Rigorous Electromagnetic Field Simulation of Two-Beam Interference Exposures for the Exploration of Double Patterning and Double Exposure Scenarios Andreas Erdmann1,a, Peter Evanschitzky1, Tim Fühner1, Thomas Schnattinger1, Cheng-Bai Xu2, and Chuck Szmanda2 1
Fraunhofer Institute of Integrated Systems and Device Technology (FhG IISB), Schottkystrasse 10, 91058 Erlangen, Germany, 2 Rohm and Haas Company, 455 Forest Street, Marlborough, MA 01752, USA ABSTRACT
The introduction of double patterning and double exposure technologies, especially in combination with hyper NA, increases the importance of wafer topography phenomena. Rigorous electromagnetic field (EMF) simulations of two beam interference exposures over non-planar wafers are used to explore the impact of the hardmask material and pattern on resulting linewidths and swing curves after the second lithography step. Moreover, the impact of the optical material contrast between the frozen and unfrozen resist in a pattern freezing process and the effect of a reversible contrast enhancement layer on the superposition of two subsequent lithographic exposures are simulated. The described simulation approaches can be used for the optimization of wafer stack configurations for double patterning and to identify appropriate optical material properties for alternative double patterning and double exposure techniques. Keywords: Double patterning and exposure, lithography simulation, wafer topography, BARC, hardmask
1. INTRODUCTION As optical lithography is pushed deeper into the sub-wavelength regime, the accurate modeling of light scattering from small features becomes increasingly important. Rigorous electromagnetic field (EMF) modeling of the light diffraction from the mask is used to investigate the impact of the mask topography and absorber stack material on process windows, through-pitch characteristics, polarization sensitivity, defect printability, and other lithographic process criteria [1]. It is common consensus that relevant EMF effects – so called mask topography effects – have to be taken into account in optical proximity correction (OPC) for the design of the mask [2]. Due to the demagnification, features on the wafer are smaller than on the mask. The exposure over patterned wafers can result in wafer topography effects such as reflective notching [3], resist footing [4], reduced efficiency of the bottom antireflective coating (BARC), and other exposure artifacts [5]. Nevertheless, the rigorous EMF modeling of light diffraction from topographic features on the wafer has attracted only little interest compared to the EMF mask modeling. The application of a BARC reduces the impact of light scattering from wafer features on lithographic exposures. Moreover, the “straightforward” application of EMF-solvers for wafer exposures is time and memory consuming [3]. Compared to the mask, the wafer is illuminated with light arriving from a considerably larger range of incidence angles. To model the partial coherence of the light and the light induced decomposition of photo acid generators (PAG), the resulting electromagnetic field components for many source points have to be stored and superposed on a fine equidistant mesh. RENFT [5] and other approaches were developed to reduce the numerical effort of rigorous EMF wafer simulations. In the hyper NA imaging regime, however, the validity of these approaches is at least questionable. The introduction of double patterning and double exposure techniques, especially in combination with hyper NA, increases the severity of wafer topography phenomena. The second lithographic exposure step in the standard dual line or dual space double patterning process is done with a patterned hardmask [6-9]. How does this hardmask pattern impact a
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[email protected] Optical Microlithography XXI, edited by Harry J. Levinson, Mircea V. Dusa, Proc. of SPIE Vol. 6924, 692452, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.772741
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the efficiency of the BARC? The resist freezing process relies on a “chemical contrast” between the frozen photoinsensitive resist feature which is created in the first lithography step and the subsequently spin-on photosensitive resist for the second lithography step [7-9]. Alignment for the second lithography step also requires an appropriate optical material contrast (different refractive indices and extinction coefficients) between the frozen and the unfrozen resist. How does this optical material contrast impact the second lithographic exposure? Double exposure schemes such as reversible contrast enhancement layers (RCEL) rely on the optical nonlinearity of photosensitive materials [9]. Which amount of nonlinearity is necessary to create a sufficient intensity contrast inside the resist? In this paper, we are using simple two beam interference exposures to explore the above questions. This approach can be considered as an equivalent of the mask diffraction analysis (or mask scatterometry) which was used to explore mask topography effects [1, 10]. Mask diffraction analysis is used to investigate the impact of the mask geometry and absorber materials on the intensity, phase, and polarization of the diffracted light, which is important for the resulting lithographic image. Here we are using simplified exposure geometries to investigate the impact of the wafer topography on the forward and backward scattered light and on resulting linewidths and swing effects in various double patterning/exposure scenarios. The paper starts with a brief description of the simulation procedure and a summary of important model parameters. Section 3 discusses relevant phenomena for the standard double patterning process. Especially the impact of the hardmask material and pattern on the linewidth after the second lithography step is investigated. Swing amplitudes for planar and patterned hardmask are analyzed to identify improved wafer stack configurations. The following section investigates the influence of the optical material contrast between frozen and unfrozen resist in a freezing technology. Simulations of double exposures using RCEL are presented in section 5. The paper concludes with a summary and an outlook on future work.
2. SIMULATION PROCEDURE AND MODEL PARAMETERS Double patterning and double exposure techniques will be employed for the aggressive reduction of half-pitches. In this situation, the image formation results from the interference of the zero and one first diffraction order only. Based on this assumption, we investigate the wafer topography for simple two beam interference scenarios. Figure 1 shows the basic setup that was used for all simulations in this paper.
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Figure 1: Schematic setup of the simulations in this paper. The following parameters are used to describe the wafer topography: dresist – resist thickness dBARC – BARC thickness dHM – hardmask thickess wHM – hardmask linewidth 2·p – pitch of hardmask lines (double of target pitch p)
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Two TE-polarized plane waves with an identical intensity are emerging from the exit pupil of the projection lens. They create a sinusoidal interference pattern in the immersion liquid (water) between the last element of the projection lens and the wafer stack. The propagation directions of the plane waves are adjusted to create an interference pattern with a pitch of 128nm. This corresponds to a target half-pitch of 32nm after the full double patterning/exposure process. The photoresist with a thickness dresist is spin-coated on the top of a bottom antireflective coating (BARC). The BARC layer
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with a thickness dBARC is deposited over a hardmask (HM) with a thickness dHM. This HM was patterned in a first lithography step. The hardmask pattern consist of lines and spaces with the linewidth wHM and a pitch 2·p which is the twice the target pitch p. For the purpose of this paper, a planar deposition of the BARC is assumed. However, the models described in the following paragraphs are not restricted to such planar deposition of BARC layers. The material below the hardmask is poly-Si. The optical constants (n and k) were taken from the RIT-Web-page [12]. The propagation of the two plane waves inside the waferstack is simulated with the finite-difference time-domain (FDTD) algorithm. Coherent superposition of the resulting electromagnetic field produces an intensity distribution – see Figure 2 for example. The intensity distribution is coupled to a standard model of a chemically amplified resist. Typical modeling parameters of a Rohm and Haas 193nm immersion resist are used for all simulations in this paper. The exposure dose was calibrated to produce resist lines with a linewidth of approximately 40nm. That takes the etch bias between the resist linewidth and the final target feature inside the hardmask/Poly-Si into account. All simulations were performed with the Fraunhofer IISB development and research lithography simulator Dr.LiTHO [13]. Compared to a “real world situation,” the described simulation approach simplifies the modeling of the mask and of the real illuminator shape. The mask is assumed to produce perfectly balanced zero and first diffraction orders. Such balanced diffraction orders produce the maximum contrast. Therefore, this situation can be considered as a mask which is obtained by a “perfect” optical proximity correction. The finite extension of the source will result in additional (nonsymmetric) two beam interferences which contribute to the image formation. As a consequence of the upper approaches, our model will not describe defocus effects and details of the variation of the scattering effects due to small variations of the incidence directions of the plane waves. However, we can expect our model to predict the dominating effects of the wafer topography induced line scattering on the dose, linewidth and placement of features. A fully rigorous model of wafer topography induced scattering requires the simulation and superposition of light scattering effects for many directions of plane waves emerging from the exit pupil of the lens [4]. Such a modeling approach is very time and memory consuming – with typical computing times between several minutes and hours on a standard PC, whereas our simplified model only requires rigorous EMF simulation for two incidence directions. This reduces simulation run times two a few seconds, facilitating extensive parameter studies and optimizations as shown in this paper.
3. STANDARD DOUBLE PATTERNING PROCESS In this section we investigate the impact of the light scattering from the patterned hardmask on the resist linewidth (CD) and its variation with resist thickness, the so called CD-swing. The hardmask pattern was created in a first lithographyetch sequence. 3.1 IMPACT OF HARDMASK PATTERN ON THE PROCESS Figure 2 compares simulated intensity distributions for a lithographic exposure over a planar (unpatterned) and for a patterned 30nm thick TiN hardmask. The thickness of the BARC layer (38nm) was optimized in order to produce a minimum standing wave effect for the planer hardmask. Such an optimization can easily be done following the standard thin film theory [14, 15]. According to Figure 2, the etched spaces in the hardmask reduce the efficiency of the BARC. Compared to the planar hardmask, more light is reflected from the bottom of the resist. Moreover, the hardmask scatters light towards the nominally dark regions of the resist. Both effects contribute to a smaller linewidth (CD) after the second lithography step compared to the linewidth after the first lithography step over a planar BARC. This impact of hardmask patterning was already observed by Robertson et al. [11]. Similar plots for hardmask materials reveal that high refractive index HM materials attract the light and reduce the light intensity in the resist. Therefore, in certain situations also larger linewidths after the second lithography step can be observed. The magnitude of the described effects depends on the optical and geometrical properties of the hardmask and the BARC.
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Figure 2: Wafer topographies and simulated intensity distributions for lithographic exposures over planar (upper row) and patterned (lower row) hardmask. Exposure conditions: target (after etch): 32nm, illumination: λ=193nm, ideal dipole, TEpolarized, mask: pitch=128nm, projector: NA=0.93i, stack: TiN-hardmask, d =30nm, d =38nm.
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Figure 3: Simulated variation of the resist linewidth (CD) against hardmask feature size wHM for different hardmask materials. Simulation setup according to Figure 1, resist thickness dresist=120nm. The thickness of the BARC was optimized to produce minimum swing behaviour for the unpatterned HM with a given thickness. SiO2: dHM=40nm, dBARC=63nm, TiN: dHM=30nm, dBARC=38nm, Si3O4: dHM=40nm, dBARC=40nm, Carbon: dHM=30nm, dBARC=75nm. Exposure parameters as specified in Figure 2.
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Figure 3 shows the simulated resist CD after the second lithography step against the feature size wHM of the hardmask. Values of wHM=0nm and wHM=128nm specify the configurations without and with an unpatterned hardmask, respectively. According to their optical properties the hardmask materials show pronounced differences in their characteristic behavior. The carbon hardmask shows the lowest sensitivity of the resist CD regarding hardmask patterns. For SiO2 and TiN an increasing CD with the hardmask feature size can be observed. The Si3N4 hardmask produces the largest CD for a hardmask feature size of about 35nm. Larger and smaller HM feature sizes result in smaller resist CDs. In real processes, the feature size of the hardmask will vary due to process fluctuations. Taking into account the etch bias between the hardmask and the substrate material, the target feature size of the hardmask will be several nanometers above the target feature size in poly-Si. Because of these two restrictions, we can typically expect hardmask feature sizes between 30 and 40nm. Compared to the other hardmask materials, both carbon and Si3N4 show a lower sensitivity of the CD to wHM in the relevant range. Figure 4 shows CD swing curves for different combinations of hardmask materials and wafer geometries. The BARC thickness is always optimized in order to produce a minimum swing effect for the planar/unpatterned hardmask. This swing effect refers to the sinusoidal modulation of the CD as a function of the resist thickness. The BARC thickness is not optimized for the waferstack without hardmask. The backreflection of light from the wafer to the resist increases the deposited dose inside the resist and results in a smaller CD. Moreover, the resist thickness dependence of the reflected light results in a more pronounced swing effect. The impact of the hardmask pattern on the CD data depends on the optical properties of the hardmask and of the BARC. The largest CD values are always obtained with an unpatterned hardmask, the smallest CD values for a process without any hardmask. The CD of the patterned hardmask is in-between that one of the other hardmask configurations. In all cases, a more pronounced CD-variation or swing effect of the pat-
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terned hardmask, in comparison to the unpatterned hardmask, can be seen. In other words: The hardmask reduces the efficiency of the BARC.
Figure 4: Simulated variation of the resist linewidth (CD) versus the resist thickness for different hardmask materials and wafer topographies (see Figure 1). Unpatterned hardmask – dashed line: wHM=2·p=128nm, patterned HM – solid line: wHM=32nm, without HM – dotted line: wHM=0nm. BARC and hardmask thickness values as given in Figure 3. 3.2 SWING AMPLITUDES AND CD SWINGS FOR PLANAR AND PATTERNED HARDMASKS In all previous simulation examples the BARC thickness was optimized to produce a low CD sensitivity to the resist thickness (swing amplitude) for the geometry of the unpatterned hardmask. For waferstacks with planar layers the optimum BARC thickness can be determined with standard thin film theory [14, 15]. Here we will generalize the optimization method for non-planar, patterned waferstacks. This enables the identification of optimum geometries and optical properties of BARCs for patterned hardmasks. For a planar wafer stack the amplitude A of the CD-swings can be computed with the well-known Brunner formula [16]: (1) A = R top ⋅ R bot ⋅ a res where Rtop and Rbot specify the reflectivity at the top and bottom of the resist, respectively. ares is the relative amount of energy which is absorbed inside the resist. For planar waferstacks, all values on the right of equation (1) can be computed with standard thin film methods. It is important to specify the direction and polarization of the incident plane wave according to the imaging conditions. This situation changes for a non-planar waferstack. According to the results in the previous section, the patterning of the hardmask modifies the reflectivity. Therefore, the bottom reflectivity has to be computed with a rigorous EMF solver. In our case, we compute Rbot with the Waveguide Method. The CD variations due to a modification of Rtop and ares by the wafer topography are comparatively small. Therefore, these values are computed with standard thin film methods for the unpatterned hardmask.
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Figure 5: Simulated swing amplitudes A for the unpatterned/planar and for the patterned hardmask, respecively, versus resist thickness dres and BARC thickness dBARC. Wafer geometry and exposure parameters according to Figures 1 and 2. Hardmask: TiN, dHM=30nm.
Figure 5 shows computed swing amplitudes versus BARC and resist thickness for an unpatterned and patterned 30nm thick TiN hardmask, respectively. For the unpatterned hardmask a pronounced minimum of A at a BARC thickness of 38nm can be seen. The position of this minimum is almost insensitive to the resist thickness. That results in a small CDswing of the unpatterned hardmask – see Figure 4. According the right of Figure 5, this minimum of A almost vanishes for the patterned hardmask. The CD-swing becomes more distinct. This can be also seen in Figure 4. Similar observations regarding the correlation of swing amplitudes (Figure 5) and CD-swings (Figure 4) can also be observed for other hardmask materials and patterns. As discussed above, the dominating effect of the hardmask patterning is the modification of Rbot. Figure 6 shows computed values of Rbot versus BARC and hardmask thickness for patterned / unpatterned hardmasks and for various materials. For all analyzed materials except carbon, a pronounced difference between the patterned and the unpatterned hardmask can be seen. This correlates with the observations from Figure 4. The results shown in Figures 4 and 5 and other parameter variation studies can be used to determine optimum combinations of hardmask and BARC thickness to produce mimimum CD-swings. In the next subsection, intensity plots and CD-swings for an optimized TiN hardmask / BARC combination will be shown.
Figure 6: Simulated bottom reflectivity Rbot for unpatterned (upper row) and patterned hardmasks versus hardmask thickness dHM and BARC thickness dBARC. Wafer geometry and exposure parameters according to Figures 1 and 2. 3.3 OPTIMIZATION OF WAFER STACK PARAMETERS The method described in the previous section enables the optimization of geometry and optical parameters to minimize the CD swing. For the TiN hardmask a combination of dHM=10nm and dBARC=30nm provides the best solution. The resulting intensity plots and CD-swing curves are shown in Figure 7. Compared to Figure 2, the intensity distribution of the patterned hardmask in the center of Figure 7 shows a significantly reduced standing wave effect. Moreover, the CD-swing is less pronounced than that shown in Figure 4. The optimum hardmask thickness of 10nm may be too small for fabrication. However, variation of the optical properties of the BARC can help to identify more appropriate conditions.
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According to the simulations in this section, the patterning of the hardmask increases the minimum bottom reflectivity and shifts the position of the optimum BARC and hardmask thickness values. The magnitude of the effect depends on the hardmask material: TiN shows the most pronounced effect, amorphous carbon the weakest, SiO2 and Si3N4 are inbetween. The generalized method for the evaluation of the Brunner formula for swing amplitudes in combination with global optimization techniques can be used to find ideal wafer stacks for the second litho step. The method can also be extended to more complex illumination conditions, mask layouts, and for the optimization of two-dimensional swingcurves which take process induced global variation of resist and BARC thickness into account [17].
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Figure 7: Simulated intensity distributions and CD-swing for the optimized TiN hardmask configuration. Left: intensity distribution for the unpatterned hardmask, center: intensity distribution for the patterned hardmask, right: CD-swing. dHM=10nm, dBARC=30nm, unpatterned hardmask – dashed line, patterned hardmask – solid line, without hardmask – dotted line, all other simulation settings and parameters as given in Figures 2 and 4, respectively.
4. RESIST FREEZING This section investigates potential wafer topography effects in a resist freezing process. Such resist freezing processes reduce the process complexity by subsequent lithographic processes over the identical wafer stack. A chemical modification of the resist pattern after the first lithography step is used to make this (frozen) resist insensitive to a second lithography step using a second deposited photoresist [7]. Proper alignment for the second lithography step may require an optical material contrast (different refractive index n and/or extinction k) between the frozen and the unfrozen resist. Figure 8 shows the corresponding wafer geometry and simulated intensity distributions for different optical properties of the frozen and the unfrozen resist, respectively. The large differences ∆n and ∆k between the optical parameters of the frozen and unfrozen resist in Figure 8 were chosen to illustrate the resulting effects. Compared to the intensity distribution in the center of the upper row of Figure 8 all modifications of the optical properties of the frozen resist show a more or less pronounced impact on the resulting intensity distribution. A higher refractive index in the frozen resist attracts the light and reduces the intensity in the unfrozen resist. Therefore, we can expect a larger resist linewidth after the second lithography step. The refractive index configuration ∆n
