Angle Resolved Optical Metrology

Angle Resolved Optical Metrology R. M. Silver, B. M. Barnes*, A. Heckert, R. Attota, R. Dixson, and J. Jun* National Institute of Standards and Technology Gaithersburg, MD 20899 KT Consulting Inc, Antioch, CA 94509

*

Abstract There has been a substantial increase in the research and development of optical metrology techniques as applied to linewidth and overlay metrology for semiconductor manufacturing. Much of this activity has been in advancing scatterometry applications for metrology. In recent years we have been developing a related technique known as scatterfield optical microscopy, which combines elements of scatterometry and bright field imaging. In this paper we present the application of this technique to optical system alignment, calibration, and characterization for the purpose of accurate normalization of optical data, which can be compared with optical simulations involving only absolute measurement parameters. We show a series of experimental data from lines prepared using a focus exposure matrix on silicon and make comparisons between the experimental and theoretical results. The data show agreement on the nanometer scale using parametric simulation libraries and no “tunable” parameters.

1. Introduction Recently, there has been significant research investigating new optical technologies for overlay measurement and critical dimension metrology for the 45 nm node and beyond. This work has been focused in two primary areas, scatterometry and more recently, scatterfield microscopy, a technique which combines well-defined angular resolved illumination with image forming optics [1-3]. This new approach is based on a Köhler illuminated system having an accessible conjugate back focal plane on the illumination side of the optical train, which enables control and engineering of the illumination. The fundamental limits of optical scatterometry/light scattering with respect to feature size and sensitivity are still several generations out [4]. Measurement limitations are driven by sample irregularity and experimental parametric uncertainties. Many of the practical scatterometry limits and engineering limitations are being effectively addressed. Sophisticated modeling approaches that vary numerous parameters are now being successfully implemented. However, there are some intrinsic limitations or barriers; target size, single target per acquisition, averaging over a given target, illumination beam spot size limits, and target under fill and background-induced limitations. A related alternative optical technique that addresses many of these limitations is scatterfield microscopy. Adding high magnification optics to a scatterometry-type platform has a number of advantages: smaller targets, multiple targets can be measured simultaneously (linearity targets), intra-target sampling and analysis, and imaging the target gives specific knowledge of the location in the target where specific measurement data were acquired [5]. The primary disadvantage or technical challenge is that the optical column must be accurately characterized which can lead to modeling inaccuracies. Another very important advantage is that the scatterfield technique enables accurate microscope characterization. One of the primary obstacles to the adoption of optical techniques for many high-resolution applications is the need for accurate simulation tools. These are needed for modeling optical measurements of critical dimension and some overlay metrology applications as well as for measurement system improvements that rely on simulations for guidance. The angle-resolved imaging technique addresses and solves a number of these obstacles, which have limited the accuracy of optical imaging techniques for a number of years. There are three primary applications for angle-resolved microscopy. The first, and perhaps most important is optical tool characterization. Angle-resolved illumination is essential to accurate tool characterization for conventional microscopy

Metrology, Inspection, and Process Control for Microlithography XXII, edited by John A. Allgair, Christopher J. Raymond Proc. of SPIE Vol. 6922, 69221M, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.777131

Proc. of SPIE Vol. 6922 69221M-1 2008 SPIE Digital Library -- Subscriber Archive Copy

and in more advanced frequency-resolved microscopy applications [6]. Characterization based on angle- and polarization-resolved illumination enables the illumination and collection optical paths to be fully quantified as a function of illumination angle, polarization, intensity and wavefront across the field of view. Angle-resolved illumination analysis has proven to be an essential and sensitive tool to achieve and analyze optical system alignment and symmetry as well as to correct for previously uncompensated errors and effects in optical microscopes, which substantially compromise measurement accuracy. The second application is to enable structured illumination for image-based overlay measurements e.g. dipole illumination, quadrapole illumination etc. to increase image information content. Different illumination schemes have been used such as dipole illumination or stepped plane wave illumination configuration, for example. Also, structured or angle resolved illumination can improve measurement performance by altering the way the light interacts/scatters off the sample enhancing the image profile or controlling the frequency information at the Fourier plane. In this application angle resolved illumination enables tailoring of the illumination to a specific target or type of metrology measurement to be performed. Recent results show scatterfield overlay targets can be measured with substantially improved resolution and image information content [7]. The third application is angle-resolved, stepped, or scanned illumination, to enable critical dimension (CD) and overlay type scatterometry measurements on a high-magnification, optics-based platform. In this application nominally plane waves of illumination are stepped through a range of angles and images captured as a function of angle. The images are then analyzed to produce intensity values and plotted versus angle creating essentially angle resolved scatterometry profiles. The intensity profiles at the image plane may contain only specular, zero order reflected intensity or may contain higher-order optical content as well, depending on the measurement wavelength, sample pitch or detailed geometrical aspects. Although the resulting image field can be broken into sub-fields, each analyzed independently thus yielding in parallel an array of angle-resolved scatterometry profiles, the data and analysis presented here is performed on full field arrays with the intent of demonstrating the experimental technique with subsequent quantitative comparisons to simulation. The acquisition of data in this mode with normalization and accurate modeling of the data forms the main body of this publication.

2. The Optical Hardware Configuration The new suite of scatterfield microscopy techniques we are developing are based on an optical platform that enables engineering the electromagnetic field at a illumination Fourier plane (conjugate back focal plane) resulting in structured illumination fields at the sample. These techniques are fundamentally based on the ability to prepare and define the illumination in angle space by scanning or stepping the illumination in position space at the illumination Fourier plane resulting in angle-resolved illumination. In a Köhler configured illumination system, each point on the back focal plane maps nominally to a plane wave of illumination at the sample plane. Therefore, a finite aperture placed at the back focal plane produces a narrow cone of plane waves, each of which illuminates the entire field of view if one chooses an appropriate field aperture. Although the optical instrumentation hardware has been described in detail previously, a brief description is given here (see Figure 1) to facilitate understanding of the scatterfield technique as it is applied to CD and overlay metrology [8]. A relay lens group relays out the back focal plane, which is physically located in the objective. A subsequent lens group magnifies this relayed conjugate back focal plane (CBFP) to a diameter of 9.8 mm, large enough to place physical apertures which can be manipulated with appropriate scanning or stepping motion hardware. For the data presented in this paper, only the primary axes are scanned with a single aperture, as shown in the figure inset. This simplifies elements of the simulation that are encountered when modeling conical or oblique incidence illumination. Polarization states can be defined at the CBFP with respect to the sample and imaging optics. The use of the primary axes allows us to produce well-defined polarization states at the sample. Since the work presented in this paper is focused on simulation-to-experiment agreement, only the subset of primary axis polarization states are used, although more complex off-axis, oblique illumination has been used and has its advantages in some applications. The collection optics are conventional high-magnification bright-field imaging optics with a numerical aperture (NA) of 0.95. This is also the limiting NA for the illumination and therefore defines the maximum angles of illumination. In this

Proc. of SPIE Vol. 6922 69221M-2

implementation a plane just above the sample is imaged to an image plane at the charge-coupled acquisition device (CCD). A high-resolution, well-calibrated CCD is used to collect the intensity at the imaging plane. The back focal plane position to illumination angle relationship has also been well characterized and calibrated. ysample xsample

LED

aperture

relay lens

objective

Figure 1. A schematic layout of the illuminator. The inset figure defines the two scan axes. Polarization is also defined relative to the x and y axes of the inset.

3. Optical System Characterization and Calibration One of the challenges in utilizing these types of optical techniques is that they fundamentally rely on accurate modeling to achieve proper measurement and data interpretation, although there are some recent results based on empirical analysis. Techniques based on scanning light as a function of angle or wavelength have been shown to have tremendous sensitivity to changes in linewidth or sidewall angle, for example [9,10]. The challenge, however, implied by this sensitivity is a commensurate sensitivity to other aspects of the sample or optical tool. It is therefore critical to develop techniques that accurately model the optical tool to enable accurately modeled results. Comprehensive measurements that fully characterize the instrumentation are necessary to achieve modeling results that simulate the physical measurement being made. One important characterization tool enabled by the scatterfield technique is that we can analyze the optical tool as a function of illumination angle, thereby characterizing the optical path independently for each isolated angle of illumination. This is similarly carried out for each polarization state. This turns out to be essential to fully characterize the optical tool and accurately model the optical measurements. In this section, we present our comprehensive analysis of illumination misalignment, inhomogeneity, and dependence of the illumination fields on polarization and illumination angle. These illumination errors are mapped to a functional dependence, which can be used as an input to either the electromagnetic simulation tools or, alternatively, to normalize the experimental data thereby removing the various instrumentation effects for subsequent comparison between normalized experimental results and modeling outputs. This is an important step in improving optical model-to-experiment agreement. The procedure we use to characterize the optical train is to measure the tool function, which includes source inhomogeneity, transmission errors as a function of angle and position, and transmission errors as a function of polarization. We also measure system glare and background scatter as well as a careful CCD characterization. This data is acquired in such a way as to allow separation of the illumination path errors and collection path errors. The resulting tool function is then used to normalize the CCD acquired data. The data in Figure 2 show reflected intensity as a function of angle for refection off of a bare silicon surface and a dielectric mirror. The dielectric mirror chosen has excellent polarization independent reflectivity and angle insensitivity to about 45o. The data shown in the figure are raw reflectivity as a function of angle.


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Figure 2. On the left are two experimental silicon reflectivity curves, for the x and y scan directions. On the right are reflectivity curves for a highly reflecting dielectric mirror. Error bars represent 3σ repeatability distributions. The figures show unpolarized (unpol), parallel polarization (pol para), and perpendicular polarization (pol perp) with respect to the line array.

The difference in the curves on the left and right in Figure 2 is the result of the optical constants and the reflectivity as a function of angle for the two materials. The shape of the angle dependent curves of the dielectric mirror is due to optical system transmissivity effects, glare, polarization effects and sample components. The upper two sets of data are for the x scan direction and the lower two are for the y scan direction showing the scan axis symmetry. In each plot the upper curves are for unpolarized light and the lower two are for the polarizations as labeled. Next, we divide the silicon data by the dielectric mirror data point-by-point to obtain normalized reflectivity curves for silicon. These data are shown on the left in Figure 3. On the right, theoretical reflectivity curves are shown for silicon calculated using our simulation package. The data are absolute and only normalized using the procedure described here with no tunable parameters. The agreement for the constant offset levels is excellent near normal incidence and the discrepancies above 40o result from the dielectric mirror reflectance and polarization errors as compared to the well-known silicon reflectivity behavior. Bare Si divided by Mirror - Y

sample

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Ic error bars

Simulated Reflectivity for Unpatterned Si - Y

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Figure 3. On the left are dielectric mirror normalized silicon reflectivity curves, taken from the data in Figure 2. The data on the right are theoretical values for silicon reflectivity. While the data on the left are close to the correct values as smaller angles of incidence, errors from the dielectric mirror and tool at higher angles introduce errors in comparison to the theoretical values on the right.


As we are interested in patterned silicon targets on the same wafer, we can divide the raw silicon data by the known silicon reflectivity data and obtain a tool normalization function, which can be used on profiles from these targets. We then compare the resulting silicon-derived tool function to that which results from the dielectric mirror. These results are shown on the left in Figure 4. The two sets of tool normalization functions are very close in shape indicating both methods independently return similar tool functions. The differences at the higher angles are critical though as the small differences can have a large effect when normalizing high angle, low signal strength data. The next step is to measure the tool function for the isolated illumination path. This allows separation of the illumination and the collection functions. This is very important since the illumination data are typically based on a single illumination aperture position in the CBFP. This is contrary to the collection of the scattered fields as although only a single illumination angle is traversed in the illumination path, multiple paths in the collection optics may be followed if higher optical orders are present. The problem can be well approximated as a linear normalization when a dense zeroorder-only reflecting target is used since only a specular reflected beam is observed, symmetric with the illumination beam. However, if higher-order diffraction is present, the collected optical signal must be normalized appropriately for the range of angles collected. However, in qualitative comparisons, the collection path typically results in a much flatter normalization function. For the purposes of this initial analysis, the collection function has been treated as independent of angle. Measured vs. ideal - X

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Figure 4. Two scan directions shown, on the top are perpendicular to the lines and on the bottom are the parallel scan profiles. The top curves in each individual plot are unpolarized and the lower curves are parallel and perpendicular polarizations as labeled in the figure. On the left tool functions are shown and on the right illumination path normalization curves are shown.


4. Experimental Results A single 300 mm wafer with a focus exposure matrix fabricated by Sematech was used for the experiments in this paper. Reference metrology was completed using a commercial critical dimension atomic force microscope (CD-AFM) [11]. This tool, which uses a flare-shaped CD tip, has been calibrated and characterized by NIST for traceable dimensional metrology. The details of this implementation and the resulting uncertainties have been published elsewhere [12]. Examples of the AFM measurement results and wafer layout are shown in Figure 5. The measurements were all reported with 3σ uncertainties. Line width, sidewall geometry, line height and pitch were all measured values. Three die were selected for each type of line array for comprehensive analysis, (0,-1), (0,0) and (-1,-1). Although details of the AFM analysis are not presented here, the 3σ uncertainties were used to determine parametric ranges in the analysis presented later.

Die

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height: 230.35 nm w(top): 120.96 nm w(mid): 116.91 nm w(bot): 130.31 nm Die

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height: 229.68 nm w(top): 120.81 nm w(mid): 116.65 nm w(bot): 130.66 nm


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Die (-1,-1) height: 230.36 nm w(top): 115.53 nm w(mid): 111.55 nm w(bot): 122.99 nm

Die (0,-1) height: 228.92 nm w(top): 116.09 nm w(mid): 112.31 nm w(bot): 125.07 nm

Die (1,-1) height: 228.09 nm w(top): 115.21 nm w(mid): 111.39 nm w(bot): 123.99 nm

Die (-1,-1) height: 228.71 ± 0.22 nm w(top): 102.14 nm w(mid): 117.06 nm w(bot): 128.91 nm

Die (0,-1) height: 227.19 ± 0.39 nm w(top): 111.76 nm w(mid): 118.43 nm w(bot): 131.92 nm

Die (1,-1) height: 227.62 ± 0.22 nm w(top): 109.85 nm w(mid): 116.46 nm w(bot): 130.02 nm

118.6 nm 114.7 nm 128.8 nm

Si

Si

Si

Si

Si

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120.4 nm 125.8 nm 139.5 nm Si


Si

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Figure 5. Wafer layout by die for the focus exposure matrix (FEM) line arrays. Two sets of line arrays with differing pitches of 300 nm and 600 nm were selected. The pitch values and focus/exposure values resulted in the sidewall variations shown.

Wafers were placed in the optical tool and repeatability measurements used to establish system repeatability. Next, three die for each of the 300 nm pitch targets were measured. The data in Figure 6 show good sensitivity to nanometer scale changes in feature dimensions. It is important to note that the dimensional changes are a combination of lateral dimension changes and sidewall angle. These changes are captured in the AFM reference data as top, middle, and bottom widths. Analysis of the sensitivity plots in the figure reveal which polarizations and scan axes have the best sensitivity to changes in the dimensions of interest. The top two plots show curves for line widths differing by 2.5 nm while the lower plots are for line width differences of less than 1 nm. Larger signal differences are observed for the larger width differences, as expected. The 300 nm pitch targets showed little variation in sidewall angle as seen in the top, mid and bottom AFM width measurements. Similar data for the 600 nm pitch targets are shown in Figure 7. Unlike the 300 nm pitch targets, these targets have higher-order diffraction peaks present for all angles and scan directions. The x scan direction, that perpendicular to the line grating, shows the best sensitivity for the larger pitch target gratings. For the targets used in this study, the overall target dimension was larger than the imaged field of view. The illumination field size was also larger than the imaged field of view. Again, this is not necessary as although more complex target layouts and multiple targets per field can be readily used, we have chosen to simply the measurements since the intent is to establish baseline measurement accuracy.


LIOOP300 - Dies (0,0) vs. (0,-I) 0.7 Die (D,D) x axis pal perp. Die (D,D) a axis, pal pare.

—Die (D,-1)x axis pal perp. —Die (D,-1)x axis, pal para.

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LIOOP300-Dies (0,-I) vs. (-1,-I) -Y5 0.7 Die (D,-1)x axis pal perp. Die (D,-1) a axis, pal pare.

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Figure 6. Sensitivity data for three die with 300 nm pitch targets. The data show repeatable sensitivity to nanometer changes in target dimension. Preferred polarization and scan directions can be seen in the data. The curves shown are the mean of repeated measurements. Die 0,0) a axis pal perp. Die 0,0) a axis, pal para.

Die (0,-i) a axis pal perp. Die (0,-i) a axis, pal para.

—Die (-i-i) a axis pal perp. —Die (-i-i) a axis, pal para.

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LIOOP600 - Dies (0,0) vs. (-1,-I) - Y In

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Figure 7. Sensitivity data for three die with 600 nm pitch targets. The data show repeatable sensitivity to nanometer changes in target dimension. Preferred polarization and scan directions can be seen in the data.


5. Parametric Modeling Elements A rigorous coupled waveguide analysis (RCWA) model was used for the results presented here [13-15]. To ensure the model was behaving correctly, we routinely compared model RCWA outputs to a finite difference time domain (FDTD) model [16]. Both models have been extensively tested, compared and validated in earlier work [4]. The modeling approach used was a parametric variation about the known values based on the AFM results. The parametric analysis included variation of n and k, the optical constants, CD based on AFM data, height variation and pitch variation, again based on the AFM data. The parametric simulations did not account for a nominal 1.7 nm thick native oxide. The height and pitch values varied throughout the measured AFM fields, typically by ± 1 nm. The sidewall variation on the other hand was coupled to the CD variation since the sidewalls did not vary randomly throughout the measurement area based on the AFM data. Rather, the entire CD would vary due to line edge roughness while maintaining a constant sidewall geometry. The specific sidewall geometry, however, did depend on the focus and exposure values but even more strongly on the pitch values, 300 nm versus 600 nm. Parametric simulation curves were generated to evaluate sensitivity to line height and line width for both polarizations and scan directions for the range of angles from 0o to 60 o. The data show very little sensitivity to line height and pitch for the geometries measured in this study. Although the parametric modeling runs did full floating variations for the CD, pitch, and height, of these three parameters only CD and sidewall angle showed substantial sensitivity. The next figure shows a compilation of parametric CD variations ranging from 102 nm to 120 nm top width, 117 nm to 126 nm mid width, and 129 nm to 139.5 nm bottom width, the range of variation as determined by the AFM data. These data show significantly more intensity variation and sensitivity as a function of CD and angle. Both scan directions and polarizations show sensitivity to CD and sidewall. Similar results were observed for the 300 nm pitch patterns with small variation in the CDs and sidewall angles. CD variation - LIOOP600 - X

CD variation - LI 00P600 - Y

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Figure 8. A compilation of parametric CD variations for both polarization states and both scan directions.

Figure 9 shows sensitivity to the optical constants, n and k. We have not included a comprehensive parametric variation of the optical constants since these targets are etched silicon with well-known optical parameters. We ran these simulations to get a sense of the effects of the optical parameters and the importance of accurately measuring them. The plot shown on the right is for the perpendicular scan direction. At angles just above 30o, the first order is rocked into the imaging optics and can be seen as the inflection point in the data. In more complex materials stacks, we will use fitted reflectivity curves from blanket materials to determine and verify the optical parameters used. These parameters will then float in the parametric analysis as required.


LI 00P300 - X

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n = 4.6 p01. para. x ••••n = 4.6 p01. perp. x 0.6 n = 4.8 p01. para. x n = 4.8 pol. perp. x n = 5.0 pol. para. x 0.5 n = 5.0 pol. perp. x

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Figure 9. The n and k parameters have a substantial effect on the intensity curves. Both polarizations and scan directions are shown with the perpendicular scan direction shown on the left.

6. Experiment to Theory Comparisons Parametric simulations were completed using the methodology described above. The next two figures show the best matches between the experimental data and the parametric evaluations. In both figures the experimental data is shown on the left side while simulation results are shown on the right. The simulation results each include the three curves from the parametric runs that are closest to the experimental data. On the left side of the figures the AFM measured top width values are shown as insets while on the right side the three simulation top width values are shown in the lower part of each plot. Although only the top widths are shown here, all simulations were run with appropriate sidewall angles and variations as described earlier. The parallel scan directions are shown on the left sides while the perpendicular data is shown on the right. Each plot contains both polarizations as labeled in the figure. In these comparisons, it should be noted that the results are to determine nominal nanometer scale agreement and that full uncertainties have not yet been determined. The upper two plots in Figure 10 show the experiment-to-simulation comparison for the (-1,-1) die and 300 nm pitch. The best fit to data is seen with the 116 nm top width simulations for both scan directions. The measured AFM values are 115.5 nm and are very close. The data show a small offset for the parallel polarization which has not yet been fully understood. It is likely that this offset is due to edge runnout at the bottom of the lines which is not measurable using the AFM. The sensitivity for these data are clearly best for the perpendicular polarization with both scan directions showing similar sensitivity. The lower two plots show modeling fits for the (0,0) die, 118.6 nm top CD. For these data the best fit is seen between the 117 nm data and the 118 nm data. Again, agreement with the AFM data is observed to within a nanometer with no tunable parameters.


LIOOP300 (-1,-I) -y- with Si Theory correction and Fitting

LIOOP300 (-1,-I) -x- with Si Theory correction and Fitting

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AFM values Top = 115.5 nm -20 0 20 Angle of Incidence (degrees) LIOOP300 (0,0) - y- with Si Theory correctioe aed Fittieg

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Figure 10. Two scan directions shown, on the left is parallel to the lines and the right side is the perpendicular scan direction.

The next figure shows results from the 600 nm pitch targets. The upper plots are from the (0,-1) die with AFM top width values of 111.8 nm. The simulation data show poor sensitivity for the parallel scan direction and best sensitivity using the perpendicular scan direction. The simulation results show best agreement for the 107 nm top width runs. It should be noted however that the simulation for the 107 nm top width has a 117.5 nm mid width and a 130.5 nm bottom width while the AFM data for the 111.8 nm top width has a 118.4 nm mid and 131.9 nm bottom widths. So again the agreement is quite reasonable with a 4 nm discrepancy for the top width and 1 nm agreement otherwise. The lower set of results in Figure 11 are for the 600 nm pitch, (-1,-1) die. Similar sensitivities are seen to the (0,-1) die although the top widths agree much better, AFM values showing 102.1 nm and the simulation having best agreement and the best fit simulation data at 102 nm. In all of the examples shown here, bracket runs of 5 nm either larger or smaller were completed to ensure we were not comparing at a local minimum and that as we simulated the larger or smaller offsets, the resulting fits became quite poor.


LIOOP600 (0,-I) - y- with Si Theory correctioe aed Fittieg

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CD:112 ll2nm

AFM values Top = 102.1 nm -40

107 107 nm 102 102 nm

-20 20 Angle of Incidence (degrees)

40

60

Figure 11. Two scan directions shown, on the left is parallel to the lines and the right side is the perpendicular scan direction.

7. Summary An angle-resolved technique has been demonstrated which enables scatterometry type measurements on a highmagnification optical platform. This technique enables measurements of very small targets, in chip applications, reduced scribe line target size, and parallel measurements of multiple targets using scanned illumination and imaging optics. Nanometer scale sensitivity measurements can be achieved using angle resolved microscopy for nominally 100 nm sized lines and pitches of 300 nm and 600 nm. Quantitative parametric modeling results demonstrated consistent agreement on the nanometer scale with AFM reference metrology. Strong sensitivity to changes in critical dimensions and sidewall angles were observed. The simulations show measurements are largely insensitive to height and pitch variation, for the target parameters studied. Sensitivity to n and k, the optical parameters, is substantial and indicates the importance of accurately knowing these values. Nanometer scale agreement was achieved between modeled measurements and the known reference values. The next step is statistical evaluation of the parametric modeling results and the experimental data. Future work will also investigate the differences between simulation and experiment and include a parametric analysis of edge runout, corner rounding, and subtle bottom width effects not captured by the AFM measurements. These results demonstrate that accurate optical measurements can be achieved using high magnification optics if the illumination and collection paths are accurately characterized. This must include a full analysis of the flare, glare, angleresolved optical transmission, and polarization dependences. The scatterfield technique is based on an instrument configuration that allows access to the illumination fields as a function of angle and polarization. This is critical to


proper profile normalization. As a result, accurate simulation results can be achieved if accurate input functions are used. Future research applications research will include quantitative, simultaneous CD and overlay measurements using arrayed target designs.

8. Acknowledgements The authors would like to thank Richard Quintanilha, Heather Patrick and Egon Marx of the National Institute of Standards and Technology (NIST) for very useful discussions. The authors acknowledge Thom Germer of NIST for model development. The NIST Office of Microelectronics Programs is gratefully acknowledged for financial support as well as the NIST Scatterfield Competence project. The authors thank Sematech for wafer fabrication and measurement support.

9. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

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* Certain instrumentation and hardware are identified in this paper to enable proper understanding of the technical work. There is no endorsement or suggestion that this equipment is the best available for the purpose identified.
