Note: Symmetric modulation methodology applied in improving the performance of scanning tunneling microscopy Bing-Feng Ju, Wu-Le Zhu, and Wei Zhang Citation: Review of Scientific Instruments 84, 126107 (2013); doi: 10.1063/1.4854476 View online: http://dx.doi.org/10.1063/1.4854476 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/84/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Construction and performance of a dilution-refrigerator based spectroscopic-imaging scanning tunneling microscope Rev. Sci. Instrum. 84, 013708 (2013); 10.1063/1.4788941 High temperature electrochemical scanning tunneling microscope instrument Rev. Sci. Instrum. 73, 102 (2002); 10.1063/1.1425776 Application of scanning tunneling microscopy to aluminum nanocluster deposition on silicon J. Vac. Sci. Technol. B 17, 265 (1999); 10.1116/1.590548 Synthesis and structure of Al clusters supported on TiO 2 (110): A scanning tunneling microscopy study J. Vac. Sci. Technol. A 16, 2562 (1998); 10.1116/1.581382 An improved control technique for the electrochemical fabrication of scanning tunneling microscopy microtips Rev. Sci. Instrum. 68, 3811 (1997); 10.1063/1.1148032
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REVIEW OF SCIENTIFIC INSTRUMENTS 84, 126107 (2013)
Note: Symmetric modulation methodology applied in improving the performance of scanning tunneling microscopy Bing-Feng Ju, Wu-Le Zhu, and Wei Zhang The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, People’s Republic of China
(Received 7 July 2013; accepted 9 December 2013; published online 26 December 2013) A symmetric modulation methodology is proposed to combine robust control of external disturbance, rapid response to steep sidewalls with the high speed of a traditional scanning tunneling microscopy. The 1400 × 200 μm2 topography of a comb-like steep sidewalls micro-structure with the depth of 23 μm was acquired at a high scanning speed of 120 μms−1 and the detectable slope angle is up to 85◦ . The total measuring time was only 17 min. In addition, a 4 × 4 mm2 aluminum dual-sinusoidal array has been successfully measured with a scanning speed up to 500 μms−1 . It improved the performance of the normal scanning tunneling microscope and enables efficient and stable measurement of large-area complex micro-structures, and thus can be introduced to engineering applications. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4854476] The scanning tunneling microscope (STM) is a powerful tool used for the characterization and analysis of structures on a nanometer scale with atomic resolution. The tough working conditions, such as ultra-high vacuum (UHV),1 high pressure,2 or extremely low temperature3 make the normal STM mostly used in the laboratory. Besides, it is not suitable for measuring complex micro-structures with a trench depth of tens of micrometers and planar non-uniformity of hundreds of micrometers. There are three main barriers that prevent STM from measuring the ultra-precision micro-structures, such as optical arrays4 machined by fast tool servo (FTS), or micro components with deep trench. First, if STM works under atmospheric pressure and external vibrations, the fluctuations of the tunneling current would increase,5 resulting in tip-sample wear and image degradation. Second, most of the microstructures are required to be fabricated in an area larger than several square millimeters. Limited by low scanning speed and small range, normal STM system is difficult for overall imaging. Third, many existing micro-structures are ones with deep trench of tens of micrometers. The normal STM cannot meet the metrology requirements of such micro-structures in terms of scanning speed, measuring range, and detecting angle. Sawano et al.6 developed a STM-based coordinate measuring machine (CMM) system with a long traveling range, but typically tens of micrometers’ lateral scanning range was in practical use and the scanning speed was limited to 10 μms−1 . Large area scanning probe microscope (SPM),7 developed by PTB Germany, had a high resolution, but it was limited to about 2 μm measuring range in the vertical direction and the typical scanning speed was less than 20 μms−1 . Wang et al.8 measured micro-structures with sidewalls of micrometers height at a speed of 2 μms−1 , and the detectable angle was only 40◦ . Accordingly, even the up-to-date SPMs are not able to achieve high speed scanning of large area microstructures, especially with deep trench. In this note, by comparing with Original value method and linearization method in the feedback control of tun0034-6748/2013/84(12)/126107/3/$30.00
neling current, we qualitatively and experimentally demonstrate the advantages of the symmetric modulation methodology for accurate measurement of micro-structure with deep trench and high speed scanning of a large area, ultra-precision component. As shown in Fig. 1, different relationships between the tunneling current and the tip-sample gap can be realized by three methods: Original value method, linearization process, and symmetric modulation methodology. The Original value method is based on the original current-gap curve MPQ without any transformation, which is expressed as IMP Q = I0 exp(−A(d − d0 )),
(1)
where A is a proportional constant and I0 is the set-point tunneling current at the tip-sample gap d0 . When a very small bias voltage is applied, the tunneling current, IMPQ , is exponential to tip-sample gap, d9 . For the Original value method applied in the constantcurrent mode of operation, when the probe encounters the upward sidewalls of a microstructure, the tunneling current detected as a feedback signal can instantaneously rise to approximately the positive threshold. In this case, once the large difference value between the feedback signal and set-point tunneling current is input to the proportional-integral controller, the position of the probe would be adjusted to rapidly follow the upward sidewalls to keep the tunneling current constant. In contrast, according to the asymmetric feature of the original curve MPQ, it would result in delay tracking of the downward ones. To eliminate this defect, the common method is to introduce a linearization process by linearizing the original exponential curve using logarithmic amplification, and the linearized line A P B is expressed as IA P B = −G log(IMP Q ) = GA(d − d0 )) − G log(I0 ), (2) where G is the gain of logarithmic amplifier. Through the linearization process, STM operates at a new set-point P (d0 , −Glog(I0 )). The gradient of line A P B is proportional to the gain G, which can be increased to make
84, 126107-1
© 2013 AIP Publishing LLC
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 136.165.238.131 On: Fri, 19 Dec 2014 21:50:49
126107-2
Ju, Zhu, and Zhang
Rev. Sci. Instrum. 84, 126107 (2013)
Compared with Eq. (3), three modulation constants can be calculated to be K = 2I0 , k1 = I0 2 , and k2 = 1. According to Eq. (4) and the constants, the modulation can be realized by the logarithmic, anti-logarithmic, and the operational amplification of tunneling current through analog circuits. Note that the symmetric modulation methodology can also be implemented in the digital control system directly by numerical computation. The modulation is expressed as IP N = 2I0 − I02
FIG. 1. Schematic of symmetric modulation methodology and the comparison with the Original value method and linearization process.
the STM probe more rapidly respond to the steep sidewalls. However, to avoid the tip-sample wear, the set-point tunneling current I0 is set to be small enough to keep the tip far away from the sample surface. The logarithmic amplification of the smaller tunneling current leads to a higher dynamic noise. Also, if there exists nano-level external vibration s, it would lead to a relatively large tunneling current fluctuation V2 = GAs. In this case, increasing the gain G magnifies V2 , thus introducing instability. By contrast, the fluctuation V1 ≈ I0 As from external disturbance by using the Original value method is much less than the fluctuation V2 caused by the linearization process. Therefore, the Original value method actually seems to be superior to the linearization method in measuring the upward sidewalls in terms of stability and rapid response. Combining robust control of external disturbance with rapid response to steep slopes, the symmetric modulation methodology is proposed. Based on the Original value method, the new curve MPN is generated by making symmetric transformation of exponential curve MPQ at set-point P (d0 , I0 ) to obtain more stability as well as a higher scanning speed than the linearization process. The modulated curve is expressed as I0 exp(−A(d − d0 )), d < d0 IMP N = . (3) 2I0 − I0 exp(−A(d0 − d)), d ≥ d0 In order to get the symmetric curve, we need to transform the curve PQ to PN. The corresponding modulation equation is ln(IP Q ) , d ≥ d0 . IP N = K − k1 exp − (4) k2 Substituting Eq. (1) to Eq. (4), it has k1 A exp IP N = K − (d − d0 ) , k2 exp ln(I0 )
d ≥ d0 .
k2
(5)
1 IP Q
,
d ≥ d0 .
(6)
Due to the symmetric transformation, the feedback signal peaks approximately at the positive threshold when the probe encounters the rising edge of steep sidewalls, and plummets to the negative threshold when it comes across the falling edge. The tunneling current fluctuation V3 ≈ I0 As from external vibration s is significantly decreased compared with the fluctuation V2 = GAs by linearization process, because I0 is normally on an order of pA to nA whereas the gain G of logarithmic amplifier is considerably high for enhancing the response to steep sidewalls. Furthermore, according to the symmetrically transformed curve, the tunneling current exponentially increases as the tip-sample gap deviates from the setpoint gap d0 . Due to the exponentially increasing deviations of tunneling current from set-point value, with a small control gain the probe driven by control system can quickly track the rough surface to keep the tip-sample gap constant. Besides, it still retains robust ability to external influences when scanning the smooth surface as the small set-point I0 is at the inflection point of the new curve MPN. Therefore, such a nonlinear transformation, which naturally increases the control gain for larger tip-sample gap deviations more rapidly than the linearization process, keeps a low gain around the small setpoint to avoid instability. It can also significantly increase the scanning speed, especially when measuring steep sidewalls. It makes the STM instrumentation system fast, steady, and suitable for measuring the complex micro-structures. The self-developed STM system has been embedded with the analog circuits of the symmetric modulation and a homemade tungsten probe with apex radius less than 20 nm.10 A gold-coated, comb-like micro-structure fabricated by a reaction ion etching technique with a slope angle of nearly 90◦ and the depth of 23 μm was measured. For comparison, Fig. 2 shows three measuring results of the same 1400 × 200 μm2 area of the micro-structure using the Original value method, linearization process, and analog symmetric modulation methodology, respectively. By using the Original value method, Fig. 2(a) shows that the measured slope angle of the rising edge is up to 85.1◦ , but the angle of the falling edge is only 67.2◦ . The delay in tracking the downward sidewalls limits the scanning speed to only 5 μms−1 , which greatly reduces the efficiency of a large area measurement. As shown in Fig. 2(b), under a higher gain G of a logarithmic amplifier, the linearization process can achieve a faster scanning speed of 40 μms−1 , and the detected angles of rising and falling edges are 81.5◦ and 78.3◦ , respectively. However, the high gain brings noticeable fluctuations in the smooth area, as shown in the black dashed circles in the figure. Figure 2(c) is the topography of the same area using
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 136.165.238.131 On: Fri, 19 Dec 2014 21:50:49
126107-3
Ju, Zhu, and Zhang
Rev. Sci. Instrum. 84, 126107 (2013)
FIG. 2. Scanning results of 1400 × 200 μm2 gold-coated comb-like micro-structure with steep sidewalls by using (a) Original value method, (b) linearization process, and (c) analog symmetric modulation methodology.
analog symmetric modulation methodology with a scanning speed up to 120 μms−1 , and the maximum angles of the steep sidewalls are evaluated to be equally 85.1◦ . Besides, the image without fluctuations can be acquired at the high speed. The total scanning time was only about 17 min. To demonstrate the efficient 3D measurement of a large area smooth micro-structure, a 4 × 4 mm2 aluminum, dual-
sinusoidal array fabricated by FTS on a diamond turning machine was successfully measured with a high speed of 500 μms−1 by using symmetric modulation methodology. The time consumed was about 55 min. Figures 3(a) and 3(b) are the 3D profile and its top view, respectively. The average wavelength is 578.93 μm in X direction and 577.83 μm in Y direction. The peak to valley height is 25.51 ± 0.10 μm. These three characteristics are the vital parameters of the array. Thus, the methodology also provides an effective solution for fast surface topography measurement of large area microstructures. The symmetric modulation methodology presented in this note greatly enhances the competency and efficiency of the traditional scanning tunneling microscopy. It ensures the measuring capability of large area, as well as high speed for micro-structures, especially with steep sidewalls. It can be introduced to engineering applications, and will provide an effective and nondestructive solution to the measurement of high step or deep trench micro-structures. This work is supported by the National Natural Science Foundation of China Project No. 51175467, Science Fund for Creative Research Groups of National Natural Science Foundation of China 51221004, 973 Program 2011CB706505 and 863 Program 2012AA040405, the Doctoral Program of Higher Education 20120101110059, and Zhejiang Provincial Natural Science Foundation of China Z13E050008. 1 M. S. Xu, S. Tsukamoto, S. Ishida, M. Kitamura, Y. Arakawa, R. G. Endres,
and M. Shimoda, Appl. Phys. Lett. 87, 083902 (2005). Laegsgaard, L. Osterlund, P. Thostrup, P. B. Rasmussen, I. Stensgaard, and F. Besenbacher, Rev. Sci. Instrum. 72, 3537 (2001). 3 K. Sagisakal, M. Kitahara, D. Fujita, G. Kido, and N. Koguchi, Nanotechnology. 15, S371 (2004). 4 W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, Precis. Eng. 27, 289 (2003). 5 A. Bryant, D. P. E. Smith, and C. F. Quate, Appl. Phys. Lett. 48, 832 (1986). 6 H. Sawano, T. Gokan , H. Yoshioka, and H. Shinno, Precis. Eng. 36, 538 (2012). 7 G. L. Dai, L. Koenders, F. Pohlenz, T. Dziomba, and H. U. Danzebrink, Meas. Sci. Technol. 16, 1241 (2005). 8 S. H. Wang, S. L. Tan, G. Xu, and K. Koyama, Meas. Sci. Technol. 22, 094013 (2011). 9 X. F. Feng and M. Salmeron, Appl. Phys. Lett. 102, 053116 (2013). 10 B. F. Ju, Y. L. Chen, and Y. Z. Ge, Rev. Sci. Instrum. 82, 013707 (2011). 2 E.
FIG. 3. (a) 3D view of measured profile of a 4 × 4 mm2 aluminum dualsinusoidal array was measured with a speed of 500 μms−1 . (b) Top view of the measured profile.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 136.165.238.131 On: Fri, 19 Dec 2014 21:50:49
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REVIEW OF SCIENTIFIC INSTRUMENTS 84, 126107 (2013)
Note: Symmetric modulation methodology applied in improving the performance of scanning tunneling microscopy Bing-Feng Ju, Wu-Le Zhu, and Wei Zhang The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, People’s Republic of China
(Received 7 July 2013; accepted 9 December 2013; published online 26 December 2013) A symmetric modulation methodology is proposed to combine robust control of external disturbance, rapid response to steep sidewalls with the high speed of a traditional scanning tunneling microscopy. The 1400 × 200 μm2 topography of a comb-like steep sidewalls micro-structure with the depth of 23 μm was acquired at a high scanning speed of 120 μms−1 and the detectable slope angle is up to 85◦ . The total measuring time was only 17 min. In addition, a 4 × 4 mm2 aluminum dual-sinusoidal array has been successfully measured with a scanning speed up to 500 μms−1 . It improved the performance of the normal scanning tunneling microscope and enables efficient and stable measurement of large-area complex micro-structures, and thus can be introduced to engineering applications. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4854476] The scanning tunneling microscope (STM) is a powerful tool used for the characterization and analysis of structures on a nanometer scale with atomic resolution. The tough working conditions, such as ultra-high vacuum (UHV),1 high pressure,2 or extremely low temperature3 make the normal STM mostly used in the laboratory. Besides, it is not suitable for measuring complex micro-structures with a trench depth of tens of micrometers and planar non-uniformity of hundreds of micrometers. There are three main barriers that prevent STM from measuring the ultra-precision micro-structures, such as optical arrays4 machined by fast tool servo (FTS), or micro components with deep trench. First, if STM works under atmospheric pressure and external vibrations, the fluctuations of the tunneling current would increase,5 resulting in tip-sample wear and image degradation. Second, most of the microstructures are required to be fabricated in an area larger than several square millimeters. Limited by low scanning speed and small range, normal STM system is difficult for overall imaging. Third, many existing micro-structures are ones with deep trench of tens of micrometers. The normal STM cannot meet the metrology requirements of such micro-structures in terms of scanning speed, measuring range, and detecting angle. Sawano et al.6 developed a STM-based coordinate measuring machine (CMM) system with a long traveling range, but typically tens of micrometers’ lateral scanning range was in practical use and the scanning speed was limited to 10 μms−1 . Large area scanning probe microscope (SPM),7 developed by PTB Germany, had a high resolution, but it was limited to about 2 μm measuring range in the vertical direction and the typical scanning speed was less than 20 μms−1 . Wang et al.8 measured micro-structures with sidewalls of micrometers height at a speed of 2 μms−1 , and the detectable angle was only 40◦ . Accordingly, even the up-to-date SPMs are not able to achieve high speed scanning of large area microstructures, especially with deep trench. In this note, by comparing with Original value method and linearization method in the feedback control of tun0034-6748/2013/84(12)/126107/3/$30.00
neling current, we qualitatively and experimentally demonstrate the advantages of the symmetric modulation methodology for accurate measurement of micro-structure with deep trench and high speed scanning of a large area, ultra-precision component. As shown in Fig. 1, different relationships between the tunneling current and the tip-sample gap can be realized by three methods: Original value method, linearization process, and symmetric modulation methodology. The Original value method is based on the original current-gap curve MPQ without any transformation, which is expressed as IMP Q = I0 exp(−A(d − d0 )),
(1)
where A is a proportional constant and I0 is the set-point tunneling current at the tip-sample gap d0 . When a very small bias voltage is applied, the tunneling current, IMPQ , is exponential to tip-sample gap, d9 . For the Original value method applied in the constantcurrent mode of operation, when the probe encounters the upward sidewalls of a microstructure, the tunneling current detected as a feedback signal can instantaneously rise to approximately the positive threshold. In this case, once the large difference value between the feedback signal and set-point tunneling current is input to the proportional-integral controller, the position of the probe would be adjusted to rapidly follow the upward sidewalls to keep the tunneling current constant. In contrast, according to the asymmetric feature of the original curve MPQ, it would result in delay tracking of the downward ones. To eliminate this defect, the common method is to introduce a linearization process by linearizing the original exponential curve using logarithmic amplification, and the linearized line A P B is expressed as IA P B = −G log(IMP Q ) = GA(d − d0 )) − G log(I0 ), (2) where G is the gain of logarithmic amplifier. Through the linearization process, STM operates at a new set-point P (d0 , −Glog(I0 )). The gradient of line A P B is proportional to the gain G, which can be increased to make
84, 126107-1
© 2013 AIP Publishing LLC
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126107-2
Ju, Zhu, and Zhang
Rev. Sci. Instrum. 84, 126107 (2013)
Compared with Eq. (3), three modulation constants can be calculated to be K = 2I0 , k1 = I0 2 , and k2 = 1. According to Eq. (4) and the constants, the modulation can be realized by the logarithmic, anti-logarithmic, and the operational amplification of tunneling current through analog circuits. Note that the symmetric modulation methodology can also be implemented in the digital control system directly by numerical computation. The modulation is expressed as IP N = 2I0 − I02
FIG. 1. Schematic of symmetric modulation methodology and the comparison with the Original value method and linearization process.
the STM probe more rapidly respond to the steep sidewalls. However, to avoid the tip-sample wear, the set-point tunneling current I0 is set to be small enough to keep the tip far away from the sample surface. The logarithmic amplification of the smaller tunneling current leads to a higher dynamic noise. Also, if there exists nano-level external vibration s, it would lead to a relatively large tunneling current fluctuation V2 = GAs. In this case, increasing the gain G magnifies V2 , thus introducing instability. By contrast, the fluctuation V1 ≈ I0 As from external disturbance by using the Original value method is much less than the fluctuation V2 caused by the linearization process. Therefore, the Original value method actually seems to be superior to the linearization method in measuring the upward sidewalls in terms of stability and rapid response. Combining robust control of external disturbance with rapid response to steep slopes, the symmetric modulation methodology is proposed. Based on the Original value method, the new curve MPN is generated by making symmetric transformation of exponential curve MPQ at set-point P (d0 , I0 ) to obtain more stability as well as a higher scanning speed than the linearization process. The modulated curve is expressed as I0 exp(−A(d − d0 )), d < d0 IMP N = . (3) 2I0 − I0 exp(−A(d0 − d)), d ≥ d0 In order to get the symmetric curve, we need to transform the curve PQ to PN. The corresponding modulation equation is ln(IP Q ) , d ≥ d0 . IP N = K − k1 exp − (4) k2 Substituting Eq. (1) to Eq. (4), it has k1 A exp IP N = K − (d − d0 ) , k2 exp ln(I0 )
d ≥ d0 .
k2
(5)
1 IP Q
,
d ≥ d0 .
(6)
Due to the symmetric transformation, the feedback signal peaks approximately at the positive threshold when the probe encounters the rising edge of steep sidewalls, and plummets to the negative threshold when it comes across the falling edge. The tunneling current fluctuation V3 ≈ I0 As from external vibration s is significantly decreased compared with the fluctuation V2 = GAs by linearization process, because I0 is normally on an order of pA to nA whereas the gain G of logarithmic amplifier is considerably high for enhancing the response to steep sidewalls. Furthermore, according to the symmetrically transformed curve, the tunneling current exponentially increases as the tip-sample gap deviates from the setpoint gap d0 . Due to the exponentially increasing deviations of tunneling current from set-point value, with a small control gain the probe driven by control system can quickly track the rough surface to keep the tip-sample gap constant. Besides, it still retains robust ability to external influences when scanning the smooth surface as the small set-point I0 is at the inflection point of the new curve MPN. Therefore, such a nonlinear transformation, which naturally increases the control gain for larger tip-sample gap deviations more rapidly than the linearization process, keeps a low gain around the small setpoint to avoid instability. It can also significantly increase the scanning speed, especially when measuring steep sidewalls. It makes the STM instrumentation system fast, steady, and suitable for measuring the complex micro-structures. The self-developed STM system has been embedded with the analog circuits of the symmetric modulation and a homemade tungsten probe with apex radius less than 20 nm.10 A gold-coated, comb-like micro-structure fabricated by a reaction ion etching technique with a slope angle of nearly 90◦ and the depth of 23 μm was measured. For comparison, Fig. 2 shows three measuring results of the same 1400 × 200 μm2 area of the micro-structure using the Original value method, linearization process, and analog symmetric modulation methodology, respectively. By using the Original value method, Fig. 2(a) shows that the measured slope angle of the rising edge is up to 85.1◦ , but the angle of the falling edge is only 67.2◦ . The delay in tracking the downward sidewalls limits the scanning speed to only 5 μms−1 , which greatly reduces the efficiency of a large area measurement. As shown in Fig. 2(b), under a higher gain G of a logarithmic amplifier, the linearization process can achieve a faster scanning speed of 40 μms−1 , and the detected angles of rising and falling edges are 81.5◦ and 78.3◦ , respectively. However, the high gain brings noticeable fluctuations in the smooth area, as shown in the black dashed circles in the figure. Figure 2(c) is the topography of the same area using
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 136.165.238.131 On: Fri, 19 Dec 2014 21:50:49
126107-3
Ju, Zhu, and Zhang
Rev. Sci. Instrum. 84, 126107 (2013)
FIG. 2. Scanning results of 1400 × 200 μm2 gold-coated comb-like micro-structure with steep sidewalls by using (a) Original value method, (b) linearization process, and (c) analog symmetric modulation methodology.
analog symmetric modulation methodology with a scanning speed up to 120 μms−1 , and the maximum angles of the steep sidewalls are evaluated to be equally 85.1◦ . Besides, the image without fluctuations can be acquired at the high speed. The total scanning time was only about 17 min. To demonstrate the efficient 3D measurement of a large area smooth micro-structure, a 4 × 4 mm2 aluminum, dual-
sinusoidal array fabricated by FTS on a diamond turning machine was successfully measured with a high speed of 500 μms−1 by using symmetric modulation methodology. The time consumed was about 55 min. Figures 3(a) and 3(b) are the 3D profile and its top view, respectively. The average wavelength is 578.93 μm in X direction and 577.83 μm in Y direction. The peak to valley height is 25.51 ± 0.10 μm. These three characteristics are the vital parameters of the array. Thus, the methodology also provides an effective solution for fast surface topography measurement of large area microstructures. The symmetric modulation methodology presented in this note greatly enhances the competency and efficiency of the traditional scanning tunneling microscopy. It ensures the measuring capability of large area, as well as high speed for micro-structures, especially with steep sidewalls. It can be introduced to engineering applications, and will provide an effective and nondestructive solution to the measurement of high step or deep trench micro-structures. This work is supported by the National Natural Science Foundation of China Project No. 51175467, Science Fund for Creative Research Groups of National Natural Science Foundation of China 51221004, 973 Program 2011CB706505 and 863 Program 2012AA040405, the Doctoral Program of Higher Education 20120101110059, and Zhejiang Provincial Natural Science Foundation of China Z13E050008. 1 M. S. Xu, S. Tsukamoto, S. Ishida, M. Kitamura, Y. Arakawa, R. G. Endres,
and M. Shimoda, Appl. Phys. Lett. 87, 083902 (2005). Laegsgaard, L. Osterlund, P. Thostrup, P. B. Rasmussen, I. Stensgaard, and F. Besenbacher, Rev. Sci. Instrum. 72, 3537 (2001). 3 K. Sagisakal, M. Kitahara, D. Fujita, G. Kido, and N. Koguchi, Nanotechnology. 15, S371 (2004). 4 W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, Precis. Eng. 27, 289 (2003). 5 A. Bryant, D. P. E. Smith, and C. F. Quate, Appl. Phys. Lett. 48, 832 (1986). 6 H. Sawano, T. Gokan , H. Yoshioka, and H. Shinno, Precis. Eng. 36, 538 (2012). 7 G. L. Dai, L. Koenders, F. Pohlenz, T. Dziomba, and H. U. Danzebrink, Meas. Sci. Technol. 16, 1241 (2005). 8 S. H. Wang, S. L. Tan, G. Xu, and K. Koyama, Meas. Sci. Technol. 22, 094013 (2011). 9 X. F. Feng and M. Salmeron, Appl. Phys. Lett. 102, 053116 (2013). 10 B. F. Ju, Y. L. Chen, and Y. Z. Ge, Rev. Sci. Instrum. 82, 013707 (2011). 2 E.
FIG. 3. (a) 3D view of measured profile of a 4 × 4 mm2 aluminum dualsinusoidal array was measured with a speed of 500 μms−1 . (b) Top view of the measured profile.
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