Facile extraction of scanning probe shape for improved deconvolution of tip-sample interaction artifacts

Atomic Force Microscopy (AFM) has intrinsic tip-sample convolution artifacts. Commercially available tip-check samples are used to obtain only the tip radius, which can be used to deconvolute surface profiles or to quantify tip wear by relying on AFM alone. When the sample height is of the order of 100 nm or more, not only the tip radius but also the overall tip shape plays a key role in imaging. Therefore, it is necessary to know the overall tip shape, which requires a structured sample that is much larger than tip-check samples. Here, we propose to use deep reactive ion-etched holes of 1 µ diameter and 5 µ height to reconstruct the overall tip shape of three different AFM probes, namely conical, pyramidal and tetrahedral. The proposed cylindrical hole structure seems promising, as simple inversion of AFM images can provide sufficient collective features to be used for deconvolution and image enhancement.


Introduction
In the fields of semiconductors, biology and materials science, the precise determination of the surface morphology of samples is crucial [1].The accurate measurement of physical properties such as height, width, and side angles is technically important in these fields [2,3].To satisfy these requirements, various surface imaging techniques have been developed, including Optical Microscopy (OM), Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), and Atomic Force Microscopy (AFM).OM is user-friendly and nondestructive but offers relatively low resolution [1].In contrast, SEM provides excellent nanometer resolution and a wide field of view but requires complex sample preparation and additional coating for non-conductive samples in a high vacuum environment [4][5][6][7].TEM is suitable for structural analysis but does not provide topographical information [8].
AFM offers nanoscale lateral resolution and sub-angstrom vertical resolution, allowing for non-destructive acquisition of three-dimensional topographical information [9].However, the use of AFM can lead to convolution artifacts due to the interaction between the tip and the sample, creating features in the image that do not exist on the actual surface, making it difficult to obtain accurate surface morphology [9][10][11][12][13][14][15][16].This issue is particularly critical in applications involving high aspect ratio structures, where precise three-dimensional measurements are required.The entire height of the probe is crucial in these contexts.This includes semiconductor manufacturing, where the accurate profiling of deep trenches and tall features is essential.The overall shape of the probe influences the accuracy of the measurements in such contexts.Commercial tip check samples are only used to measure the tip radius, but when the sample height exceeds 100 nm, the complete tip shape also plays a crucial role in imaging [13][14][15][16][17][18][19][20].Additionally, during the *Correspondence: Jungchul Lee jungchullee@kaist.ac.kr 1 Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Daejeon 34141, Republic of Korea production process of AFM tips, variations can occur in the shape of the tips, which means the shapes provided in datasheets may differ from the actual configurations.Therefore, a method for accurate determination of the tip shape is necessary [21][22][23][24][25].This requires much larger structured samples than traditional tip-check samples.
This study proposes to reconstruct the entire tip shapes of three different AFM probes-conical, pyramidal, and tetrahedral-formed by deep reactive ion etching with 1 µm diameter and 5 µm height.The proposed cylindrical hole structures can provide sufficient collective features by simple inversion of AFM images for effective deconvolution and image enhancement.This research is expected to make a significant contribution to improving the accuracy and reliability of AFM technology.

Sample preparation for measurement
The samples used in this study were fabricated from p-type 100 silicon wafers, and were developed in our previous work [26].The size of the wafers was 20 mm × 20 mm × 0.5 mm , featuring a hole pattern of 1 µm diameter and 5 µm height, spaced at 1 µm inter- vals, created using deep reactive ion etching (DRIE) technique.This microstructure over the entire silicon wafer provides an ideal sample for precise tip shape measurement and analysis, allowing for the measurement of tip shapes with an uncertainty of approximately 10 nm.This error range is due to the adhesion forces between the tip and the sample as discussed by Van Noort et al. [27].The samples were cut from the wafer for SEM and AFM characterization, each piece containing hundreds of microhole patterns.

AFM characterization and analysis
The AFM used in this study was the Nanosurf Flex AFM system, operated at standard ambient temperature and pressure and all images are acquired in tapping mode (under amplitude modulation) for each probe at the pixel resolution of 256 × 256 .Our AFM probe selec- tion includes representative types commonly used in the AFM imaging society.They are tetrahedral Dyn190Al (Nanosurf, Switzerland) probes, conical qp-HBC-10 (Nanosensors, Switzerland) probes, and pyramidal PNP-TRS-20 (NanoWorld, Switzerland) probes.The scanning speed along the fast scan axis is set to be 1 µm/s and the set point of 60% with the free vibration amplitude of 33 nm are used considering optimal imaging conditions.
AFM image analysis was performed using the data processing program Gwyddion [28].This analysis aimed to eliminate the effects of external factors such as sample tilt and to evaluate the structure of the tips through image inversion.It was conducted by setting a reference height aligned with the flat baseline plane of the substrate to analyze tip height and angles in AFM images.All AFM images received only the first-order plane fit correction to eliminate sample tilt, ensuring that potential artifacts from other image processing steps were minimized as much as possible.

SEM characterization
SEM measurements were conducted to verify the accuracy of the tip shapes estimated using AFM.These measurements were performed using Hitachi's field emission scanning electron microscope (SU8230).This study characterized the shapes of AFM tips and the cross-sections of holes patterned by DRIE.To effectively reduce charging effects, the accelerating voltage was set to 10 kV, which enabled direct observation of insulating samples without the need for sputtering a conductive layer.The working distance was set at approximately 13.36 mm.All SEM images were recorded at a magnification of 12, 000× and an emission current of 5 µA , using a secondary elec- tron detector.

Tip shape estimation
This research utilized a method of estimating tip shape through deep hole structure measurement.When a tip with a width 'a' and height 'b' passes through a hole structure measuring 1 µm in width and 5 µm in height, the tip side touches the hole structure's corner, forming the tip's shape.In this case, the measured shape's width 'a*' and height 'b*' maintain the same proportions as the tip's original width and height.The estimation process is divided into two stages: a measurement phase, where the hole pattern is scanned using AFM to capture the image of the tip's shape, and an inversion phase, where this captured image is used to deduce the original tip shape (see Fig. 1).

SEM characterization of tip shapes
This study conducted detailed analysis on various AFM tip shapes.As seen in Fig. 2, three types of probes-Dyn190Al's tetrahedral tip, qp-HBC-10's conical tip, and PNP-TRS-20's pyramidal tip-each exhibit distinct geometric characteristics.These tips were imaged using high-resolution SEM, and each image clearly shows the ends of the tips.

Tip shape estimation by AFM result
Figure 3A shows AFM images measured using the DRIE hole pattern for each tip, and through a simple inversion method, the shape of the tips was estimated as shown in B. This estimation process involved quantitatively comparing the images obtained with SEM to the actual tip shapes, measuring each tip's width 'a*' and height 'b*' from estimated tip shape and each tip's width 'a' and height 'b' from SEM images.Tip aspect ratios (b/a) measured by SEM and those measured by the AFM inversion method (b*/a*) were compared in Fig. 4. The aspect ratios from the proposed tip estimation method of each tip were found to be estimated with an average deviation of 13.28% compared to aspect ratios from SEM images.

Deconvolution results
Figure 5 presents the AFM measured result of calibration sample (TGXYZ03) using the PNP-TRS-20 probe and the deconvolution results using tip shapes obtained from various sources.This measurement was conducted on a cylindrical pillar structure (width 3 µm , height 0.5 µm ) of the calibration sample, and the results are shown in the top left of Fig. 5.The top right image shows the result of the deconvolution using the tip shape obtained through the proposed estimation method, the bottom left shows the result of the deconvolution using the tip shape constructed from datasheet information, and the bottom right shows the result of the deconvolution using the tip shape obtained from SEM(tip radius is from data sheet due to resolution of SEM measured result).The data sheet for each tip shape is presented in Table 1.All deconvolution processes were conducted using the Gwyddion program.
To quantitatively compare the results of the deconvolution, the side wall slope and Full Width at Half Maximum (FWHM) for each result were compared.The crosssection's location is shown in Fig. 6A, and the side wall slope and FWHM measurements are shown in Fig. 6B. Figure 6C and D respectively show the results of comparing the side wall slopes and FWHMs, confirming that the deconvolution result using the proposed tip shape estimation method approximate the actual cylindrical pillar shape of the calibration sample more closely.Using the proposed method to estimate the tip shape for deconvolution showed improvement of up to 5.16% based on FWHM and improvement of up to 44.37% based on the lateral slope compared to using a tip estimated by other methods.These results suggest that the proposed method is highly effective in precisely estimating tip shapes and in restoring accurate shapes through deconvolution.

Conclusion
The simple inverse tip estimation method proposed in this study presents a new approach to effectively identify the shape of the tip through AFM measurements.This method can estimate tip shapes with high accuracy without SEM measurements and provides superior results for deconvolution compared to those using tip shapes estimated with SEM and provided in datasheets.When performing deconvolution, proposed method showed a maximum improvement of 5.16% based on FWHM and an improvement of up to 44.37% based on the lateral slope.The proposed method through this research is expected to improve imaging and analysis capabilities at the nanoscale.

Fig. 1
Fig. 1 Schematic of the tip shape estimation process using a deep hole structure, accompanied by a scanning electron microscopy (SEM) image showing the cross-section of the deep hole.When a tip with a width 'a' and height 'b' passes through a hole structure measuring 1 µm in width and 5 µm in height, the tip side touches the hole's corner, forming the tip's shape.In this case, the measured shape's width 'a*' and height 'b*' maintain the same proportions as the tip's original width and height.Scale bar is 1 µm

Fig. 3 AFig. 4
Fig. 3 A Results of measuring deep hole structure using probes with three different tip shapes.B Side view of the tip shape predicted through simple inversion of the result of measuring the deep hole structure.All scale bars are 1 µm

Fig. 5
Fig. 5 AFM measurement using the PNP-TRS-20 probe for a calibration sample (TGXYZ03) with a height of 500 nm.(top right) Tip shape obtained from proposed estimation method, (bottom left) obtained from the datasheet, (bottom right) obtained from SEM image (tip radius from data sheet).All scale bars are 1 µm

Fig. 6 A
Fig. 6 A The cross-section's location on the AFM measurement.B The side wall slope and FWHM on the cross-sectional view of the AFM measurement.C Side wall slope at left (L) and right (R) positions shown in A and D width for each data source (present work, datasheet, and SEM).Error bars are included for all data points, with the following error values: Raw L (0.06928), Present work L (1.25698), Datasheet L (0.10825), SEM L (0.19919), Raw R (0.5317), Present work R (1.25698), Datasheet R (0.05629), SEM R (0.17628).Due to the small size of some error values, certain error bars may not be visible in the figure.Raw represents raw data without deconvolution

Table 1
Tip properties on data sheet