Towards smart scanning probe lithography: a framework accelerating nano-fabrication process with in-situ characterization via machine learning

Scanning probe lithography (SPL) is a promising technology to fabricate high-resolution, customized and cost-effective features at the nanoscale. However, the quality of nano-fabrication, particularly the critical dimension, is significantly influenced by various SPL fabrication techniques and their corresponding process parameters. Meanwhile, the identification and measurement of nano-fabrication features are very time-consuming and subjective. To tackle these challenges, we propose a novel framework for process parameter optimization and feature segmentation of SPL via machine learning (ML). Different from traditional SPL techniques that rely on manual labeling-based experimental methods, the proposed framework intelligently extracts reliable and global information for statistical analysis to fine-tune and optimize process parameters. Based on the proposed framework, we realized the processing of smaller critical dimensions through the optimization of process parameters, and performed direct-write nano-lithography on a large scale. Furthermore, data-driven feature extraction and analysis could potentially provide guidance for other characterization methods and fabrication quality optimization.


Supplementary Note 1 Design of the XY compliant nano-manipulator
Compliant nano-manipulators (CNMs) are well suited for the applications with nanometric precision thanks to their features such as friction-free, maintenance-free and compact desktop-size.The desired compliant nano stages should have the following characteristics: nanometric motion quality (< 100 nm) [S1], large stroke (> 1 mm) [S1-S3], high speed [S3, S4], small parasitic rotation [S2, S3], small cross-axis coupling [S5, S6], and high linearity [S3].It is very challenging for the existing compliant XY motion stages to achieve nanometric precision, large range and other good features simultaneously.Although considerable advances have been made, it is still difficult to achieve both nanometric precision and macro range for a planar layout leaf-spring based motion stage through comprehensively considering parasitic rotation, cross-axis coupling and appropriate natural frequencies.
A conceptual design of the XY CNM is provided to achieve nanometric precision and large range.As shown in Fig. S1a, the manipulator consists of the guiding mechanism, the redundant constraint one, the decoupling one and the motion stage.The dimensions of each leaf spring are labeled in Fig. S1b.

Actuator
Motion stage

Decoupling mechanism
Guiding mechanism Based on the design and modelling, the size parameters of the CNM are determined.The overall size of the compliant manipulator is 300 mm × 300 mm × 14 mm, which keeps the manipulator desktop-level.The geometric parameters and values are shown in Tab.S1.With the above design, we need to model the proposed compliant manipulator to determine its static and dynamic features.By design, the linearity of the load-displacement curve is usually good within the travel range, and hence the stiffness matrix model can be adopted in the static analysis [S7].Fig. S2 shows a flexure beam with its coordinates.The forces and moments in/around certain axes are exerted on certain points, and the relationship between displacements and loads are formulated as follows, where T are the sets of forces/moments and translational displacements/rotational angles, respectively, and K is the stiffness matrix, and the compliance matrix C = K −1 is of the following form The compliance matrix C j at coordinate xo i y can be obtained by transforming the compliance matrix C i at the local coordinate xo i y where matrix P(r i ) is the transformation matrix from the local coordinate to a global coordinate, matrix R(θ i ) is the direction transformation matrix.Matrices P(r i ) and R(θ i ) can be expressed as follows where vector r i = [x i , y i , z i ] T is the one from the local coordinate o i to the global coordinate o j , and and The compliance matrix method is used to model the CNM.The redundant constraint mechanism is a quadruple parallelogram module, the minimum unit of the module is modeled, and then the compliance matrix of the whole module is obtained with the transformation and superposition of the compliance matrix.Fig. S3a shows the minimum unit -the parallelogram module, and Fig. S3b presents the right half of the whole module, and Fig. S3c displays the whole module.Based on the compliance matrix of the flexure beam, the stiffness matrix of the parallelogram module is given by where C p1 and C p2 are the compliance matrices of the two beams, respectively.Hence the compliance matrix of the double parallelogram module can be calculated by where θ di and r di are the transformation angles and transformation vectors, respectively.Thus, the compliance matrix of the quadruple parallelogram module is given by where C d1 and C d2 are the compliance matrices of the two double parallelogram modules, respectively.
Similarly, the stiffness matrix of the guiding mechanism K g , the stiffness matrix of the parallelogram mechanism K p , and the stiffness matrix of the double parallelogram mechanism K dp can be obtained.The compliance matrix of a quarter of the CNM can be expressed as follows, Since the manipulator contains four identical parts, the total stiffness matrix of the manipulator K S can be written as follows where θ i is the transformation angles.By simplifying the elements of matrix K S , it can be found K S1,1 = K S2,2 , the axial stiffness in the X direction is the same as the one in the Y direction.The axial stiffness of the CNM is shown as follows, The CNM is simplified to a single-degree-of-freedom mass-stiffness system as shown in Eq. ( 17), of which the natural frequency is calculated by Eq. ( 18) where M S is the equivalent mass of the stage.

Supplementary Note 3 Finite element analysis of the CNM
To validate the analytical model and the comprehensive performance of the CNM, the finite element analysis (FEA) is implemented using the software ANSYS ® .
According to the static model shown in Eq. ( 16), the theoretical relationship between the axial force and displacement are plotted in Fig. S4  The errors between the simulation results of axial stiffness and the theoretical model of the X axis and Y axis are 1.17 % and 1.13 %, respectively.The simulation results further verify the validity of linear stiffness matrix model.
The dynamic features of the compliant manipulator are investigated with the modal analysis.And the results are shown in Fig. S5, where the first and second modals represent the translation of the motion stage in the X and Y axis, respectively.The first and second natural frequencies are 60.57Hz and 60.68 Hz, respectively, which are significantly higher than those of the existing leaf-spring based compliant manipulators.Comparing to the natural frequency calculated by Eq. ( 18), the errors between theoretical dynamic model and FEA simulation are less than 1%.As shown in Fig. S7, the real-time control is implemented by using the dSPACE-R1103 rapid prototyping system.The sampling time applied in the servo is 10 kHz.A laser interferometer (attocube IDS3010) is utilized to measure the displacement difference of two sides of the motion stage to calibrate the two linear optical encoders.To evaluate the effectiveness of the semantic segmentation network, we compute seven metrics for evaluation purposes.These metrics include pixel accuracy (PA), precision, average precision (AP), intersection over union (IoU), mean intersection over union (MIoU), frequency weighted intersection over union (FWIoU), and F 1 -score (F 1 ).The PA metric indicates the percentage of pixels that are classified correctly in the image.Precision provides information about the purity of positive detections with respect to the ground truth.AP is the average precision across all classes.The IoU metric measures the intersection between the predicted and target masks, divided by the total number of pixels in both masks.The MIoU is the average IoU across all classes.FWIoU is the average weighted IoU based on the frequency of each class.The F 1 score represents the harmonic mean of precision and recall.The following are the definitions of each of these metrics: where k is the number of categories of the segmentation target, TP, TN, FP and FN are true positive, true negative, false positive, and false negative, respectively.
To assess the quality of the segmentation results for each case presented in the test set, we compute the evaluation metrics outlined in Eqs. ( 19)-( 26), and report the results in Tab.S2.The evaluation demonstrates that the proposed method successfully achieves precise segmentation of nano-structures, and the trained model can be readily utilized to optimize the conditions and parameters of the nano-lithography process.We detail the traditional SPL process parameter optimization method and the proposed one based on ML to show sufficient evidence demonstrating the benefits of the proposed framework.Fig. S8 shows the flow chart of traditional SPL process parameter optimization method.First, the initial process parameters need to be given.In this example, we select two typical parameters, scan speed (v i ) and setpoint (s i ), for demonstration.After nanolithography and in situ characterization, AFM images are obtained.Nano-fabrication results often exhibit variations across different locations, even when subjected to identical process parameters.We present the height distribution of two cross-sectional lines of the "Manual measurement" part in Fig. S8.It is evident that the width and depth of the same groove in nano-lithography vary at different locations.To describe the width of the nano-grooves, the parameter of full width at half maximum (FWHM) is usually adopted.The conventional approach is to select one or several cross-sectional lines for manual measurement of the FWHM of the nano-structures.However, it is very errorprone, time-consuming and usually difficult to fully characterize and measure the entire nano-structures manually.As a result, it remains challenging to optimize the process of nano-lithography without an accurate and reasonable metric.With the results of the manual measurement, the process parameters are adjusted for optimization.The inaccuracy associated with manual measurement and the lack of clear direction in adjusting process parameters significantly hinder the efficiency and results of the optimization process.
To tackle the above challenges, we propose the framework to accelerate nano-fabrication process with in-situ characterization via machine learning.Fig. S9 shows the flow chart of the proposed SPL process parameter optimization method.In contrast to the conventional approach, which involves specifying two typical parameters, the proposed method employs a matrix of parameters.This facilitates rapid experimentation with multiple sets of parameters.The proposed framework allows for the automatic processing of AFM topological images using ML to extract a multitude of information.Here we show a nano-lithography result as an example to demonstrate the credible and comprehensive statistical and analytical results automatically obtained based on the framework, as shown in the "Automatic measurements for global information" part in Fig. S9.For each set of parameters, the information (e.g., FWHM and pitch) can be obtained automatically for each position in each etched area.Different from traditional SPL techniques that rely on manual labeling-based experimental methods, the proposed framework intelligently extracts reliable and global information for statistical analysis to fine-tune and optimize process parameters.The matrix of parameters is further refined to find the optimal parameters (coarse-to-fine nano-lithography process method).

Start
Regarding additional process parameters, more experiments are usually required to complete the optimization process.Therefore, additional variables will complicate the optimization process.The proposed ML-based framework can still accelerate the optimization of multi-parameters with automatic and accurate measurement of nanofabrication results (e.g., FWHM and pitch).The proposed framework still has significant advantages in terms of efficiency and accuracy compared to process parameter optimization methods using manual measurement methods.
The proposed framework offers essential advantages and benefits, which can be summarized as follows: ⋆ The proposed ML-based framework focuses on the extraction of nano-structures and the automated calculation of important nano-fabrication results (e.g., FWHM and pitch).Specifically, global nano-fabrication results can be automatically obtained, which provides an accurate and fast measurement method for the process parameter optimization.
⋆ We also propose a coarse-to-fine nano-lithography process method for the rapid determination of optimal process parameters.The process of reducing pitch size relies on the FWHM and pitch information automatically obtained by the ML-based framework, which speeds up the optimization process of manual methods.
In the coarse-to-fine nano-lithography process method, we conduct experiments to obtain optimized process parameters.Specifically, the tapping mode of m-SPL is chosen for nano-lithography experimentation.The driving amplitude of the probe and scanning speed are identified as critical factors that affect the machining results while maintaining constant values for other conditions.For each of the aforementioned factors, 11 values are chosen, resulting in 121 parameter pairs for the experiment, which are illustrated in Fig. S10.The area of the nano-lithography pattern is 17 × 17 µm 2 .
During the coarse step, the setpoint range is set from 0.5 to 5.5 nA, increasing at an interval of 0.5 nA.The scanning speed values, on the other hand, are selected as 0.5, 1, 5, 10, 50, 100, 300, 500, 1, 000, 2, 000, and 3, 560 µm/s, respectively.To minimize error, nine lines are generated under each parameter pair, with each parameter being processed within a range of 1 × 1 µm 2 and a parallel line spacing of 100 nm.After processing, we use the same probe to acquire surface topography data.The sample is scanned at a Speed Setpoint Fig. S11 presents the AFM topology image obtained during the coarse step of the process method.Fig. S11a showcases the topography of the sample surface after being spin-coated with PMMA before nano-lithography.Following nano-lithography and insitu characterization, the resulting nano-structures are depicted in Fig. S11b.It can be observed that the critical dimension and depth of the nano-structures vary in a gradient with the change of the nano-lithography parameters.In this regard, we select the region of interest and fine-tune its parameters to determine the optimized process parameters.The red box illustrated in Fig. S11b  In the fine step of the process method, the Setpoint value ranges from 3.0 to 4.0nA at an interval of 0.1 nA, while the scanning speed ranges from 5 to 55 µm/s at an interval of 5 µm/s.Fig. S12 illustrates the AFM topology image obtained during the fine step of the process method.Fig. S12a presents the topography of the sample surface after being spin-coated with PMMA prior to nanolithography.Following nanolithography and in-situ characterization, the nano-structures are obtained, as depicted in Fig. S12b.In the fine step of the process method, the gradient variation of the critical dimension and depth decrease.By utilizing this process method, the process parameters associated with the desired nano-structure can be attained.with a pitch of 500 mm.The proposed SPL system supports millimeter-level stroke, thus enabling direct processing of this pattern without stitching.However, conventional AFMs typically have a scanning range of less than 100 × 100 µm 2 , and the existing approaches face challenges when directly applied to large-area fabrication and characterization.In order to showcase the SPL results in a stitched manner, the aforementioned large-area pattern is subdivided into 25 sub-patterns, each spanning an area of 200 × 200 µm 2 .These sub-patterns are sequentially processed and subsequently stitched together to form a complete large-area pattern.Fig. S18a and Fig. S18b show the SEM images of the large-area patterns.The speed of nanolithography is 1 mm/s.The stitchless method takes a total of 86 minutes and 43 seconds.And the stitched method takes a total of 166 minutes and 50 seconds.Compared with the stitched method, the stitchless nano-lithography result demonstrates an absence of stitching error, and the throughput is increased by 48%.Fig. S21 shows the SEM image of the junction of the four sub-patterns in a stitched manner.Among them, the four corners belong to four different sub-patterns.It can be seen that there are obvious stitching errors at the junction of each sub-pattern using the stitched manner.
Fig. S22a and Fig. S22b show the partial enlarged SEM images of the above two largearea patterns processed by different methods using the same probe.Following several hours of utilization, both patterns produced through SPL exhibit critical dimensions of approximately 20 nm.Experiments verify that SPM can support large-area and long-time etching, and the accuracy is almost unaffected.To study the effect of substrate hardness on SPL results, we further choose polished silicon wafers as substrates.The Tap300DLC probe is chosen, which is the same as the previous probe in the experiments on copper substrates.The lithography speed is 0.3 µm/s.Fig. S28 shows the SPL results on silicon substrate.The pattern is an array of parallel lines with a pitch of 500 nm.Fig. S29 shows the height information of A-A crosssection line in Fig. S28.The critical dimension of the lines is 109.6 nm.And the depth is 1.107 nm.The aspect ratio is calculated to be 0.010.The experimental aspect ratio of the silicon substrate is only 27.8% of that of the copper substrate (0.036).Compared with the soft material (PMMA, aspect ratio: 0.373), as shown in Figs.S30-S31, the harder substrate, the smaller aspect ratio.We compare the SPL results with other lithography methods, as shown in Tab.S3 [S8].
Note that the processing results (resolution and speed) are not standard, we list typical data of different nano-lithography methods in Tab.S3.It is evident that SPL exhibits substantially higher throughput compared to EBL and FIB.Furthermore, SPL achieves a smaller critical dimension than common photolithography.Additionally, SPL offers advantages in terms of environmental conditions and cost considerations.

Figure S1 :
Figure S1: A conceptual design of an XY CNM. a Top view.b Top view with labeled geometric parameters.

Figure S2 :
Figure S2: Coordinates of the flexure beam.

Figure S3 :
Figure S3: Schematic diagram and coordinates of compliant mechanisms.a Parallelogram module.b Double parallelogram module.c Quadruple parallelogram module.

Figure S8 :Figure S9 :
Figure S8: Flow chart of traditional SPL process parameter optimization method.

Figure S10 :Figure S11 :
Figure S10: Lithography pattern in the coarse-to-fine process method.

Figure S12 :
Figure S12: The AFM topology images in the fine step of the process method.a Before nano-lithography.b After nano-lithography.

Figure S13 :
Figure S13: AFM probe in the SPL system.

FigFigure S14 :Figure S15 :Figure S16 :Figure S17 :
Fig. S13 presents a cross-sectional view of the nano-lithography results for the parameter set with setpoint of 3.3 nA and speed of 25 µm/s.The FWHM of the structure with nano-lithography is approximately 25 nm.

Figure S18 :
Figure S18: SEM images of the large-area patterns.a SEM image of the large-area pattern in a stitchless manner (1 × 1 mm 2 ).b SEM image of the large-area pattern in a stitched manner (1 × 1 mm 2 ).

FigFigure
Fig. S19 and Fig. S20 show the partial enlarged views of the upper left corner and the upper right corner of the large-area patterns, respectively.One can clearly see the SPL Figure S21: SEM image of the junction of the four sub-patterns in a stitched manner.

Figure S22 :
Figure S22: Partial enlarged views of the large-area patterns.a SEM image of the largearea pattern in a stitchless manner.b SEM image of the large-area pattern in a stitched manner.

Figure S27 :
Figure S27: Height information of A-A cross-section line in Fig. S26.
Figure S28: SPL results on silicon substrate.

Figure S29 :
Figure S29: Height information of A-A cross-section line in Fig. S28.

Figure
Figure S30: SPL results on PMMA substrate.

Figure S31 :
Figure S31: Height information of A-A cross-section line in Fig. S30.

Table S1 :
Geometric dimensions of the XY CNM Supplementary Note 2 Modelling of the CNM

Table S2 :
Evaluation metrics for segmentation result of nano-structures.
1 Background 2 Nano-structures Supplementary Note 6 Comparison of traditional SPL process parameter optimization method and the proposed one