Angular scatterometry is a fast, in-line, noncontact, and nondestructive nanoscale metrology tool that is widely used in manufacturing processes. As scatterometry is a potential metrology technique for next generation semiconductor manufacturing and for other emerging large-area (roll-to-roll) nanotechnology products such as wire grid polarizers (WGPs) and nanostructured metamaterials, it is necessary to study its fundamental sensitivity and accuracy limitations. Two different samples are simulated using rigorous coupled-wave analysis. One is a high index contrast aluminum WGP structure, and the other is a low-index contrast resist grating on a polycarbonate substrate. During modeling, the sample structure is scaled by simultaneously scaling both the line width and the height of the grating with a fixed pitch and all linear dimensions, including pitch, line width, and grating height, of the structure. Two metrics are chosen to define the limits: the first is the comparison with experimental limits, that is, if the reflection difference for a 5% scaling variation is larger than the experimental noise floor, scatterometry has sufficient resolution to recover the metrology information; the second is the comparison with effective medium models, that is, if the simulated angular scatterometry signature differs from an effective medium model signature, again within experimental noise limits, scatterometry is judged to have sufficient resolution to determine the feature parameters. Using a 405 nm source, scatterometry provides sufficient information to analyze a 20 nm pitch WGP structure using a 405 nm laser source (wavelength/pitch = 20), while the minimum pitch resist grating is ∼24 nm (wavelength/pitch = 16.8).
Metrology is an essential aspect of nanoscale manufacturing because of the need to monitor procedures and provide process control. As the scale of today’s semiconductor products is smaller than ∼10 nm, metrology faces a significant challenge and is becoming a more significant factor in advanced manufacturing.1–4 Recently, additional nanoscale fabrication steps have been added to the manufacturing process to obtain denser electronics requiring complex 3D structures (e.g., FinFETs).5 For example, double patterning (litho-etch-litho-etch, LELE), self-aligned double patterning (SADP), or self-aligned quadruple patterning (SAQP) is used to extend 193-nm based optical lithography, but the number of steps, the required alignment between steps, and the need for metrology increase in comparison to single-step lithography processes.6 Additionally, with the introduction of FinFETs, 3D structural information is required.7,8 Because more features and steps need to be monitored, metrology has become a very expensive and time-consuming aspect of manufacturing. Hybrid metrology techniques have been explored as a solution to a complete quality control process.9 Therefore, there is an urgent need to develop and improve the current metrology technologies to meet the industry’s requirements, to keep pace with the development of new manufacturing technologies, and to understand the fundamental limitations of various techniques. Modern integrated circuit manufacturing operations are based on a well-developed mature tool set and crystalline substrates for which off-line statistical process control can provide adequate information for yield control. In contrast, roll-to-roll tools are just now approaching manufacturing at nanoscale dimensions and hence demand real-time monitoring as a consequence of the greater degrees of freedom associated with flexible substrates and nanofluidic surface interactions.10–12
After nearly 30 years of development,13 optical scatterometry has proven to be one of the most effective solutions for metrology at the 14 nm node.15–23 There are two dominant approaches to scatterometry: (1) Mueller matrix ellipsometric (MME)-based scatterometry and (2) angular scatterometry. Both approaches are based on diffraction from periodic structures. In ellipsometric scatterometry, the angle of incidence is fixed and the wavelength is varied, usually using a broadband, incoherent source. In angular scatterometry, the angle of incidence is varied, while a fixed wavelength source, usually a high brightness laser source, is used. Both techniques have demonstrated resolution to feature sizes relevant to advanced manufacturing needs. Each technique has advantages. Ellipsometric scatterometry has greater sensitivity (ellipsometry can provide submonolayer information24) but (a) requires detailed knowledge and control of the properties of all the involved materials as a function of wavelength (particularly in the ultraviolet spectral region where absorption can vary greatly with stoichiometry) and (b) requires a long measurement time because of restrictions on optical power density and spot size imposed by an extended, broadband incoherent source.25 Angular scatterometry has the potential for a faster response since it uses a much brighter (power/wavelength-cm2-solid-angle) coherent laser source that can be focused using small dimensions as needed by metrology targets and offers much higher power densities, allowing larger bandwidth receivers to accommodate higher speeds. Additionally, angular scatterometry only requires knowledge of the optical properties at a single wavelength, usually well removed from spectral regions of high material variability, which makes the interpretation of the scattering signature vs angle more robust. In particular, there is an emerging need for in-line metrology tools for high volume, roll-to-roll (R2R) manufacturing tools and processes with ∼millisecond or lower speed requirements. Angular scatterometry uniquely fits this requirement.14
Scatterometry can measure 1D structures (e.g., gratings), 2D periodic structures (e.g., dots/holes/grids), and 3D periodic structures (e.g., FinFET channels and other complex structures). Scatterometry measurement is an indirect, nonimaging process that takes place in two steps: measurement and simulation. As angular scatterometry is a potential high-speed in-line metrology technique for emerging R2R nanoscale manufacturing, it is necessary to explore its fundamental limitations. We had previously reported the experimental results on two nanoscale 1D sample types: (1) a high contrast Al wire grid polarizer (WPG) on a silica substrate and (2) a low-contrast photoresist grating on a flexible polycarbonate substrate,26,27 both with a ∼100 nm pitch using a 405-nm-laser-based angular scatterometry arrangement. A good agreement between the inferred structures from angular scatterometry measurements and destructive cross-section SEM images was obtained. In this contribution, we extend the modeling for both sample types by scaling (1) the feature dimensions, keeping the period fixed, and (2) the feature dimensions and the pitch. Two metrics are used to determine limitations: (1) an experimentally based metric with a noise floor based on our previous experimental results and (2) a modeling metric where the variations in the scatterometry signature are compared with an effective medium model which only depends on the refractive indices and the fill factor without invoking any structural information.
A. WGP structure definition
The WGP sample before scaling is a nominal 100-nm pitch periodic grating structure with a ∼200-nm thick Al grating on a fused silica substrate. From previous studies, seven parameters are needed to define and characterize the symmetric WGP structure: pitch (P), bottom width (BW), top width (TW), Al height (Al), fused silica undercut (FS), horizontal rounding (HR), and vertical rounding (VR), as well as an Al2O3 layer that forms over the Al on exposure to air (AlO) (see Fig. 1). In this paper, a 4-nm thick layer of Al2O3 is added to the simulation. As discussed in our previous papers, two low reflectivity measurement conditions when the grating (lines) direction and polarization are perpendicular to each other (low reflectivity, high transmission) are chosen for the analysis. The high reflectivity polarization conditions do not offer a sufficient dynamic range for metrology purposes.
B. Resist grating structure definition
The resist grating sample has a nominal ∼130 nm pitch and ∼100 nm height resist grating on a polycarbonate substrate before scaling. Five parameters are used to define the resist grating structure. They are pitch (P), bottom width (BW), top width (TW), resist height (H), and residual layer thickness (RT) (see Fig. 2). The substrate for the resist grating samples was a polycarbonate, which is a flexible, high optical transmission material with an optical refractive index comparable to glass. It has been shown previously that for scatterometry of symmetrical line patterns, independent data can be collected at 0° and 90° angles relative to the grating direction.28
When the grating directions are perpendicular to the polarization directions, a strong Fabry-Perot effect is observed in the scatterometry measurement, which causes uncertainties in the fitting. For the resist grating samples, the measurement was carried out at the condition that grating directions are parallel to the polarization directions and opposite to the WGP conditions (TM polarization with a horizontal grating and TE polarization with a rotated, vertical grating, see Fig. 3). Since this is not a high reflectivity structure, the dynamic range issues evident in the WGP case are not significant.
C. Noise level
An essential aspect of investigating the limits of scatterometry is to determine the noise level of the measurement system. When scatterometry reaches its limitation, it means that the structure information in the scatterometry signature of the sample surface does not emerge from the measurement noise as the simulation parameters are changed. The variance for changing parameters is defined as the maximum difference between the data points between the initial parameter sets for a ±5% variation of the parameters. If the variation is larger than the system noise level, the parameter change is considered as “measureable” by scatterometry.
In order to obtain the noise level of our scatterometry system, we measured a sample five times and then calculated the root mean square (rms) difference for this measurement. The first measurement data points were chosen as the reference. The average rms difference is calculated by the following equation:
where xn is the measurement data point at the n’th incident angle, xi,n is the first measurement data point at the same incident angle, N is the total number of data points, and M is the number of measurement repeats. This rms evaluation shows the reflection variation between several measurements over an angular range of 8°–80° for the same sampled area having an uncertainty of 6.4 × 10−4. Clearly, this noise level could be improved with additional experimental attention to the elimination of noise sources. Therefore, the limits discussed below should be considered as upper bounds that can be improved upon.
D. Limitation for the WGP structure
For studying the limitations of scatterometry applied to the WGP, we shrink the structure size in the simulation. A reflection difference is calculated for the scaled structure and a similar structure with a 5% variation of one of its parameters for TM polarization with vertical grating and TE polarization with horizontal grating (the same definition as presented for the WGP is shown in Sec. II A). The maximum difference across the angle range from 0.1° to 79.1° is compared with the noise level of our system. We used two different approaches to scaling: (1) fixing the pitch at 100 nm and individually decreasing either the line width of the grating or the Al thickness to study the influence of variation of these two parameters and (2) decreasing all parameters simultaneously (e.g., linewidth, pitch, and grating thickness), keeping the line width equal to a half of the pitch and the Al thickness equal to the pitch. All the simulation work is performed assuming a 405 nm wavelength. These two conditions are discussed separately.
E. Limitation for resist grating
For resist grating, two similar scaling approaches were investigated: (1) independently decreasing the line width and the resist thickness at a 130 nm fixed pitch and (2) shrinking the pitch from 130 nm to 5 nm, scaling both the line width and the resist height proportionately. With a scaled structure, simulations for each structure and a 5% variation of the structure are calculated for both TM polarization with horizontal grating and TE polarization with vertical grating (the same conditions are defined in Sec. II C).
F. Effective medium
Scatterometry is an indirect measurement; the structure information is encoded into the reflection/transmission vs angle data. The best match between forward simulations for the reflection vs angle curves for many parameter sets are used to evaluate the structural information. For this to be effective, the measurements must contain information on the structure. However, as the feature sizes become much less than the wavelength (λ/p ≫ 1), the composite structure will eventually optically behave as an effective medium without any structural information. In this case, the grating structure is simply a plane layer with an effective refractive index, and all the structure information except the fill factor (critical dimension/pitch) and the thickness of the grating are lost to the scatterometry measurement. Before we moved to the process of fitting our scatterometry measurements, the measurement results were compared with an effective medium approach to ensure that the measurements are able to monitor the details of our WGP samples. Additionally, as the structure scales in both transverse dimensions and thickness, the scatterometry measurement is dominated by the signature of the substrate, and again, the structure information is lost within the measurement noise limits.
There are several approaches to evaluating the effective medium approximation for a first medium with refractive index n1, an inclusion medium with refractive index n2, and a volume fraction σ of the inclusion medium. The volume fraction is between zero and unity (0 < σ < 1). We chose two frequently used methods to compare to our measurement results: the Maxwell-Garnett and Bruggeman models.29 For the Maxwell-Garnett model, the equation to calculate the effective index is as follows:
For Bruggeman’s model, the equation to calculate effective index is
where n1 is the index of the first medium, which is air (n1 = 1) for the WGP, n2 is the index of the inclusion medium, which is the index of Al for the WGP, nAl = 0.479 51 + 4.772 4i at a wavelength of 405 nm, and σ is the fraction of the inclusion medium, which is set at 0.5.
After obtaining the effective refractive index, it underwent rigorous coupled-wave analysis (RCWA) to calculate the reflection as the angle of incidence is varied from 0.1° to 79.1°. Since the film is simply represented by a composite refractive index in the effective medium approximation, this is equivalent to a straight-forward thin-film-coating reflectivity calculation. The fill fraction coefficient chosen for the WGP was 0.5, and the thickness of this effective medium was equal to the 200 nm thickness of the Al grating. Figure 4 shows the comparison of our measurement results (which closely match the RCWA simulation results) with those from the Maxwell-Garnett and Bruggeman’s models. The figure indicates that the Maxwell-Garnett model based on TE and TM (reflectometry parameters) simulation is more suited for our WGP structure and shows a closer approximation result. There is a significant difference between the scatterometry measurements and the effective medium approximations, which indicates that there is structure information in the scatterometry measurements when using a 405 nm wavelength source for this 200 nm thick, 100 nm pitch Al grating.
Extending these results to thinner films, it is important to determine the thicknesses when the film information is swamped by the reflectivity of the surface without a film; to this end, in Fig. 5, we show the difference between the Maxell-Garnett effective medium reflectivity and the reflectivity of a bare silica surface as the effective medium.
Similar results were obtained for the photoresist grating, which are shown in Fig. 6. For this lower contrast system, the difference between the effective medium and the bare substrate is distinguishable only to about 50 nm for the TE and TM polarizations. Ellipsometry can, of course, extend these limits.
III. RESULTS AND DISCUSSION
For studying the limitation of WGP and resist grating structure, we shrink the structural dimensions of the sample in the simulation. A reflection difference is calculated between the scaled structure and a 5% variation of one of its parameters for TM polarization and TE polarization (the same definition as presented above). At each parameter value change, the maximum difference across the 0.1°–79.1° angular range is picked to present the sensitivity performance for each parameter set. This maximum difference is compared with the noise level of our system.
A. WGP structure results—100 nm pitch
The initial structure we defined in the simulation is for a line width BW = TW = 70 nm, Al thickness Al = 200 nm, and pitch P = 100 nm with 4-nm thick Al2O3 added on the surface of the Al lines. We fix the pitch of the WGP at 100 nm, and (1) we scale the Al grating width from 70 nm to 10 nm (see Figs. 7 and 8) and (2) scale the Al grating thickness from 200 nm to 10 nm (see Figs. 9 and 10).
Both simulation results indicate that scatterometry with a 405 nm wavelength laser is sufficient to measure a grating width down to ∼10 nm on a 100 nm pitch structure. At smaller scales, the difference between 5% parameter variations is still greater than our noise level but becomes very small. In Figs. 8 and 10, the variation suddenly increases when the feature size is ∼10 nm for Al thickness and bottom width. This is due to the fixed 4-nm thick Al2O3 layer, which dominants the simulation at these small Al linewidths. For the Al thickness variation, although TM polarization and TE polarization have lost sensitivity at ∼25 nm Al thickness (see Fig. 9), this can be solved by switching to another wavelength laser.
B. WGP results—100nm–5 nm pitch variation
The pitch is varied from 100 nm to 5 nm. As the pitch varies, the line width of the grating changes simultaneously so that the line width is fixed at half the size of the pitch and the Al thickness is fixed equal to the pitch in the simulation.
Figure 11 shows the result as the pitch of the WGP is varied from 100 nm to 10 nm. The difference between TM and TE polarization conditions at pitch = 100 nm is much greater than the noise level. It indicates that the scatterometry measurement is very sensitive and sufficient for our current WGP sample with a pitch = 100 nm. Figure 12 demonstrates that scatterometry still retains sensitivity at a 20 nm feature size with a 405 nm wavelength laser (λ/p = 20) for TM polarization, and the measureable feature size could be smaller with a lower noise system. This indicates the impressive potential capability of scatterometry. Both polarizations exhibit sharp changes at P ∼ 20 nm. This is likely caused by surface resonance which is a very common phenomenon for a metal grating structure with wavelength ≫ pitch.30 When the pitch of the WGP grating approaches 6 nm, the signatures have a similar shape and reflection intensity as the Maxwell-Garnet effective medium results. Figure 13 demonstrates that all WGP structure information is lost at a pitch of 6 nm and there is only effective refractive index information in the scatterometry signature.
C. Resist results—130 nm pitch
Next, we report the simulations for the resist grating. The initial structure we defined in the simulation is that the line width BW = TW = 100 nm and the resist thickness H = 100 nm. We fix the pitch of the resist grating at 130 m, and we (1) scale the resist grating width from 100 nm to 10 nm (see Figs. 14 and 15) and (2) scale the resist grating thickness from 120 nm to 10 nm (see Figs. 16 and 17).
As expected, the limits are not as small as those of the WGP because of the lower index contrast of this sample. TE polarization has a better sensitivity for parameter variation for resist grating at pitch = 130 nm. Comparing these with WGP results, scatterometry is less sensitive for the resist grating because of the lower index contrast, but simulations, shown in Figs. 14 and 16, indicate that scatterometry with a 405 nm laser is still sufficient for line width determinations at 10 nm and resist thickness at 30 nm.
D. Resist results—130–10 nm pitch variation
The pitch is varied from 130 nm to 10 nm, and line width is fixed at half of the pitch; the resist thickness is equal to the pitch because for resist grating, there is a stronger surface tension between gratings with a smaller pitch, and gratings are likely to collapse with a high ratio of resist grating thickness over pitch.
Similar to the results provided in the last section, TE polarization has more sensitivity than TM polarization. Scatterometry loses sensitivity at ∼24 nm for both TM and TE polarization (shown in Figs. 18 and 19). Although a pitch of 24 nm is the limit of resist grating under the current noise level, the signatures are still different from the effective medium approach (Maxwell-Garnett model). However, when the pitch of the resist grating approaches 14 nm, the signatures have a similar shape and reflection intensity as the Maxwell-Garnet effective medium results. Figure 20 demonstrates that all resist grating and WGP structure information is lost at a pitch of 20 nm and there is only effective refractive index information in the scatterometry signature.
IV. SUMMARY AND CONCLUSIONS
Scatterometry simulations are presented for two different 1D (grating) sample types: an Al grating on fused silica and a resist grating on a polycarbonate as the samples are scaled to ∼10 nm dimensions. The study demonstrates that a 405 nm wavelength laser can provide a sufficient measurement for all three samples with 50 nm half pitch features. A limitation study on the WGP and resist grating structure indicates that angular scatterometry with the 405 nm laser can provide a sufficient measurement for ∼20 nm Al features (λ/p = 20) and ∼24 nm resist features (λ/p = 17) with the current system noise level. For resist grating on a polycarbonate, at a pitch of 20 nm, scatterometry does not provide any grating structure information, and the scatterometry signature is indistinguishable from the effective medium result.
This work is based on the work supported primarily by the National Science Foundation under Cooperative Agreement No. EEC-1160494. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.