, and for an asymmetric signal it is approximately proportional to the inaccuracy. It should be noted that the quality metric detects any signal asymmetry, including asymmetry originating from asymmetries in the optics. Such optics induced signal asymmetry corresponds to TIS. Thus, for an optical system with significant TIS, it is recommended to use TIS corrected overlay in the definition of the quality metric in order to evaluate target induced overlay inaccuracy. How can we use the measurement quality metric to improve the accuracy of overlay metrology? In this work we present two methodologies to do this, which can be used separately or simultaneously. The first one is outlier removal, while the second one is recipe optimization for enhanced accuracy. Outlier removal addresses the situation where few of the overlay marks on the wafer have a particularly high asymmetry and stand out from the rest of the marks on the same wafer. In this case, the values of the quality metric of these marks will be at the far tails of the distribution of quality metric values of all the sites on the wafer. An analysis of this distribution easily identifies these outliers and they are removed. Recipe optimization farther improves the accuracy of the metrology by selecting optimal parameters of the recipe such as focus position, color filter, etc. In the next section we explain these methodologies and validate them using simulations. Experimental validation is presented in Guy Cohen et al., Overlay Quality Metric, Proceedings of SPIE (2012), paper 8324-71 (current proceedings). 4.
MEASUREMENT QUALITY METRIC VALIDATION
Figure 6 is a wafer map of overlay inaccuracy obtained from simulations of overlay marks with varying degree of asymmetry which depends on position on the wafer. This map associates a vector with each site, whose X and Y components are the inaccuracy in X overlay and Y overlay correspondingly. Three sites (marked in red) show a particularly high inaccuracy and can be considered as outliers. The values of the quality metric calculated from the simulated signals we used to generate Figure 6 are shown in Figure 7. Here each point corresponds to one of the sites on the wafer. The X (Y) coordinate of the point corresponds to the quality metric of the X (Y) portion of the overlay mark at this site. This cloud of quality metric values can be generated for each wafer and then the sites which deviate significantly from the cluster of points within the cloud are considered as outliers and are removed before correctibles are calculated. To validate that this procedure indeed removes sites with particularly high inaccuracy, we circled in red in Figure 7 the points which correspond to the sites with the red vectors (high inaccuracy) in Figure 6. Clearly, these points deviate significantly from the cluster.
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Overlay inaccuracy wafer map
Figure 6. Wafer map of overlay inaccuracy calculated from simulations of asymmetric overlay mark with an asymmetry which depends on wafer coordinates. The X and Y components of the arrows correspond to the inaccuracy in X and Y overlay correspondingly. Sites with particularly large inaccuracy are marked in red.
Wafer quality metric cloud 1 0
Quality metric Y
5
0 - 1 0
- 5
0
5
1 0
1 5
2 0
2 5
3 0
3 5
4 0
- 5
- 1 0
- 1 5
- 2 0
- 2 5
- 3 0
Quality metric X Figure 7. Cloud of points, where each point corresponds to the X and Y quality metric value of a site on the simulated wafer. The three sites marked as red arrows in Figure 6 are circled in red in the current figure. These sites have exceptionally large overlay inaccuracy as seen in Figure 6 and show up as excursions from the cloud in the current figure.
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To demonstrate recipe optimization for accuracy, we generated two different quality metric clouds for the same simulated wafer, which correspond to two different color filters. We removed outliers in both cases and obtained the clusters of points seen in Figure 8. It is obvious from this figure that color filter 2 generates a narrower and tighter distribution of quality metric values than color filter 1. We therefore select color filter 2 as the one that should give better overlay accuracy. In order to verify that this recipe setup is optimal, we calculated (from the same simulation) the wafer inaccuracy maps that correspond to the two color filters. These maps are shown in Figure 9 for color filter 1 and in Figure 10 for color filter 2. It is evident that color filter 2 indeed produces significantly more accurate overlay values.
8
6
Quality metric Y
4
2
0 - 1 0
- 5
0
5
1 0
1 5
2 0
Color filter 1
- 2
Color filter 2
- 4
- 6
- 8
- 1 0
- 1 2
Quality metric X Figure 8. Two quality metric clouds, similar to the one shown in Figure 7, which correspond to simulations of measurements of the same wafer with two different color filters. Outliers have been removed, using the values of the quality metric, as explained above.
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OVL inaccuracy: Color filter 1
Figure 9. Wafer map of overlay inaccuracy calculated from a simulation which corresponds to color filter 1, whose quality metric cloud is shown in green in Figure 8.
OVL inaccuracy: Color filter 2
Figure 10. Wafer map of overlay inaccuracy calculated from a simulation which corresponds to color filter 2, whose quality metric cloud is shown in black in Figure 8.
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5.
SUMMARY AND CONCLUSIONS
In this work we show that overlay mark imperfections have a large impact on overlay accuracy, and may lead to inaccuracy of several nanometers if not addressed properly. Theoretical analysis and simulations reveal that high sensitivity of the metrology to overlay mark asymmetry induces inaccuracy beyond the usually small geometrical ambiguity, and that DBO is more sensitive to mark asymmetry than imaging overlay. The concept of overlay measurement quality is proposed as a solution to improve overlay accuracy in the case of an asymmetric overlay mark. It is shown in simulations that the use of the quality metric enables efficient removal of outliers as well as effective optimization of recipe parameters, thus leading to a significantly better accuracy.
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