Mechanical system and dynamic control in photolithography for nanoscale fabrication: A critical review

As one of the most advanced and precise equipment in the world, a photolithography scanner is able to fabricate nanometer‐scale devices on a chip. To realize such a small dimension, the optical system is the fundamental, but the mechanical system often becomes the bottleneck. In the photolithography, the exposure is a dynamic process. The accuracy and precision of the movement are determined by the mechanical system, which is even more difficult to control compared with the optical system. In the mechanical system, there are four crucial components: the reticle and wafer stages, the linear motor, the metrology system, and the control system. They work together to secure the reticle and substrate locating at the correct position, which determines the overlay and alignment performance in the lithography. In this paper, the principles of these components are reviewed, and the development history of the mechanical system is introduced.


| INTRODUCTION
Following Moore's law, the integrated density of the transistors on a chip becomes double every 24 months, which means the critical dimensions (CDs) of the devices keep shrinking. As a key process in the chip manufacturing, photolithography determines the minimum CD of the devices. In the photolithography, one important parameter is CD. The frequently discussed 5 nm, 3 nm nodes refer to the minimum CD of a transistor gate. Another important parameter is the overlay, which defines the relative positioning between two adjacent layers. If two layers are misaligned, it will lead to a performance loss or even a failure of the device. In the photolithography, overlay is more difficult to control as compared to CD, because it is affected by not only the optical system but also the mechanical system. In the mechanical system of the photolithography, the dynamic control is always a big challenge.
In a photolithography tool, the reticle and wafer move at an extremely high speed and acceleration, which further increases the difficulty. In this situation, to realize a desired dynamic control, it needs a collaboration of the movement platform, motor, metrology and control system. The movement platform, which is also called the stage, is mainly classified into three types: mechanical guide, aerostatic guide, and maglev guide. 1,2 The mechanical guide is a traditional guide, which suffers from friction and is not able to achieve very high accuracy. Aerostatic guide uses a air bearing to avoid direct contact, and can effectively reduce the friction. Maglev has been introduced in the recent decade for the nanometer-scale locating.
Linear motors are applied to guide the movement, and make sure the stage moves in the correct direction, vertically or horizontally.
Iron-core and ironless linear motors are implemented for different applications, with respect to the cogging effect, thrust fluctuation, and dynamic response. [3][4][5][6][7][8][9][10][11][12] In a mechanical system, it is expected that the movement is always accurate. However, in reality, there always exists offsets between the design and the real operation. These offsets bring errors to the final devices, and the errors accumulate to cause failure. Proper metrology methods are needed to measure the offsets, and feedback could be applied to minimize the errors. Generally, interferometer is the standard metrology tool for the movement and locating. [13][14][15][16] Two optical signals are collected by an interferometer. One is collected by a static light path and used as a reference signal. The other is collected from the moving stage as the measurement signal. Then the location can be decided by comparing the phase difference between the two signals. Based on the traditional interferometer, the grating interferometer was proposed, which is also called linear encoder. High precision gratings are utilized to program the optical signal, which can further improve the metrology resolution. Meanwhile, dual frequencies are applied by the interferometers for solving the 2π phase shift issue in a broad measurement range. With the next step, the metrology result is treated as feedback to the photolithography, and the measured movement error can be compensated by the dynamic control of the stage. [17][18][19] 2 | WAFER STAGE Wafer stage is one of the core technological units of photolithography system, which has a long history of technical development. The accuracy and efficiency of the photolithography process are directly determined by the control precision and scanning speed of the wafer stage.
Mechanical guideways have been commonly used for early photolithography wafer stages. A typical structure of wafer stage fitted with a mechanical guide is shown in Figure 1.
The wafer stage mainly consists of a base, a cross structure, an X-Y table and a wafer clamping plate. As the X-Y table moves along the Y axis, the Y slider bar slides in a square channel along the Y guide plane, and then the X guide bar forces the X-Y table to move. For the movement along the X axis, the X plane in the X-Y table moves along the X guide bar. 20 Figure 2 shows the structure of Canon FPA-2000 photolithography system. In this system, movements in X-, Y-, and Z-directions are controlled precisely by double-layer mechanical guide, which has been used in the 0.5 μm process. 21 The performance of mechanical guideway workpieces are limited by the following factors. First, due to the gap between the die and the lead screw, the mechanical guide rail can only maintain the positioning accuracy at the sub-micron level. Second, the mechanical system has the inevitable friction, in which resulting particles can also contaminate subsequent processes. Finally, the mechanical guide is bulky and needs more complex processing techniques, for which the maintenance is costly.
With the upgrading of technology, the aerostatic guide gradually has replaced the mechanical guide and has become the main displacement device of the wafer stage. Aerostatic guide technology has been widely used in the major scanning photolithography systems, which is owned by the world's three largest photolithography manufacturers: Canon, Nikon and ASML. The introduction of air bearing effectively isolates the actuator and rotor, and reduces the repeated friction between them. The zerofriction feature of the air floating guide almost does not generate additional heat, which can be integrated with the servo actuators and sensors to form a closed-loop system, and achieve highprecision displacement positioning. Figure 3 shows a typical X-Y direction air-floating platform.
The air floating platform consists of an X-direction platform and a Y-direction platform. The side of the platform was also equipped with a vertical guide rail and a laser diode for ranging. The gas F I G U R E 1 Typical structure of wafer stage fitted with a mechanical guide. Adapted with permission. 20  Magnetic-levitation (maglev) guide is also one of the common technologies used in the wafer stage. With the increasing technological requirements, researchers put forward higher standards for the vacuum degree of the photolithography systems, where the floating rail technology was no longer applicable. Maglev guide is widely used in the wafer stage of the latest generation of photolithography system. Figure 4 shows a wafer stage with maglev guide. In this model, the permanent magnets and the coils were arranged around the motor center in a circle. The magnet array was formed in the Halbach mode along the rotor circumference. 23 Figure 5 shows the NXT:1950i photolithography system of ASML with maglev stages. 24 In addition, for the design and manufacture of advanced photolithography system, the modeling and simulation of the wafer stage system are particularly important. The wafer stage consists of a complex mechanical structure and dynamic characteristics, which have a great impact on its motion and measurement accuracy. Figure 6 shows a design framework supporting the dynamic design of nano-precision positioning stages. 25 According to the system simulation, researchers get the relationship between the stiffness of the air floating and the thickness of the gas film, which is the basis to design the mass center of the actuator accordingly, as shown in   Air-core motor is a common driving device to support and control the movement in the Z-direction in the photolithography. The photolithography with an air-core motor possesses the advantage of low vibrations, low acoustic noise, high precision and low power loss. [3][4][5][6][7][8][9][10][11][12] Tanaka designed an air levitation (bearing) system, composed of Lorentz forced planar motors with three degrees of freedom (DOF).

Dynamics test indicates that servo bandwidth is limited around
25 Hz due to a 75 Hz mechanical resonance frequency. The coupling between horizontal force and vertical force activated by the planar motor is less than 10%. 3 Chen et al. developed an ultra-precision drive machine with air bearing, as shown in Figure 9. The dynamic performances of the driving machines with short stroke motor and long stroke motor are compared. The results show that the vibration amplitude of drive machine with short stroke motor may decrease by 95.2% (from −2.8 μm movement to 0.1 μm movement), compared with drive machine with long stroke motor. 6 As a result, another disadvantage of air-core motor is that it is not suitable for photolithography with large stroke or large area. Alternatively, the magnetically levitated planar motor is more suitable for the photolithography with large stroke and large area.
To achieve a minimal fringing field influence on the working performance of photolithography system, Paul et al. investigated a maglev linear motor with a relatively short distance between the fringing fields and actuators. The dynamic characterization experiment shows that the photolithography system with this motor can realize high resonant frequency and high-precision movements. [26][27][28][29] Zhang et al. developed a novel magnetically levitated planar motor for the photolithography system, as shown in Figure 10. The researchers used the scalar magnetic potential to investigate the magnetic system in a planar motor, with the differential equations simulated by the finite element method (FEM). Dynamic characterization experiment shows that the F x in the photolithography system may tend to be stable in 30ms, and the F z may tend to be stable immediately. Meanwhile, the stable forces of the F z and F x are 1600 and 900 N, respectively; and the force vibration amplitude is within 100 N, implying the capacity of driving a wafer stage with a large stroke and large area. 26 With the demand for ultrahigh-precision lithography technology and 3D lithography technology, piezoelectric ceramic motors have In addition to the movement in the Z-direction, the motor controlling the horizontal movement of the work piece table also determines the performance of the photolithography system. [31][32][33][34] At present, long stroke motors used in the photolithography system can be classified into ironless linear motors and iron-core linear motors. The coreless permanent magnet linear synchronous motor has the advantages of no cogging effect, low thrust fluctuation, and high dynamic response. However, if it is applied to the double-workpiece stage of a photolithography system, some problems still need to be solved, such as achieving high thrust volume density, increasing thrust copper loss ratio, and thrust fluctuations.
As a result, the horizontal movement in the photolithography system is usually realized by the iron-core linear motors.
To reduce the noise effect induced by the iron-core linear motors, Jun et al. presented a novel low-noise high-force linear motor for photolithography system, as shown in Figure 12. Usually, the spatial-frequency magnetic field is the main root cause leading to the vibration of the work piece. In that paper, the author reduces the spatial-frequency magnetic field by optimizing electromagnetic field design. The results show that this new type of motor can achieve 28% higher shear stress, compared to a common motor, and its output power can reach 500 W/mm. 34 Although the iron-core linear motors can realize long stroke, to achieve a nano-level precision motion in a photolithography system, it requires linear motors combined with the advantages of other motors. Take ASML photolithography system Twinscan XT 1950i as an example, the maximum speed of the Y-direction long-stroke linear F I G U R E 9 Schematic view of air-bearings in X-direction. Reproduced with permission. 6  motor of the mask table is greater than 2 m/s, the maximum acceleration is greater than 60 m/s 2 , the peak thrust is greater than 1200 N, and the positioning accuracy is ±1 μm. Macro movement of Twinscan XT 1950i is realized by the iron-core linear motors. Furthermore, with the development of high-precision laser direct writing photolithography systems, such as a two-photon laser direct writing equipment, researchers directly used piezoelectric ceramics as actuators to complete the photolithography process. [35][36][37][38][39][40] Brussel et al. designed a work piece with the piezoelectric ceramics, as shown in Figure 13, and the work piece possesses the advantage of high-speed positioning, high precision. Dynamic characterization experiment shows the maximum speed of prototype linear motor can exceed 100 mm/s with the movement range within 3 μm. 39 On the premise of maintaining accuracy, Gao et al. designed a dual mechanism multimodal linear motor to enlarge the movement range. Besides a piezoelectric motor, an electromagnetic motor can also be found in the linear motor. Dynamic characterization test experiment prototype shows that the nanomotor can reach 2 nm under the high speed of 50 mm/s. 38 In addition to the electromagnetic motor and piezoelectric ceramic motor, pneumatic motor is also a new development direction for the photolithography system. Worktable driven by pneumatic motor in laser direct writing photolithography system, as shown in

| STAGE POSITION MEASUREMENT
Stage positioning is the alignment accuracy of the wafer stage and reticle stage, which can be well positioned to each other. An independent measurement system is needed to control the stage movement precision. Therefore, it is important to establish a precise method to measure the position and orientation of the stage directly.
As the solutions, heterodyne laser interferometers and grating interferometers are widely used as metrology tools for ultra-precision displacement measurements. 43 Interferometers have been applied in the industry as the stage position measurement system for more than 20 years. [13][14][15][16] The typical principle of an interferometer is to measure an optical path difference between two beams, which are separated by a Wollaston prism or F I G U R E 12 A linear stage testbed with a fine-tooth motor. A magnet track is mounted on the bottom surface of the moving stage. Reproduced with permission. 34 Copyright 2021, The Authors, published by IEEE F I G U R E 13 (left) Actuator lay-out, (right) picture of actual piezo motor. Adapted with permission. 39 Copyright 2021, The Authors, published by Elsevier other optical splitters. One is an external beam reflected by a stage mirror, and another one is an internally beam reflected by a mirror inside the interferometer. 44,45 As shown in Figure 16A, these two reflected beams will produce interference fringes composed of bright and dark bands. 46 The optical path change of the external beam can be calculated by counting the number of fringes. To further enhance the resolution, a new design was proposed based on the traditional laser interferometer. As illustrated in Figure 16B, a mirror in front of the detector input gate is added, and it switches to the model with the same gate for input and output beams. As a result, a twofold enhanced measurement resolution was obtained, but the maximum velocity of the measured target was reduced to half.
To apply this method on stage position measurement of a photolithography system, it is necessary to know the frequency of the external beam propagating in the air. If the changes in the refractive index of the air are not compensated, they will cause measurement noise and errors, especially in the region 0.5-50 Hz. 47 Even in a system with a very stable environment, these noise and errors will still be larger than 1 nm. They are mainly cause by complex physical processes during the movement of stage itself. For example, the changes such as the local pressure, temperature, and air composition, will cause interruption to the beam. The refractive index changes during these processes, and thus leads to positioning errors. It is noticed that, the laser beam of interferometer is parallel to the stage, which means to measure the motions at different directions, a laser interferometer must have several sub-systems placed around the measured stage. This will increase the complexity of the measurement system. 48,49 The laser interferometer measurement system implemented on the ASML XT system is shown in Figure 17(top), with a signal error of 0.9 nm (3σ). 24 A dramatically reduced sensitivity to refractive index changes can be realized by using grating interferometers (GIs). [50][51][52] The grating is placed vertically or with a certain angle to the incident lasers. Therefore, with a single grating, a GI can achieve up to 6 DOF measurement in a compact area. 48,53 A general system of the GI is composed of a laser light source, a read head, a grating, and a signal processing module. 54 The development of GI has experienced an exploration from homodyne to heterodyne interferometry, and then spatially separated heterodyne interferometry.
A typical Michelson-type homodyne GI uses a single frequency laser source, composed of a fixed reference grating and a flexible measuring grating, as shown in Figure 18A. 55 The single-frequency laser beam with a frequency f is divided into two paths by a nonpolarized beam splitter (NPBS), working as the measuring beam and reference beam. The measuring beam is diffracted by the measuring grating, and the reference beam is diffracted by the reference grating. These two diffracted beams are converged to the NPBS and detected by a photodetector (PD) module. The single PD is shown in Figure 18B. It can realize only homodyne interference displacement measurements, but not able to distinguish the direction of motion. 56 To achieve the direction measurement, a quadratic phase detector module and a quadrature phase detector module are implemented, as shown in Figure 18C,D. The movement of the measuring grating generates the diffraction beams on the surface. Due to the optical Doppler effect, the movement will cause a frequency shift of diffraction beams, causing a phase difference between the reference beam and the measuring beam. 57 When the interference beam is formed by these two beams with a phase difference, the actual motion phase can be acquired from interferential phase signals, from which the length and direction of the grating displacement can be calculated. Now, there is an issue for this structure, the sensitivity of the homodyne GI. To achieve a high sensitivity, the phase sensitive detector requires a more complex optical structure, including multiple PDs for the phase-sensitive detection. 56 To solve the sensitivity issue of the homodyne GI, a heterodyne GI with a dual-frequency laser source has been proposed. A Michelsontype interferometer can also be formed by a heterodyne GI, as shown in Figure 19. 55 A polarized laser beam with two frequencies f 1 and f 2 is produced by a dual-frequency laser. The light is split into two beams by a NPBS, one beam is detected by the PD r to form a reference signal, the other beam is divided into two parts by a polarized beam splitter (PBS) and enters the reference grating and the measuring grating respectively. Then the interference light formed in the beam splitter is collected by the PD m . For a heterodyne GI, the frequency difference (f 1 − f 2 ) contains displacement information, which makes it possible to use a single PD to determine the direction. 56 Due to ellipticity and nonorthogonality of the light source and misalignment or imperfection of the PB, 58 periodic nonlinear errors exist in the practical GIs. As shown in Figure 20, the spatially separated heterodyne GI has been proposed to reduce these errors. 59 This configuration avoids the frequency mixing with two acoustic optic modulators, which modulates the two beams by using two different frequencies, f 1 and f 2 , separately. To implement a GI on the stage position measurement in a photolithography system, the measurement resolution needs to be further enhanced. There are mainly two ways to enhance the optical resolution, decreasing the grating pitch or increasing the optical fold factor. However, the decrease of the grating pitch is limited by the fabrication capability. Therefore, the efficient way to improve the optical resolution is increasing optical fold factor. Multifold diffraction has been applied to achieve a high optical resolution by using a differential optical structure, where the diffracted beams are reflected onto the grating and diffract each time. 60,61 In addition to a high optical resolution, a multi-DOF measurement of the stage position is also needed in a photolithography system. Many optical structures for multi-DOF measurements have been proposed, based on different types of GIs. It includes inplane displacement measurement, 62,63 out-of-plane displacement measurement, 64,65 and rotational measurement. 66,67 The GI system is implemented onto the ASML NXT platform with a signal error of 0.22 nm (3σ), as shown in Figure 17(bottom). 24 Compared with a laser interferometer, the encoder has many benefits, including no In the design, the encoder is connected to the chuck and measures the optical signal from the grating supported by a grid frame. This is maintained by a vibration isolated metrology frame. The metrology frame also holds the exposure lens and measuring equipment, the sensors on the frame also measure the alignment and focus at the area.
One encoder head measures 2 DOF: the translation in the grating plane, and the distance between the encoder head and grating.
An encoder head is place on the corner of each chuck. A grating plane F I G U R E 17 Schematic views of a traditional interferometer system with long variable beams (top) and the encoder system with short fixed beam interferometers and grid-plates (bottom). The left plotting is the noise levels of both systems. Reproduced with permission. 24 The Authors, published by SPIE F I G U R E 18 A homodyne grating in a Michelson-type interferometer: (A) an optical structure of reading head; (B) a single photodetector; (C) a quadratic phase detector module; (D) a quadrature phase detector module with a non-polarized beam splitter (NPBS). Reproduced with permission. 55  consisting of a 2-dimensional grating is used as the reference for the encoder measurement, as shown in Figure 21. 47 Due to the thermal expansion effect of the chuck, the measurement direction is selected tangent to the center of the chuck, which improves the thermal stability of the position measurement. Finally, ASML points out that the new bidirectional encoder-design is a improvement of the uni-directional encoders, which has been used in the reticle stage for more than 5 years.

| CONTROL OF OVERLAY
With a continuous development of the integrated circuits, the CD of the semiconductor manufacturing continues to shrink. In this situation, there are many challenges in the photolithography technology, and a crucial issue is the distortion of wafer patterns. 68 The quality of the wafer pattern is determined by many factors, including but not limited to the light source quality, reflective reticle, reflective optics and vacuum environment. 69 Meanwhile, the synchronization errors caused by the scanning and projection modes of the exposure module also greatly impact the wafer pattern fidelity.
In particular, the synchronization between the wafer stage and the reticle stage is a key factor of the exposure. 70 Here the reticle stage is defined as the master stage, holding the reticle with a pattern on a quartz plate. And the wafer stage is defined as the follower stage, holding the wafer covered by the photo resist. In an ideal condition, the reticle stage and the wafer stage keep a precise synchronization during the scanning exposure.
However, the external disturbance and the dynamic performance may introduce a relative error between the reticle stage and the wafer stage at the scanning direction. 71 In addition, the response speed of the wafer stage and the reticle stage may differ due to the weight difference, and it further increases the difficulty of the control system. 72 To secure the precise synchronization for both long and short distances, 73 a feedback control strategy has been applied. It solves the synchronization problem by compensating the positioning errors during the movement process. [17][18][19] Figure 22 shows the structure of a photolithography scanner.
The reticle stage and the wafer stage are located at the high and the low levels of the base frame. The coarse stage is driven by a linear motor, which responses for the fast and long distance motions; and the fine stage is driven by a voice coil motor (or Lorenz plane motor), which responses for the fine motion.
The structure of a synchronized control system is shown in Figure 23, in which two stages move with a fixed velocity while maintaining a synchronized position. 72 The synchronization error is minimized with the assistance of a position close loop and feedback synchronization. Then a flexible and efficient control can be realized.
Here P R and P W define the models of two stages, C R and C W define the feedback controllers of two stages, and ILC defines the synchronization controller. e s (t) defines the synchronization error. y R (t) and y W (t) define the position outputs of the two stages. For the control effort (N) of the reticle stage, u R (t) is a sum of the feedback control input u f (t) and the feed-forward control input u s (t).
where T is the exposure time and e(t) is the position error as a function of time t.
However, the positioning accuracy also depends on some nonlinear factors, such as the cogging force and force ripple, 71 while the driven motor is involved in the control model. Considering the behavior of the linear motor, the control process can be approximated as a second-order dynamic system. With a rigorous modeling, the reticle stage system can be expressed as where M is the effective mass, The state space of the reticle stage could be expressed in the matrix form as where As a result, the law of synchronization control during each iteration can be expressed as where k is the iteration number and α is the step size. To further reduce the position error, a system with feedback and feedforward control has been developed, and the experimental setup is shown in Figure 31. 80  The time response trend of the stage position change is shown in Figure 33. In Figure 33A, the green curve shows a 20 mm stage motion set-point and actual position, with a scaled acceleration by the red curve which is limited by a value of 10 m/s 2 . In Figure 33B, the corresponding imaging error is plotted, which is constrained in a F I G U R E 22 Structure of a photolithography scanner. Reproduced with permission. 71   In addition, during the lithography process, the accuracy of the image transfer from the reticle to the wafer is also impacted by the optical elements. Then an optical element, such as a high precision phase detector, is applied to ensure the phase measurement accuracy of interference fringes. 82 The accuracy of a homodyne detector is constrained by three factors: the DC offsets, the unequal AC amplitudes, and the quadrature phase-shift error in the detected quadrature signals. 82 Figure 35A shows the correction of phase error, which dramatically decreases from 45.5 to 8.1 nm. However, the corrected phase signal is still not perfect, mainly due to the residual phase locking error. 88 The eliminated nonlinearity error is given in Figure 35B, with the value of 39.0 nm. Figure 35C shows the results of the spectrum analysis. The amplitudes of the first and the second-order periodic errors are attenuated by 27.8 and 46.5 dB.
F I G U R E 27 QQ plot of sample data versus standard normal in X direction. Reproduced with permission. 79   The combination of a maglev guide working platform and a grating interferometer based linear encoder pushes the photolithography capability to the range below 10 nm resolution and locating, which also requires a less-than-1 nm CD control and a less-than-3 nm overlay control.
In the near future, as the technical node of the integrated circuits approaches 3 nm and below, and the wide application of 3D stacking, new technologies will be required to further improve the mechanical system and its dynamic control. Multiple frequency optical interferometer or even X-ray interferometer can increase the metrology precision and reliability. High order calibration models will be applied to the control per exposure, with both inter and intra field optimization.