- Email: [email protected]
A simple method for AFM tip characterization by polystyrene spheres
ARTICLE IN PRESS Ultramicroscopy 108 (2008) 975– 980
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
A simple method for AFM tip characterization by polystyrene spheres Zhi-gang Zeng a, Guo-dong Zhu a, Zhang Guo b, Li Zhang a, Xue-jian Yan a,, Qiang-guo Du b, Ran Liu c a b c
Department of Materials Science, Fudan University, 220 Handan Road, Shanghai 200433, China Department of Macromolecular Science, Fudan University, 220 Handan Road, Shanghai 200433, China School of Microelectronics, Fudan University, 220 Handan Road, Shanghai 200433, China
a r t i c l e in fo
abstract
Article history: Received 14 December 2007 Received in revised form 20 March 2008 Accepted 8 April 2008
An AFM image would not be the true topography of a surface because of the limitation of a finite size of the tip. The true topography of the surface can be deduced if we can know the tip shape. In this paper a simple method has been established to determine the profile of an AFM tip. A geometrical model for the tip and a spherical object has been proposed to show the procedure for deducing the tip shape from AFM images. Isolated spheres and closely packed spheres with different diameters have been observed to confirm the tip shape by this method. It is a non-destructive method to determine the tip shape and the results can be used for future reconstruction of an AFM image. & 2008 Elsevier B.V. All rights reserved.
PACS: 06.30.Bp 61.16.Ch 07.05.Tp Keywords: AFM Tip characterization Polystyrene spheres
1. Introduction Atomic force microscopy (AFM) has occupied a key place in nanometer-scale metrology in both research and industrial applications. It is widely used to obtain topographic information and quantitative data of sample surface in the nanometer scale. However, it is well known that in lateral direction the distortion or artifact [1–10] caused by the non-vanishing size of AFM tip may broaden the measured peaks, especially in the scanning of some surfaces with high aspect ratio surface features. Tip-induced artifacts in AFM observations can usually be modified by using a sharper tip [1,2], or by the algorithms method to reconstruct the AFM images [3–8]. Chen et al. [2] have reported that the AFM tip made of carbon nanotube is available to optimize the image resolution. For the reconstruction method, a conventional way to mathematically remove the tip effect from the acquired images is based on tip characterizers. By this method, an object whose geometry and dimensions are well defined, such as spheres, is firstly scanned by AFM. Secondly, the shape information of the tip, such as the apex radius, is generally deduced from the obtained image. Thirdly, another AFM image of an unknown surface is obtained using the same tip. Finally, the
Corresponding author. Tel.: +86 021 6564 2872.
E-mail address: [email protected] (X.-j. Yan). 0304-3991/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2008.04.001
‘‘true’’ topography of sample surface can be acquired by algorithms to remove the convolution of the determined tip. Therefore, in order to deduce the ‘‘true’’ topography of the sample surface, it is important to determine the tip profile primarily. The shape of the tip can be directly observed by SEM or TEM, but it is a destructive method because of the deposition of conductive coating. For a non-destructive determination there are several suitable mediums as tip characterizers, including small spheres whose diameter is under 100 nm [3–5], large spheres of several hundred nanometers in diameter [6], samples with sharp protrusions [7,8] and so on. However, all of these tip characterizers are not powerful enough to determine both body and apex information of the tip. Large spheres and samples with sharp protrusions are excellent for the measurement of body information but are poor for apex determination [6]; in contrast, small spheres are better for apex determination but give less body information of the tip [3,6,7]. In order to obtain the entire information (both on body and apex) of the tip, it is necessary to integrate different kinds of tip characterizers, but large errors may be introduced into such an integration system. In this paper, we propose a simple model that only uses large spheres for the determination of the body and the apex information of the tip and this model is verified experimentally by polystyrene (PS) spheres with different diameters. It is a non-destructive method which can provide precise data of the profile of an AFM tip for the following reconstruction of the AFM images.
ARTICLE IN PRESS 976
Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
2. Modeling In our model, isolated spheres and closely packed spheres are selected as tip characterizers; the profile of the AFM tip is supposed to be of a pyramidal shape with an asymmetrical structure [10], and the tip apex to be of a spherical shape with a certain curvature, as shown in Fig. 1. The visualization of the AFM tip has three steps as follows: Firstly, for the isolated spheres, as shown in Fig. 1a, if the tip scans a single sphere from the left to the right, the left-half apparent width (wL) is influenced by the right slope angle of the tip (yR), while the right-half apparent width (wR) is decided by the left slope angle of the tip (yL). Because the height of the isolated spheres is determined correctly, the summit of the apparent spheres can be considered as a cut-off point to separate the lefthalf and the right-half apparent width. In geometry, the broadened width includes the width (x1+x2, Fig. 1b) introduced by the body of tip and the width (x3) induced by the tip apex, so the right-half apparent width can be expressed as follows: wR ¼ R cos yL þ Rðsin yL þ 1Þ tan yL þ rðcos ec yL 1Þ tan yL 1 þ sin yL 1 sin yL ¼R þr cos yL cos yL
(1)
Secondly, for closely packed spheres, as shown in Fig. 2a, the lateral measurement of this periodical structure is hardly affected by the tip and this kind of closely packed spheres can be considered as a calibration standard for SEM and AFM [11]. However, the measured altitude difference (between the dashed lines shown in Fig. 2a) of the periodical profile is shrunk and smaller than the radius of spheres because of the tip effect, and this shrunk altitude will be taken into consideration for the determination of the tip shape. Besides, the assumed tip (as shown in Fig. 1a) is asymmetrical and the slopes are not the same, so the lowest point is off-center and not directly above the contact point between two spheres. In order to simplify the calculation, the altitude h (as shown in Fig. 2b) at the point above the contact point (corresponding to the point D) between two spheres is considered instead of the supreme altitude hmax (from the lowest point of the AFM tip scanning curve to the maximal point of the sphere, as shown in Fig. 2a). In addition, because the right slope angle is larger than the left one, the right-half slope angle is a dominating parameter to affect the altitude difference. In this case, the geometrical relationship is depicted in Fig. 2b, when the tip detects the contact point D. Thus, h can be expressed as h ¼ R ðy1 y2 þ y3 Þ ¼ R ½R sin yR Rð1 cos yR Þ= tan yR þ rðcos ec yR 1Þ
where R is the radius of spheres and r is the curvature radius of the tip apex. Analogously, the left-half apparent width can be deduced:
sin yR þ cos yR 1 1 sin yR r h¼R sin yR sin yR
1 þ sin yR 1 sin yR þr . wL ¼ R cos yR cos yR
Finally, the profile of the AFM tip can be deduced from the formulas above. From formulas (2) and (3), the right slope angle
(2)
(3)
Fig. 1. Schematic diagrams of (a) a scanning an isolated sphere by an AFM tip and (b) a geometrical broadening of the sphere’s dimension by the tip. x1 is the projected length between the center of the sphere and the contact point (A) of the sphere and the tip, x2 is the projected length from point (A) to the crossing point (B) of the substrate surface and the extended line from the tip body, x3 is the projected length from point (B) to the contact point (C) of the tip apex and the substrate. yL is the left slope angle of the tip.
Fig. 2. Schematic diagrams of (a) scanning closely packed spheres by an AFM tip and of (b) the geometrical relationship of the profile when the tip detects the contact point between adjacent spheres. Point A is the projected point on the Y-axis of the contact point of the tip’s right-half body and the sphere. Point B is the tip apex. Point C is the crossing point of the Y-axis and the extended line from the tip’s right-half body. D is the contact point of two spheres. yR is right slope angle of the tip.
ARTICLE IN PRESS Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
can be deduced as yR ¼ arctg
wL R 2R h
(4)
Then, the curvature radius (r) of tip apex can be calculated by substituting yR to formula (2) and the left slope angle (yL) can be obtained by substituting r to formula (1).
3. Experimental Aqueous suspensions of monodispersed PS latex spheres with average diameter of 199 nm (Duke Scientific Corporation) and 430 nm (homemade) were used. The substrates were glass slides (1 cm 1 cm) which were immerged into the intermixture of sulfuric acid (98%) and hydrogen peroxide (H2SO4:H2O2 ¼ 3:1) overnight to obtain hydrophilic surfaces.
977
The isolated spheres were prepared as follows: the glass slide was immersed into the PS suspensions (0.5 wt%) for 2 min. And then the glass slide was withdrawn and re-immersed mildly into the deionized water to remove the spheres that were weakly absorbed on the substrate. Finally, the glass slide was dried by air flow at room temperature. The closely packed spheres were made by the spin-coating method. The spheres might self-assemble into ordered structures after the evaporation of water. In our experiments, the volume of PS suspensions (0.5 wt%) and the spin speed were mainly controlled to obtain a monolayer film. The volume of PS suspensions and the spin speed were 50 mL and 100 rpm, respectively, for homemade spheres (430 nm), and 25 mL and 170 rpm for Duke spheres (200 nm). A gold layer with thickness about 10–15 nm was deposited onto these spheres. The Au layer can make the spheres much more stable on the substrate and more universal for the observation by SEM, TEM and STM and so on. Because the Au layer might have some influence on the size of these spheres, the sphere samples
Fig. 3. SEM images (a, b), AFM images (c, d) and typical cross-sections (e, f) of isolated spheres. (a), (c) and (e) are obtained from 430 nm spheres and (b), (d) and (f) are from 200 nm spheres. The scan range of (c) and (d) is 5 mm 5 mm.
ARTICLE IN PRESS 978
Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
were re-calibrated by SEM in Shanghai Institute of Measurement and Testing Technology (SIMT), China. The statistical diameters of these samples were 20075 and 430713 nm, respectively. The AFM data were acquired by UltraObjective AFM (SIS, Germany) with the tapping mode. The AFM parameters were carefully set to minimize the pressure of tip on the spheres, and the Au layer also could enhance the non-deformability of spheres against the tip pressure [12]. The commercial Si3N4 tip was used, which was pyramidal in shape with the nominal apex radius of about 30 nm, and the tilted angle of the cantilever was about 81 during scanning (from the manual of SIS GmbH). The collected AFM data were statistically analyzed to calculate the profile of the tip. Over 50 isolated spheres were counted to obtain the apparent width (wL and wR) and over 200 closely packed spheres were considered to acquire the altitude difference (h and hmax).
4. Results and discussions 4.1. Topography of isolated spheres The SEM and AFM images of the isolated spheres are shown in Fig. 3. The spheres in the SEM images were regular and symmetric both for 430 nm (Fig. 3a) and 200 nm spheres (Fig. 3b). The AFM images (Fig. 3c and d) of these spheres were distorted by the AFM tip and the distortion was even worse for 430 nm spheres (Fig. 3c). From the typical cross-section analysis of the isolated spheres (Fig. 3e and f), an asymmetrical structure and linear regions on both sides were demonstrated. The asymmetrical structure in the AFM images would be caused by the asymmetrical body of the AFM tip because the spheres were of regular spherical shape, as shown in the SEM images (Fig. 3a and b).
Fig. 4. SEM images (a, b), AFM images (c, d) and typical cross-sections (e, f) of closely packed spheres. (a), (c) and (e) are obtained from 430 nm spheres and (b), (d) and (f) are from 200 nm spheres. The scan range of (c) and (d) is 5 mm 5 mm and 2 mm 2 mm, respectively.
ARTICLE IN PRESS Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
979
Table 1 Experimental data and consequently calculated tip parameters Diameter D (from SEM)(nm)
Experimental results hmax (nm)
20075 430713
39.472.1 121.677.2
h (nm)
36.271.9 108.676.8
Calculated results wL (nm)
219.676.8 424.7710.9
4.2. Topography of closely packed spheres The SEM and AFM images of the closely packed spheres are demonstrated in Fig. 4. The spheres were closely packed as hexagonal structures with some defects. The shapes of the spheres in the AFM images (Fig. 4c and d) were almost regular like that in the SEM images (Fig. 4a and b) and did not show any distortion like that of isolated spheres (Fig. 3(c) and (d)). The average diameters measured by AFM were 432.5 and 201.2 nm, respectively, which were well consistent with the results measured at SIMT. It is illustrated that the size information of these closely packed spheres in the lateral direction was hardly affected by the tip. The typical cross sections of closely packed spheres (Fig. 4e and f) clearly depicted that the altitude difference was affected by the tip and was less than the radius of the corresponding spheres. The altitude difference (h and hmax) can be directly read from the cross-sections, and h is the altitude of the midpoint between two maximal point of spheres. Because the spheres were not absolutely uniform and there were some assembling defects, both h and hmax were statistically averaged for the calculation of our model.
4.3. Tip characterization In the experiments, some factors may greatly affect the accuracy of our measurements, such as the diameter distribution of spheres, the AFM scan parameters, the processing of AFM images and so on. The diameter distribution is an important factor that can directly enlarge the deviation of the AFM measurements. In our experiments, the diameter distribution is 2.5% for 200 nm spheres and 3.0% for 430 nm spheres. However, monodispersed spheres with a smaller diameter distribution are available in the market, and use of those spheres may improve the accuracy of the AFM tip characterization. Besides, in order to inhibit the further deviation induced by the image processing, the acquired AFM images were not processed by any offline algorithms except for the plane correction to remove the information of the tilted background. Because of these factors, the experimental results were obtained statistically over 50 isolated spheres and 300 closely packed spheres. The statistic data and calculated results according to our model are listed in Table 1. The slope angles and apex radius of the tip were calculated by the mean value. The results calculated from hmax were also listed in order to make comparisons. Because the tip is asymmetrical and the lowest point is offcenter, the value of h is about 90% of the value of hmax in our experiments. Comparing the calculated results from h with that from hmax, it can be found that the slope angle alters a little but the curvature radius of the tip apex shows more sensitivity to the value of the altitude difference, especially for the 430 nm spheres. It implies that h is a key parameter to obtain the correct curvature radius of the tip apex, so suitable scan size and speed [13] should be taken into consideration
wR (nm)
180.274.2 355.576.9
From hmax
From h
yL (deg)
yR (deg)
r (nm)
yL (deg)
yR (deg)
r (nm)
23.9 24.3
36.7 34.2
40.7 35.0
22.8 22.4
36.1 33.1
44.8 51.2
to carefully determine the maximal point of spheres and the value of h. As shown in Table 1, the curvature radius of the tip apex was 44.8 nm calculated from 200 nm spheres and 51.2 nm from 430 nm spheres. The calculated radii of the tip apex were a little larger than the nominal value (30 nm) reported in the manual. The total tip vertex angle obtained from 200 nm spheres was 58.91 and the right slope angle was 13.31 larger than the left one; the total tip vertex angle acquired from 430 nm spheres was 55.51 and the right slope angle was 10.71 larger than the left one. The calculated slope angles were well consistent. It should be noted that in our model the tilted angle of the cantilever during scanning is assumed to be 01, while, in most situations, the inclination of the cantilever (the tilted angle is about 81 in our experiments) may induce the tip to cause a slight inclination of the tip to the sample surface [4]. Thus, the calculated asymmetry of the tip in our model has included the influence of the inclination of the cantilever. Additionally, the tip actually is not so ideal and the electrical noise may be introduced when the tip is scanning, so these factors may also have some contribution to the experimental errors. However, the calculated profile of the AFM tip from 200 nm spheres is well consistent with that from 430 nm spheres, and we believe that our proposed method is efficient to determine the slope angle of the AFM tip and the curvature radius of the tip apex. The acquired data of the tip shape can be used to reconstruct the AFM images, and the reconstruction will be conducted in our further work. 5. Conclusion In conclusion, a simple model based on isolated spheres and closely packed spheres as the characterizers has been proposed to determine the profile of the AFM tip. Monodispersed PS spheres with diameters of 200 and 430 nm have been utilized to verify this model. The total vertex angle of the tip obtained from our model was 58.91 and the right slope angle was 13.31 larger than the left one by using the data obtained from 200 nm spheres; the total vertex angle of the tip was 55.51 and the right slope angle was 10.71 larger than the left one from 430 nm spheres. The curvature radius of the tip apex was 44.8 nm from 200 nm spheres and 51.2 nm from 430 nm spheres. The results indicate that the calculated profiles are well consistent with each other, which means that our model is efficient and non-destructive to obtain both the body information and apex radius of tips. Acknowledgments This work was supported by the project of STCSM (No. 0652NM028), the Shanghai Leading Academic Discipline Project (B113) and the International Research Training Group (IRTG).
ARTICLE IN PRESS 980
Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
References [1] [2] [3] [4] [5] [6]
Y. Martin, K. Wickramasinghe, Appl. Phys. Lett. 64 (1994) 2498. L. Chen, C.L. Cheung, P.D. Ashby, C.M. Lieber, Nano Lett. 4 (2004) 1725. S. Xu, M.F. Arnsdorf, J. Microsc. 187 (1997) 43. P. Markiewicz, M.C. Goh, Langmuir 10 (1994) 5. K. Shiramine, S. Muto, J. Appl. Phys. 101 (2007) 033527. P. Markiewicz, S.R. Cohen, A. Efimov, D.V. Ovchinnikov, A.A. Bukharaev, Probe Microsc. 1 (1999) 355.
[7] L. Montelius, J.O. Tegenfeldt, Appl. Phys. Lett. 62 (1993) 2628. [8] V. Bykov, A. Golaganov, V. Shevyakov, Appl. Phys. A 66 (1998) 499. [9] L.S. Dongmo, J.S. Villarrubia, S.N. Jones, T.B. Renegar, M.T. Postek, J.F. Song, Ultramicroscopy 85 (2000) 141. [10] K.A. Ramirez-Aguilar, K.L. Rowlen, Langmuir 14 (1998) 2562. [11] Y. Li, S.M. Lindsay, Rev. Sci. Instrum. 62 (1991) 2630. [12] D. Alliata, C. Cecconi, Rev. Sci. Instrum. 67 (1996) 748. [13] H.G. Abdelhady, S. Allen, S.J. Ebbens, C. Madden, N. Patel, C.J. Roberts, J. Zhang, Nanotechnology 16 (2005) 966.
Contents lists available at ScienceDirect
Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic
A simple method for AFM tip characterization by polystyrene spheres Zhi-gang Zeng a, Guo-dong Zhu a, Zhang Guo b, Li Zhang a, Xue-jian Yan a,, Qiang-guo Du b, Ran Liu c a b c
Department of Materials Science, Fudan University, 220 Handan Road, Shanghai 200433, China Department of Macromolecular Science, Fudan University, 220 Handan Road, Shanghai 200433, China School of Microelectronics, Fudan University, 220 Handan Road, Shanghai 200433, China
a r t i c l e in fo
abstract
Article history: Received 14 December 2007 Received in revised form 20 March 2008 Accepted 8 April 2008
An AFM image would not be the true topography of a surface because of the limitation of a finite size of the tip. The true topography of the surface can be deduced if we can know the tip shape. In this paper a simple method has been established to determine the profile of an AFM tip. A geometrical model for the tip and a spherical object has been proposed to show the procedure for deducing the tip shape from AFM images. Isolated spheres and closely packed spheres with different diameters have been observed to confirm the tip shape by this method. It is a non-destructive method to determine the tip shape and the results can be used for future reconstruction of an AFM image. & 2008 Elsevier B.V. All rights reserved.
PACS: 06.30.Bp 61.16.Ch 07.05.Tp Keywords: AFM Tip characterization Polystyrene spheres
1. Introduction Atomic force microscopy (AFM) has occupied a key place in nanometer-scale metrology in both research and industrial applications. It is widely used to obtain topographic information and quantitative data of sample surface in the nanometer scale. However, it is well known that in lateral direction the distortion or artifact [1–10] caused by the non-vanishing size of AFM tip may broaden the measured peaks, especially in the scanning of some surfaces with high aspect ratio surface features. Tip-induced artifacts in AFM observations can usually be modified by using a sharper tip [1,2], or by the algorithms method to reconstruct the AFM images [3–8]. Chen et al. [2] have reported that the AFM tip made of carbon nanotube is available to optimize the image resolution. For the reconstruction method, a conventional way to mathematically remove the tip effect from the acquired images is based on tip characterizers. By this method, an object whose geometry and dimensions are well defined, such as spheres, is firstly scanned by AFM. Secondly, the shape information of the tip, such as the apex radius, is generally deduced from the obtained image. Thirdly, another AFM image of an unknown surface is obtained using the same tip. Finally, the
Corresponding author. Tel.: +86 021 6564 2872.
E-mail address: [email protected] (X.-j. Yan). 0304-3991/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2008.04.001
‘‘true’’ topography of sample surface can be acquired by algorithms to remove the convolution of the determined tip. Therefore, in order to deduce the ‘‘true’’ topography of the sample surface, it is important to determine the tip profile primarily. The shape of the tip can be directly observed by SEM or TEM, but it is a destructive method because of the deposition of conductive coating. For a non-destructive determination there are several suitable mediums as tip characterizers, including small spheres whose diameter is under 100 nm [3–5], large spheres of several hundred nanometers in diameter [6], samples with sharp protrusions [7,8] and so on. However, all of these tip characterizers are not powerful enough to determine both body and apex information of the tip. Large spheres and samples with sharp protrusions are excellent for the measurement of body information but are poor for apex determination [6]; in contrast, small spheres are better for apex determination but give less body information of the tip [3,6,7]. In order to obtain the entire information (both on body and apex) of the tip, it is necessary to integrate different kinds of tip characterizers, but large errors may be introduced into such an integration system. In this paper, we propose a simple model that only uses large spheres for the determination of the body and the apex information of the tip and this model is verified experimentally by polystyrene (PS) spheres with different diameters. It is a non-destructive method which can provide precise data of the profile of an AFM tip for the following reconstruction of the AFM images.
ARTICLE IN PRESS 976
Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
2. Modeling In our model, isolated spheres and closely packed spheres are selected as tip characterizers; the profile of the AFM tip is supposed to be of a pyramidal shape with an asymmetrical structure [10], and the tip apex to be of a spherical shape with a certain curvature, as shown in Fig. 1. The visualization of the AFM tip has three steps as follows: Firstly, for the isolated spheres, as shown in Fig. 1a, if the tip scans a single sphere from the left to the right, the left-half apparent width (wL) is influenced by the right slope angle of the tip (yR), while the right-half apparent width (wR) is decided by the left slope angle of the tip (yL). Because the height of the isolated spheres is determined correctly, the summit of the apparent spheres can be considered as a cut-off point to separate the lefthalf and the right-half apparent width. In geometry, the broadened width includes the width (x1+x2, Fig. 1b) introduced by the body of tip and the width (x3) induced by the tip apex, so the right-half apparent width can be expressed as follows: wR ¼ R cos yL þ Rðsin yL þ 1Þ tan yL þ rðcos ec yL 1Þ tan yL 1 þ sin yL 1 sin yL ¼R þr cos yL cos yL
(1)
Secondly, for closely packed spheres, as shown in Fig. 2a, the lateral measurement of this periodical structure is hardly affected by the tip and this kind of closely packed spheres can be considered as a calibration standard for SEM and AFM [11]. However, the measured altitude difference (between the dashed lines shown in Fig. 2a) of the periodical profile is shrunk and smaller than the radius of spheres because of the tip effect, and this shrunk altitude will be taken into consideration for the determination of the tip shape. Besides, the assumed tip (as shown in Fig. 1a) is asymmetrical and the slopes are not the same, so the lowest point is off-center and not directly above the contact point between two spheres. In order to simplify the calculation, the altitude h (as shown in Fig. 2b) at the point above the contact point (corresponding to the point D) between two spheres is considered instead of the supreme altitude hmax (from the lowest point of the AFM tip scanning curve to the maximal point of the sphere, as shown in Fig. 2a). In addition, because the right slope angle is larger than the left one, the right-half slope angle is a dominating parameter to affect the altitude difference. In this case, the geometrical relationship is depicted in Fig. 2b, when the tip detects the contact point D. Thus, h can be expressed as h ¼ R ðy1 y2 þ y3 Þ ¼ R ½R sin yR Rð1 cos yR Þ= tan yR þ rðcos ec yR 1Þ
where R is the radius of spheres and r is the curvature radius of the tip apex. Analogously, the left-half apparent width can be deduced:
sin yR þ cos yR 1 1 sin yR r h¼R sin yR sin yR
1 þ sin yR 1 sin yR þr . wL ¼ R cos yR cos yR
Finally, the profile of the AFM tip can be deduced from the formulas above. From formulas (2) and (3), the right slope angle
(2)
(3)
Fig. 1. Schematic diagrams of (a) a scanning an isolated sphere by an AFM tip and (b) a geometrical broadening of the sphere’s dimension by the tip. x1 is the projected length between the center of the sphere and the contact point (A) of the sphere and the tip, x2 is the projected length from point (A) to the crossing point (B) of the substrate surface and the extended line from the tip body, x3 is the projected length from point (B) to the contact point (C) of the tip apex and the substrate. yL is the left slope angle of the tip.
Fig. 2. Schematic diagrams of (a) scanning closely packed spheres by an AFM tip and of (b) the geometrical relationship of the profile when the tip detects the contact point between adjacent spheres. Point A is the projected point on the Y-axis of the contact point of the tip’s right-half body and the sphere. Point B is the tip apex. Point C is the crossing point of the Y-axis and the extended line from the tip’s right-half body. D is the contact point of two spheres. yR is right slope angle of the tip.
ARTICLE IN PRESS Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
can be deduced as yR ¼ arctg
wL R 2R h
(4)
Then, the curvature radius (r) of tip apex can be calculated by substituting yR to formula (2) and the left slope angle (yL) can be obtained by substituting r to formula (1).
3. Experimental Aqueous suspensions of monodispersed PS latex spheres with average diameter of 199 nm (Duke Scientific Corporation) and 430 nm (homemade) were used. The substrates were glass slides (1 cm 1 cm) which were immerged into the intermixture of sulfuric acid (98%) and hydrogen peroxide (H2SO4:H2O2 ¼ 3:1) overnight to obtain hydrophilic surfaces.
977
The isolated spheres were prepared as follows: the glass slide was immersed into the PS suspensions (0.5 wt%) for 2 min. And then the glass slide was withdrawn and re-immersed mildly into the deionized water to remove the spheres that were weakly absorbed on the substrate. Finally, the glass slide was dried by air flow at room temperature. The closely packed spheres were made by the spin-coating method. The spheres might self-assemble into ordered structures after the evaporation of water. In our experiments, the volume of PS suspensions (0.5 wt%) and the spin speed were mainly controlled to obtain a monolayer film. The volume of PS suspensions and the spin speed were 50 mL and 100 rpm, respectively, for homemade spheres (430 nm), and 25 mL and 170 rpm for Duke spheres (200 nm). A gold layer with thickness about 10–15 nm was deposited onto these spheres. The Au layer can make the spheres much more stable on the substrate and more universal for the observation by SEM, TEM and STM and so on. Because the Au layer might have some influence on the size of these spheres, the sphere samples
Fig. 3. SEM images (a, b), AFM images (c, d) and typical cross-sections (e, f) of isolated spheres. (a), (c) and (e) are obtained from 430 nm spheres and (b), (d) and (f) are from 200 nm spheres. The scan range of (c) and (d) is 5 mm 5 mm.
ARTICLE IN PRESS 978
Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
were re-calibrated by SEM in Shanghai Institute of Measurement and Testing Technology (SIMT), China. The statistical diameters of these samples were 20075 and 430713 nm, respectively. The AFM data were acquired by UltraObjective AFM (SIS, Germany) with the tapping mode. The AFM parameters were carefully set to minimize the pressure of tip on the spheres, and the Au layer also could enhance the non-deformability of spheres against the tip pressure [12]. The commercial Si3N4 tip was used, which was pyramidal in shape with the nominal apex radius of about 30 nm, and the tilted angle of the cantilever was about 81 during scanning (from the manual of SIS GmbH). The collected AFM data were statistically analyzed to calculate the profile of the tip. Over 50 isolated spheres were counted to obtain the apparent width (wL and wR) and over 200 closely packed spheres were considered to acquire the altitude difference (h and hmax).
4. Results and discussions 4.1. Topography of isolated spheres The SEM and AFM images of the isolated spheres are shown in Fig. 3. The spheres in the SEM images were regular and symmetric both for 430 nm (Fig. 3a) and 200 nm spheres (Fig. 3b). The AFM images (Fig. 3c and d) of these spheres were distorted by the AFM tip and the distortion was even worse for 430 nm spheres (Fig. 3c). From the typical cross-section analysis of the isolated spheres (Fig. 3e and f), an asymmetrical structure and linear regions on both sides were demonstrated. The asymmetrical structure in the AFM images would be caused by the asymmetrical body of the AFM tip because the spheres were of regular spherical shape, as shown in the SEM images (Fig. 3a and b).
Fig. 4. SEM images (a, b), AFM images (c, d) and typical cross-sections (e, f) of closely packed spheres. (a), (c) and (e) are obtained from 430 nm spheres and (b), (d) and (f) are from 200 nm spheres. The scan range of (c) and (d) is 5 mm 5 mm and 2 mm 2 mm, respectively.
ARTICLE IN PRESS Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
979
Table 1 Experimental data and consequently calculated tip parameters Diameter D (from SEM)(nm)
Experimental results hmax (nm)
20075 430713
39.472.1 121.677.2
h (nm)
36.271.9 108.676.8
Calculated results wL (nm)
219.676.8 424.7710.9
4.2. Topography of closely packed spheres The SEM and AFM images of the closely packed spheres are demonstrated in Fig. 4. The spheres were closely packed as hexagonal structures with some defects. The shapes of the spheres in the AFM images (Fig. 4c and d) were almost regular like that in the SEM images (Fig. 4a and b) and did not show any distortion like that of isolated spheres (Fig. 3(c) and (d)). The average diameters measured by AFM were 432.5 and 201.2 nm, respectively, which were well consistent with the results measured at SIMT. It is illustrated that the size information of these closely packed spheres in the lateral direction was hardly affected by the tip. The typical cross sections of closely packed spheres (Fig. 4e and f) clearly depicted that the altitude difference was affected by the tip and was less than the radius of the corresponding spheres. The altitude difference (h and hmax) can be directly read from the cross-sections, and h is the altitude of the midpoint between two maximal point of spheres. Because the spheres were not absolutely uniform and there were some assembling defects, both h and hmax were statistically averaged for the calculation of our model.
4.3. Tip characterization In the experiments, some factors may greatly affect the accuracy of our measurements, such as the diameter distribution of spheres, the AFM scan parameters, the processing of AFM images and so on. The diameter distribution is an important factor that can directly enlarge the deviation of the AFM measurements. In our experiments, the diameter distribution is 2.5% for 200 nm spheres and 3.0% for 430 nm spheres. However, monodispersed spheres with a smaller diameter distribution are available in the market, and use of those spheres may improve the accuracy of the AFM tip characterization. Besides, in order to inhibit the further deviation induced by the image processing, the acquired AFM images were not processed by any offline algorithms except for the plane correction to remove the information of the tilted background. Because of these factors, the experimental results were obtained statistically over 50 isolated spheres and 300 closely packed spheres. The statistic data and calculated results according to our model are listed in Table 1. The slope angles and apex radius of the tip were calculated by the mean value. The results calculated from hmax were also listed in order to make comparisons. Because the tip is asymmetrical and the lowest point is offcenter, the value of h is about 90% of the value of hmax in our experiments. Comparing the calculated results from h with that from hmax, it can be found that the slope angle alters a little but the curvature radius of the tip apex shows more sensitivity to the value of the altitude difference, especially for the 430 nm spheres. It implies that h is a key parameter to obtain the correct curvature radius of the tip apex, so suitable scan size and speed [13] should be taken into consideration
wR (nm)
180.274.2 355.576.9
From hmax
From h
yL (deg)
yR (deg)
r (nm)
yL (deg)
yR (deg)
r (nm)
23.9 24.3
36.7 34.2
40.7 35.0
22.8 22.4
36.1 33.1
44.8 51.2
to carefully determine the maximal point of spheres and the value of h. As shown in Table 1, the curvature radius of the tip apex was 44.8 nm calculated from 200 nm spheres and 51.2 nm from 430 nm spheres. The calculated radii of the tip apex were a little larger than the nominal value (30 nm) reported in the manual. The total tip vertex angle obtained from 200 nm spheres was 58.91 and the right slope angle was 13.31 larger than the left one; the total tip vertex angle acquired from 430 nm spheres was 55.51 and the right slope angle was 10.71 larger than the left one. The calculated slope angles were well consistent. It should be noted that in our model the tilted angle of the cantilever during scanning is assumed to be 01, while, in most situations, the inclination of the cantilever (the tilted angle is about 81 in our experiments) may induce the tip to cause a slight inclination of the tip to the sample surface [4]. Thus, the calculated asymmetry of the tip in our model has included the influence of the inclination of the cantilever. Additionally, the tip actually is not so ideal and the electrical noise may be introduced when the tip is scanning, so these factors may also have some contribution to the experimental errors. However, the calculated profile of the AFM tip from 200 nm spheres is well consistent with that from 430 nm spheres, and we believe that our proposed method is efficient to determine the slope angle of the AFM tip and the curvature radius of the tip apex. The acquired data of the tip shape can be used to reconstruct the AFM images, and the reconstruction will be conducted in our further work. 5. Conclusion In conclusion, a simple model based on isolated spheres and closely packed spheres as the characterizers has been proposed to determine the profile of the AFM tip. Monodispersed PS spheres with diameters of 200 and 430 nm have been utilized to verify this model. The total vertex angle of the tip obtained from our model was 58.91 and the right slope angle was 13.31 larger than the left one by using the data obtained from 200 nm spheres; the total vertex angle of the tip was 55.51 and the right slope angle was 10.71 larger than the left one from 430 nm spheres. The curvature radius of the tip apex was 44.8 nm from 200 nm spheres and 51.2 nm from 430 nm spheres. The results indicate that the calculated profiles are well consistent with each other, which means that our model is efficient and non-destructive to obtain both the body information and apex radius of tips. Acknowledgments This work was supported by the project of STCSM (No. 0652NM028), the Shanghai Leading Academic Discipline Project (B113) and the International Research Training Group (IRTG).
ARTICLE IN PRESS 980
Z.-g. Zeng et al. / Ultramicroscopy 108 (2008) 975–980
References [1] [2] [3] [4] [5] [6]
Y. Martin, K. Wickramasinghe, Appl. Phys. Lett. 64 (1994) 2498. L. Chen, C.L. Cheung, P.D. Ashby, C.M. Lieber, Nano Lett. 4 (2004) 1725. S. Xu, M.F. Arnsdorf, J. Microsc. 187 (1997) 43. P. Markiewicz, M.C. Goh, Langmuir 10 (1994) 5. K. Shiramine, S. Muto, J. Appl. Phys. 101 (2007) 033527. P. Markiewicz, S.R. Cohen, A. Efimov, D.V. Ovchinnikov, A.A. Bukharaev, Probe Microsc. 1 (1999) 355.
[7] L. Montelius, J.O. Tegenfeldt, Appl. Phys. Lett. 62 (1993) 2628. [8] V. Bykov, A. Golaganov, V. Shevyakov, Appl. Phys. A 66 (1998) 499. [9] L.S. Dongmo, J.S. Villarrubia, S.N. Jones, T.B. Renegar, M.T. Postek, J.F. Song, Ultramicroscopy 85 (2000) 141. [10] K.A. Ramirez-Aguilar, K.L. Rowlen, Langmuir 14 (1998) 2562. [11] Y. Li, S.M. Lindsay, Rev. Sci. Instrum. 62 (1991) 2630. [12] D. Alliata, C. Cecconi, Rev. Sci. Instrum. 67 (1996) 748. [13] H.G. Abdelhady, S. Allen, S.J. Ebbens, C. Madden, N. Patel, C.J. Roberts, J. Zhang, Nanotechnology 16 (2005) 966.