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Phase variation experiments in non-contact dynamic force microscopy using phase locked loop techniques
Applied Surface Science 140 Ž1999. 287–292
Phase variation experiments in non-contact dynamic force microscopy using phase locked loop techniques Ch. Loppacher ) , M. Bammerlin, M. Guggisberg, F. Battiston, R. Bennewitz, S. Rast, A. Baratoff, E. Meyer, H.-J. Guntherodt ¨ Institute of Physics, UniÕersity of Basel, CH-4056 Basel, Switzerland Received 21 July 1998; accepted 17 August 1998
Abstract This work presents constant amplitude Dynamic Force Microscopy ŽDFM. measurements under ultra-high vacuum conditions performed with home-built digital electronics based on the principle of phase locked loop ŽPLL. techniques. In DFM so-called topography is often measured in constant frequency shift Ž D f . mode. This study describes the influence of phase shifts on constant D f imaging. Therefore, phase variation experiments were acquired, leading to information about the cantilever resonance behaviour close to the surface. As sample, an evaporated thin film of NaCl on a CuŽ111. substrate was chosen in order to obtain a heterogeneous system with clean Cu and NaCl areas. The atomic structure of both materials was resolved, which is the first time true atomic resolution was obtained on a metal. Large apparent topography variations are observed on this heterogeneous sample when changing the phase between the excitation and oscillation of the cantilever end. Such artefacts can be explained by comparison with phase variation experiments. q 1999 Elsevier Science B.V. All rights reserved. PACS: 61.16.C; 07.79.L Keywords: Non-contact AFM; Dynamic force microscopy; DFM; Phase locked loop; PLL; Damping; Phase variation; True atomic resolution; Surface structure of metal
1. Introduction Our home-built w1x scanning probe microscope 1 is operated under ultra-high vacuum conditions with
) Corresponding author. Tel.: q41-61-267-3762; Fax: q41-61267-3784; E-mail: [email protected] 1 For an overview in force microscopy see Ref. w2x.
the new digital electronics based on phase locked loop ŽPLL. and FM-detection techniques w3–5x. All results presented in this paper are acquired in noncontact Dynamic Force Microscopy Žnc-DFM. in constant frequency shift Ž D f . mode, the cantilever is controlled at constant, large Ž) 1 nm. amplitude w6–8x. In nc-DFM the D f of the cantilever depends on many parameters, such as interaction forces, oscillation amplitude A 0 and phase w between the
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 5 4 2 - X
288
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
exciting sinusoidal amplitude A exc and the cantilever response. The aim of this work is to investigate the influence of w , when using PLL techniques.
2. Phase variation technique Usually the properties of a cantilever are measured by frequency sweep spectra where the frequency is swept with constant excitation A exc , whereas the amplitude A 0 and the phase w of the cantilever response are recorded ŽFig. 1a,b.. For small amplitudes the frequency sweep spectra is used to determine the cantilever resonance curve w9x. As interactions close to the surface can affect A 0 , the cantilever oscillation must be kept constant for large amplitudes during scanning at constant tip–sample interaction or D f. Our new digital electronics provide the possibility to obtain information contained
in frequency sweep curves but from a cantilever oscillating at constant amplitude. Fig. 1c,d shows D f and the corresponding change of A exc induced by sweeping the phase between the cantilever response and the excitation signal. For correlation with frequency sweep spectra as shown in Fig. 1a,b, A exc and w are plotted vs. the measured frequency change. Out of the equation of motion ŽI.
z¨ q
2p f 0 Q
2
z˙ q Ž 2p f 0 . z s 0
Ž I.
where Q is the quality factor with the ansatz ŽII. for the free oscillating cantilever, z s z Ž t . y z 0y A exc cos Ž 2p fty w . where z Ž t . s A 0 sin Ž 2p ft .
Ž II .
Fig. 1. A 0 and A exc vs. f Ža,c. and w vs. f curves Žb,d.. Ža,b. were acquired with a network analyzer ŽHP-3589 A. by sweeping the frequency at constant excitation. The cantilever dimensions are l s 500 mm, w s 4 mm, t s 0.45 mm, f 0 s 2500 Hz, c s 1 mNrm. Žc,d. were acquired with our home-built PLL by varying the phase at constant oscillation amplitude A 0 . The used cantilever is provided by Wolter, f 0 s 317 kHz.
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
289
A exc ŽIII. and w ŽIV. as functions of the frequency f can be calculated. A exc s
)
Ž f 2 y f 02 .
w s arctan
ž
2
f 02 y f 2 f0 f
q
/
f 02 f 2 A 0
Q .
Q2
f 02
Ž III . Ž IV .
The curves calculated out of formula ŽIII. and ŽIV. look the same than the measured ones in Fig. 1c,d, showing that the energy required to keep A 0 constant is minimised for 908 phase between cantilever oscillation and excitation. These phase variation experiments show that in a PLL a phase shift results in an additional D f, driving the cantilever slightly off its resonance, and in a large increase of A exc to maintain a constant cantilever oscillation. Thus it is important to adjust the phase in order to stay ‘in resonance’.
3. The sample The polished Ž111. surface of a Cu single crystal was prepared by repeated cycles of Arq sputtering
Fig. 2. NaCl Ž1 ml. evaporated on CuŽ111.. 460=460 nm2 topography image acquired at constant D f sy36 Hz Žnc-DFM.. Ž f 0 s 317 kHz; Ubias sq0.3 V..
Fig. 3. 3=3 nm2 topography image in nc-DFM mode of CuŽ111. with an atomic-sized defect Žsulphur impurity.. Ž f 0 s 362 kHz; D f sy269 Hz; as 2.3 nm; Ubias sq0.4 V..
and annealing at 850 K. Typically, the surface topography shows terraces with widths between 30 nm to 80 nm, which are separated by steps of a height of Ž0.20 " 0.02. nm, corresponding to the bulk distance
Fig. 4. 6=6 nm2 topography image of NaClŽ001. Žnc-DFM.. Ž f 0 s156 kHz; D f sy126 Hz; Ubias sq0.24 V..
290
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
with true atomic resolution in constant D f mode ŽFigs. 3 and 4..
4. Experiments Phase variation was now used to investigate contrast mechanisms on evaporated thin films of NaCl on CuŽ111.. Fig. 5 presents distance dependent phase variation experiments measured on pure CuŽ111.. The oscillating cantilever is approached to a setpoint of D f s y65 Hz. Then, the distance controller is stopped and the phase is swept by "368. For every step back from the surface, phase variation curves are acquired. These data show, that the optimum phase w 0 , where A exc reaches its minimum, slightly changes, and the whole A exc curve increases when the tip is closer to the sample indicating an increase in damping which is also consistent with the decreased slope of w vs. D f. The following experiments show the effect of a phase different from the optimum w 0 on constant D f imaging. The upper half of Fig. 6 displays the same area of the sample than Fig. 2, with the dark copper Fig. 5. Distance dependent phase variation curves on CuŽ111. for three different distances.
between Ž111. layers of 0.21 nm. A closer inspection of the surface reveals atomic sized defects with a density of about 3.5 = 10y1 6 cmy2 . Auger spectra taken on the surface show significant peaks only for copper and sulphur, whereupon we assume that the atomic sized defects represent sulphur impurities. NaCl was then evaporated for 3 min from a Knudsen cell at a temperature of 660 K, the Cu substrate temperature was 330 K. Calibration with a quartz microbalance yielded an evaporation rate of 0.15 nmrmin assuming similar sticking coefficients for the quartz balance and the CuŽ111. surface. The pressure in the ultra-high vacuum chamber during evaporation was lower than 5 = 10y1 0 mbar. After deposition of the NaCl film the sample was transferred into the analysis chamber with a base pressure below 5 = 10y1 1 mbar and examined with the DFM. Fig. 2 shows the topography of the sample, some areas are pure copper, others are pure NaCl. The atomic structure of both sample areas was resolved
Fig. 6. Constant D f images. Upper half with w s 308, lower half with w sy368; Ž D f sy36 Hz and Ubias sq0.3 V for both pictures..
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
291
in Fig. 7b and on NaCl in Fig. 7c show markedly different slopes at the setpoint of D f s y65 Hz which is due to different interactions. Hence, a phase change of 308 for example will cause a displacement D z about twice as large on copper than on sodium, when the feedback reacts to the induced D f.
5. Conclusions Owing to differing dependencies of D f on distance, and applied voltage, the apparent contrast mechanisms on heterogeneous materials can be complex. In order to understand topography and especially A exc images one must learn more about the influence of interactions on the resonance behaviour of the cantilever close to the surface. Phase variation experiments and other spectroscopic measurements are the key to distinguish between different damping mechanisms in nc-DFM. The described phase variation curves have shown changes of the optimum phase w 0 and of A exc upon approach i.e., increasing interaction. This indicates that the model of a harmonic oscillator for a cantilever close to the surface must be modified. Experiments and calculations are in progress to characterize the resonance behaviour and energetic losses of the cantilever close to the surface.
Acknowledgements
Fig. 7. Phase variation curves Ža. on CuŽ111. and NaClŽ001. show almost the same D f Ž w . dependence, whereas D f vs. D z on CuŽ111. Žb. are different from curves on NaClŽ001. Žc..
area in the corner right low. Upon changing the phase from 308 to y368 the contrast on the copper area inverts. This reversal in contrast can be explained by different variations about D f, the same setpoint of the distance controller on both materials. The phase vs. frequency curves in Fig. 7a show about the same D f for a changing phase on CuŽ111. and NaCl. But the D f vs. distance curves on CuŽ111.
The technical help from D. Muller, H.-R. Hidber ¨ and R. Maffiolini is gratefully acknowledged. This work was supported by the ‘Kommission zur Forderung der wissenschaftlichen Forschung’, the ¨ Swiss National Science Foundation and the Swiss Priority Program ‘MINAST’.
References w1x L. Howald, E. Meyer, R. Luthi, H. Haefke, R. Overney, H. ¨ Rudin, H.-J. Guntherodt, Appl. Phys. Lett. 63 Ž1993. 117. ¨ w2x H.-J. Guntherodt, D. Anselmetti, E. Meyer ŽEds.., Forces in ¨ Scanning Probe Methods, NATO ASI Series E: Applied Sciences Vol. 286, Kluwer Academic, 1995.
292
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
w3x T.R. Albrecht, P. Grutter, D. Horne, D. Rugar, J. Appl. Phys. ¨ 69 Ž1991. 668. w4x U. Durig, H.R. Steinauer, J. Appl. Phys. 82 Ž1997. 3641. ¨ w5x Ch. Loppacher, M. Bammerlin, F. Battiston, M. Guggisberg, D. Muller, H.-R. Hidber, R. Luthi, ¨ ¨ E. Meyer, H.-J. Guntherodt, ¨ Appl. Phys. A 66 Ž1998. 215. w6x F.J. Giessibl, Science 267 Ž1995. 68.
w7x Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, Science 270 Ž1995. 1646. w8x M. Bammerlin, R. Luthi, E. Meyer, A. Baratoff, J. Lu, ¨ ¨ M. Guggisberg, Ch. Gerber, L. Howald, H.-J. Guntherodt, Probe ¨ Microscopy 1 Ž1997. 3. w9x R. Erlandsson, L. Olsson, Appl. Phys. A 66 Ž1998. 879.
Phase variation experiments in non-contact dynamic force microscopy using phase locked loop techniques Ch. Loppacher ) , M. Bammerlin, M. Guggisberg, F. Battiston, R. Bennewitz, S. Rast, A. Baratoff, E. Meyer, H.-J. Guntherodt ¨ Institute of Physics, UniÕersity of Basel, CH-4056 Basel, Switzerland Received 21 July 1998; accepted 17 August 1998
Abstract This work presents constant amplitude Dynamic Force Microscopy ŽDFM. measurements under ultra-high vacuum conditions performed with home-built digital electronics based on the principle of phase locked loop ŽPLL. techniques. In DFM so-called topography is often measured in constant frequency shift Ž D f . mode. This study describes the influence of phase shifts on constant D f imaging. Therefore, phase variation experiments were acquired, leading to information about the cantilever resonance behaviour close to the surface. As sample, an evaporated thin film of NaCl on a CuŽ111. substrate was chosen in order to obtain a heterogeneous system with clean Cu and NaCl areas. The atomic structure of both materials was resolved, which is the first time true atomic resolution was obtained on a metal. Large apparent topography variations are observed on this heterogeneous sample when changing the phase between the excitation and oscillation of the cantilever end. Such artefacts can be explained by comparison with phase variation experiments. q 1999 Elsevier Science B.V. All rights reserved. PACS: 61.16.C; 07.79.L Keywords: Non-contact AFM; Dynamic force microscopy; DFM; Phase locked loop; PLL; Damping; Phase variation; True atomic resolution; Surface structure of metal
1. Introduction Our home-built w1x scanning probe microscope 1 is operated under ultra-high vacuum conditions with
) Corresponding author. Tel.: q41-61-267-3762; Fax: q41-61267-3784; E-mail: [email protected] 1 For an overview in force microscopy see Ref. w2x.
the new digital electronics based on phase locked loop ŽPLL. and FM-detection techniques w3–5x. All results presented in this paper are acquired in noncontact Dynamic Force Microscopy Žnc-DFM. in constant frequency shift Ž D f . mode, the cantilever is controlled at constant, large Ž) 1 nm. amplitude w6–8x. In nc-DFM the D f of the cantilever depends on many parameters, such as interaction forces, oscillation amplitude A 0 and phase w between the
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 5 4 2 - X
288
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
exciting sinusoidal amplitude A exc and the cantilever response. The aim of this work is to investigate the influence of w , when using PLL techniques.
2. Phase variation technique Usually the properties of a cantilever are measured by frequency sweep spectra where the frequency is swept with constant excitation A exc , whereas the amplitude A 0 and the phase w of the cantilever response are recorded ŽFig. 1a,b.. For small amplitudes the frequency sweep spectra is used to determine the cantilever resonance curve w9x. As interactions close to the surface can affect A 0 , the cantilever oscillation must be kept constant for large amplitudes during scanning at constant tip–sample interaction or D f. Our new digital electronics provide the possibility to obtain information contained
in frequency sweep curves but from a cantilever oscillating at constant amplitude. Fig. 1c,d shows D f and the corresponding change of A exc induced by sweeping the phase between the cantilever response and the excitation signal. For correlation with frequency sweep spectra as shown in Fig. 1a,b, A exc and w are plotted vs. the measured frequency change. Out of the equation of motion ŽI.
z¨ q
2p f 0 Q
2
z˙ q Ž 2p f 0 . z s 0
Ž I.
where Q is the quality factor with the ansatz ŽII. for the free oscillating cantilever, z s z Ž t . y z 0y A exc cos Ž 2p fty w . where z Ž t . s A 0 sin Ž 2p ft .
Ž II .
Fig. 1. A 0 and A exc vs. f Ža,c. and w vs. f curves Žb,d.. Ža,b. were acquired with a network analyzer ŽHP-3589 A. by sweeping the frequency at constant excitation. The cantilever dimensions are l s 500 mm, w s 4 mm, t s 0.45 mm, f 0 s 2500 Hz, c s 1 mNrm. Žc,d. were acquired with our home-built PLL by varying the phase at constant oscillation amplitude A 0 . The used cantilever is provided by Wolter, f 0 s 317 kHz.
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
289
A exc ŽIII. and w ŽIV. as functions of the frequency f can be calculated. A exc s
)
Ž f 2 y f 02 .
w s arctan
ž
2
f 02 y f 2 f0 f
q
/
f 02 f 2 A 0
Q .
Q2
f 02
Ž III . Ž IV .
The curves calculated out of formula ŽIII. and ŽIV. look the same than the measured ones in Fig. 1c,d, showing that the energy required to keep A 0 constant is minimised for 908 phase between cantilever oscillation and excitation. These phase variation experiments show that in a PLL a phase shift results in an additional D f, driving the cantilever slightly off its resonance, and in a large increase of A exc to maintain a constant cantilever oscillation. Thus it is important to adjust the phase in order to stay ‘in resonance’.
3. The sample The polished Ž111. surface of a Cu single crystal was prepared by repeated cycles of Arq sputtering
Fig. 2. NaCl Ž1 ml. evaporated on CuŽ111.. 460=460 nm2 topography image acquired at constant D f sy36 Hz Žnc-DFM.. Ž f 0 s 317 kHz; Ubias sq0.3 V..
Fig. 3. 3=3 nm2 topography image in nc-DFM mode of CuŽ111. with an atomic-sized defect Žsulphur impurity.. Ž f 0 s 362 kHz; D f sy269 Hz; as 2.3 nm; Ubias sq0.4 V..
and annealing at 850 K. Typically, the surface topography shows terraces with widths between 30 nm to 80 nm, which are separated by steps of a height of Ž0.20 " 0.02. nm, corresponding to the bulk distance
Fig. 4. 6=6 nm2 topography image of NaClŽ001. Žnc-DFM.. Ž f 0 s156 kHz; D f sy126 Hz; Ubias sq0.24 V..
290
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
with true atomic resolution in constant D f mode ŽFigs. 3 and 4..
4. Experiments Phase variation was now used to investigate contrast mechanisms on evaporated thin films of NaCl on CuŽ111.. Fig. 5 presents distance dependent phase variation experiments measured on pure CuŽ111.. The oscillating cantilever is approached to a setpoint of D f s y65 Hz. Then, the distance controller is stopped and the phase is swept by "368. For every step back from the surface, phase variation curves are acquired. These data show, that the optimum phase w 0 , where A exc reaches its minimum, slightly changes, and the whole A exc curve increases when the tip is closer to the sample indicating an increase in damping which is also consistent with the decreased slope of w vs. D f. The following experiments show the effect of a phase different from the optimum w 0 on constant D f imaging. The upper half of Fig. 6 displays the same area of the sample than Fig. 2, with the dark copper Fig. 5. Distance dependent phase variation curves on CuŽ111. for three different distances.
between Ž111. layers of 0.21 nm. A closer inspection of the surface reveals atomic sized defects with a density of about 3.5 = 10y1 6 cmy2 . Auger spectra taken on the surface show significant peaks only for copper and sulphur, whereupon we assume that the atomic sized defects represent sulphur impurities. NaCl was then evaporated for 3 min from a Knudsen cell at a temperature of 660 K, the Cu substrate temperature was 330 K. Calibration with a quartz microbalance yielded an evaporation rate of 0.15 nmrmin assuming similar sticking coefficients for the quartz balance and the CuŽ111. surface. The pressure in the ultra-high vacuum chamber during evaporation was lower than 5 = 10y1 0 mbar. After deposition of the NaCl film the sample was transferred into the analysis chamber with a base pressure below 5 = 10y1 1 mbar and examined with the DFM. Fig. 2 shows the topography of the sample, some areas are pure copper, others are pure NaCl. The atomic structure of both sample areas was resolved
Fig. 6. Constant D f images. Upper half with w s 308, lower half with w sy368; Ž D f sy36 Hz and Ubias sq0.3 V for both pictures..
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
291
in Fig. 7b and on NaCl in Fig. 7c show markedly different slopes at the setpoint of D f s y65 Hz which is due to different interactions. Hence, a phase change of 308 for example will cause a displacement D z about twice as large on copper than on sodium, when the feedback reacts to the induced D f.
5. Conclusions Owing to differing dependencies of D f on distance, and applied voltage, the apparent contrast mechanisms on heterogeneous materials can be complex. In order to understand topography and especially A exc images one must learn more about the influence of interactions on the resonance behaviour of the cantilever close to the surface. Phase variation experiments and other spectroscopic measurements are the key to distinguish between different damping mechanisms in nc-DFM. The described phase variation curves have shown changes of the optimum phase w 0 and of A exc upon approach i.e., increasing interaction. This indicates that the model of a harmonic oscillator for a cantilever close to the surface must be modified. Experiments and calculations are in progress to characterize the resonance behaviour and energetic losses of the cantilever close to the surface.
Acknowledgements
Fig. 7. Phase variation curves Ža. on CuŽ111. and NaClŽ001. show almost the same D f Ž w . dependence, whereas D f vs. D z on CuŽ111. Žb. are different from curves on NaClŽ001. Žc..
area in the corner right low. Upon changing the phase from 308 to y368 the contrast on the copper area inverts. This reversal in contrast can be explained by different variations about D f, the same setpoint of the distance controller on both materials. The phase vs. frequency curves in Fig. 7a show about the same D f for a changing phase on CuŽ111. and NaCl. But the D f vs. distance curves on CuŽ111.
The technical help from D. Muller, H.-R. Hidber ¨ and R. Maffiolini is gratefully acknowledged. This work was supported by the ‘Kommission zur Forderung der wissenschaftlichen Forschung’, the ¨ Swiss National Science Foundation and the Swiss Priority Program ‘MINAST’.
References w1x L. Howald, E. Meyer, R. Luthi, H. Haefke, R. Overney, H. ¨ Rudin, H.-J. Guntherodt, Appl. Phys. Lett. 63 Ž1993. 117. ¨ w2x H.-J. Guntherodt, D. Anselmetti, E. Meyer ŽEds.., Forces in ¨ Scanning Probe Methods, NATO ASI Series E: Applied Sciences Vol. 286, Kluwer Academic, 1995.
292
Ch. Loppacher et al.r Applied Surface Science 140 (1999) 287–292
w3x T.R. Albrecht, P. Grutter, D. Horne, D. Rugar, J. Appl. Phys. ¨ 69 Ž1991. 668. w4x U. Durig, H.R. Steinauer, J. Appl. Phys. 82 Ž1997. 3641. ¨ w5x Ch. Loppacher, M. Bammerlin, F. Battiston, M. Guggisberg, D. Muller, H.-R. Hidber, R. Luthi, ¨ ¨ E. Meyer, H.-J. Guntherodt, ¨ Appl. Phys. A 66 Ž1998. 215. w6x F.J. Giessibl, Science 267 Ž1995. 68.
w7x Y. Sugawara, M. Ohta, H. Ueyama, S. Morita, Science 270 Ž1995. 1646. w8x M. Bammerlin, R. Luthi, E. Meyer, A. Baratoff, J. Lu, ¨ ¨ M. Guggisberg, Ch. Gerber, L. Howald, H.-J. Guntherodt, Probe ¨ Microscopy 1 Ž1997. 3. w9x R. Erlandsson, L. Olsson, Appl. Phys. A 66 Ž1998. 879.