OPTICAL LITHOGRAPHY INTO THE MILLENNIUM: SENSITIVITY TO ABERRATIONS, VIBRATION AND POLARIZATION

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1 OPTICAL LITHOGRAPHY INTO THE MILLENNIUM: SENSITIVITY TO ABERRATIONS, VIBRATION AND POLARIZATION Donis G. Flagello a, Jan Mulkens b, and Christian Wagner c a ASML, 8555 S. River Parkway, Tempe, AZ 858, USA b ASML, de Run 111, 553 LA Veldhoven, The Netherlands c Carl Zeiss, D-7366 Oberkochen, Germany This paper was first presented at SPIE The 5th Annual International Symposium on Microlithography February 7-March 3, Santa Clara, CA, U.S.A.

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3 OPTICAL LITHOGRAPHY INTO THE MILLENNIUM: SENSITIVITY TO ABERRATIONS, VIBRATION AND POLARIZATION Donis G. Flagello a, Jan Mulkens b, and Christian Wagner c a ASML, 8555 S. River Parkway, Tempe, AZ 858, USA b ASML, de Run 111, 553 LA Veldhoven, The Netherlands c Carl Zeiss, D-7366 Oberkochen, Germany ABSTRACT Various factors, such as lens aberrations, system vibration and the choice of illumination polarization can degrade the level of modulation, and hence, image quality. This paper discusses the sensitivity of multiple feature types to these factors. It is shown that aberration sensitivity increases linearly with decreasing resolution, scaled to the Rayleigh criteria. An analysis of the vibration tolerance is done for transverse and axial vibration planes, where the effects on the process window and CD uniformity are measured. The vibration is shown to decrease the process window greater for low contrast images and is shown to scale directly with the resolution. The new millennium will usher in optical systems with very high NA lenses (>.75 NA) for 8 nm, 193 nm and 157 nm. This paper re-examines the role of the polarization on required specifications of the exposure tool optics. It is found that tight polarization specifications with <1% residual polarization will be needed for future systems. 1. INTRODUCTION The next decade, within the new millennium, will likely see the extension of optical lithography down to 5 nm resolution for isolated gates and possibly periodic structures. This may be accomplished using NA >.75, wavelengths down to 157 nm and a plethora of techniques such as phase shift masks, nonconventional illumination and advanced photoresist processes. The success of manufacturing processes at these sub-wavelength resolutions will rely on the ability either to print low modulation images or the ability to increase the image modulation to a level that will give acceptable lithographic yield. Typically the industry has used the Rayleigh criterion to judge the resolution and depth of focus capability of a process. These equations, given by Resolution λ λ = k and DOF = k NA NA (1) have their basis in fundamental imaging equations and allow the process difficulty level to be described by the constant k 1. Image modulation is best described by contrast or the logarithm of the aerial image slope in the vicinity of the feature edge (also called the log-slope). The contrast is defined by Contrast I max I min = I max + I min () where the image irradiance I is a function of position in the image field. Previously, a contrast level for viable manufacturing would have limited the working contrast and modulation levels to 6% through focus. This is roughly comparable to the Rayleigh criterion of k 1 >.5. However, within the past few years, there has been a tremendous advance of photoresist, reticle and lens technology, which has resulted in so-called image enhancement. The consequence of this is successful lithographic printing of features that would have produced contrast levels of well below 6%. The future of lithography shows that this trend will continue unabated until there is very little working modulation. Figure 1 shows evidence of this by plotting NA, k 1 and contrast as a function of the year and resolution. This is based on the 1999 ITRS projections for the DRAM resolution introduction into manufacturing. The contrast numbers are based on an aerial image simulation of periodic lines with a 5% duty cycle and a partial coherence of σ=.7. The authors have made some assumptions concerning NA and wavelength based on industry tendencies and expectations. Ideally, one would not want the k 1 or contrast to continually decrease since this implies more difficult processes. As can be seen, the decrease in wavelength and increase in NA only temporarily mitigates the loss of contrast. The minimum k 1 keeps dropping until the introduction of EUV technology. To create an aerial image modulation at low levels will either require low lens aberration levels and high contrast photoresist processes or fundamental change in wavelength technology when the image is no longer viable. 1

4 metric i-line DUV 139nm 157nm EUV '97 '99 '1 '3 '5 '7 '9 ' Figure 1 NA k 1 contrast '13 year CD[nm Expected NA, k 1 and contrast as a function of time. Based on the DRAM resolution targets of the 1999 SIA roadmap. Contrast is simulated for a periodic array with 5% duty cycle and a partial coherence of σ=.7. At low k 1 (<.5), one or more image enhancement technologies will be needed to sustain the image through focus. A partial list of these technologies would consists of phase shift masks, advanced optical proximity correction, advanced photoresists, pupil filtering, double exposures and exotic illumination. At k 1 <. the modulation of the image will be extremely sensitive to a multitude of parameters. Various factors, such as lens aberrations, system vibration and the choice of illumination polarization will degrade the level of modulation, and hence, image quality. Wagner [1] gives a detailed discussion of the technology needed to achieve working lithography in these regimes. The work presented here will discuss the sensitivity of multiple feature types to various imaging detractors using simulation analysis. The stability of the photoresist image in the presence of lens aberrations will be reviewed, and the effects on feature types will be examined using binary and phase-shifted masks with varying degrees of lens pupil filling. The resultant metrics will be CD performance by Monte Carlo and pattern shift. An analysis of the vibration tolerance for the transverse and axial vibration planes is also done by observing the decrease in the overall process window as resolution and vibration are increased. Finally, the millennium will usher in optical systems with very high NA lenses (>.75 NA) for 8 nm, 193 nm and 157 nm. This necessitates a re-examination of the polarization requirements, especially for low-k 1 lithography. We will review the polarization effects with emphasis on required specifications of the exposure tool optics. I-153.ILL. SCALING AND IMAGING Understanding the sensitivity of imaging metrics to various factors is facilitated by an examination of the partial coherent imaging equations written in terms of a linear systems approach. [] This is given by,, I ( rz ; ) (3) s ρ J ρ = d ( ) FT Õ( ρ ρ )P ( ρ)f ( ρ; z)h( ρ; Z ) i i i where the image, I, in a given film such as photoresist, is a function of position, r and specific for a given focus position z. This equation is valid for all NAs and the image is the summation of overall polarization states, i. The integral is over the source distribution, defined by J. Of interest to us in this work is the Fourier term within brackets. This represents the electric field distribution at the exit pupil. We note that the terms are the object spectrum of the reticle pattern, a polarization function, a film function and a pupil function given by, H( ρ; z ) = A ρ ( )e ik z γ e ik W ( ρ) γinput γ where A is the amplitude distribution, W describes the wavefront aberrations, and γ input and γ are direction cosines at the entrance and exit pupils. The terms can be considered approximately separable, allowing a general independent analysis of the effects. The ability to scale the various imaging effects in lithography has the advantage that we can determine cause and effect relationships at a specific set of parametric conditions, either by experimentation or simulation, and predict the effect by scaling at another set of conditions. Perhaps the most common scaling rule in lithography is the Rayleigh equations in (1). The resolution can be scaled in units of k 1 or NA/λ, while the DoF is scaled in units of NA /λ. Although an earlier work [3] has shown that these expressions are not exact for aerial images at very high NA, they still provide a reasonable approximation for examining general properties considering partial coherent illumination. The image scaling for resolution is a good approximation for aerial images for NA<.9 and close to exact for TE polarization. The DoF actually scales with a cosine function; hence the breakdown occurs due to a high NA simplification and not polarization considerations; however, it still provides a valid nd order approximation for NA<.85. If we consider the pupil filling of the lens by the object spectrum and the source, the resolution scaling does produce an exact, normalized angular relationship. ()

5 Figure Isolated lines with varying levels of aberration and scaled resolution. At k 1 -., there is catastrophic failure such that most aberration levels destroy the lithographic image. Therefore, for a given value of resolution in terms of k 1, the object spectrum convolved with the source always has the same distribution within the lens pupil. Each scaled resolution will also have approximately the same contrast. For example, consider cases with different wavelengths: 1) λ=193 nm with NA=.75 and dense line width=1 nm, and ) λ=157 nm with NA=.8 and dense linewidth=1 nm. Both of these cases will have a contrast. with the same relative pupil distribution when the partial coherence has a value of σ=.7. Figure illustrates this with 3 different views of a lens pupil with varying scaled resolutions of a periodic object with 5% duty cycle. The k 1 defines the position of the orders in the pupil, while the main effect of lowering k 1 is to proportionately lower the resolution and also lower the contrast. Aberrations directly affect the pupil function by equation (3) and (), with the secondary impact being on the aerial image and contrast. Therefore, aberrations will scale with the proportion of the pupil being used or with k 1. On the other hand, vibrations generally occur outside of the imaging lens and do not directly enter the image equation. We would expect that vibrations would somehow scale with the size of the aerial image. The expectation is that the transverse vibration should scale with the resolution, while the axial vibration should scale with the DoF. This implies that the axial vibration would also be sensitive, indirectly, to the value of the NA and the lens pupil filling. Finally the effects of polarization and high NA are analyzed by observing the terms in the full imaging equation. The film function and the polarization function in equation (3) have the strongest influence on the resultant image. The effects with the polarization term tend to scale with the cosine of the angle; however, partial coherence and varying film stacks complicate any simple scaling. The approach here will be to use a vector simulation and vary the NA but keep the k 1 constant and the photoresist thickness to.5 λ/na, maintaining a constant pupil distribution for NA comparisons. 3. STUDY I: ABERRATION EFFECTS This study looks at the impact that aberrations have on imaging as scaled resolution is decreased using a Monte Carlo technique. [] The metrics of interest are change in CD from an aberration free reference and 3

6 image shift from an aberration free reference. The various cases that are examined are listed in Table 1. Dense lines (5% duty cycle), isolated lines and an end-of-line feature are simulated. The method of analysis uses an approach whereby 5 random combinations of Zernike aberrations are created to provide wavefront RMS values that range from λ to.8λ. Each combination is fed into a commercial lithography simulator (e.g., Solid-C from Sigma-C or Prolith from Finle Technologies) and a measurement of the photoresist linewidth and average photoresist pattern shift is output. This is done for each scaled resolution of interest. Additional parameters are listed in Table. A full photoresist model is used that has been calibrated to an in-house DUV process. To minimize extreme photoresist effects such as standing waves, a generic film stack was created using a matched substrate. Figure 3 and Figure shows an example output from the CD simulation for dense and isolated lines, and Figure 5 shows an example plot of the image shift data. This data has been normalized to the CD and image shift for RMS=. The CD data generally shows greater CD changes with decreasing scaled resolution, while the image shift data shows only slightly higher sensitivity. The CD data is consistent with the fact that a lower k 1 with a given process stresses the outer areas of the lens pupil, increasing sensitivity to aberrations. Also, the dense lines have a linewidth that increases with aberration level while the isolated lines decrease. This is due to the fact that various processes and features may have iso-focal regions, or perhaps more correct iso-aberrational regions close to the target CD value. [5] Isolated lines tend to have a quadratic functionality of CD though focus such that their iso-aberrational region is far above the target CD. Therefore, aberrations decrease their line width. The dense lines may have this region very close to the target CD, as is the case here, where the image shift data shows a linear behavior for the maximum effect. Table 1 Case studies describing the features and resolution of interest Case Feature/Reticle type Resolution (k 1 range) Dense lines, binary reticle Dense lines, 6% attenuated PSM Dense lines, alternating PSM Isolated lines, binary reticle Isolated lines, alternating PSM Isolated lines, alternating PSM end-of-line structure (EOL), binary reticle (measured as space between the end of lines) Partial Coherence, σ Table.. Simulation parameters Parameter Numerical aperture, NA wavelength, l 8 nm Photoresist index n= i Substrate index n= i Photoresist film thickness, λ/na.688 µm Exposure and Focus Value.6 Centered for each case and resolution

7 Figure 3 Photoresist line shift or dense lines, normalized to aberration case. We can further reduce the data by fitting by defining the maximum change as a function of RMS. This is given by the average plus the mean absolute deviation (MAD) corrected for the average. Figure 6 shows an example of this as a surface that is a function of scaled resolution and wavefront RMS for the dense line case. Once reasonable functions are obtained, an comparison of all cases can be made by defining a target or specification. For a CD change, it seems reasonable to allow up to 5% CD change due to the maximum lens aberration. For the pattern shift, a rule of thumb is usually defined as 1% of the target resolution. Once the RMS aberration level is obtained pertaining to a specific target, aberration sensitivity is defined by taking the reciprocal of the RMS, resulting in sensitivity number with units of λ -1. This metric has the advantage of increasing with heightened aberration effect. Figure 7 shows this data, where the limiting feature for aberration sensitivity is the isolated PSM with respect to pattern shift. The EOL and isolated features show the highest sensitivity for CD change. The isolated PSM cases have the highest resolution and therefore show data at k 1 =.5 and.. The aberration RMS values with CD change have an approximate linear functionality on k 1, verifying our original hypothesis. However, the image shift only shows a linear behavior for the isolated case. The dense cases have a constant behavior with resolution. There are opposing factors that explain this phenomena with dense lines: 1) the image shift is proportional to the transverse aberration, and therefore, the sensitivity must decrease with increasing NA, where NA is defined by first diffraction orders of the dense lines, and ) the absolute resolution requires that the specification will be less as k 1 is lowered. The net effect is that the% change in pattern shift remains constant with scaled resolution for dense lines. The choice of illumination is a critical factor in any aberration sensitivity analysis. Case 5, the isolated PSM 5

8 resolution =.6 resolution =.5 resolution = contrast =.8 contrast =.7 contrast =. irradiance I-1533.ILL position Figure position -.. position Top row shows the pupil distributions for a given resolution in units of NA/ λ or k 1. The bottom row gives the respective irradiance, I, of the aerial image as a function of normalized position in units of k 1. feature, uses a small partial coherence that strongly influenced the aberration effects. Small increases in the illumination size quickly change the iso-aberrational region and influence the sensitivity of the feature type as evidenced by Case 6, where the partial coherence has been slightly increased. This small change resulted in slightly reducing the CD sensitivity to aberrations but greatly influencing the pattern shift sensitivity. There are also aberration combinations, even with high levels of RMS that will have effects much lower than the maximum CD change. Hence, Figure 7 and Figure 8 represent worst case examples and are not necessarily indicative of any one lens. Currently, Zeiss is improving the lens technology such that the maximum RMS level will be <.5λ for advanced step and scan systems.. STUDY II: VIBRATION EFFECTS Since vibrations have a direct impact on the aerial image, their effect in a lithographic system can be approximated by the convolution of the image given in equation (3) with a probability density function of the vibrations. [6] Hence, any aerial images with the same overall shape, contrast, and/or log-slope will behave in a similar fashion with vibration. For example, an image formed with phase masks will behave the same as an image made with conventional illumination if their aerial images were similar before vibration. Also, unlike lens aberrations, vibrations, especially on a scanning exposure system, do not often produce systematic intrafield CD errors, unless the non-correctable distortional lens errors are high (<15 nm). Their impact is to lower the process window and the CD uniformity, where the effects can be seen as field-to-field, wafer-to-wafer and tool-to-tool. In this work, we only consider Gaussian vibration, looking at both the transverse and axial vibration. Vibration is given in terms of the moving standard deviation (MSD), which is a common metric for the optical scanners. The analysis here considers a pupil filling using conventional illumination with a partial coherence of σ=.7. The hypothesis being that, as we lower the scaled resolution, the contrast levels of the 6

9 Figure 5 Dense lines with varying levels of aberration and scaled resolution for partial coherence σ=.7. There is no viable process to sustain the images beyond k 1 =.35. image decreases and the sensitivity to vibrations increase. Figure 8a shows this impact of transverse MSD on an isolated line by analyzing the log-slope of the aerial image. Figure 8b shows the same data but, now the vibration is normalized to the scaled resolution, all points plot approximately on the same curve, which implies that vibration scales inversely with resolution While aerial image studies provide invaluable image information, it is often difficult to extrapolate to a photoresist response. This is studied by analyzing the response of dense and isolated features to various levels of vibration using the parameter set of Cases 1 and in Table II. The simulation is done through a range of exposure and focus for transverse vibrations with MSD X = nm, nm, nm, and 8 nm and longitudinal or axial vibrations with MSD Z = nm, 5 nm, 5 nm, 1 nm, and nm. The simulation outputs exposure-defocus curves from which the exposure latitude (EL) and DoF can be extracted. Figure 9a and Figure 9b gives an example of these curves for the isolated line case at a scaled resolution of., where the area under the curves decreases with increasing MSD. Additionally, we note that Figure 9b shows the maximum DoF increasing with the highest axial MSD. This is the effect called focus drilling ; however, the overall process window does not improve due to a large loss in exposure latitude. The process window can be defined as the area under the EL vs. DoF curves, i.e., the process area (PA), approximated here by ( EL( DOF = ) DOF( EL = ) PA = (5) Figure 1a and Figure 1b shows this as a percent of the PA that is lost as the normalized MSD increases for both transverse and axial vibration. The normalization for the axial MSD is done using the Rayleigh approximation for DoF, i.e., λ/na, where the dense line NA is calculated from the positions of the ±1 diffraction orders, given by λ/pitch. The data shows an approximately linear functionality for process window; however, an estimate of CD uniformity shows that the 7

10 CD change [%] I-1536.ILL resolution.5 3 resolution RMS [mwaves] Figure 6 Dense line sensitivity to scaled resolution and wavefront aberration RMS. shift change [%] RMS [mwaves] aberration sensitivity res =.6 res =.5 res =. res =.35 res =.3 res =.5 res =. aberration sensitivity dense dense att. dense alt. isolated iso. alt.pc =.35 iso. alt.pc =.5 EOL dense dense att. I-1537.ILL dense alt. isolated iso. alt.pc =.35 iso. alt.pc =.5 Figure 7 (a) Sensitivity to RMS wavefront aberrations for the various features, where the reciprocal of the sensitivity is the RMS wavefront in wavelengths: (a) aberration sensitivity for a 5% CD change (b) aberration sensitivity for a 1% pattern shift. (b) 8

11 MSD x = MSD z = I-1539.ILL exposure latitude 1 MSD x = 8 nm exposure latitude 1 MSD x = nm DoF [µm] DoF [µm] (a) (b) Figure 8 Process window for an isolated line with a scaled resolution =.: (a) varying transverse MSD levels, and (b) varying axial MSD levels resolution=.5 resolution=. resolution= resolution=.5 resolution=. resolution=.35 I-1538.ILL 1 1 log-slope loss [%] log-slope loss [%] MSDx [nm] normalized MSDx [nm] (a) (b) Figure 9 The percentage change in the log-slope of an isolated line aerial image as a function of the transverse vibration: (a) the MSD in units of nm, and (b) the MSD normalized to the resolution functionality with MSD is only linear for normalized MSD below., as shown in Figure 11a and Figure 11b. The percentage CD uniformity was calculated by assuming a process with a total exposure variation of 6% and extracting the resultant CD range for best focus. The data is then normalized to MSD= to produce the results. Finally, we end this section with an estimate of a target specification for isolated lines. It is obvious from the data 9

12 8 isolated line dense line 16 isolated line dense line I-15.ILL process area loss [%] 6 process area loss [%] normalized MSDx normalized MSDz (a) (b) Figure 1 The change in the process area as function of the: (a) normalized transverse MSD, and (b) the normalized axial MSD CD uniformity change [%] isolated line dense line CD uniformity change [%] isolated line dense line I-151.ILL normalized MSDx normalized MSDz (a) (b) Figure 11 The percentage loss in the CD uniformity as a function of the: (a) normalized transverse MSD, and (b) the normalized axial MSD that the longitudinal vibration is less sensitive to change than the transverse vibration, but the isolated lines are more sensitive to longitudinal vibration than the dense lines. If we choose a PA<1%, we end up in the region of normalized MSD x =.1 or approximately 1% of the resolution, which would also give us a CD uniformity loss<1%. Our normalized longitudinal vibration would need to be MSD z =.18 or 18% of the Rayleigh DoF. For example, to determine vibration targets for a system with NA=.7, λ=8 nm and k 1 =., our CD would be 1 nm and DoF.5 µm. Our vibration targets should be MSD x <1 nm and MSD z <1 nm. 1

13 5. STUDY III: HIGH NA EFFECTS AND POLARIZATION The loss in DoF with high NA is well known according to equation (1) and will not be explored here. However, the polarization targets for high NA partially coherent systems have not been widely examined. According to equation (3), high NA imaging is intrinsically linked with the polarization state and the thin film structure, where the electric field coupling and the absorbed power by a photoresist film can be drastically altered. Therefore, from a manufacturer point of view, it is important to understand the extent of this effect, such that proper targets can be determined. Before looking at the influence of imaging, we examine the effect of polarization on the absorbed power due to incident plane waves on a photoresist film with a perfect absorbing substrate. The absorbed power in a photoresist film will be proportional to the exposure necessary to develop. Figure 1 gives the result of a simulation where the incident angles are given in units of NA and the absorbed power has been normalized to the unpolarized state. The orthogonal polarization states diverge extensively at higher NA up to a 5% power change. An imaging system would contain a multitude of incident angles, reducing this effect; however, alternating PSMs often require a small partial coherence which will restrict the total number of angles and could produce similar exposure changes. For this study, we examined imaging configurations to explore the effects. To obtain a valid comparative analysis, we restrict the pupil filling by the object to be identical for each NA that is examined. Hence, we the fix the k 1 =. and vary the NA and the feature size. Since the effects of the photoresist thickness on the DoF should also be minimized, the thickness is fixed to.5 λ/na. Table III gives the feature conditions, where the simulation is based on λ=8 nm. The results of the simulation are shown in Figure 13. The CD difference from a completely polarized state and the unpolarized state is plotted as a percentage of the unpolarized CD. Clearly, dense lines with an alternating PSM is the most critical feature. This is expected since the pupil configuration essentially produces -beam interference at the wafer level. This case will tend to maximize the polarization effects. If we target NA=.85 and wanted to limit the systematic CD error due to polarization to <3%, we would limit the residual polarization to 1% as shown in Figure 1. The simulation results also indicate that the level of pupil filling and partial coherence can lessen the polarization effects. This is evidenced by the small polarization influence on the features using conventional illumination. power change [%] TE polarization TM polarization I-15.ILL CD change [%] dense PSM isolated PSM dense isolated I-153.ILL Figure NA Power percentage change as a function of the incident angle in NA units. This is proportional to exposure change in resist for orthogonal polarization states NA Figure 13 CD percentage change from the completely polarized state to the unpolarized state as a function of NA. 11

14 Table 3 Simulation parameters for polarization study REFERENCES Case Feature/Reticle 1 Dense.7 Dense with alternating PSM.3 3 Isolated.7 Isolated with alternating PSM.3 CD change [%] polarized dense PSM 1% polarized dense PSM polarized dense 1% polarized dense Partial Coherence, σ I-15.ILL [1] C. Wagner et. al., Advanced technology for extending optical lithography, SPIE vol., () [] D. Flagello et. al., Theory of high-na imaging in homogeneous thin films, J. Opt. Soc. Am A 13, 53-6 (1996) [3] D. Flagello and A.E. Rosenbluth, Lithographic tolerances based on vector diffraction theory, J. Vac. Sci. Technol. B 1(6), (199) [] C. Progler and D. Wheeler, Optical lens specifications from the user s perspective, SPIE vol. 333, 56-68, (1998) [5] R. Schenker, Effects of phase masks on across field linewidth control, SPIE vol. 3679, 18-6, (1999) [6] J. Bischoff et. al., Simulations on step & scan optical lithography, SPIE vol. 197, , (199) 5 Figure NA Cd percentage change for the dense line cases showing fully polarized and 1% CD limits. 6. CONCLUSIONS Lithography into the new millennium will be challenging. Imaging using k 1 <.5 will be commonplace in manufacturing environments. This will require due diligence on all effects that stress the integrity of the aerial image and impact contrast. As we use more and more phase masks and imaging technology that will demand small coherence levels, we may have to deal with aberration specifications <.λ. This will necessitate newer metrology technologies for the lens manufacturer. Vibration effects have the potential to lower the overall process window as we drive the contrast and linewidths to smaller regimes. Finally, high NA polarization effects will result in extremely tight specifications on illumination polarization on future tools. This will influence the complexity of illuminators and lenses for high NA systems. 1

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