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Abstract
Vibrations of the reticle and wafer stage are inevitable due to the high speed and acceleration required during the exposure movement of the lithography system. Previous studies have shown that these vibrations have an impact on both overlay and imaging quality. Furthermore, as the integrated circuit industry continues to develop and extreme ultraviolet (EUV) lithography is increasingly utilized, the size of the exposure image continues to decrease, making the stability of the reticle and wafer stage motion increasingly important. This paper establishes a model of the reticle and wafer stage motion under the influence of vibration based on the advanced process node of EUV lithography. We investigate the relationship between variations in vibration amplitude and frequency and their effects on imaging contrast and line edge roughness (LER). Additionally, we simulate the quantitative relationship between the vibration of the reticle and wafer stage and the imaging quality of through-pitch line/space structures, tip-to-tip (T2T) structures, and tip-to-line (T2L) structures under extreme exposure conditions of EUV lithography using a computer.
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1. Introduction
The rapid development of integrated circuits is closely linked to the continuous upgrading of lithographic tools. The renewal of lithography tools is primarily driven by advancements in the wavelength of the exposure source, the projection system, and the wafer and reticle stages. For instance, the exposure source has evolved from the g-line (436 nm) using filtered Hg arc lamps to the i-line (365 nm) in the ultraviolet band, and then to excimer lasers KrF (248 nm) and ArF (193 nm) in the deep ultraviolet band. Currently, water immersion ArF lithography and the most advanced EUV lithography using extreme ultraviolet of 13.5 nm have also entered high-volume manufacturing. The exposure system in lithography tools has undergone three periods: contact printing, near-contact printing, and projection printing. Similarly, the wafer stage has been improved from a single stage to a more efficient dual stage [1–3].
The emergence of the EUV lithography system has significantly reduced the complexity of processes below the 7 nm node, but the system's structure is more precise and complex. It comprises several parts, such as a source that can generate EUV, an illumination system, a projection system, and a stage system [4]. The stage system consists of a reticle stage and a wafer stage. For increasingly fine lithography patterns, the stage system in the lithography tool must have extremely high acceleration, fast speed, and high accuracy. However, with the reduction of process nodes, the vibration of the stage during exposure has become one of the significant factors affecting imaging. Many researchers have invested in this area over the years. In 1994, Joerg et al. studied and classified the causes of contrast reduction in photolithography and proposed a method to estimate and compare mechanical vibrations using transfer functions. They established an analytical method for modeling spatial images with scanning interference and evaluated the effect of vibrations on contrast and process window (PW) parameters [5]. In 2000, Flagello et al. discussed the sensitivity of different mask structures to vibration, aberration, and polarization-induced image quality degradation. They investigated the impact of transverse and longitudinal vibrations on PW and critical dimension (CD) uniformity for different periodic line structures [6]. Later in 2002, Emmanuel et al. introduced asymmetric magnification and asymmetric rotation in the exposure process to simulate transverse vibrations. They experimentally studied the tolerance of 0.18 µm and 0.12 µm gate patterns to transverse vibrations during scanning on KrF and ArF lithography tools and further investigated the relationship between CD, energy latitude (EL), PW, and other imaging parameters of line structures with transverse vibrations at this node [7].
Currently, EUV lithography has also been put into mass production in advanced process nodes below 7 nm. As the line width continues to decrease, the vibration of the stage in the lithography system has an increasingly significant impact on the imaging quality [8]. In the following content of this paper, building on previous research progress, we provide a modeling analysis of the vibration of the reticle and wafer stage during the exposure movement of the lithography system. Additionally, we conduct experiments using a variety of test masks to investigate the influence of stage vibration on the imaging quality in the advanced process nodes of the EUV lithography system.
2. Modeling and analysis of vibration of lithographic tool stages
2.1 EUV lithography exposure principle
The EUV lithography system uses a total reflection light path because most materials have strong absorption for extreme ultraviolet light. The exposure schematic diagram is shown in Fig. 1, where during the exposure process, the reticle and wafer stages move synchronously at high speed according to a specific relationship [9]. The exposure process adopts a scan and step mode, where the wafer is divided into many exposure fields, and the exposure process in each area is completed by scanning. During the scanning process, the movement of the reticle and wafer stage can be divided into four steps: 1. acceleration step; 2. steady speed step; 3. uniform exposure step; and 4. deceleration step [10–12]. After the exposure of each field is completed, the reticle and wafer stages repeat the scanning process by stepping to the next exposure field, and the entire wafer is exposed by scan and step. During the exposure process, the reticle stage and the wafer stage need to maintain high-speed and high-acceleration movements, resulting in mechanical vibrations with different characteristics. It is, therefore, difficult to ensure that the alignment accuracy of the reticle stage and the wafer stage is in the nanometer order, which seriously affects the imaging quality and overlay of the lithography tool.
2.2 Descriptive parameters of stage vibration
The reticle stage and wafer stage are two relatively independent motion systems. However, during the exposure process, it is crucial to maintain a high degree of synchronous motion accuracy between the two stages. The synchronization performance of the wafer stage and reticle stage is described by their synchronization position deviation, and the freedom of movement required for synchronization performance is in the x, y, and z directions, respectively. To illustrate this, let's consider the X direction, where synchronization deviation can be defined as:
where ${x_w}$ represents the position of x on the wafer at time t, ${x_j}$ represents the position of x on the mask at time t.In the process of exposure, the synchronization error changes all the time. The moving average (MA) and moving standard deviation (MSD) of synchronization error are often used to describe the influence of reticle and wafer stage system on lithography imaging during exposure. Still taking the x direction as an example, the definitions of MA and MSD are as follows [13,14]:
During the exposure process, mechanical vibrations can cause synchronous errors between the reticle stage and the wafer stage. The complex vibrations in practical applications can be represented as a combination of simple sine functions through Fourier decomposition, so, we describe the synchronization error caused by the vibration using Eq. (4). And by analyzing Eqs. (2) and (3), we can derive the relationship between MA and MSD with respect to the amplitude a and vibration frequency ν of the wafer stage, as shown in Eqs. (5) and (6).
It is easy to obtain $\mathop {\lim }\limits_{\nu \to \infty } MA = 0$ and $\mathop {\lim }\limits_{\nu \to \infty } MSD = \frac{{\sqrt 2 }}{2}a$ from Eqs. (5) and (6). Therefore, high-frequency vibration has no effect on MA and MSD becomes a constant value that does not vary with frequency. Here we consider the motion parameters of the reticle and wafer stage, taking the scanning speed of the wafer stage as 500 mm/s, the width of the slit as 1.8 mm, and the vibration amplitude of the stage as 3 nm. The variation of MA and MSD with frequency is shown in Fig. 2. It can be seen that mainly low-frequency vibration causes changes in MA, while high-frequency vibration causes changes in MSD. The definition of high and low frequency is related to the scanning speed and the width of the slit.
Fig. 2. When the vibration amplitude of the stage is 3 nm, the relationship between MA and MSD with the vibration frequency. (a) is the change of MA with the vibration frequency, (b) is the change of MSD with the vibration frequency.
2.3 Simulation of vibration of stage
We classified the vibration of the reticle and wafer stage into two types: parallel to the wafer surface and perpendicular to the wafer surface, recognizing that these two types of vibration have different effects on imaging. Specifically, the vibration parallel to the wafer surface is referred to as transverse vibration, while the vibration perpendicular to the wafer surface is referred to as longitudinal vibration. To ensure the realism and reliability of our simulation results, we used the relevant parameters of EUV lithography, as shown in Table 1 [15,16], during the modeling and analysis process.
Table 1. Parameters related to step scanning motion of EUV lithography system
We consider the case of a single exposure field exposure subjected to high frequency stage vibration. The light from the source arrives at the reticle stage through the illumination system carrying the mask pattern information, after which the light passes through the exposure slit to transfer the mask pattern to the wafer, and we define the light intensity at this point as the static light intensity ${I_0}(\overrightarrow r ,t)$, while the light intensity after the scanning exposure process is disturbed by the reticle and wafer stage vibration is defined as the dynamic light intensity $I(\overrightarrow r ,t)$. Since we only discuss the position shift and contrast change of the spatial image due to the vibration of the reticle and wafer stage, it is assumed that the image quality during exposure is perfect in all aspects except for the vibration of the reticle and wafer stage. For the relationship between the effect of the reticle and wafer stage vibration on the aerial image, the vibration in the transverse direction can be approximated by the convolution of the static light intensity with the probability density function of the vibration [6], which is expressed in the following equation:
The probability density function of the transverse vibration of the reticle and wafer stage is denoted by $D(x,y)$, and a Gaussian distribution is used to represent it. The one-dimensional case is given by the following equation. As stated earlier, MSD is the standard deviation of the synchronized position changes between the reticle stage and the wafer stage during the exposure process. And MSD is used to represent the high-frequency variation of the synchronized position, which is essentially the synchronization error caused by the reticle and wafer stage vibration. When we use a Gaussian distribution to describe the vibration, MSD is equivalent to the parameter σ in the distribution.
The longitudinal vibration of the reticle and wafer stage actually makes the position on the wafer surface to be exposed fluctuate near the focal plane all the time. According to optical knowledge, different defocusing situations correspond to different aerial images, represented by ${I_0}(x,{z_i})$, where ${z_i}$ represents different defocus. We calculate multiple aerial images within a suitable range near the focal plane, and then perform weighted summation to represent the effect of different vertical vibrations (MSDz) on the aerial images. The specific expression is given by Eq. (9), where the weighting coefficient $D({z_i} - {z_0})$ is given by the Gaussian distribution, and ${z_0}$ represents the focal plane position.
After understanding the mathematical relationship between vibration and imaging, and the results are as follows.
During simulation, we set the graphics as lines with a width of 13 nm, and the blank spaces are set to 13 nm, 31 nm, and 65 nm, respectively, which represents the dense, semi-dense and iso patterns. The relationships between the intensity of the spatial image and the MSD for the above three patterns are shown in Fig. 3. It can be seen that as the MSD increases, the intensity of the spatial image becomes smaller, further confirming the influence of vibration on the image. Comparing the relationship between transverse and longitudinal vibrations, it can be seen that transverse vibrations have a much more serious impact on the image than longitudinal vibrations. In actual exposure, dense-line should be given priority, and the exposure conditions of dense-line should be used as the basis. It can be seen that under this process rule, MSD has a significant impact on the CD control of semi-line and iso-line, and further optimization using computational lithography is needed to complete the exposure.
Fig. 3. Relationship between aerial image and MSD. (a) The aerial image of the line with CD = 13 nm and pitch = 26 nm changes with the transverse MSD, (b) The aerial image of the line with CD = 13 nm and pitch = 44 nm changes with the transverse MSD, (c) The aerial image of the line with CD = 13 nm and pitch = 78 nm changes with the transverse MSD, (d) The aerial image of the line with CD = 13 nm and pitch = 26 nm changes with the longitudinal MSD, (e) The aerial image of the line with CD = 13 nm and pitch = 44 nm changes with the longitudinal MSD, (f) The aerial image of the line with CD = 13 nm and pitch = 78 nm changes with the longitudinal MSD.
We further investigate the distribution of light intensity for a single line structure parallel to the scanning direction during a single scan, taking into account the influence of reticle and wafer stage vibration. Our aim is to study the relationship between the amplitude and frequency of the vibration in different directions and the LER. We use the sine function to model the vibration in each scanning direction. Figure 4 shows the light intensity distribution within a single exposure field. Our simulation results indicate that even small perpendicular vibrations (3 nm) can significantly affect the LER, with the effect decreasing as the vibration frequency increases. Conversely, the effect of parallel vibration on the LER is relatively small. Under the conditions mentioned above, a vibration amplitude of several hundred nanometers is required to produce a significant effect, while longitudinal vibration also needs to reach several hundred nanometers to cause a significant change in the LER.
3. MSD impact on 13 nm imaging with EUV lithography
In this section, we aim to analyze the impact of reticle and wafer stage vibration on parameters such as CD, PW, and LER. To achieve this, we have selected several representative test mask graphics, including through-pitch line/space structures, tip-to-tip structures, and tip-to-line structures.
3.1 One-dimensional through-pitch line/space structures
Figure 5 shows the illumination conditions and test mask used in the experiment. Dipole illumination with an inner diameter of 0.7 and an outer diameter of 0.9 is used, and the line width of the mask is set to 13 nm. The period of the lines varies from 26 nm to 130 nm. The experimental results focus on elucidating the relationship between CD, PW, LER, and MSD of line structures.
Fig. 5. Diagram of illumination and test mask. (a) Dipole, (b)dense-line, (c)semi-line, (d)iso-line.
The results of the reticle and wafer stage vibration effect on the CD of the line/space structure are shown in Fig. 6. From Fig. 6(a), we can see that transverse vibrations have a severe impact on the CD of the line/space structure. For lines with width of 13 nm and pitch larger than 52 nm, a change in MSD from 2 nm to 3 nm can cause a CD variation of around 1 nm. This implies that different OPC (Optical Proximity Correction) is required to correct the mask for different MSD values of lithography tools under the condition of 13 nm line width. For line structures with pitch between 26 nm and 41 nm, the tolerance range can be relaxed to 2-4 nm, and a small MSD within this period range can produce a beneficial result in line CD. A comparison of Fig. 6(a) and Fig. 6(b) shows that the effect of longitudinal vibration on line CD is much less than that of transverse vibration, and the MSD can be relaxed to 48 nm between pitches of 26 nm and 41 nm. As the pitch of the line continues to increase (greater than 41 nm) the tolerance to longitudinal MSD drops to less than 32 nm.
Fig. 6. The relationship between CD of line structure and MSD. (a) shows the effect of transverse vibration on CD, while (b) shows the effect of longitudinal vibration on CD.
As process nodes continue to shrink, the impact of reticle and wafer stage vibration on image quality becomes increasingly severe. Reducing this impact through computational lithography is crucial in promoting the development of smaller process nodes. We compared the CD imaging results of MSDx and MSDz without OPC optimization to those optimized by OPC, as shown in Fig. 7. The results demonstrate that OPC processing has a significant effect on improving the impact of MSD on CD, moreover, the influence of vibration in transverse direction on CD is improved more than that in longitudinal direction. Additionally, once the lithography tool is determined, its MSD value is challenging to change. Therefore, we illustrated the rule of through-pitch line/space patterns after OPC processing with a determined MSD in Fig. 8. As illustrated, increasing MSD leads to different changes in CD, and optimizing CD through OPC processing is achievable.
Fig. 7. Relationship diagram of OPC to improve the influence of MSD on CD. (a) and (c) mask pattern without OPC processed, (b) and (d) mask pattern with OPC processed.
Fig. 8. OPC rules of through-pitch line/space patterns under different MSD. The MSD is 0, 2, 3 and 4 nm for (a) to (d), respectively.
The effect of stages vibration on the PW of line structures in lithography is shown in Fig. 9. For dense line structures, the depth of focus (DOF) range is large, so the vibration of the stages has a small effect on the DOF, but has a severe impact on the energy margin. For semi-dense and iso structures, the vibration of the stages leads to a significant decrease in both energy margin and defocus, making them more susceptible to the impact of vibration on the process window. The different effects of transverse and longitudinal vibration can also be observed from the change in the process window. The effect of longitudinal vibration is smaller, and the effect of transverse vibration 10 times larger is approximately equal to that of longitudinal vibration.
Fig. 9. Diagram of the influence of vibration on PW. (a) is the influence of transverse-MSD on dense-line (CD = 13 nm, pitch = 26 nm), (b) is the influence of transverse-MSD on semi-line (CD = 13 nm, pitch = 44 nm), (c) is the influence of transverse-MSD on iso-line (CD = 13 nm, pitch = 78 nm), (d) is the influence of longitudinal-MSD on dense-line (CD = 13 nm, pitch = 26 nm), (e) is the influence of longitudinal-MSD on semi-line (CD = 13 nm, pitch = 44 nm), (f) is the influence of longitudinal-MSD on iso-line (CD = 13 nm, pitch = 78 nm).
As shown in the previous simulations, stages vibration has a certain impact on the line edge roughness (LER), which can also be inferred from the relationship between contrast and roughness. According to the work of Gallatin et al. [17–19], it can be obtained that the LER is inversely proportional to the square root of the dose right at the edge of the developed line (${D_{edge}}$), inversely proportional to the diffusion length of the acid in the photoresist (${L_d}$), and inversely proportional to the image log slope (ILS). Assuming that the photoresist remains constant, values for the ${D_{edge}}$ and ${L_d}$ can be determined, allowing us to focus solely on establishing the relationship between LER and image log slope (ILS). If the ILS is normalized by multiplying the linewidth L, the normalized image log-slope (NILS) can be obtained using Eq. (11). From the Eqs. (10) and (11), it can be concluded that LER is also inversely proportional to NILS.
The influence of reticle and wafer stage vibration on the NILS and LER of line structures in lithography is shown in Fig. 10, which illustrates the relationship between NILS and line pitch under MSD effect. As MSD increases, the contrast of aerial image decreases and NILS decreases as well. It is easy to see that LER becomes more severe with the aggravation of reticle and wafer stage vibration. Additionally, it can be seen that transverse vibration has a more severe effect on the NILS of iso-line structures, making the LER of iso-line structures more prone to deterioration due to vibration [20]. Longitudinal vibration is more likely to affect the LER of semi-dense and sparse line structures. According to the research on design rules by Y. Li et al. [21], the NILS of line structures under extreme conditions should be at least 1.8. According to the requirements of the process, it is necessary to ensure that the transverse vibration of the wafer stage is less than 3 nm and the longitudinal vibration is below 40 nm to meet the need for such NILS.
Fig. 10. Diagram of the influence of vibration on NILS and LER. (a) shows the change of NILS of the line structure with respect to the period and transverse MSD, (b) shows the change of NILS with respect to the period and longitudinal MSD, (c) shows the change of LER with respect to the period and transverse MSD, and (d) shows the change of LER with respect to the period and longitudinal MSD.
3.2 Two-dimensional structure
In this subsection, we use the tip-to-tip (T2T) and tip-to-line (T2L) structures as test masks to investigate the relationship between the effect of transverse and longitudinal vibrations on the CD and PW of 2D patterns. As shown in Fig. 11, the illumination method is dipole, where the inner diameter is 0.7 and the outer diameter is 0.9, and the CD of the line is 13 nm and the pitch is 26 nm, while the gap increases from 13 nm to 25 nm.
The results of the effect of vibration on the CD at the T2T and T2L structure gaps are shown in Fig. 12. From Fig. 12(a), it can be seen that as the gap width decreases, the effect of vibration in the transverse direction on the CD at the gap of the T2T structure is more severe. The reason for the bulge phenomenon when the gap is wider is that the energy threshold appears above the isofocal point as the vibration changes. From Fig. 12(b), we can see that the longitudinal vibration makes the CD of T2T decreasing, but it is obvious that the effect of longitudinal vibration is much less than that of transverse vibration. From both Fig. 12(a) and (b), we can see that the actual energy threshold deviates from the standard energy threshold, which can effectively mitigate the effect of vibration on CD. In Fig. 12(c) we can see that the transverse vibration causes a deviation from the CD of the T2L structure, which specifically leads to an increase or decrease in relation to the selection of the energy threshold and the width of the standard CD. In Fig. 12(d) we can see that the longitudinal vibration causes a slight increase in the CD of the T2L structure, which has a smaller effect in the same range.
Fig. 12. Relationship between 2D structure CD and MSD. (a) is the influence of transverse-MSD on T2T patterning, (b) is the influence of longitudinal-MSD on T2T patterning, (c) is the influence of transverse-MSD on T2L patterning, (d) is the influence of longitudinal-MSD on T2L patterning.
The results of the effect of vibration on the process windows of T2T and T2L structures are shown in Fig. 13. From Fig. 13(a) and (c), it can be seen that with the increase of MSD, the ELmax and DOF of T2T and T2L structures are decreasing, resulting in smaller PWs, with the decrease of T2L being larger than that of T2T structure. From Fig. 13(b) and (d), it can be seen that the effect of longitudinal vibration within a reasonable range on the PW of the 2D structure remains small, and the DOF values also appear to widen with the increase of MSD.
Fig. 13. PW diagram of 2D structure. (a) is the influence of transverse-MSD on T2T patterning, (b) is the influence of longitudinal-MSD on T2T patterning, (c) is the influence of transverse-MSD on T2L patterning, (d) is the influence of longitudinal-MSD on T2L patterning
4. Conclusion
In this study, we introduce the exposure principle of scan-step lithography as an example and construct a motion model of the reticle and wafer stage during the exposure process. We then model and simulate the transverse and longitudinal vibration during the reticle and wafer stage motion from the perspective of imaging. By taking a line structure with CD = 13 nm as an example, we investigate the spatial image variation law of three different cycles of single line patterns with the vibration of the reticle and wafer stage. We also investigate the variation law of the LER of the line structure with the vibration amplitude and frequency of the reticle and wafer stage by simulating the spatial image distribution in a single exposure field. Furthermore, we investigate the relationship between the vibration of the reticle and wafer stage and the parameters of CD, PW, and LER using through-pitch line/space structures, T2T, and T2L structures as test masks. Through simulation and analysis, we found that high-frequency vibration of the reticle and wafer stage mainly weakens the exposure energy and decreases contrast, while low-frequency vibration has a more serious impact on the LER. For a line width of 13 nm, the tolerable transverse vibration of the reticle and wafer stage cannot be higher than 3 nm, while the influence of longitudinal vibration on the imaging quality of the pattern is weaker than that of transverse vibration, which can be relaxed to about ten times that of transverse vibration. Finally, as the process node continues to shrink, vibration will become an important factor affecting the imaging quality, which needs to be further resolved.
Funding
University of Chinese Academy of Sciences (Grant# 118900M032); Fundamental Research Funds for the Central Universities (Grant# E2ET3801).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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