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AFM tip characterization by using FFT filtered images of step structures
Author’s Accepted Manuscript AFM tip characterization by using FFT filtered images of step structures Yongda Yan, Bo Xue, Zhenjiang Hu, Xuesen Zhao
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To appear in: Ultramicroscopy Received date: 24 September 2013 Revised date: 9 October 2015 Accepted date: 12 October 2015 Cite this article as: Yongda Yan, Bo Xue, Zhenjiang Hu and Xuesen Zhao, AFM tip characterization by using FFT filtered images of step structures, Ultramicroscopy, http://dx.doi.org/10.1016/j.ultramic.2015.10.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Title: AFM tip characterization by using FFT filtered images of
step structures
Author names and affiliations: Yongda Yan1,2, Bo Xue1,2, Zhenjiang Hu2, Xuesen Zhao2
1
Key Laboratory of Micro-systems and Micro-structures Manufacturing of Ministry of Education,
Harbin Institute of Technology, Harbin, Heilongjiang 150001, P.R. China 2
Center For Precision Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001,
P.R. China
Corresponding author: Y. D. Yan E-mail: [email protected] Tel.: +86-451-86412924 Fax: +86-451-86415244
Present/permanent address: P.O. Box 413 Harbin Institute of Technology, Harbin, Heilongjiang 150001, P.R. China
Abstract The measurement resolution of an atomic force microscope (AFM) is largely dependent on the radius of the tip. Meanwhile, when using AFM to study nanoscale surface properties, the value of the tip radius is needed in calculations. As such, estimation of the tip radius is important for analyzing results taken using an AFM. In 1
this study, a geometrical model created by scanning a step structure with an AFM tip was developed. The tip was assumed to have a hemispherical cone shape. Profiles simulated by tips with different scanning radii were calculated by fast Fourier transform (FFT). By analyzing the influence of tip radius variation on the spectra of simulated profiles, it was found that low-frequency harmonics were more susceptible, and that the relationship between the tip radius and the low-frequency harmonic amplitude of the step structure varied monotonically. Based on this regularity, we developed a new method to characterize the radius of the hemispherical tip. The tip radii estimated with this approach were comparable to the results obtained using scanning electron microscope imaging and blind reconstruction methods.
Keywords: atomic force microscope, step structure, spectrum of image, tip characterization
1. Introduction The atomic force microscope (AFM) is an important research tool in the fields of surface science, materials science, electrochemistry, biology, and metrology. The heart of an AFM is a sharp tip that interacts with the sample’s surface on the atomic level, using a normal force. With this interaction, not only can three-dimensional nanoscale topographies be obtained, but nanotribology [1,2] and nanomechanics [3-5] can also be studied. The fabrication process for new tips yields a radius generally ~8–10 nm wide in the shape of a hemisphere. Thus, the tip geometry is always involved in the testing results and may wear out during continuous contact. The wear of a tip will not only degrade the measurement resolution, but can also introduce error into the experimental results [6,7]. In addition, for nanomechanics studies, the tip radius value needs to be known to calculate the surface parameters [4,5]. Therefore, being more aware of the shape of the tip will lead to more accurate analysis of the results using an 2
AFM. Evaluation of the tip radius has been the focus of our work. General methods for tip characterization are scanning electron microscopy (SEM) [8,9] or transmission electron microscopy (TEM) [10,11]. From the images obtained, the tip radius can be approximated. However, imaging of worn tips using SEM or TEM must be performed before and after the AFM imaging experiments [12], which interrupts the continuous scanning with the tip. Meanwhile, radiation damage from the electron beams used in TEM and SEM can increase both wear on the tip and the tip radius [13]. Moreover, because of the tip dilation effect on the AFM image, a blind reconstruction method has been under development for several years [14-19]. In this method, not only can the shape of the tip be extracted from the AFM image itself [14,15], but the AFM image can also be reconstructed more accurately [14,16]. However, the blind reconstruction method is very sensitive to spikes in the data (noise) that result during the imaging process from external interferences and the scanning parameter settings; these spikes affect the estimation of the results and lead to an underestimated tip radius [17,18]. To improve this characterization, methods to reduce the influence of noise on the reconstruction results were investigated [18]. In addition, the parameter settings for the reconstruction process were optimized to increase the characterization method’s
ease
of
use
[19].
Some
researchers
[12,20]
have
used
the
Derjaguin-Muller-Toporov theory of contact mechanics to analyze tip wear. A worn tip has an increased contact area with the water film between the tip and sample, leading to an increase in the adhesive force F (F=2πWR, where W is the work of adhesion and R is the tip radius) between them. With the other conditions unchanged, the adhesive force varies with a change in the tip radius, and this observation is employed as a method to estimate the tip apex geometry. Another tip characterization method frequently used is based on scanning defined reference surfaces on which there are structures in special geometries, such as a sphere [6], peaks [21], a cylinder [22], and the grating [23]. The tip radii can be calculated from the images obtained using the established tip-sample interaction geometrical model. However, some 3
models are complicated, requiring complex calculations. The models were developed under ideal conditions where the structures had accurate dimensions, which may induce errors caused by the difference between the actual and theoretical conditions. In addition, preparation of the special structures adds difficulty to this method. New methods to estimate the tip apex geometry are still required. The random height distribution of the surface topography makes it difficult to extract the tip radius quantitatively and accurately directly from the AFM images. Liu et al. [24] found that the power spectral density curve of the AFM image obtained with a blunt tip was lower than that with a sharper tip, indicating a decline in resolution with a worn tip. By using this method they qualitatively evaluated the tip wear through estimation of the tip radius. It seemed that the frequency domain analysis method had good potential as a way to estimate the tip radius. For defined structure surfaces, the tip radius can be directly calculated from the sample image artifacts caused by the tip-sample interaction, but artifacts introduced by instrumental noise and poor response to the AFM control system may degrade the accuracy of this method. Fast Fourier transform (FFT) analysis can separate the noise signal (usually high frequency) from the useful component. As such, spectrum analysis for the tip assessment may decrease the error. Our objective here is to develop a simple and effective FFT analysis method for AFM images of the defined structure to quantitatively evaluate the AFM tip radius. In the present study, a nano-stepped structure that has accurate and simple dimensions was chosen as the tip characterizer. The geometrical model based on the AFM tip scanning the step structure was established. The shape of the AFM tip in the model was assumed to be a hemispherical cone, which is the frequently presented shape in AFM experiments. In addition, this hemispherical tip is often used as an indenter for nanoindentation [4,5]. Tips with different radii were simulated to scan the step structure and the FFT results of the corresponding scanned contours were calculated. The relationships between the tip radius and variations in the harmonics of the step structure were also investigated. 4
2. Modeling and estimation methods based on FFT analysis 2.1. Modeling the interaction between the tip apex and step structure First, the geometrical interaction model was built to simulate the AFM imaging process on a step with different tip radii, as shown in Fig. 1. For the simulation, it is assumed that the tip apex had a semicircular arc with a radius of curvature R tangential to the tip edges. The edges are at an angle α from the vertical. The step structure has an ideal right angle. As shown in Fig. 1(a) and (b), there are two conditions described as follows: first, when the height of the semicircular tip apex (the distance between tangent points of the semicircle and the edges and the semicircle vertex) is higher than the step height, the step sidewall is only scanned by the tip of the semicircle. Figure 1(a) shows, from the geometrical model, the artifact height, which can be expressed as: y R2 x2 h R ,
(1)
where y is the artifact height, h is the step height, and x is the horizontal distance between the arc center and the step edge. Second, when the semicircular height is less than the step height, both the tip of the semicircle and edge would be in contact with the step sidewall during scanning. In this case, an artifact comprises effects of them both. The arc effect is the same as above. Figure 1(b) illustrates the effect of the tip edge, which can be given as: y h (R
x R ). tan sin
（2）
Fig. 1 Geometrical model of the interaction between the tip apex and the step.
Generally, the new commercial tip used for measurement has an approximately 5
8-nm tip radius. Therefore, to guarantee that the tip arc affects the scanning result, the distance between two scanning pixels should be less than 8 nm. Because a larger tip radius results in wider artifacts along the horizontal direction, the scan length should be enough to include the artifact. When considering the convenience for practical experiments, larger scan lengths would require more sampling points, which is time consuming. Therefore, a 2-μm scan length was preferred in this study. To be consistent with the subsequent experiment, in the simulations, the step height was set to 180 nm and the scan length was 2 μm, which contains 512 points with a sampling interval of 3.9 nm. The edge inclination angle α was 33° (with a half angle of 25° along the tip edge given by the manufacturer plus an 8° inclination angle caused by mounting). The theoretical measurement profile data of the step based on equations (1) and (2) and the corresponding FFT data were calculated using Matlab software. 2.2. FFT analysis of the simulated data The simulated profiles of the step (red lines) with different tip radii are shown in Fig. 2, showing the effect of the tip shape on the scanning results. Through the Fourier transform, the step contours were decomposed into different frequency harmonics (black lines), as shown in Fig. 2. It can be seen in Fig. 2(a) that a standard step can be considered as a square wave signal that does not have even harmonics. However, because of the tip radius and tip edge effects, for the scanning results, not only even harmonics are introduced, but the amplitude and phase of each harmonic and DC component have also varied as shown in Fig. 2(b)−(d). The DC component influences only the contour position in the vertical axis, while the component harmonics dictate the contour shape, in which the low-frequency harmonics play a leading role. Meanwhile, as the tip radius increases, the amplitudes and phases of the low-frequency harmonics change more obviously. For a fixed step height, with an increase in the tip radius, the tip artifact in the scanned result contains more components of the arc than the edge of the tip because of the dilation of the surface by the tip, and vice versa. The amount of tip edge contained in the simulated result is decided by the size of the tip radius. Therefore, the overall impact of tip shape on 6
scanning results can be represented by the tip radius.
Fig. 2 The simulation results of step based on the model and the corresponding component harmonics. (a) standard step, (b) result under 100-nm tip radius scanning, (c) 200 nm and (d) 300 nm.
To further analyze the impact of the tip radius on the harmonics, the simulated contours were calculated using the FFT approach to obtain the phase and amplitude of each harmonic, as shown in Fig. 3. It can be seen that the tip radius had a significant effect on spectra in the low-frequency region. However, the high-frequency harmonics also changed slightly with the variation of tip radius. For the long-wavelength harmonics, both amplitudes and phases varied monotonically with the tip radius, outlined in the insets in Fig. 3. Meanwhile, it can be seen that the harmonic amplitude is more susceptible to tip radius than the phase. Therefore, we focused on the relationship between the tip radius and the harmonic amplitude in our tip evaluation.
7
Fig. 3 The corresponding spectra of the simulation results with different tip radii. (a) phase spectra, (b) amplitude spectra.
To establish a function between the tip radius and the harmonic amplitude to estimate the tip radius value, a larger sample of tip radii from 8 to 300 nm (the interval is 1 nm) was employed. By analyzing the influence of tip radius on the amplitude of each harmonic, it was found that the amplitudes of the first four harmonics (the highest frequency is 2 μm-1 of the 4th harmonic) varied monotonically with increasing tip radius, while harmonic frequencies above the 4th harmonic (2 μm-1) did not display monotonic variation. Figure 4 shows the amplitude variation for the first six harmonics of the simulated profiles with increasing radii. It can be seen that the first four harmonics showed monotonic variations with an increase in the tip radius R, but the 5th and 6th harmonics did not. Therefore, the amplitudes of the first four harmonics had corresponding relationships with the tip radius, which could be used as evaluating functions to calculate the tip radius. The higher harmonics (>2 μm-1) were not taken into consideration. To obtain a mathematical equation for this relationship, the curves between the amplitudes of the first four harmonics and the tip radius were fitted with a polynomial. The corresponding fitting curves and expressions are represented by the blue lines in Fig. 4(a)−(d). In these four quadratic functions, the independent variable x represents the tip radius R and the dependent variable y represents the amplitude spectrum. Therefore, for a tip with an unknown radius, such as a worn tip or a new tip, the profile of the normal step imaged with the tip was processed using the FFT method. Then, the tip radius could be estimated based on these equations in Fig. 4(a)−(d). 8
The 2nd and 4th harmonic amplitudes had a larger coefficient for one power term, indicating that they varied more monotonically with the radius. The following two functions were used in this study to evaluate the tip radius R. y=-7.5475e-05x2+0.0966x+9.9811
(3)
y=-1.4625e-04x2+0.0912x+9.5048
(4)
Fig. 4 Functions of the tips with radii from 8 nm to 300 nm and the amplitudes of (a) the first, (b) second, (c) third, (d) fourth, (e) fifth, and (f) sixth harmonics.
The step is a deterministic structure in which the component harmonics can be known. When tips with different degrees of wear are employed to scan, different measurement results would be obtained because of the different tip shapes. The tip shape would result in variation of thee component harmonics, especially for low-frequency harmonics. Meanwhile, the amplitudes of 2nd (1-μm wavelength) and 4th (0.5-μm wavelength) harmonics vary linearly as the tip radius increases, which can be expressed by the equations and are appropriate for tip characterization. However, the wavelengths of low-frequency harmonics are related to the scan length and sampling points. Although changing these two parameters would also result in altering coefficients in equations (3) and (4), linear relationships between low-frequency harmonics and tip radius remain. Therefore, to evaluate the tip using equations (3) and (4) in subsequent experiments, a 2-μm scan length and 512 sampling points should be strictly fixed. 9
In the actual situation, because of the fabrication factor and the wear generated in use, the edges and corners of the step cannot be completely sharp, but have an arc with certain size, as shown in Fig. 5(a). This corner radius would undermine the final estimate of the tip radius, which should be taken into account. Through the analysis it can be shown that for a step with r corner radius, when the radius of the scanning tip is R (Fig. 5(a)), the corresponding measurement result is equal to the condition that the tip with (R+r) radius scans a sharp step (Fig. 5(b)). Therefore, the estimate of the tip radius obtained by the method mentioned above would be more accurate after subtracting the step corner radius.
Fig. 5 Effect of the step corner radius on tip characterization.
3. Experimental details Experiments were carried out using a Dimension Icon AFM (Bruker Company) in the tapping mode under ambient conditions. Two used and worn single crystal silicon tips (RTESP; Bruker Company), named tip-1 and tip-2, respectively, were used to scan the step for evaluation. A nano grating sample with step structures was employed: a platinum-coated silicon substrate with a square pit array on its surface (VGRP-15M; Bruker Company). Dimensions of each pit were 10 μm in length and 180 nm in depth. For each scan, a 50×50 μm2 (256×256 pixels) scan size on the pit array sample was first captured and then a selected local area of 0.5×2 μm2 (128×512 pixels) in the imaged area was employed for characterization, as shown in Fig. 6(a) and (b), respectively. SEM imaging and blind reconstruction were also used to 10
estimate the size of the tips used to verify this method. The sample used for the blind reconstruction approach was a rough titanium sample, which produced many sharp features (RS-15M; Bruker Company). Because in the FFT method the data used for evaluating the tip radius is the AFM image scanned by the corresponding tip, the scanning quality would affect the accuracy of the evaluation result. If the feedback loop of the AFM system is slow, the tip can be off track of the height variation of step structure, and hence the artifact (low frequency) would appear in the AFM image, which in turn misleads the subsequent tip evaluation. To minimize this error, the response of the measuring system to the height variation of the step structure should be evaluated. In our AFM (Dimension Icon), the differences between the round-trip scanning lines for each measuring profile were used to examine the tip tracing state [25]. The scan parameters were adjusted to obtain the minimum difference between the round-trip scanning lines, which renders the measuring results more accurate and lowers the influence of feedback system property. In this case, the scanning results were used for calculating the tip radii.
Fig. 6 AFM images of the grating sample. (a) A wide range scan of the pit array and (b) the local step structure
used for characterization.
4. Results and discussion Using offline AFM processing software (NanoScope Analysis), a matrix containing an image with 128×512 points was captured with each tip. In these 11
matrices each row represented the step outline measured along the fast-scan direction and every column was the data captured along the low-scan direction. The fast- and slow-scan directions are illustrated in Fig. 6(b). An average step outline was calculated by adding all the rows together and then dividing by the number of columns. A tilt error was caused when the sample was mounted, resulting in a difference between the experimental and theoretical results. To reduce this error, we chose to study the sidewall component of the step, and the other data of the scanned step were replaced by the horizontal points to eliminate the tilt. Then the modified height points were calculated by FFT to get the amplitude values of the 2nd and 4th harmonics; these two values were substituted into equations (3) and (4) to evaluate the tip radius. The mean solution value of the two equations is used as the estimated value of the tip radius. The corner radius of the step needs to be known first. A new tip (about 8-nm radius) was used to scan the step structure before evaluating other tips. The corresponding scanned result, as shown in Fig. 7(a), was then analyzed by the above method, resulting in an estimated corner radius of 31.5 nm. With this estimated value, the simulation could be conducted. Figure 7(b) is a comparison of the scanned contour and the reconstructed contour, which shows good coincidence between the two lines. Referring to Fig. 5, the estimated value includes the tip radius and corner radius. Therefore, as the 8-nm tip radius was known, the corner radius of the step can be estimated as 23.5 nm. This value was used for amending the following tip characterization.
12
Fig. 7 (a) The experimental result, (b) the comparison for the experimental and the theoretical.
The estimated radii of tip-1 and tip-2 were 79.2 nm and 98.7 nm, respectively. The red lines in Fig. 8 depict the simulation contours achieved with the established model with tip radii of 79.2 nm and 98.7 nm, respectively. Both of the simulation results are in good agreement with the experimental data. However, there are still some errors between them. This may be caused by the assumption that the hemisphere of the tip apex was at a tangent to the tip edges, which may be inconsistent with the actual condition. The arc and edges may intersect, and the shape of the tip apex may be ellipsoidal rather than spheroidal. Moreover, deviation of the tip edge inclination angle α may also cause a difference between the experimental and simulation data. After eliminating the effect of step corner radius, the final evaluated value is obtained as tip-1 55.7 nm and tip-2 75.2 nm.
Fig. 8 Comparison of the experimental and simulated scan results.
To verify this method, these two tips were used to scan the characterizer sample RS-15M. Each tip was used to scan two positions on the sample surface to obtain two tip evaluations. With commercial image processing software (NanoScope Analysis), the 3D morphology of the tip apex (Fig. 9) could be estimated from the captured AFM images. The cross-sections (blue lines) along the fast-scan direction (Fig. 6(b)) were selected to estimate the tip radius, coinciding with the FFT characterization direction. The top of every cross-section was fitted with a circle by the least squares fit. Upon fitting, the radii estimates of tip-1 were calculated as 45.2 nm (Fig. 9(a)) and 57.4 nm (Fig. 9(b)). For tip-2, the corresponding values were 61.7 nm (Fig. 9(c)) and 60.4 nm 13
(Fig. 9(d)), showing much better consistency. The values obtained with this method were lower than the values estimated with the FFT method. The other direction cross-sections were analyzed as shown in Fig. 9(b) and (d) black lines. For tip-1, there was little difference between radii along the two directions, which indicates the tip apex could be approximately seen as a spheroid. However, tip-2 showed evidence for a worse geometric symmetry – a large difference in radii between the two directions. This blind reconstruction method could be used to obtain visual 3D images of the tips and the radii along different directions, but is susceptible to sharpness features on the sample surface, which should be much sharper than the tip apex. The sharp degree of the feature would result in a misleading evaluation of the tip radius, as shown in Fig. 9(a) and (b). Meanwhile, the image quality obtained while scanning the characterizer sample could also affect the accuracy of the assessment. For each tip, the tip side as shown in Fig. 9(e), which interacts with the scanned structure, was imaged by SEM. The SEM images of the two tips are shown in Fig. 9(f). The two tips were both worn, and tip-2 was more severely worn. The apex of tip-1 shows a better spheroid, which can be seen as tangential to the edges, while the arc of tip-2 apex is more like a section of an ellipsoid. Though SEM imaging can reflect the real topography of the tip, it cannot directly obtain the quantitative radii from images. In Fig. 9(f), the white circles were drawn to coincide with the top arc profiles of tip-1 and tip-2 for estimating the tip radii. Referring to the scale bar, the arc radii of tip-1 and tip-2 could be estimated approximately as 50 nm and 70 nm, respectively. In general, the tip radii values obtained using SEM were comparable to the values achieved with the FFT method, which also served to verify the accuracy of the corner radius estimation. Here, in our evaluating process, only one direction step (one side of the ridge structure) was scanned, and hence the radius represented the cross-section along the scanning direction. If the tip apex is approximated to be symmetric (tip-1), scanning one direction step would be enough. However, if the tip apex is asymmetric, such as for tip-2, the tip radius would vary along different cross-sections. Therefore, to obtain 14
more information about the tip apex, different direction steps should be scanned and evaluated by the FFT method to get tip radii of different cross-sections.
Fig. 9 The estimated 3D topographies of tip apexes obtained by blind reconstruction and the cross-sections of apexes, and SEM images for tips.
5. Conclusion As there was instrumental noise emerging in the high-frequency range, analysis in the low-frequency range lowered this influence on the characterization. By analyzing the effects of the tip radius on the low-frequency spectral region of the simulated scan results, it was found that as the tip radius increases, the amplitudes of the first four harmonics of the step contours varied monotonically; from this observation two functions were built to use as a tip assessment method. Through the comparison with the blind reconstruction and SEM imaging methods, the effectiveness of this tip characterization was verified. In addition, as we set the tip to have a hemispherical cone shape in the geometrical model, the tip radius mainly affects the amplitudes of low-frequency 15
harmonics, and the evaluating function was derived from the relationship between the tip radius and the amplitude of the low-frequency harmonics. If the tip apex is not spherical, the variation of the scanned contour spectra caused by the tip would mainly occur in the high-frequency components, and the eventual result using this method would not be correct. Therefore, this method is more applicable to quantitatively evaluating the radius of the tip whose apex has a hemispherical shape.
Acknowledgments: The authors gratefully acknowledge financial support from the Foundation for National Natural Science Foundation of China (51222504), the Author of National Excellent Doctoral Dissertation of PR China (201031), the Fundamental Research Funds for the Central Universities (HIT.BRETIV.2013.08) and the Heilongjiang Postal Doctoral Foundations.
References [1] D. Marchetto, A. Rota, L. Calabri, G.C. Gazzadi, C. Menozzi, S. Valeri, AFM investigation of tribological properties of nano-patterned silicon surface, Wear 265 (2008) 577-582. [2] I. Szlufarska, M. Chandross, R.W. Carpick, Recent advances in single-asperity nanotribology, J. Phys. D: Appl. Phys 41 (2008) 123001. [3] M. Kopycinska-Muller, R.H. Geiss, D.C. Hurley, Contact mechanics and tip shape in AFM-based nanomechanical measurements, Ultramicroscopy 106 (2006) 466-474. [4] J. Song, D. Tranchida, G.J. Vancso, Contact mechanics of UV/ozone-treated PDMS by AFM and JKR testing: mechanical performance from nano- to micrometer 16
length scales, Macromolecules 41 (2008) 6757-6762. [5] C.A. Clifford, N. Sano, P. Doyle, M.P. Seah, Nanomechanical measurements of hair as an example of micro-fibre analysis using atomic force microscopy nanoindentation, Ultramicroscopy 114 (2012) 38-45. [6] K.A. Ramirez-Aguilar, K.L. Rowlen, Tip characterization from AFM images of nanometric spherical particles, Langmuir 14 (1998) 2562-2566. [7] S.B. Velegol, S. Pardi, X. Li, D. Velegol, B.E. Logan, AFM imaging artifacts due to bacterial cell height and AFM tip geometry, Langmuir 19 (2003) 851-857. [8] N. Tayebi, Y. Zhang, R.J. Chen, Q. Tran, R. Chen, Y. Nishi, Q. Ma, V. Rao, An ultraclean tip-wear reduction scheme for ultrahigh density scanning probe-based data storage, ACS Nano 4 (2010) 5713-5720. [9] P.C. Fletcher, J.R. Felts, Z. Dai, T.D. Jacobs, H. Zeng, W. Lee, P.E. Sheehan, J.A. Carlisle, R.W. Carpick, W.P. King, Wear-resistant diamond nanoprobe tips with integrated silicon heater for tip-bases nanomanufacturing, ACS Nano 4 (2010) 3338-3344. [10] K.H. Chung, Y.H. Lee, D.E. Kim, Characteristics of fracture during the approach process and wear mechanism of a silicon AFM tip, Ultramicroscopy 102 (2005) 161-171. [11] T. Larsen, K. Moloni, F. Flack, M.A. Eriksson, M.G. Lagally, C.T. Black, Comparison of wear characteristics of etched-silicon and carbon nanotube atomic-force Microscopy probes, Appl Phys Lett 80 (2002) 1996-1998. [12] J.J. Liu, J.K. Notbohm, R.W. Carpick, K.T. Turner, Method for characterizing nanoscale wear of atomic force microscope tips, ACS Nano 4 (2010) 3763-3772. [13] R.F. Egerton, P. Li, M. Malac, Radiation damage in the TEM and SEM, Micro 35 (2004) 399-409. [14] J.S. Villarrubia, Algorithms for scanned probe microscope, image simulation, surface reconstruction and tip estimation, J. Res. Natl. Inst. Stand. Technol 102 17
(1997) 425-454. [15] L.S. Dongmo, J.S. Villarrubia, S.N. Jones, T.B. Renegar, M.T. Postek, J.F. Song, Experimental test of blind tip reconstruction for scanning probe microscopy, Ultramicroscopy 85 (2000) 141-153. [16] M. Xu, D. Fujita, K. Onishi, Reconstruction of atomic force microscopy image by using nanofabricated tip characterizer toward the actual sample surface topography, Rev. Sci. Instrum 80 (2009) 043703. [17] D. Tranchida, S. Piccarolo, R.A.C Deblieck, Some experimental issues of AFM tip blind estimation: the effect of noise and resolution, Meas. Sci. Technol 17 (2006) 2630-2636. [18] G. Jozwiak, A. Henrykowski, A. Masalska, T. Gotszalk, Regularization mechanism in blind tip reconstruction procedure, Ultramicroscopy 118 (2012) 1-10. [19] E.E. Flater, G.E. Zacharakis-Jutz, B.G. Dumba, I.A. White, C.A. Clifford, Towards easy and reliable AFM tip shape determination using blind tip reconstruction, Ultramicroscopy 146 (2014) 130-143. [20] H. Bhaskaran, B. Gotsmann, A. Sebastian, U. Drechsler, M.A. Lantz, M. Despont, P. Jaroenapibal, R.W. Carpick, Y. Chen, K. Sridharan, Ultralow nanoscale wear through atom-by-atom attrition in silicon-containing diamond-like carbon, Nat. Nano 5 (2010) 181-185. [21] V. Bykov, A. Gologanov, V. Shevyakov, Test structure for SPM tip shape deconvolution, Appl. Phys. A 66 (1998) 499-502. [22] Y. Wang, X.Y. Chen, Carbon nanotubes: A promising standard for quantitative evaluation of AFM tip apex geometry, Ultramicroscopy 107 (2007) 293-298. [23] H. Itoh, T. Fujimoto, S. Ichimura, Tip characterizer for atomic force microscopy, Review of Scientific Instruments 77 (2006) 103704. [24] J. Liu, D.S. Grierson, K. Sridharan, R.W. Carpick, K.T. Turner, Assessment of 18
the mechanical integrity of silicon and diamond-like carbon coated silicon atomic force microscope probes, Proc. of SPIE 7767 (2010) 776708. [25] B. Xue, Y.D. Yan, Z.J. Hu, X.S. Zhao, Study on effects of scan parameters on the image quality and tip wear in AFM tapping mode, Scanning 36 (2014) 263-269. Highlights The AFM tips with different radii were simulated to scan a nano step structure. The spectra of the simulation scans under different radii were analyzed. The monotonic variations between tip radius and harmonic amplitude were used for tip characterization. The comparisons with blind reconstruction and SEM imaging methods were conducted to verify the effectiveness of this evaluation method.
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To appear in: Ultramicroscopy Received date: 24 September 2013 Revised date: 9 October 2015 Accepted date: 12 October 2015 Cite this article as: Yongda Yan, Bo Xue, Zhenjiang Hu and Xuesen Zhao, AFM tip characterization by using FFT filtered images of step structures, Ultramicroscopy, http://dx.doi.org/10.1016/j.ultramic.2015.10.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Title: AFM tip characterization by using FFT filtered images of
step structures
Author names and affiliations: Yongda Yan1,2, Bo Xue1,2, Zhenjiang Hu2, Xuesen Zhao2
1
Key Laboratory of Micro-systems and Micro-structures Manufacturing of Ministry of Education,
Harbin Institute of Technology, Harbin, Heilongjiang 150001, P.R. China 2
Center For Precision Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001,
P.R. China
Corresponding author: Y. D. Yan E-mail: [email protected] Tel.: +86-451-86412924 Fax: +86-451-86415244
Present/permanent address: P.O. Box 413 Harbin Institute of Technology, Harbin, Heilongjiang 150001, P.R. China
Abstract The measurement resolution of an atomic force microscope (AFM) is largely dependent on the radius of the tip. Meanwhile, when using AFM to study nanoscale surface properties, the value of the tip radius is needed in calculations. As such, estimation of the tip radius is important for analyzing results taken using an AFM. In 1
this study, a geometrical model created by scanning a step structure with an AFM tip was developed. The tip was assumed to have a hemispherical cone shape. Profiles simulated by tips with different scanning radii were calculated by fast Fourier transform (FFT). By analyzing the influence of tip radius variation on the spectra of simulated profiles, it was found that low-frequency harmonics were more susceptible, and that the relationship between the tip radius and the low-frequency harmonic amplitude of the step structure varied monotonically. Based on this regularity, we developed a new method to characterize the radius of the hemispherical tip. The tip radii estimated with this approach were comparable to the results obtained using scanning electron microscope imaging and blind reconstruction methods.
Keywords: atomic force microscope, step structure, spectrum of image, tip characterization
1. Introduction The atomic force microscope (AFM) is an important research tool in the fields of surface science, materials science, electrochemistry, biology, and metrology. The heart of an AFM is a sharp tip that interacts with the sample’s surface on the atomic level, using a normal force. With this interaction, not only can three-dimensional nanoscale topographies be obtained, but nanotribology [1,2] and nanomechanics [3-5] can also be studied. The fabrication process for new tips yields a radius generally ~8–10 nm wide in the shape of a hemisphere. Thus, the tip geometry is always involved in the testing results and may wear out during continuous contact. The wear of a tip will not only degrade the measurement resolution, but can also introduce error into the experimental results [6,7]. In addition, for nanomechanics studies, the tip radius value needs to be known to calculate the surface parameters [4,5]. Therefore, being more aware of the shape of the tip will lead to more accurate analysis of the results using an 2
AFM. Evaluation of the tip radius has been the focus of our work. General methods for tip characterization are scanning electron microscopy (SEM) [8,9] or transmission electron microscopy (TEM) [10,11]. From the images obtained, the tip radius can be approximated. However, imaging of worn tips using SEM or TEM must be performed before and after the AFM imaging experiments [12], which interrupts the continuous scanning with the tip. Meanwhile, radiation damage from the electron beams used in TEM and SEM can increase both wear on the tip and the tip radius [13]. Moreover, because of the tip dilation effect on the AFM image, a blind reconstruction method has been under development for several years [14-19]. In this method, not only can the shape of the tip be extracted from the AFM image itself [14,15], but the AFM image can also be reconstructed more accurately [14,16]. However, the blind reconstruction method is very sensitive to spikes in the data (noise) that result during the imaging process from external interferences and the scanning parameter settings; these spikes affect the estimation of the results and lead to an underestimated tip radius [17,18]. To improve this characterization, methods to reduce the influence of noise on the reconstruction results were investigated [18]. In addition, the parameter settings for the reconstruction process were optimized to increase the characterization method’s
ease
of
use
[19].
Some
researchers
[12,20]
have
used
the
Derjaguin-Muller-Toporov theory of contact mechanics to analyze tip wear. A worn tip has an increased contact area with the water film between the tip and sample, leading to an increase in the adhesive force F (F=2πWR, where W is the work of adhesion and R is the tip radius) between them. With the other conditions unchanged, the adhesive force varies with a change in the tip radius, and this observation is employed as a method to estimate the tip apex geometry. Another tip characterization method frequently used is based on scanning defined reference surfaces on which there are structures in special geometries, such as a sphere [6], peaks [21], a cylinder [22], and the grating [23]. The tip radii can be calculated from the images obtained using the established tip-sample interaction geometrical model. However, some 3
models are complicated, requiring complex calculations. The models were developed under ideal conditions where the structures had accurate dimensions, which may induce errors caused by the difference between the actual and theoretical conditions. In addition, preparation of the special structures adds difficulty to this method. New methods to estimate the tip apex geometry are still required. The random height distribution of the surface topography makes it difficult to extract the tip radius quantitatively and accurately directly from the AFM images. Liu et al. [24] found that the power spectral density curve of the AFM image obtained with a blunt tip was lower than that with a sharper tip, indicating a decline in resolution with a worn tip. By using this method they qualitatively evaluated the tip wear through estimation of the tip radius. It seemed that the frequency domain analysis method had good potential as a way to estimate the tip radius. For defined structure surfaces, the tip radius can be directly calculated from the sample image artifacts caused by the tip-sample interaction, but artifacts introduced by instrumental noise and poor response to the AFM control system may degrade the accuracy of this method. Fast Fourier transform (FFT) analysis can separate the noise signal (usually high frequency) from the useful component. As such, spectrum analysis for the tip assessment may decrease the error. Our objective here is to develop a simple and effective FFT analysis method for AFM images of the defined structure to quantitatively evaluate the AFM tip radius. In the present study, a nano-stepped structure that has accurate and simple dimensions was chosen as the tip characterizer. The geometrical model based on the AFM tip scanning the step structure was established. The shape of the AFM tip in the model was assumed to be a hemispherical cone, which is the frequently presented shape in AFM experiments. In addition, this hemispherical tip is often used as an indenter for nanoindentation [4,5]. Tips with different radii were simulated to scan the step structure and the FFT results of the corresponding scanned contours were calculated. The relationships between the tip radius and variations in the harmonics of the step structure were also investigated. 4
2. Modeling and estimation methods based on FFT analysis 2.1. Modeling the interaction between the tip apex and step structure First, the geometrical interaction model was built to simulate the AFM imaging process on a step with different tip radii, as shown in Fig. 1. For the simulation, it is assumed that the tip apex had a semicircular arc with a radius of curvature R tangential to the tip edges. The edges are at an angle α from the vertical. The step structure has an ideal right angle. As shown in Fig. 1(a) and (b), there are two conditions described as follows: first, when the height of the semicircular tip apex (the distance between tangent points of the semicircle and the edges and the semicircle vertex) is higher than the step height, the step sidewall is only scanned by the tip of the semicircle. Figure 1(a) shows, from the geometrical model, the artifact height, which can be expressed as: y R2 x2 h R ,
(1)
where y is the artifact height, h is the step height, and x is the horizontal distance between the arc center and the step edge. Second, when the semicircular height is less than the step height, both the tip of the semicircle and edge would be in contact with the step sidewall during scanning. In this case, an artifact comprises effects of them both. The arc effect is the same as above. Figure 1(b) illustrates the effect of the tip edge, which can be given as: y h (R
x R ). tan sin
（2）
Fig. 1 Geometrical model of the interaction between the tip apex and the step.
Generally, the new commercial tip used for measurement has an approximately 5
8-nm tip radius. Therefore, to guarantee that the tip arc affects the scanning result, the distance between two scanning pixels should be less than 8 nm. Because a larger tip radius results in wider artifacts along the horizontal direction, the scan length should be enough to include the artifact. When considering the convenience for practical experiments, larger scan lengths would require more sampling points, which is time consuming. Therefore, a 2-μm scan length was preferred in this study. To be consistent with the subsequent experiment, in the simulations, the step height was set to 180 nm and the scan length was 2 μm, which contains 512 points with a sampling interval of 3.9 nm. The edge inclination angle α was 33° (with a half angle of 25° along the tip edge given by the manufacturer plus an 8° inclination angle caused by mounting). The theoretical measurement profile data of the step based on equations (1) and (2) and the corresponding FFT data were calculated using Matlab software. 2.2. FFT analysis of the simulated data The simulated profiles of the step (red lines) with different tip radii are shown in Fig. 2, showing the effect of the tip shape on the scanning results. Through the Fourier transform, the step contours were decomposed into different frequency harmonics (black lines), as shown in Fig. 2. It can be seen in Fig. 2(a) that a standard step can be considered as a square wave signal that does not have even harmonics. However, because of the tip radius and tip edge effects, for the scanning results, not only even harmonics are introduced, but the amplitude and phase of each harmonic and DC component have also varied as shown in Fig. 2(b)−(d). The DC component influences only the contour position in the vertical axis, while the component harmonics dictate the contour shape, in which the low-frequency harmonics play a leading role. Meanwhile, as the tip radius increases, the amplitudes and phases of the low-frequency harmonics change more obviously. For a fixed step height, with an increase in the tip radius, the tip artifact in the scanned result contains more components of the arc than the edge of the tip because of the dilation of the surface by the tip, and vice versa. The amount of tip edge contained in the simulated result is decided by the size of the tip radius. Therefore, the overall impact of tip shape on 6
scanning results can be represented by the tip radius.
Fig. 2 The simulation results of step based on the model and the corresponding component harmonics. (a) standard step, (b) result under 100-nm tip radius scanning, (c) 200 nm and (d) 300 nm.
To further analyze the impact of the tip radius on the harmonics, the simulated contours were calculated using the FFT approach to obtain the phase and amplitude of each harmonic, as shown in Fig. 3. It can be seen that the tip radius had a significant effect on spectra in the low-frequency region. However, the high-frequency harmonics also changed slightly with the variation of tip radius. For the long-wavelength harmonics, both amplitudes and phases varied monotonically with the tip radius, outlined in the insets in Fig. 3. Meanwhile, it can be seen that the harmonic amplitude is more susceptible to tip radius than the phase. Therefore, we focused on the relationship between the tip radius and the harmonic amplitude in our tip evaluation.
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Fig. 3 The corresponding spectra of the simulation results with different tip radii. (a) phase spectra, (b) amplitude spectra.
To establish a function between the tip radius and the harmonic amplitude to estimate the tip radius value, a larger sample of tip radii from 8 to 300 nm (the interval is 1 nm) was employed. By analyzing the influence of tip radius on the amplitude of each harmonic, it was found that the amplitudes of the first four harmonics (the highest frequency is 2 μm-1 of the 4th harmonic) varied monotonically with increasing tip radius, while harmonic frequencies above the 4th harmonic (2 μm-1) did not display monotonic variation. Figure 4 shows the amplitude variation for the first six harmonics of the simulated profiles with increasing radii. It can be seen that the first four harmonics showed monotonic variations with an increase in the tip radius R, but the 5th and 6th harmonics did not. Therefore, the amplitudes of the first four harmonics had corresponding relationships with the tip radius, which could be used as evaluating functions to calculate the tip radius. The higher harmonics (>2 μm-1) were not taken into consideration. To obtain a mathematical equation for this relationship, the curves between the amplitudes of the first four harmonics and the tip radius were fitted with a polynomial. The corresponding fitting curves and expressions are represented by the blue lines in Fig. 4(a)−(d). In these four quadratic functions, the independent variable x represents the tip radius R and the dependent variable y represents the amplitude spectrum. Therefore, for a tip with an unknown radius, such as a worn tip or a new tip, the profile of the normal step imaged with the tip was processed using the FFT method. Then, the tip radius could be estimated based on these equations in Fig. 4(a)−(d). 8
The 2nd and 4th harmonic amplitudes had a larger coefficient for one power term, indicating that they varied more monotonically with the radius. The following two functions were used in this study to evaluate the tip radius R. y=-7.5475e-05x2+0.0966x+9.9811
(3)
y=-1.4625e-04x2+0.0912x+9.5048
(4)
Fig. 4 Functions of the tips with radii from 8 nm to 300 nm and the amplitudes of (a) the first, (b) second, (c) third, (d) fourth, (e) fifth, and (f) sixth harmonics.
The step is a deterministic structure in which the component harmonics can be known. When tips with different degrees of wear are employed to scan, different measurement results would be obtained because of the different tip shapes. The tip shape would result in variation of thee component harmonics, especially for low-frequency harmonics. Meanwhile, the amplitudes of 2nd (1-μm wavelength) and 4th (0.5-μm wavelength) harmonics vary linearly as the tip radius increases, which can be expressed by the equations and are appropriate for tip characterization. However, the wavelengths of low-frequency harmonics are related to the scan length and sampling points. Although changing these two parameters would also result in altering coefficients in equations (3) and (4), linear relationships between low-frequency harmonics and tip radius remain. Therefore, to evaluate the tip using equations (3) and (4) in subsequent experiments, a 2-μm scan length and 512 sampling points should be strictly fixed. 9
In the actual situation, because of the fabrication factor and the wear generated in use, the edges and corners of the step cannot be completely sharp, but have an arc with certain size, as shown in Fig. 5(a). This corner radius would undermine the final estimate of the tip radius, which should be taken into account. Through the analysis it can be shown that for a step with r corner radius, when the radius of the scanning tip is R (Fig. 5(a)), the corresponding measurement result is equal to the condition that the tip with (R+r) radius scans a sharp step (Fig. 5(b)). Therefore, the estimate of the tip radius obtained by the method mentioned above would be more accurate after subtracting the step corner radius.
Fig. 5 Effect of the step corner radius on tip characterization.
3. Experimental details Experiments were carried out using a Dimension Icon AFM (Bruker Company) in the tapping mode under ambient conditions. Two used and worn single crystal silicon tips (RTESP; Bruker Company), named tip-1 and tip-2, respectively, were used to scan the step for evaluation. A nano grating sample with step structures was employed: a platinum-coated silicon substrate with a square pit array on its surface (VGRP-15M; Bruker Company). Dimensions of each pit were 10 μm in length and 180 nm in depth. For each scan, a 50×50 μm2 (256×256 pixels) scan size on the pit array sample was first captured and then a selected local area of 0.5×2 μm2 (128×512 pixels) in the imaged area was employed for characterization, as shown in Fig. 6(a) and (b), respectively. SEM imaging and blind reconstruction were also used to 10
estimate the size of the tips used to verify this method. The sample used for the blind reconstruction approach was a rough titanium sample, which produced many sharp features (RS-15M; Bruker Company). Because in the FFT method the data used for evaluating the tip radius is the AFM image scanned by the corresponding tip, the scanning quality would affect the accuracy of the evaluation result. If the feedback loop of the AFM system is slow, the tip can be off track of the height variation of step structure, and hence the artifact (low frequency) would appear in the AFM image, which in turn misleads the subsequent tip evaluation. To minimize this error, the response of the measuring system to the height variation of the step structure should be evaluated. In our AFM (Dimension Icon), the differences between the round-trip scanning lines for each measuring profile were used to examine the tip tracing state [25]. The scan parameters were adjusted to obtain the minimum difference between the round-trip scanning lines, which renders the measuring results more accurate and lowers the influence of feedback system property. In this case, the scanning results were used for calculating the tip radii.
Fig. 6 AFM images of the grating sample. (a) A wide range scan of the pit array and (b) the local step structure
used for characterization.
4. Results and discussion Using offline AFM processing software (NanoScope Analysis), a matrix containing an image with 128×512 points was captured with each tip. In these 11
matrices each row represented the step outline measured along the fast-scan direction and every column was the data captured along the low-scan direction. The fast- and slow-scan directions are illustrated in Fig. 6(b). An average step outline was calculated by adding all the rows together and then dividing by the number of columns. A tilt error was caused when the sample was mounted, resulting in a difference between the experimental and theoretical results. To reduce this error, we chose to study the sidewall component of the step, and the other data of the scanned step were replaced by the horizontal points to eliminate the tilt. Then the modified height points were calculated by FFT to get the amplitude values of the 2nd and 4th harmonics; these two values were substituted into equations (3) and (4) to evaluate the tip radius. The mean solution value of the two equations is used as the estimated value of the tip radius. The corner radius of the step needs to be known first. A new tip (about 8-nm radius) was used to scan the step structure before evaluating other tips. The corresponding scanned result, as shown in Fig. 7(a), was then analyzed by the above method, resulting in an estimated corner radius of 31.5 nm. With this estimated value, the simulation could be conducted. Figure 7(b) is a comparison of the scanned contour and the reconstructed contour, which shows good coincidence between the two lines. Referring to Fig. 5, the estimated value includes the tip radius and corner radius. Therefore, as the 8-nm tip radius was known, the corner radius of the step can be estimated as 23.5 nm. This value was used for amending the following tip characterization.
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Fig. 7 (a) The experimental result, (b) the comparison for the experimental and the theoretical.
The estimated radii of tip-1 and tip-2 were 79.2 nm and 98.7 nm, respectively. The red lines in Fig. 8 depict the simulation contours achieved with the established model with tip radii of 79.2 nm and 98.7 nm, respectively. Both of the simulation results are in good agreement with the experimental data. However, there are still some errors between them. This may be caused by the assumption that the hemisphere of the tip apex was at a tangent to the tip edges, which may be inconsistent with the actual condition. The arc and edges may intersect, and the shape of the tip apex may be ellipsoidal rather than spheroidal. Moreover, deviation of the tip edge inclination angle α may also cause a difference between the experimental and simulation data. After eliminating the effect of step corner radius, the final evaluated value is obtained as tip-1 55.7 nm and tip-2 75.2 nm.
Fig. 8 Comparison of the experimental and simulated scan results.
To verify this method, these two tips were used to scan the characterizer sample RS-15M. Each tip was used to scan two positions on the sample surface to obtain two tip evaluations. With commercial image processing software (NanoScope Analysis), the 3D morphology of the tip apex (Fig. 9) could be estimated from the captured AFM images. The cross-sections (blue lines) along the fast-scan direction (Fig. 6(b)) were selected to estimate the tip radius, coinciding with the FFT characterization direction. The top of every cross-section was fitted with a circle by the least squares fit. Upon fitting, the radii estimates of tip-1 were calculated as 45.2 nm (Fig. 9(a)) and 57.4 nm (Fig. 9(b)). For tip-2, the corresponding values were 61.7 nm (Fig. 9(c)) and 60.4 nm 13
(Fig. 9(d)), showing much better consistency. The values obtained with this method were lower than the values estimated with the FFT method. The other direction cross-sections were analyzed as shown in Fig. 9(b) and (d) black lines. For tip-1, there was little difference between radii along the two directions, which indicates the tip apex could be approximately seen as a spheroid. However, tip-2 showed evidence for a worse geometric symmetry – a large difference in radii between the two directions. This blind reconstruction method could be used to obtain visual 3D images of the tips and the radii along different directions, but is susceptible to sharpness features on the sample surface, which should be much sharper than the tip apex. The sharp degree of the feature would result in a misleading evaluation of the tip radius, as shown in Fig. 9(a) and (b). Meanwhile, the image quality obtained while scanning the characterizer sample could also affect the accuracy of the assessment. For each tip, the tip side as shown in Fig. 9(e), which interacts with the scanned structure, was imaged by SEM. The SEM images of the two tips are shown in Fig. 9(f). The two tips were both worn, and tip-2 was more severely worn. The apex of tip-1 shows a better spheroid, which can be seen as tangential to the edges, while the arc of tip-2 apex is more like a section of an ellipsoid. Though SEM imaging can reflect the real topography of the tip, it cannot directly obtain the quantitative radii from images. In Fig. 9(f), the white circles were drawn to coincide with the top arc profiles of tip-1 and tip-2 for estimating the tip radii. Referring to the scale bar, the arc radii of tip-1 and tip-2 could be estimated approximately as 50 nm and 70 nm, respectively. In general, the tip radii values obtained using SEM were comparable to the values achieved with the FFT method, which also served to verify the accuracy of the corner radius estimation. Here, in our evaluating process, only one direction step (one side of the ridge structure) was scanned, and hence the radius represented the cross-section along the scanning direction. If the tip apex is approximated to be symmetric (tip-1), scanning one direction step would be enough. However, if the tip apex is asymmetric, such as for tip-2, the tip radius would vary along different cross-sections. Therefore, to obtain 14
more information about the tip apex, different direction steps should be scanned and evaluated by the FFT method to get tip radii of different cross-sections.
Fig. 9 The estimated 3D topographies of tip apexes obtained by blind reconstruction and the cross-sections of apexes, and SEM images for tips.
5. Conclusion As there was instrumental noise emerging in the high-frequency range, analysis in the low-frequency range lowered this influence on the characterization. By analyzing the effects of the tip radius on the low-frequency spectral region of the simulated scan results, it was found that as the tip radius increases, the amplitudes of the first four harmonics of the step contours varied monotonically; from this observation two functions were built to use as a tip assessment method. Through the comparison with the blind reconstruction and SEM imaging methods, the effectiveness of this tip characterization was verified. In addition, as we set the tip to have a hemispherical cone shape in the geometrical model, the tip radius mainly affects the amplitudes of low-frequency 15
harmonics, and the evaluating function was derived from the relationship between the tip radius and the amplitude of the low-frequency harmonics. If the tip apex is not spherical, the variation of the scanned contour spectra caused by the tip would mainly occur in the high-frequency components, and the eventual result using this method would not be correct. Therefore, this method is more applicable to quantitatively evaluating the radius of the tip whose apex has a hemispherical shape.
Acknowledgments: The authors gratefully acknowledge financial support from the Foundation for National Natural Science Foundation of China (51222504), the Author of National Excellent Doctoral Dissertation of PR China (201031), the Fundamental Research Funds for the Central Universities (HIT.BRETIV.2013.08) and the Heilongjiang Postal Doctoral Foundations.
References [1] D. Marchetto, A. Rota, L. Calabri, G.C. Gazzadi, C. Menozzi, S. Valeri, AFM investigation of tribological properties of nano-patterned silicon surface, Wear 265 (2008) 577-582. [2] I. Szlufarska, M. Chandross, R.W. Carpick, Recent advances in single-asperity nanotribology, J. Phys. D: Appl. Phys 41 (2008) 123001. [3] M. Kopycinska-Muller, R.H. Geiss, D.C. Hurley, Contact mechanics and tip shape in AFM-based nanomechanical measurements, Ultramicroscopy 106 (2006) 466-474. [4] J. Song, D. Tranchida, G.J. Vancso, Contact mechanics of UV/ozone-treated PDMS by AFM and JKR testing: mechanical performance from nano- to micrometer 16
length scales, Macromolecules 41 (2008) 6757-6762. [5] C.A. Clifford, N. Sano, P. Doyle, M.P. Seah, Nanomechanical measurements of hair as an example of micro-fibre analysis using atomic force microscopy nanoindentation, Ultramicroscopy 114 (2012) 38-45. [6] K.A. Ramirez-Aguilar, K.L. Rowlen, Tip characterization from AFM images of nanometric spherical particles, Langmuir 14 (1998) 2562-2566. [7] S.B. Velegol, S. Pardi, X. Li, D. Velegol, B.E. Logan, AFM imaging artifacts due to bacterial cell height and AFM tip geometry, Langmuir 19 (2003) 851-857. [8] N. Tayebi, Y. Zhang, R.J. Chen, Q. Tran, R. Chen, Y. Nishi, Q. Ma, V. Rao, An ultraclean tip-wear reduction scheme for ultrahigh density scanning probe-based data storage, ACS Nano 4 (2010) 5713-5720. [9] P.C. Fletcher, J.R. Felts, Z. Dai, T.D. Jacobs, H. Zeng, W. Lee, P.E. Sheehan, J.A. Carlisle, R.W. Carpick, W.P. King, Wear-resistant diamond nanoprobe tips with integrated silicon heater for tip-bases nanomanufacturing, ACS Nano 4 (2010) 3338-3344. [10] K.H. Chung, Y.H. Lee, D.E. Kim, Characteristics of fracture during the approach process and wear mechanism of a silicon AFM tip, Ultramicroscopy 102 (2005) 161-171. [11] T. Larsen, K. Moloni, F. Flack, M.A. Eriksson, M.G. Lagally, C.T. Black, Comparison of wear characteristics of etched-silicon and carbon nanotube atomic-force Microscopy probes, Appl Phys Lett 80 (2002) 1996-1998. [12] J.J. Liu, J.K. Notbohm, R.W. Carpick, K.T. Turner, Method for characterizing nanoscale wear of atomic force microscope tips, ACS Nano 4 (2010) 3763-3772. [13] R.F. Egerton, P. Li, M. Malac, Radiation damage in the TEM and SEM, Micro 35 (2004) 399-409. [14] J.S. Villarrubia, Algorithms for scanned probe microscope, image simulation, surface reconstruction and tip estimation, J. Res. Natl. Inst. Stand. Technol 102 17
(1997) 425-454. [15] L.S. Dongmo, J.S. Villarrubia, S.N. Jones, T.B. Renegar, M.T. Postek, J.F. Song, Experimental test of blind tip reconstruction for scanning probe microscopy, Ultramicroscopy 85 (2000) 141-153. [16] M. Xu, D. Fujita, K. Onishi, Reconstruction of atomic force microscopy image by using nanofabricated tip characterizer toward the actual sample surface topography, Rev. Sci. Instrum 80 (2009) 043703. [17] D. Tranchida, S. Piccarolo, R.A.C Deblieck, Some experimental issues of AFM tip blind estimation: the effect of noise and resolution, Meas. Sci. Technol 17 (2006) 2630-2636. [18] G. Jozwiak, A. Henrykowski, A. Masalska, T. Gotszalk, Regularization mechanism in blind tip reconstruction procedure, Ultramicroscopy 118 (2012) 1-10. [19] E.E. Flater, G.E. Zacharakis-Jutz, B.G. Dumba, I.A. White, C.A. Clifford, Towards easy and reliable AFM tip shape determination using blind tip reconstruction, Ultramicroscopy 146 (2014) 130-143. [20] H. Bhaskaran, B. Gotsmann, A. Sebastian, U. Drechsler, M.A. Lantz, M. Despont, P. Jaroenapibal, R.W. Carpick, Y. Chen, K. Sridharan, Ultralow nanoscale wear through atom-by-atom attrition in silicon-containing diamond-like carbon, Nat. Nano 5 (2010) 181-185. [21] V. Bykov, A. Gologanov, V. Shevyakov, Test structure for SPM tip shape deconvolution, Appl. Phys. A 66 (1998) 499-502. [22] Y. Wang, X.Y. Chen, Carbon nanotubes: A promising standard for quantitative evaluation of AFM tip apex geometry, Ultramicroscopy 107 (2007) 293-298. [23] H. Itoh, T. Fujimoto, S. Ichimura, Tip characterizer for atomic force microscopy, Review of Scientific Instruments 77 (2006) 103704. [24] J. Liu, D.S. Grierson, K. Sridharan, R.W. Carpick, K.T. Turner, Assessment of 18
the mechanical integrity of silicon and diamond-like carbon coated silicon atomic force microscope probes, Proc. of SPIE 7767 (2010) 776708. [25] B. Xue, Y.D. Yan, Z.J. Hu, X.S. Zhao, Study on effects of scan parameters on the image quality and tip wear in AFM tapping mode, Scanning 36 (2014) 263-269. Highlights The AFM tips with different radii were simulated to scan a nano step structure. The spectra of the simulation scans under different radii were analyzed. The monotonic variations between tip radius and harmonic amplitude were used for tip characterization. The comparisons with blind reconstruction and SEM imaging methods were conducted to verify the effectiveness of this evaluation method.
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