Novel Technique for Critical Dimension Measurements of Phase-shift Masks Using Broadband Transmittance Spectra in Conjunction with RCWA
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1 Novel Technique for Critical Dimension Measurements of Phase-shift Mass Using Broadband Transmittance Spectra in Conjunction with RCWA Alexander Gray University of California at Davis, CA John C. Lam and Stanley Chen n& Technology, nc., Santa Clara, CA ABSTRACT For the first time Rigorous Coupled Wave Analysis (RCWA) has been applied to the analysis of the transmittance spectra for the determination of critical dimension (CD) of phase-shift photomass. The use of transmittance spectra proved to be instrumental in improving the sensitivity of the measurement to minor (sub-nanometer) changes in the width of the trench. We present a novel unique metrology solution based on the simultaneous measurement of broadband reflectance and transmittance, covering a wavelength range from 19 to 1 nm, in one nanometer intervals. The analyses of both types of spectra are performed simultaneously, using Forouhi-Bloomer dispersion equations, in conjunctions with RCWA. The method provides accurate and repeatable results for critical dimensions, thicness, and optical properties (n and spectra from 19 1 nm) for all materials present in the structure. n the current study, the method described above was used to examine grating structures on AC (After-Clean nspection) phase-shift mas. The use of transmittance spectrum proved to be essential for the accurate measurement of the CD, since the transmittance spectrum is more sensitive to the change in line width, compared to the reflectance spectrum. The results were compared with the measurements taen on the same sample using conventional CD-SEM. The CD linearity study demonstrated excellent correlation with CD-SEM. The advantages of the optical reflectance and transmittance method are high throughput, non-destructive nature of the measurements and capability to measure a wider variety of structures pertinent to the photomas manufacturing process. Keywords: Optical metrology, transmittance measurements, critical dimensions, broadband reflectometry, Forouhi- Bloomer dispersion equations, RCWA, CD linearity, repeatability.. NTRODUCTON Measurement of the critical dimensions (CD) on phase-shift photomass has become one of the central problems in modern-day metrology. Vast amounts of resources are being channeled towards the efforts to improve the accuracy, sensitivity and reliability of the esting techniques and development of the new ones. Conventional techniques, such as CD-SEM, AFM and nterferometry are being replaced by faster, non-destructive, non-contact optical techniques. A number of techniques based on optical reflectometry have proven to be successful in CD measurements, however, problems with measurement sensitivity push the metrology companies to explore new hardware solutions and develop new computational analysis algorithms. n this article we present a new metrology method, based on broadband measurements of reflectance and transmittance spectra. For the first time Rigorous Coupled Wave Analysis (RCWA) is applied to the analysis of the transmittance spectra for the determination of critical dimensions of phase-shift photomass. Section (Sensitivity and Resolution) underlines the necessity of the new technique. n Section (RCWA Method for Transmittance Spectra) the new calculation algorithm is described. Sections V and V outline the methodology and the measurement results. Photomas Technology 6, edited by Patric M. Martin, Robert J. Naber, Proc. of SPE Vol. 6349, , (6) X/6/$15 doi: / Proc. of SPE Vol
2 . SENSTVTY AND RESOLUTON As the product specifications become tighter, the question of measurement resolution and sensitivity becomes more and more critical. The conventional reflectance-based scatterometry is often limited by the fact that a small variation in line width does not correspond to a measurable change in the spectral reflectance. As a result of this, it is sometimes impossible to resolve the difference between acceptable and defective products. Tools that use monochromatic sources are particularly limited in that sense, since for certain pitches and materials a small variation in line width might have virtually no effect on the reflectivity measured at 193, 48, 365 or 633 nanometers. The following figure illustrates a typical variation in the polarized reflectance spectra (R s and R p ) due to 4 nm variation in line width of a 6 nm pitch grating. Twenty R s spectra and twenty R p spectra are plotted - each one corresponding to a nm increase in line width (from 8 nm to 3 nm). The mamum sensitivity to the change in width is observed at ~44 nm wavelength. At 193, 48, 365 and 633 nm wavelengths the variations would be simply impossible to resolve. Even at the optimal wavelength of ~44 nm a repeatable measurement would be difficult to accomplish due to low reflectivity and possible noise problems. R s 5:: 5s: x Es: is: ::: :: ;cavelength fta) Figure 1: Typical variation in the polarized reflectance spectra (R s and R p ) due to 4 nm variation in line width of a 6 nm pitch grating. R p Overlooing this issue may cause significant reduction in yield. Understanding this issue will lead to a search for an alternate metrology solution. n this case, instruments with the widest measurement wavelength range, variable measurement angle and variable polarization of sampling radiation will have the advantage over other tools. n other words, the most versatile instrument will occupy the top place in the list of possible metrology solutions. The use of transmittance spectra proved to be instrumental in improving the sensitivity of the measurement to minor (sub-nanometer) changes in the width of the trench. The study demonstrated that transmittance spectrum is more sensitive to the variation in line width, compared to the reflectance spectrum. The following figure illustrates a typical variation in the polarized transmittance spectra (T s and T p ) due to 4 nm variation in line width of a 6 nm pitch grating. Twenty T s spectra and twenty T p spectra are plotted - each one corresponding to a nm increase in line width (from 8 nm to 3 nm). Right away, the contrast with the previous graph is obvious. The variation in the spectral intensity is very high, compared to the variations in the reflectance spectra. Virtually any wavelength between 19 and 5 nm can be used to resolve the difference between the trenches of various line widths. The wavelengths of 193, 48, 44 and 465 nm are particularly sensitive to the variation and therefore are particularly useful. Proc. of SPE Vol
3 T p T s - E:. :s:,::. 55: :-: s: s:-: :: ;cavelength fta) 7:-: 7&: p[:. py=. :5:. - Figure : Typical variation in the polarized transmittance spectra (T s and T p ) due to 4 nm variation in line width of a 6 nm pitch grating. The discovery of this type of sensitivity opens new portals in CD metrology. The improved resolution maes it possible to detect Angstrom-level variations in trench width. This technique, however, would be impossible to use without a robust physically-valid analysis model, which would interpret the shape of the spectrum and quantify the grating geometry. The model of choice for the characterization of the optical properties of the materials present in the grating structure are the Forouhi-Bloomer dispersion relations, which provide a physically valid solution for the index of refraction and extinction coefficient spectra of thin films in the interband region. The most appropriate technique for the analysis of the grating geometry (trench depth, line width, sidewall angle, etc.) is the Rigorous Coupled Wave Analysis technique, introduced by Moharam 1 in Until now, however, this technique has never been applied to analyze measured transmittance spectra. The next section gives an overview of the RCWA method for the analysis of the transmittance spectra.. RCWA METHOD FOR TRANSMTTANCE SPECTRA n RCWA method, as shown in Moharam s paper, for different polarization state of incident beam, Maxwell s equations in the grating region can be transferred as finding the eigenvalue of the matrix: Where B x K x, = EK xe A = B E (1) K x for s polarization x, for p polarization () And E is the matrix formed by the permittivity harmonic components (ε i ), with the i, j elements equals to ε i-j ; K x is a diagonal matrix with the elements equal to. is the wave vector of i-th diffraction order in x direction, and is the wave number in free space. For a grating with a thicness of d (in z-direction), electromagnetic field in the grating region can be written in Fourier expression as 1 M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 1, 168- (1995). Proc. of SPE Vol
4 E H y x = = N N { } + ( j x) w c exp( q z) + c [ q ( z d )] exp (3) i= 1 m= 1 N N i, m m m m exp { } + ( j x) v c exp( q z) + c [ q ( z d )] exp (4) i= 1 m= 1 i, m m m m exp m m Where w im and q m are the elements of eigenvector matrix W and the positive square root of the eigenvalues of matrix A; V = WQ is the matrix with elements v im ; Q is the diagonal matrix with the elements q m. N is the truncation number of the diffraction orders. The boundary condition in the surface (z=) and bottom of the grating (z = d) lead to δ i + jn cosθδ i W X V X jk W C V C + [ R] W = V = jk T WX C VX C + (6) (5) Where R, T are vectors of reflectance and transmittance; C +, C - + are vectors with the elements c m, c m separately; X is a diagonal matrix with the elements exp( qmd ); K, K are diagonal matrices with the elements, (for s, or ( n ),, for p-polarization), and, n for p-polarization) separately; is the identity matrix; n, n are the refractive index of the incident and substrate media; and l, = (for s, or ( ) [ nl ( ) ] 1, real( l, ) > imag( l, ) j [( ) n ] 1, real( ) < imag( ) l l, l, (7) for l =, separately. Let Where + C = ac + b = W ( Xa ), g V ( Xa ) f + a = (8) = (9) ( V + jk W ) ( V jk W )X (1) b = ( V + jk W ) j( K + n cosθ ) δ i (11) Then the transmittance can be found by eq.(5), (6) as ( gf jk ) ( gf W V )Xb T = (1) Proc. of SPE Vol
5 For the multi-layer problem, consider the approach of partial solution (in J. Opt. Soc. Ame. A/Vol. 1, No.5, 1995, p ), let W =, V = jδ i f ( θ ), f =, g = jk, C = R b = δ i, X = ; Where, n cosθ, for s polarization f ( θ ) = (13) cosθ n, for p polarization And eep the relation of eq.(8)~(11) for each layer, the transmittance can be found as T L ( g L + jk f L ) BL = f (14) Where L is the number of layers, in the l-th layer (l = 1,, L), l ( Vl + gl fl Wl ) X l ( Vl + gl 1 fl 1Wl ) B B (15) = l With the eq.(14), (15), reflectance for all the multi-layer diffraction grating with different polarization states can be found with a good data stability and converging rate. V. MEASUREMENT METHOD For the current study we used a spectrophotometer-based instrument, capable of collecting four continuous spectra during one measurement two polarized reflectance spectra (R s and R p ) and two polarized transmittance spectra (T s and T p ). The light source of the spectrophotometer was equipped with a rotating polarizer, facilitating TE and TM polarization of the measurement beam. The measurement wavelength range was from 19 nm to 1 nm, with in one nanometer intervals. n general, the described method can be used to analyze any combination of polarized and unpolarized reflectance and transmittance spectra. n fact, before this study, the measurement of polarized transmittance spectra were not particularly instrumental in the characterization of small-pitch gratings, since the RCWA technique for the analysis of the measured data was not yet developed. Therefore, in the past, only reflectance spectra were used for the determination on the critical dimensions in small-pitch gratings, and the transmittance spectra were used strictly for the characterization of the optical properties of the materials used in the film structure. Addition of a transmittance spectrophotometer was originally intended to facilitate extra raw data, which helps to constrain the calculation model and provide more stable and accurate results. t turned out, however, that transmittance spectra do not only carry additional information about the structure, but are in general more useful in providing highresolution, high-sensitivity CD measurement, compared to the reflectance spectra. After the raw data is collected, all four spectra are simultaneously analysed using the Forouhi-Bloomer dispersion relations, in conjunction with RCWA, to extract the values of n and, film thicness, and trench dimensions. The analysis model generates calculated reflectance and transmittance spectra using the nominal parameters, and then optimizes the values, using nonlinear regression analysis in order to obtain the best match between the measured and calculated spectra. Each parameter in the model can be either varied or fixed at a nown value. The following figure depicts a typical fit between four measured spectra and four calculated spectra, generated by the analysis software. Proc. of SPE Vol
6 Rs & Rp / Ts & Tp (%) Rs-exp Rs-cal Rp-exp Rp-cal Ts-exp Ts-cal Tp-exp Tp-cal Wavelength (nm) Figure 3: Typical fit between four measured spectra (R s -exp, R p -exp, T s -exp, T p -exp) and their calculated counterparts (R s -cal, R p -cal, T s -cal, T p -cal). Generally, it is not practical to vary the optical properties of the films present in the grating structure. n most cases n and of the films can be obtained by collecting the measurements on the blanet areas of the sample. The determined optical properties then can be used in the model for the trench structure, reducing the number of variables in the model. Typically, in the case of the chromium, photoresist, and the phase shift materials (MoSi), the n and spectra are premeasured from the uniform area and then fixed during the CD measurement. V. APPLCATON TO THE MEASUREMENT OF AC PHOTOMASKS n the current study, the method described above was used to measure the CD linearity on an AC (After Cleaning nspection) photomas. A typical AC structure consists of a single patterned MoSi layer deposited on a fused silica substrate (see the figure below). Figure 4: Typical AC trench structure. During the etching process, the substrate is usually slightly overetched into (~3A). The parameter of interest at this stage of the process is the width of MoSi lines in the trench pattern. However, in the process of measurement, other parameters, such as n and of the substrate and the MoSi layer, and trench depth are also determined. Furthermore, if desired, the method can be used to determine a detailed profile of the periodic grating structure. The following figure illustrates an example of such analysis applied to the characterization of the profile of the photoresist lines on chrome (AD structure). The cross section of the same grating structure obtained using SEM is displayed on the right. 3 5ir;L Figure 5: Typical AD trench profile obtained using the technique described above. Proc. of SPE Vol
7 For this particular study, an array of twenty-one grating structures was measured on an AC photomas. The pitch of the grating structure was 6 nm. The nominal line widths varied from 8 nm to 3 nm with -nanometer interval. The following figure depicts the schematic top view of the measured grating arrays. 8 nm 8 nm 84 nm 86 nm 88 nm 9 nm 9 nm 94 nm 96 nm 98 nm 3 nm 3 nm 34 nm 36 nm 38 nm 31 nm 31 nm 314 nm 316 nm 318 nm 3 nm Figure 6: Schematic top view of the measured trench structures. Each square pad is a mm mm grating array. The same structures were re-measured using a conventional CD-SEM. The following plot illustrates the correlation between the results obtained using the two techniques. CD Correlation Plot Line Width (CD-SEM) R = Line Width (n& Analyzer) Figure 7: Correlation of the line width values obtained using the optical technique and the CD-SEM. t is evident that the results obtained using the new transmittance RCWA technique exhibit excellent correlation with a conventional CD-SEM. The major advantage of the optical technique, however, is high throughput (several seconds per point) and versatility. Along with the line width, other parameters such as trench depth, optical properties of the MoSi and phase shift at 193 nm and 48 nm were obtained during the same measurement. Furthermore, due to the fact that the intensity of the transmitted measurement beam is about fives time higher than the intensity of the reflected measurement beam, the improved signal-to-noise ratio guarantees a much better repeatability of the results. The following table illustrates a typical improvement in the short-term load-unload repeatability of the AS and binary Cron-Quartz mass. Proc. of SPE Vol
8 1X Short Term Load-Unload Repeatability (3σ) Measurement Mode AS Cr on Quartz Polarized Reflectance 1.1 nm.9 nm Polarized Transmittance.5 nm.1 nm Figure 8: mprovement in the repeatability of the CD measurement due to the use of transmittance spectra. Evidently, the repeatability of the measured CD values improves due to the inclusion of the higher-intensity transmittance spectra in the analysis. V. SUMMARY For the first time Rigorous Coupled Wave Analysis (RCWA) has been applied to the analysis of the transmittance spectra for the determination of critical dimension (CD) of phase-shift photomass. A spectrophotometer-based instrument (n& R-T Scatterometer), capable of collecting four continuous spectra during one measurement two polarized reflectance spectra (R s and R p ) and two polarized transmittance spectra (T s and T p ) was used for the measurement of the 6 nm pitch gratings on an AC mas. The light source of the spectrophotometer was equipped with a rotating polarizer, facilitating TE and TM polarization of the measurement beam. The measurement wavelength range was from 19 nm to 1 nm, in one nanometer intervals. The use of transmittance spectra proved to be instrumental in improving the sensitivity of the measurement to minor (sub-nanometer) changes in the width of the trench. The linearity study using a new technique demonstrated an excellent correlation with a conventional CD-SEM measurements and an improved repeatability, compared to the traditional reflectance-only measurement. The advantages of the optical method are high throughput, non-destructive nature of the measurements and capability to measure a wider variety of structures pertinent to the photomas manufacturing process. Acnowledgements We would lie to than Dr. Yo-Han Choi and Dr. Kyoung-Yoon Bang of Samsung Electronics, Korea, for providing the samples and CD-SEM results for the study. We would also lie to than Dr. Rahim Forouhi and Dr. George Li of n& Technology for supervising the measurements and the analysis of the samples. Proc. of SPE Vol
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