Langmuir 1995,11, 1065-1067
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Artifacts in Force Measurements with the Atomic Force Microscope Due to Digitalization Peter Siedle and Hans-Jiirgen Butt* Max-Planck-Institut fur Biophysik, Kennedyallee 70, 60596 Frankfurt a m Main, Germany Received November 29,1994. In Final Form: February 14,1995@ The atomic force microscope has become a standard tool to measure surface forces. Force-versusdistance curves taken with an atomic force microscope often show a hysteresis in the noncontact region between approach and retraction. The hysteresis can be caused by the discrete, stepwise motion of the sample due to digitalization. Since in the presence of liquids cantilever and sample are coupled, the cantilever oscillates after each step. Depending on when a data point is recorded during this oscillation, the amplitude of the cantilever deflection measured may deviate from the equilibrium value. This might cause a hysteresis and other misleading results in force-versus-distancemeasurements. Especially when attractive forces are measured, cantilever oscillations can severely change the results.
After the invention of the atomic force microscope (AFMl), it soon became apparent that the instrument can also be used for measuring surface forces (e.g., refs 2-14). A cantilever with a n attached tip senses surface forces betwen the tip and a flat sample. The deflection of the cantilever is usually detected by a laser beam, which is reflected off the backside of the cantilever toward a segmented photo diode. For force measurements the sample is attached to a piezo scanner which moves the sample periodically up and down. The deflection of the cantilever is recorded, multiplied with the spring constant of the cantilever, and plotted versus the height ( 2 )position of the sample. In this way the so-called force curve is obtained. A force curve starts at a point where tip and sample are far apart, surface forces acting between tip and sample are negligible, and the cantilever is not deflected. When the sample approaches the tip, a variety of attractive and repulsive forces deflect the cantilever. Since the tip does not touch the sample, this region is called the noncontact region. Finally sample and tip get into contact and the deflection of the cantilever follows the movement of the sample. This is the contact region. During retraction of the sample, adhesion often causes the tip to stick to the sample until it is strongly pulled away. Normally a hysteresis between the approaching and retracting portions of force curves is observed. In the contact region friction effects and piezo-artifacts are probably the reason
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for the hysteresis; in the noncontact region the hysteresis is caused by the viscosity of the medium in which the measurements are made.I6J6 In this paper we would like to point to a possible source of artifacts in force measurements that is due to digitalization. Normally the sample is moved in discrete steps due to the fact that the piezo is controlled by digital signals. The stepwise approach of the sample can cause oscillations of the cantilever which might give rise to a hysteresis in the noncontact region. Cantilever oscillations can also lead to erroneous measurements of attractive forces. The force measurements were done with a Nanoscope I1 AFM (Digital Instruments, Santa Barbara, California) using SisNd-cantilevers of approximately 200 pm length and a spring constant of about 0.06 N/m." The scanner used had a z-sensitivity of 7.2 nmN. To show the effect of the stepwise movement of the sample, force curves were recorded in two ways. First, we used the standard software of the manufacturer. In this case the piezo was moved up and down by the stepped voltage ramp supplied by the AFM controller. Second, with an oscilloscope connected to a personal computer the cantilever deflection and the voltage applied to the piezo were measured. Up to 4000 data points per cycle were recorded and analyzed. In this case the piezo was moved either by the stepped voltage ramp supplied by the AFM controller or by a n external, smooth voltage ramp. When a stepped, discrete voltage ramp was used to move the sample, the cantilever oscillated aRer each step of the piezo (Figure 1). The amplitude of the oscillations increased with step height. I t could reach up to 100 nm. The oscillations of typically 10-15 kHz were damped by the fluid and decayed with a typical time constant of 0.15 ms. Probably, a step in the piezo movement caused the cantilever to oscillate since piezo and cantilever are coupled via the liquid. This hypothesis is supported by the observation that force curves taken in air showed almost no hysteresis in the noncontact region. If the cantilever was replaced by a tilted mirror, the oscillations disappeared. Hence, the effect is not caused by the electronics. The frequency of the cantilever oscillations was higher than the value reported previously (2.2 kHz).18 This might be caused by the fact that the whole length of
(10)Tsao, Y.H.; Evans, D. F.; Wennerstriim, H. Science 1993,262, 547. (11)Biggs, S.;Mulvaney, P. J. Chem. Phys., in press. (12)Ducker, W. A.;Xu, Z.; Israelachvili, J. N. Langmuir 1994,10, 3279. (13)Radmacher, M.; Cleveland, J. P.; Fritz, M.; Hansma, H. G.; Hansma, P.K. Biophys. J. 1994,66,2159. (14)Rabinovich, Y.I.; Yoon, R. H. Lungmuir 1994,10,1903.
(15)Hues, S.M.; Draper, C. F.; Lee, K. P.; Colton, R. J. Rev. Sci. Instrum. 1994,65,1561. (16)Hoh, J. H.; Engel, A. Langmuir 1993,9, 3310. (17)Similar problems were observed with the Nanoscope 111,but the manufacturer has recently described a simple change to a software parameter file that can be used to substantially reduce the digitization artifacts.
* To whom correspondence should be addressed.
* Abstract published in Advance ACS Abstracts, April 1,1995.
(1)Binnig, G.; Quate, C. F.; Gerber, C. Phys. Reu. Lett 1986,56,930. (2)Bumham, N. A.;Colton, R. J. J . Vac. Sci. Technol. A 1989,7 , 2906. (3)Mate, C. M.;Lorenz, M. R.; Novotny, V. J. J . Chem. Phys. 1989, 90, 7550. (4)Weisenhom, A. L.; Hansma, P. K.; Albrecht, T . R.; Quate, C. F. Appl. Phys. Lett. 1989,54, 2651. (5)Ducker, W. A.;Senden, T . J.; Pashley, R. M. Nature 1991,353, 239. ~ . . ( 6 ) Butt, H.-J. Biophys. J. 1991,60,1438. (7)OShea, S.J.;Welland, M. E.; Rayment, T.AppZ.Phys.Lett. 1992, en 2.156. (8) Larson, I.; Drummond, C. J.; Chan, D. Y. C.; Grieser, F. J.Am. Chem. SOC.1993,115,11885. (9)Lin, X.-Y.; Creuzet, F.; Arribart, H. J. Phys. Chem. 1993,97, - - I
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0743-7463/95/2411-1065$09.Q0lQ 0 1995 American Chemical Society
Letters
1066 Langmuir, Vol. 11, No. 4,1995
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Figure 1. Voltage applied to the piezo (bottom,0.5 V/div, 3.6 nddiv) and cantileverdeflection (top,2V/div, 15nddiv)versus time (0.2 ms/div). The cycle period was 440 ms, the totalz-scan range of the piezo was 100 V. The piezo signal is part of the triangular ramp which moves the sample up and down. The measurement was taken in distilled water. The cantilever reacted with a damped oscillation t o each step of the piezo movement.
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Figure 2. Typical force curve measured in distilled water on mica. Shown is the height position of the sample versus the deflection of the cantilever. The full line consists of 4000 data points. The oscillations of the cantilever can be seen. After reduction of the 4000 data points to 400 data points, the oscillations reduce t o those force curves seen with normal microscope software. Instead of oscillations there appear to be a hysteresis between approaching and retracting curve. Note that in the noncontact region there is also a true hysteresis which is not caused by the oscillations. The cycle period was 1040 ms, the total z-scan range of the piezo was 66 V.
the cantilever is coupled to the piezo movement, and thus higher harmonics can be induced. A force curve measured with 4000 points shows the effect of cantilever oscillations (Figure 2). Force curves obtained depended critically on the delay time between a step of the piezo and sampling the cantilever deflection. The phase of the cantilever oscillation is reversed when the direction of the piezo is reversed. Therefore, if the sampled data point is situated on an extreme of the cantilever oscillations,the hysteresis between approaching and retracting curve will be large. If it is situated near the zero passage, the hysteresis will be small. (18)Butt, H.-J.; Siedle, P.; Seifert, K.; Fendler, K.; Seeger, T.; Bamberg, E.; Weisenhorn, A. L.; Goldie, K.; Engel, A. J.Microsc. 1993, 169,75.
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13,9 nm / Div Figure 3. A series of force curves measured on a gold surface with the standard electronics and software. The approach is the solid line in the non-contact region, the retraction is the dashed line. The cycle periods were from top t o bottom 80,120, 160, and 440 ms. The total z-scan range of the piezo was 39 V. Cantilever oscillations due to the stepwise movement of the piezo can cause a t least two misinterpretations: attractive forces and the viscous effect of the liquid on the cantilever might be over- or underestimated. This is demonstrated with a series of force curves measured with different cycle speeds on a gold surface (Figure 3). These measurements were done with a stepwise, discrete voltage ramp. In the approaching curves a n attractive force, probably the van der Waals force, is visible. The difference between approaching and retracting curves in the noncontact region and the strength of the attractive force varied with cycle speed in a n unsystematic way. At the smallest cycle period of 80 ms the attractive force, measured during the approach, is visible. At a cycle period of 120 ms the attractive force almost disappeared; at a period of 160 ms it is again present. The hysteresis in the noncontact region is large a t short cycle periods, then becomes small, large, and finally zero with increasing cycle period. Probably those force curves taken with a long cycle period (440ms) are the most reliable ones since one can measure cantilever deflection a t the end of each step. For attractive force curves a serious problem remains: Due to the oscillation, a t a certain time the tip is closer
Langmuir, Vol.11, No. 4,1995 1067
Letters to the sample than one would expect from the height position of the sample. If at this point the gradient of the attractive forces exceeds the spring constant plus the gradient of repulsive forces, the tip jumps onto the sample.lg Hence, the jump-in occurs a t too large a distance. One possibility to remove cantilever oscillations was to ramp the sample by a n external, smooth signal without steps. Another simple possibility consists in filtering the voltage applied to the piezo by a low-pass filter with a rise time of typically 1ms. (19) Burnham,N. A.;Colton, R.J.;Pollock, H.M.J.VUC. Sci. Technol. A 1991,9, 1991.
Not all of the hysteresis in the noncontact regime is caused by cantilever oscillations. When the piezo was moved by a n external smooth voltage ramp, a small hysteresis was still apparent in the noncontact region. This hysteresis increased linearly with the sample approach speed. At a speed of 5 p d s in water the hysteresis was about 8 nm, which roughly agrees with ref 16. Acknowledgment. We thank E. Bamberg, M. Jaschke, and F. Schabert for their help and R. Schubert and H. Volk for excellent drawings and photographs. This work was supported by the Deutsche Forschungsgemeinschaft Schwerpunktprogra" Neue mikroskopische Techniken fur Biologie und Medizin. LA940942F
