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Studies of tip wear processes in tapping mode™ atomic force microscopy
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Ultramicroscopy 97 (2003) 135–144
Studies of tip wear processes in tapping modet atomic force microscopy Chanmin Su, Lin Huang*, Kevin Kjoller, Ken Babcock Digital Instruments/Veeco Metrology Group, 112 Robin Hill Road, Santa Barbara, CA 93117, USA Received 25 June 2002; received in revised form 7 October 2002
Abstract Tip integrity is crucial to atomic force microscope image quality. Tip wear not only compromises image resolution but also introduces artifacts. However, the factors that govern wearing have not been systematically studied. The results presented here of tip wearing on a rough titanium surface were determined by monitoring changes in tip shape and the evolution of histograms of complex surface curvatures under different control parameters. In contrast with the common assumption that operating at a low set point (the ratio of tapping amplitude to free oscillation amplitude) wears the tip quickly, we observed that a low set point actually minimizes tip wear on a hard surface regardless of the free amplitude. The results can be interpreted qualitatively with theoretical calculations based on momentum exchange at tapping impact. Operating at a low set point allows more robust scanning than with a high set point (tapping near free amplitude), providing a method to slow down tip wear. Another advantage of a low set point is that amplitude error grows faster than with a high set point by nearly an order of magnitude, permitting an increase in scanning speed. r 2003 Elsevier Science B.V. All rights reserved.
1. Introduction For all scanning probe related techniques, the tip radius of a probe is considered as the most critical factor that determines image resolution. In the majority of applications, the tips are in direct or proximate contact with sample surfaces. The contact can be either transient as in tapping mode or sustained as in contact mode. Tip wear has been an inevitable byproduct of atomic force microscopy (AFM) imaging. In practical applications, the consequences of tip wear or tip damage can be severe. Most obviously, image resolution degrades, yielding false data if tip shape is substantially modified. In metrology applications not only can *Corresponding author. E-mail address: [email protected] (L. Huang).
tip wear be confounded with sample wear, reducing apparent production yield, but it also contributes significant systematic error to step height measurements [1]. Although tip wear cannot be avoided, tip wear processes can be understood and their controlling parameters optimized to minimize tip degradation. There are two processes causing tip damage: engaging the tip to a surface and scanning on the surface; in this study we focus on the latter process. Existing tip wear studies are surprisingly limited with regard to tapping mode imaging parameters, despite tapping mode being the most widely used AFM technique under ambient conditions. Skarman et al. used a high-resolution scanning electron microscope (SEM) to study tip shape directly as it evolves during tapping [2]. They were able to correlate image deterioration
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with tip cracking, tip contamination and tip supply vendors, though for some tips wear and image quality were not well correlated. Ho and West [3] also examined the geometry of AFM probes using an SEM before and after scanning in tapping mode to determine whether the scanning technique had an effect on the geometry of the probe tip. They concluded that if a probe oscillates such that it contacts the surface during each cycle, substantial damage or ‘‘wear’’ to the probe occurs and significant image degradation is observed. When probes are operated in so-called ‘‘near-contact’’ tapping mode (very small oscillation amplitude), image quality can be well preserved after prolonged scanning. However, the supporting measurements made for the study were performed at different drive amplitudes and set points, as is apparent from the noise levels of the cases compared. The factors that can affect tip wear are complicated and interrelated. For example, a higher noise level forces the AFM feedback loop to average more data, so reduces its responsiveness. As a result, the control error increases; leading to unintended and potentially damaging tip motion. Another tip wear factor is the set point of the feedback, the root mean square value of probe cantilever oscillation targeted by the control system. Cantilever response changes with set point, independently of tip/surface interaction and can lead to an entirely different data acquisition environment, modifying the progress of tip wear. It is therefore important that tip wear studies be performed in well-controlled environments that take into account feedback loop parameters and system noise in addition to tip and sample selection. In this paper, we approach tappinginduced tip wear through closely controlled AFM operating conditions. The objectives of the current study are to define the optimum operating conditions for high-efficiency feedback loop control while extending the useful ‘‘life’’ of the tip.
2. Tip/sample interaction in tapping mode imaging There are two main concerns in tapping mode imaging: sample damage if the hardness of the tip
is higher than that of the sample, and tip wear if the sample is comparable or harder than the tip. In this paper, we limit our scope to probes interacting with a relatively hard sample surface. There have been numerous investigations of tip/ sample interaction during tapping [4]. We focus on those works where the impact force or the speed of the tip upon impact is explicitly calculated. Salapaka et al. modeled the tapping process as a damped spring with a concentrated mass. In their calculation, the impact is simulated as a ball bouncing away from a hard wall with the reflection speed determined by the coefficient of restitution [5]. When the coefficient is 1, the reflection speed is equal to the impact speed. The impact speed is found to increase monotonically as the separation between the sample surface and the oscillating mass is reduced, confirming the general presumption that low set point produces harder tapping on sample surfaces. In contrast to Salakapa’s calculation, Anczykowski et al. simulated the tip impact process based on the MYD/BHM model, which is derived from first principles, taking elastic deformation and attractive forces into account [6]. They calculated the average force at the reversal point as a tip taps a surface. It was shown that this force is low at tapping amplitudes close to the free amplitude, so is normally referred to as ‘‘light tapping.’’ However, as the set point is reduced until it approaches the limit of ‘‘hard tapping’’ at low set point, the force goes through a maximum and descends to a value as low as that for ‘‘light tapping.’’ Since tapping force is proportional to momentum change within the duration of the impact, for a given tip/cantilever equivalent mass this force is also proportional to impact speed. In another modeling of tapping interaction, Tamayo and Garcia simulated tapping on the surfaces by van der Waals force at near-surface distance and Hertz model during indentation [7]. The average force of tapping was found to go through a maximum as the relative set point is decreasing, yielding similar results as those by Anczykowski et al. It is obvious that the above results of the calculation disagree with each other in predicting tapping force. None of them attempted to correlate this force with tip wear. As we know, this force will determine local stresses causing tip
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deformation during impact and will eventually lead to tip wear; it is important to obtain experimental data directly from tip wear tests based on the control conditions described in the simulation models. From the imaging control system point of view it is well established that in order to protect either sample or tip, it is most straightforward to select a tapping imaging set point very close to the free oscillation amplitude, for light tapping, which is also referred to as tapping with high relative set point (Rs ¼ Atapping =Afree close to 1, Afree and Atapping representing cantilever amplitude in free and tapping oscillation, respectively). The other extreme setting of operating parameter Rs ; much smaller than 1, is referred to as low relative set point. The drawback of high relative set point operation is that the amplitude error generation rate (the speed of amplitude growth) is low and the transient time for amplitude error to reach equilibrium increases exponentially as Atapping =Afree approaches 1. As a consequence, AFM feedback on true error due to surface topographic change has to run much slower through proportional (P) and integral (I) gain adjustment, limiting bandwidth for high relative set point operation. Any time the amplitude error contains transient components they are (falsely) interpreted as surface position, the feedback loop may oscillate. As a result, the control system loses track of the surface and the probe may impact surface out of control during feedback oscillation, damaging the tip in most cases. It is therefore interesting, in light of Anczykowski and Tomayo’s calculation, to verify that low relative set point operation does not subject a tip to extra impact forces. Another simple way to visualize impact force is to calculate tip speed before it taps the surfaces. Because the contact time during tapping is nearly a constant for relative hard sample materials, the impact force, which is momentum change divided by contact time, is then proportional to the tip impact speed. Our approximation of tapping speed treats each period after impact as a new start (see Fig. 1 for two values of cantilever mechanical Q). The dotted lines in Figs. 1a and b are cantilever deflection data sampled while tapping surfaces. Assuming the surface is instantaneously with-
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drawn at t0 ; the cantilever amplitude continues to grow as shown in the case for Q ¼ 32 (the solid curves are sampled data of unobstructed cantilever amplitude). The cantilever then has a whole period to accelerate and decelerate as it approaches the surface. If no surface is present, the deceleration is completed at higher amplitude than the last period and the amplitude continues to grow exponentially. The presence of a surface stops the downward motion of the cantilever before the cantilever spring decelerates the tip speed to zero, ending the period prematurely. The tip therefore impacts the surface with a finite speed that depends on where the downward oscillation is terminated. The speed based on this simple model can be
Fig. 1. Deflection of an MESP cantilever during tapping as a function of time. The resonance frequency of the lever is approximately 87 kHz. (a) Dotted line: data points sampled as tapping proceeds; solid line: the calculated amplitude increase assuming the surface is withdrawn after tapping at t0 : Amplitude growth is based on a lever with Q ¼ 32: Point A marks the amplitude at which the tip hits the surface. (b) Same as (a) except the Q of the lever is 298, typical of most cantilevers used in air.
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expressed as Vr ¼ 2pfAs cos1
Rs ; Rs þ ðp=QÞð1 Rs Þ
ð1Þ
where Vr is the impact velocity or residual speed immediately before tip/surface impact, f is the cantilever resonant frequency, As is the set point of the feedback loop, Rs is the relative set point and Q is the mechanical quality factor of the probe. In this model, the sample acts as an infinite energy sink and the cantilever has to accelerate from zero speed after impact. The residual speed of the tip (right before impact at point A in Fig. 1a) is plotted as a function of set point for cantilevers with different mechanical Q factors. Two features deserve attention. The first is the shape of the curves in Fig. 2: the speed is low around free oscillation (region C, Fig. 2) and increases quickly as the relative set point Rs is reduced. However, instead of a monotonic increase with descending Rs; the speed goes through a maximum (region B, Fig. 2) then drops to a comparable low level with the light tapping of a high relative set point (region A, Fig. 2). This simple model supports the calculation of Anczykowski et al. and Toyama et al. The other feature worth noting is the strong dependence of the residual speed on cantilever mechanical quality factor Q: As Q increases, the speed before impact declines for the same value of Rs ; even though the
1.8
3
Tapping Speed(mm/s)
1.6 1.4
B
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shape of the Rs dependence remains the same. Deformations of tip/sample during tapping interactions are neglected in our simple model of reflection, assuming that the tip accelerates from zero speed after impact. For these assumptions to be valid, the oscillation center of the tapping vibration should be precisely the same as that of free oscillation when the tip is not interacting with a surface. Otherwise, the additional kinetic energy upon reflection shifts the oscillation center with respect to that of the freely vibrating cantilever.
3. Experimental We used a MultiMode AFM (Digital Instruments, Veeco Metrology Group, Santa Barbara, CA) equipped with a low-noise laser diode in this study. The photodetector signal was also directly sampled by a 12-bit analog-to-digital converter (ADC) with 5 megasamples/second data rate and 6 mV peak-to-peak (p2p) single sampling noise. The samples studied are all considered hard surfaces, such as Si and Ti coatings (TipCheckt) on Si. The probes used are OTESPA (Olympus etched Si probes with the cantilever spring constant around 40 N/m). In all the wear tests, not only the scan rate and set point, but also the feedback error was closely controlled to assure a fair comparison between cases. The amplitude control error was kept below 20 mV, which is negligible compared with the lowest set point studied, 200 mV. An extremely careful engaging procedure was used to avoid any tip damage upon first engaging. Tip size was then immediately monitored and had to qualify for the tip to continue in the trials.
2 A
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C
4. Results
0.4
1
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4.1. Cantilever oscillation
0 0
10
20
30
40
50
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Fig. 2. Calculated impact speed of the tip on a surface for a cantilever with free oscillating amplitude of 100 nm and Q ¼ 200 (curve 1), 100 (curve 2) and 50 (curve 3), respectively. The resonant frequency of the lever is 200 kHz.
To visualize cantilever deflection during the tapping process, we devised a high speed, lownoise system to sample cantilever deflection data in real time. The purpose of the experiment is to observe cantilever oscillation during low set point
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operations and compare the center of oscillation with that of the lifted cantilever where the tip is not tapping a surface. To produce conclusive data, the AFM itself must exhibit low noise, negligible drift and employ a low-noise sampling system that does not interfere with AFM signals. The sampler used has a peak-to-peak single sampling noise level well below the operating signal amplitude. With a few samples averaged, the noise can be dropped below 1 mV. The sampled data are displayed in Fig. 3. The imaging set point used corresponds to a cantilever oscillation of 255 mV pp (about 15 nm peak to peak, curve 1 in Fig. 3). The tip was then lifted by 100 nm and the cantilever allowed to reach free oscillation within a few milliseconds. Free oscillation data were sampled as shown in curve 2 of Fig. 3. To avoid any offset introduced by operational amplifiers or filters, the oscillation center is calculated by (separately) averaging the data in curves 1 and 2 (Fig. 3, curves 3 and 4 for tapping and lifted modes, respectively). System drift in the Z-direction is about 3 nm/min. Data
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acquisition for the two conditions took about 1 s. The drift-induced deflection change is therefore negligible. The average positions of tapping and free oscillation over a longer time are shown at a magnified scale for the same curves 3 and 4 in the inset of Fig. 3. Low-frequency noise is visible. However, the oscillation centers for ‘‘low set point’’ operation and free oscillation appear to coincide within approximately a millivolt. Note that, with the MultiMode, lift mode is implemented by withdrawing the sample surface from the tip, so the reflection optical path remains exactly the same as during tapping except that the sample surface no longer constrains the cantilever oscillation. The average vertical positions on the photodetectors are 132.2 and 131.8 mV for free oscillation and Rs ¼ 0:15; low set point operation, respectively. The difference is well within the noise levels of the photodetector and the ADC individually. It is concluded that the tapping oscillation of a cantilever retains the same center as when it is freely vibrating.
Fig. 3. Precision measurement of the DC offset during tapping as the set point is changed for a fixed drive amplitude. The free oscillation was performed by lifting the lever 100 nm immediately after tapping data acquisition. Curve 1: Tapping deflection at a relative set point of As =A0 ¼ 0:15: Curve 2: Free oscillation deflection after the lever is lifted 100 nm. Curve 3: (dotted line) center positions of the lever oscillation at a tapping set point of 0.15. Curve 4: (dashed line) center positions of the lever in free oscillation. Inset: center positions of tapping (curve 3, solid line) and free (curve 4, dashed line) oscillation lever in longer time scale and zoomed in vertical scale.
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The significance of this observation is that the impact of the tip on the surface transfers the majority of remanent kinetic energy to the sample, which serves as an infinite energy sink. Sample and tip deformation-induced bounce back was not observed in the cases studied. The loss of kinetic energy during impact is probably the governing factor for tip wear and tip damage in tapping mode. The preceding insight motivates the following investigation, i.e. tip wear as a function of set point, of the correlation between the remanent kinetic energy driving tip/surface impact and any observed tip wear following impact. 4.2. Tip wear Maintaining the cautions observed during cantilever oscillation measurements, OTESPA type probes were scanned on Ti flake surfaces. Fig. 4 shows images acquired on the same sample but using different tips under various relative set points as indicated by A, B and C in Fig. 2. The three images shown in the top row of Fig. 4 used a very low set point of Rs ¼ 0:1: The middle row images, where Rs ¼ 0:5; represent a medium set point and the bottom row corresponds to light tapping, where Rs ¼ 0:8: The first frame under all three operating conditions, A, B and C (the left column of images in Fig. 4), demonstrates clear feature resolution. However, by the sixth frame (the middle column of images in Fig. 4), the image resolution has degraded considerably for the medium set point, B, while the other two sets of data still maintain their original resolution. By the 21st frame, the medium set point tip was quite worn and the light-tapping tip started to show deteriorated resolution in comparison to its first frame. The image resolution of very low set point remains nearly identical throughout all the frames. Note that the data shown are only for trace. Since scanning occurs in both trace and retrace, the actual scanning frames on surfaces are doubled. The qualitative resolution difference between operating at set points A and C remains to be quantified. Given that the Ti flakes are extremely hard and sharp, image resolution deterioration was used to indicate the extent of tip wear. The shape of the tip
Frame
1
6
21
A
B
C
Fig. 4. Surface topography of Ti flakes imaged with relative set points marked as A, B and C in Fig. 2. All the other imaging conditions are identical, including free oscillation amplitude. Row A: relative set point at 0.1, images at the first, sixth and 20 first frames, tracing in the same direction. Row B: same as row A but relative set point at 0.5. Row C: relative set point at 0.8.
was reconstructed using a morphological dilation routine developed by Digital Instruments [8] from algorithms discussed in detail by Villarrubia [9]. Fig. 5 shows how the tip qualification routine works. Once sample topographic data is captured, the local peaks are identified. All such summit neighborhoods are then superimposed with their peaks aligned as shown in the bottom right cross section view. The envelope of innermost trajectories in every direction from the overlapped data is defined as the estimated tip shape through surface morphological dilation. The nominal diameters of two cuts parallel to the xy (sample) plane yield estimated tip diameters (ETD) for the two heights shown in Fig. 5. Normally, the two heights are selected as 5 and 10 nm, respectively and as displayed in Fig. 6. While ETD representation of tip shape is convenient and straightforward, we were concerned that a single peak traversal (as shown in the rightside diagram of Fig. 5) could dominate the tip shape determination. Such sharp peaks could be due to temporary mechanical/electronic drift under environmental stimulation. A statistical
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Height2 Height1
1.5
µm
Fig. 5. Schematics showing the tip qualification process. Top left: a sharp tip and rounded surface feature produce a similar trace to that from a dull tip and a sharp surface feature. Bottom left: actual image with the local maxima marked. Right: topographic data in the neighborhoods of the local maxima are superimposed, aligning the peaks. The inner envelope of the traces, projected through the summit point, is taken as the tip shape. The ETDs are the average tip cross-section diameters at height1 and height2 above the tip apex.
treatment of the data is therefore preferred. Note that simply performing a fast Fourier transform (FFT) to view the components in k-space is insufficient because even a blunt tip may yield a very sharp minimum and an FFT does not differentiate maxima from minima, so it could produce a misleading spectrum instead. The ‘‘innermost’’ data subset of the maxima is no longer necessarily continuous, therefore, performing an FFT on it becomes nontrivial. To simplify the data analysis, we generated a histogram of peak traversal neighborhood data subsets each characterized by its calculated radius of curvature. The number of image peaks measured at each radius of curvature, within a 4 nm bin size, is plotted as a function of radius in Fig. 7. The distribution curves shift systematically to higher calculated radii with increasing ETD value, implying that ETD serves as a valid representation of tip shape. Theoretically, the area under each of the three curves is identical irrespective of the associated tip radius change. However, sample drift may result in different sample areas and therefore a different total number of local maxima. Also, severe tip shape change may result in totally
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different topographic data and a changed total number of maxima. Sample drift and abrupt tip degradation may explain the lack of area conservation beneath the curves of Fig. 7. With confidence established in the data analysis algorithm, a group of tips were used to wear on the same surface but at different relative set points. Fig. 8 illustrates the progression of ETD with tip wear under different set points. The initial tips were chosen from the same batch. However, the first frames show a slightly smaller diameter as the set point is reduced. This tendency may reflect how well a tip tracks a surface. After a few frames of scanning (512 scan lines), the dependence of tip wear on set point becomes clear. The shapes of the curves of ETD as a function of relative set points (Fig. 8) generally resemble the shapes of the curves in Fig. 2 and also follow the calculation of Anzykowski et al. and Toyama et al. There is one abrupt drop point in ETD for set point Rs ¼ 0:38 at the 20th frame that may be due to hitting the surface so hard that the tip fractured. Similar measurements were also performed on a surface with polysilicon grains. Rs values within the range 0.4–0.5 were again found to be the most damaging imaging conditions. The most visible effect of tapping force was seen when imaging silver nanocrystals with a height of 3–20 nm, deposited at low temperature under UHV [10]. The particles are weakly bound to the underlying Si(1 1 1) surface. Imaging must proceed with great care to avoid moving them [11]. Fig. 9 shows, for the same probe, the difference between imaging silver nanocrystals at a very low set point, Rs ¼ 0:1; where their spherical shape is clearly distinguishable (Fig. 9a), and at a medium set point of Rs ¼ 0:5; where the particles are no longer stationary. In Fig. 9b, the tip is pushing nanocrystals along the slow scan direction, as indicated by the arrows. Note that nearly all the features in Fig. 9b are distorted along fast scan direction as well.
5. Discussion We have demonstrated that hard tapping (at a low relative set point) is the operating condition
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Fig. 6. An example of ETD determination. Top left: original data with local maxima identified. Bottom left: data measured. Top right: cross section (white area and the most inner circle) at height1. Bottom right: cross section (gray area and the innermost circle) at height2.
Fig. 7. Histograms of tip radii. Bin size for all curves: 4 nm. All data are from the same tip scanned at the relative set point of 0.5 (initial free amplitude approximately 44 nm). Curves 1–3: first frame, third frame and sixth frame. The legend shows ETD calculated for each set of data.
which best preserves the tip. The advantage of tapping at low relative set point is the potential for faster amplitude growth. The focus of an AFM control system is error growth around the set point. If the tip hits a higher feature than at the previous scan location, the surface can always stop the tip oscillation and generate error at a rate faster than the cantilever dynamics. On the other hand, when the tip reaches a new scan location that is lower than the previous one, the amplitude growth is determined by the cantilever dynamics. The growth rate is shown in Fig. 10, where the rate was measured by sudden withdrawal of the sample surface during tapping. This figure clearly shows that operating at lower set point results in much quicker error growth, therefore allowing the feedback loop to run at higher bandwidth,
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corresponding to higher P and I gains. The combination of greater bandwidth and higher gains allows a tip to track a surface while scanning faster. The drawback of the low set point operation is that it may turn into contact mode. Given a tapping amplitude of 200 mV pp, as in our case, if the feedback control error is more than 100 mV,
the tip will be on the surface with zero amplitude, scanning in contact mode before the feedback loop can respond to the error. In all our experiments, the scan rate was kept at 0.3 Hz to assure negligible control error. A much higher scan rate is desirable as a practical matter, and we have now learned that the cantilever dynamics is capable of
Fig. 8. ETD at 5 nm (height1) as a function of set point after tips were tested with the same amount of tapping on Ti surfaces. Each relative set point uses a different tip and tip wear proceeds as the number of scanned frames increases. Curves 1–6: ETD calculated from data sampled at the first, second, third, fifth, 10th and 20th frames.
Fig. 10. Amplitude error growth rate measured by sudden withdrawal of the surface when the tip is tapping, at different set points. Measurements were taken with an MESP type cantilever (resonant frequency approximately 87 kHz and Q approximately 270).
Fig. 9. Tapping mode imaging of silver nanocrystals on Si(1 1 1) surface. The free oscillation amplitude is the same for both cases shown. The scanning size is 500 nm 500 nm (a) Relative set point of 0.1, (b) relative set point of 0.5.
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providing much faster response at lower set points, most importantly, without sacrificing the tip in hard tapping. The bottleneck then becomes the feedback loop itself. Fortunately, Minne et al. developed a nested feedback loop [12], which was implemented by Digital Instruments in the Nanoscope IV Controller [13]. The combined system can lower the feedback control error by a factor of 20, greatly reducing the risk of tip degradation while running surface scans at a low set point. As for the wear mechanism, the similarity between the curves in Figs. 2 and 8 suggests that the wear process is dominated by momentum exchange between tip and surface. The residual speed of the tip hitting the surface determines the rate of tip wear. One more aspect worth noting: in practical operation, the tip should be engaged with low tapping amplitude and the cantilever drive increased after the feedback loop achieves set point control. Failing to do this may result in the tip going through the maxima in both Figs. 2 and 9 and tip damage may occur.
6. Conclusion We have proved experimentally the correlation between residual tip speed before impacting a surface and tip wear for the relatively hard samples used in this investigation. It is demonstrated that lower set point is not harmful to tips for those samples under our experimental conditions. On the other hand, the potential amplitude growth rate is greatly increased by running the microscope at lower set points, rendering faster scanning possible.
Acknowledgements The authors are indebted to Michael Serry of Digital Instruments, Veeco Metrology for his initial experimental work. We also appreciate enlightening discussion with Dr. R. Garcia and careful editing work by Alan Rice.
References [1] H. Edwards, R. McGlothlin, J. Appl. Phys. 83 (1998) 3952. [2] B. Skarman, L.R. Wallenberg, S.N. Jacobsen, U. Helmersson, C. Thelander, Langmuir 16 (2000) 6267. [3] H. Ho, P. West, Scanning 18 (1996) 339. [4] A. San Paulo, R. Garcia, Phys. Rev. B 64 (2001) 193411; O. Sahin, A. Atalar, Appl. Phys. Lett. 78 (2001) 2973; J.P. Aime, R. Boisgard, L. Nony, G. Couturier, J. Chem. Phys. 114 (2001) 4945; R. Garcia, A. San Paulo, Phys. Rev. B 60 (1999) 4961; R.G. Winkler, J.P. Spatz, S. Sheiko, M. Moller, P. Reineker, O. Marti, Phys. Rev. B 54 (1996) 8908. [5] M.V. Salapaka, D.J. Chen, J.P. Cleveland, Phys. Rev. B 61 (2000) 1106. [6] B. Anczykowski, D. Kruger, K.L. Babcock, H. Fuchs, Ultramicroscopy 66 (1996) 251. [7] J. Tamayo, R. Garcia, Langmuir 12 (1996) 4430. [8] Tip qualification application notes, published by Digital Instruments/Veeco Metrology Group. [9] J.S. Villarrubia, J. Res. Nat. Inst. Standards Technol. 102 (1997) 425. [10] L. Huang, S.J. Chey, J.H. Weaver, Phys. Rev. Lett. 80 (1998) 4095. [11] S.J. Chey, L. Huang, J.H. Weaver, Appl. Phys. Lett. 72 (1998) 2698. [12] S. Minne, US Patent #6,189,374. [13] L. Huang, K. Kjoller, C. Su, K. Babcock, D.M. Adderton, S.C. Minne, American Physical Society Meeting, March 2002.
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Studies of tip wear processes in tapping modet atomic force microscopy Chanmin Su, Lin Huang*, Kevin Kjoller, Ken Babcock Digital Instruments/Veeco Metrology Group, 112 Robin Hill Road, Santa Barbara, CA 93117, USA Received 25 June 2002; received in revised form 7 October 2002
Abstract Tip integrity is crucial to atomic force microscope image quality. Tip wear not only compromises image resolution but also introduces artifacts. However, the factors that govern wearing have not been systematically studied. The results presented here of tip wearing on a rough titanium surface were determined by monitoring changes in tip shape and the evolution of histograms of complex surface curvatures under different control parameters. In contrast with the common assumption that operating at a low set point (the ratio of tapping amplitude to free oscillation amplitude) wears the tip quickly, we observed that a low set point actually minimizes tip wear on a hard surface regardless of the free amplitude. The results can be interpreted qualitatively with theoretical calculations based on momentum exchange at tapping impact. Operating at a low set point allows more robust scanning than with a high set point (tapping near free amplitude), providing a method to slow down tip wear. Another advantage of a low set point is that amplitude error grows faster than with a high set point by nearly an order of magnitude, permitting an increase in scanning speed. r 2003 Elsevier Science B.V. All rights reserved.
1. Introduction For all scanning probe related techniques, the tip radius of a probe is considered as the most critical factor that determines image resolution. In the majority of applications, the tips are in direct or proximate contact with sample surfaces. The contact can be either transient as in tapping mode or sustained as in contact mode. Tip wear has been an inevitable byproduct of atomic force microscopy (AFM) imaging. In practical applications, the consequences of tip wear or tip damage can be severe. Most obviously, image resolution degrades, yielding false data if tip shape is substantially modified. In metrology applications not only can *Corresponding author. E-mail address: [email protected] (L. Huang).
tip wear be confounded with sample wear, reducing apparent production yield, but it also contributes significant systematic error to step height measurements [1]. Although tip wear cannot be avoided, tip wear processes can be understood and their controlling parameters optimized to minimize tip degradation. There are two processes causing tip damage: engaging the tip to a surface and scanning on the surface; in this study we focus on the latter process. Existing tip wear studies are surprisingly limited with regard to tapping mode imaging parameters, despite tapping mode being the most widely used AFM technique under ambient conditions. Skarman et al. used a high-resolution scanning electron microscope (SEM) to study tip shape directly as it evolves during tapping [2]. They were able to correlate image deterioration
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with tip cracking, tip contamination and tip supply vendors, though for some tips wear and image quality were not well correlated. Ho and West [3] also examined the geometry of AFM probes using an SEM before and after scanning in tapping mode to determine whether the scanning technique had an effect on the geometry of the probe tip. They concluded that if a probe oscillates such that it contacts the surface during each cycle, substantial damage or ‘‘wear’’ to the probe occurs and significant image degradation is observed. When probes are operated in so-called ‘‘near-contact’’ tapping mode (very small oscillation amplitude), image quality can be well preserved after prolonged scanning. However, the supporting measurements made for the study were performed at different drive amplitudes and set points, as is apparent from the noise levels of the cases compared. The factors that can affect tip wear are complicated and interrelated. For example, a higher noise level forces the AFM feedback loop to average more data, so reduces its responsiveness. As a result, the control error increases; leading to unintended and potentially damaging tip motion. Another tip wear factor is the set point of the feedback, the root mean square value of probe cantilever oscillation targeted by the control system. Cantilever response changes with set point, independently of tip/surface interaction and can lead to an entirely different data acquisition environment, modifying the progress of tip wear. It is therefore important that tip wear studies be performed in well-controlled environments that take into account feedback loop parameters and system noise in addition to tip and sample selection. In this paper, we approach tappinginduced tip wear through closely controlled AFM operating conditions. The objectives of the current study are to define the optimum operating conditions for high-efficiency feedback loop control while extending the useful ‘‘life’’ of the tip.
2. Tip/sample interaction in tapping mode imaging There are two main concerns in tapping mode imaging: sample damage if the hardness of the tip
is higher than that of the sample, and tip wear if the sample is comparable or harder than the tip. In this paper, we limit our scope to probes interacting with a relatively hard sample surface. There have been numerous investigations of tip/ sample interaction during tapping [4]. We focus on those works where the impact force or the speed of the tip upon impact is explicitly calculated. Salapaka et al. modeled the tapping process as a damped spring with a concentrated mass. In their calculation, the impact is simulated as a ball bouncing away from a hard wall with the reflection speed determined by the coefficient of restitution [5]. When the coefficient is 1, the reflection speed is equal to the impact speed. The impact speed is found to increase monotonically as the separation between the sample surface and the oscillating mass is reduced, confirming the general presumption that low set point produces harder tapping on sample surfaces. In contrast to Salakapa’s calculation, Anczykowski et al. simulated the tip impact process based on the MYD/BHM model, which is derived from first principles, taking elastic deformation and attractive forces into account [6]. They calculated the average force at the reversal point as a tip taps a surface. It was shown that this force is low at tapping amplitudes close to the free amplitude, so is normally referred to as ‘‘light tapping.’’ However, as the set point is reduced until it approaches the limit of ‘‘hard tapping’’ at low set point, the force goes through a maximum and descends to a value as low as that for ‘‘light tapping.’’ Since tapping force is proportional to momentum change within the duration of the impact, for a given tip/cantilever equivalent mass this force is also proportional to impact speed. In another modeling of tapping interaction, Tamayo and Garcia simulated tapping on the surfaces by van der Waals force at near-surface distance and Hertz model during indentation [7]. The average force of tapping was found to go through a maximum as the relative set point is decreasing, yielding similar results as those by Anczykowski et al. It is obvious that the above results of the calculation disagree with each other in predicting tapping force. None of them attempted to correlate this force with tip wear. As we know, this force will determine local stresses causing tip
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deformation during impact and will eventually lead to tip wear; it is important to obtain experimental data directly from tip wear tests based on the control conditions described in the simulation models. From the imaging control system point of view it is well established that in order to protect either sample or tip, it is most straightforward to select a tapping imaging set point very close to the free oscillation amplitude, for light tapping, which is also referred to as tapping with high relative set point (Rs ¼ Atapping =Afree close to 1, Afree and Atapping representing cantilever amplitude in free and tapping oscillation, respectively). The other extreme setting of operating parameter Rs ; much smaller than 1, is referred to as low relative set point. The drawback of high relative set point operation is that the amplitude error generation rate (the speed of amplitude growth) is low and the transient time for amplitude error to reach equilibrium increases exponentially as Atapping =Afree approaches 1. As a consequence, AFM feedback on true error due to surface topographic change has to run much slower through proportional (P) and integral (I) gain adjustment, limiting bandwidth for high relative set point operation. Any time the amplitude error contains transient components they are (falsely) interpreted as surface position, the feedback loop may oscillate. As a result, the control system loses track of the surface and the probe may impact surface out of control during feedback oscillation, damaging the tip in most cases. It is therefore interesting, in light of Anczykowski and Tomayo’s calculation, to verify that low relative set point operation does not subject a tip to extra impact forces. Another simple way to visualize impact force is to calculate tip speed before it taps the surfaces. Because the contact time during tapping is nearly a constant for relative hard sample materials, the impact force, which is momentum change divided by contact time, is then proportional to the tip impact speed. Our approximation of tapping speed treats each period after impact as a new start (see Fig. 1 for two values of cantilever mechanical Q). The dotted lines in Figs. 1a and b are cantilever deflection data sampled while tapping surfaces. Assuming the surface is instantaneously with-
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drawn at t0 ; the cantilever amplitude continues to grow as shown in the case for Q ¼ 32 (the solid curves are sampled data of unobstructed cantilever amplitude). The cantilever then has a whole period to accelerate and decelerate as it approaches the surface. If no surface is present, the deceleration is completed at higher amplitude than the last period and the amplitude continues to grow exponentially. The presence of a surface stops the downward motion of the cantilever before the cantilever spring decelerates the tip speed to zero, ending the period prematurely. The tip therefore impacts the surface with a finite speed that depends on where the downward oscillation is terminated. The speed based on this simple model can be
Fig. 1. Deflection of an MESP cantilever during tapping as a function of time. The resonance frequency of the lever is approximately 87 kHz. (a) Dotted line: data points sampled as tapping proceeds; solid line: the calculated amplitude increase assuming the surface is withdrawn after tapping at t0 : Amplitude growth is based on a lever with Q ¼ 32: Point A marks the amplitude at which the tip hits the surface. (b) Same as (a) except the Q of the lever is 298, typical of most cantilevers used in air.
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expressed as Vr ¼ 2pfAs cos1
Rs ; Rs þ ðp=QÞð1 Rs Þ
ð1Þ
where Vr is the impact velocity or residual speed immediately before tip/surface impact, f is the cantilever resonant frequency, As is the set point of the feedback loop, Rs is the relative set point and Q is the mechanical quality factor of the probe. In this model, the sample acts as an infinite energy sink and the cantilever has to accelerate from zero speed after impact. The residual speed of the tip (right before impact at point A in Fig. 1a) is plotted as a function of set point for cantilevers with different mechanical Q factors. Two features deserve attention. The first is the shape of the curves in Fig. 2: the speed is low around free oscillation (region C, Fig. 2) and increases quickly as the relative set point Rs is reduced. However, instead of a monotonic increase with descending Rs; the speed goes through a maximum (region B, Fig. 2) then drops to a comparable low level with the light tapping of a high relative set point (region A, Fig. 2). This simple model supports the calculation of Anczykowski et al. and Toyama et al. The other feature worth noting is the strong dependence of the residual speed on cantilever mechanical quality factor Q: As Q increases, the speed before impact declines for the same value of Rs ; even though the
1.8
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shape of the Rs dependence remains the same. Deformations of tip/sample during tapping interactions are neglected in our simple model of reflection, assuming that the tip accelerates from zero speed after impact. For these assumptions to be valid, the oscillation center of the tapping vibration should be precisely the same as that of free oscillation when the tip is not interacting with a surface. Otherwise, the additional kinetic energy upon reflection shifts the oscillation center with respect to that of the freely vibrating cantilever.
3. Experimental We used a MultiMode AFM (Digital Instruments, Veeco Metrology Group, Santa Barbara, CA) equipped with a low-noise laser diode in this study. The photodetector signal was also directly sampled by a 12-bit analog-to-digital converter (ADC) with 5 megasamples/second data rate and 6 mV peak-to-peak (p2p) single sampling noise. The samples studied are all considered hard surfaces, such as Si and Ti coatings (TipCheckt) on Si. The probes used are OTESPA (Olympus etched Si probes with the cantilever spring constant around 40 N/m). In all the wear tests, not only the scan rate and set point, but also the feedback error was closely controlled to assure a fair comparison between cases. The amplitude control error was kept below 20 mV, which is negligible compared with the lowest set point studied, 200 mV. An extremely careful engaging procedure was used to avoid any tip damage upon first engaging. Tip size was then immediately monitored and had to qualify for the tip to continue in the trials.
2 A
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4. Results
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0 0
10
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Fig. 2. Calculated impact speed of the tip on a surface for a cantilever with free oscillating amplitude of 100 nm and Q ¼ 200 (curve 1), 100 (curve 2) and 50 (curve 3), respectively. The resonant frequency of the lever is 200 kHz.
To visualize cantilever deflection during the tapping process, we devised a high speed, lownoise system to sample cantilever deflection data in real time. The purpose of the experiment is to observe cantilever oscillation during low set point
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operations and compare the center of oscillation with that of the lifted cantilever where the tip is not tapping a surface. To produce conclusive data, the AFM itself must exhibit low noise, negligible drift and employ a low-noise sampling system that does not interfere with AFM signals. The sampler used has a peak-to-peak single sampling noise level well below the operating signal amplitude. With a few samples averaged, the noise can be dropped below 1 mV. The sampled data are displayed in Fig. 3. The imaging set point used corresponds to a cantilever oscillation of 255 mV pp (about 15 nm peak to peak, curve 1 in Fig. 3). The tip was then lifted by 100 nm and the cantilever allowed to reach free oscillation within a few milliseconds. Free oscillation data were sampled as shown in curve 2 of Fig. 3. To avoid any offset introduced by operational amplifiers or filters, the oscillation center is calculated by (separately) averaging the data in curves 1 and 2 (Fig. 3, curves 3 and 4 for tapping and lifted modes, respectively). System drift in the Z-direction is about 3 nm/min. Data
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acquisition for the two conditions took about 1 s. The drift-induced deflection change is therefore negligible. The average positions of tapping and free oscillation over a longer time are shown at a magnified scale for the same curves 3 and 4 in the inset of Fig. 3. Low-frequency noise is visible. However, the oscillation centers for ‘‘low set point’’ operation and free oscillation appear to coincide within approximately a millivolt. Note that, with the MultiMode, lift mode is implemented by withdrawing the sample surface from the tip, so the reflection optical path remains exactly the same as during tapping except that the sample surface no longer constrains the cantilever oscillation. The average vertical positions on the photodetectors are 132.2 and 131.8 mV for free oscillation and Rs ¼ 0:15; low set point operation, respectively. The difference is well within the noise levels of the photodetector and the ADC individually. It is concluded that the tapping oscillation of a cantilever retains the same center as when it is freely vibrating.
Fig. 3. Precision measurement of the DC offset during tapping as the set point is changed for a fixed drive amplitude. The free oscillation was performed by lifting the lever 100 nm immediately after tapping data acquisition. Curve 1: Tapping deflection at a relative set point of As =A0 ¼ 0:15: Curve 2: Free oscillation deflection after the lever is lifted 100 nm. Curve 3: (dotted line) center positions of the lever oscillation at a tapping set point of 0.15. Curve 4: (dashed line) center positions of the lever in free oscillation. Inset: center positions of tapping (curve 3, solid line) and free (curve 4, dashed line) oscillation lever in longer time scale and zoomed in vertical scale.
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The significance of this observation is that the impact of the tip on the surface transfers the majority of remanent kinetic energy to the sample, which serves as an infinite energy sink. Sample and tip deformation-induced bounce back was not observed in the cases studied. The loss of kinetic energy during impact is probably the governing factor for tip wear and tip damage in tapping mode. The preceding insight motivates the following investigation, i.e. tip wear as a function of set point, of the correlation between the remanent kinetic energy driving tip/surface impact and any observed tip wear following impact. 4.2. Tip wear Maintaining the cautions observed during cantilever oscillation measurements, OTESPA type probes were scanned on Ti flake surfaces. Fig. 4 shows images acquired on the same sample but using different tips under various relative set points as indicated by A, B and C in Fig. 2. The three images shown in the top row of Fig. 4 used a very low set point of Rs ¼ 0:1: The middle row images, where Rs ¼ 0:5; represent a medium set point and the bottom row corresponds to light tapping, where Rs ¼ 0:8: The first frame under all three operating conditions, A, B and C (the left column of images in Fig. 4), demonstrates clear feature resolution. However, by the sixth frame (the middle column of images in Fig. 4), the image resolution has degraded considerably for the medium set point, B, while the other two sets of data still maintain their original resolution. By the 21st frame, the medium set point tip was quite worn and the light-tapping tip started to show deteriorated resolution in comparison to its first frame. The image resolution of very low set point remains nearly identical throughout all the frames. Note that the data shown are only for trace. Since scanning occurs in both trace and retrace, the actual scanning frames on surfaces are doubled. The qualitative resolution difference between operating at set points A and C remains to be quantified. Given that the Ti flakes are extremely hard and sharp, image resolution deterioration was used to indicate the extent of tip wear. The shape of the tip
Frame
1
6
21
A
B
C
Fig. 4. Surface topography of Ti flakes imaged with relative set points marked as A, B and C in Fig. 2. All the other imaging conditions are identical, including free oscillation amplitude. Row A: relative set point at 0.1, images at the first, sixth and 20 first frames, tracing in the same direction. Row B: same as row A but relative set point at 0.5. Row C: relative set point at 0.8.
was reconstructed using a morphological dilation routine developed by Digital Instruments [8] from algorithms discussed in detail by Villarrubia [9]. Fig. 5 shows how the tip qualification routine works. Once sample topographic data is captured, the local peaks are identified. All such summit neighborhoods are then superimposed with their peaks aligned as shown in the bottom right cross section view. The envelope of innermost trajectories in every direction from the overlapped data is defined as the estimated tip shape through surface morphological dilation. The nominal diameters of two cuts parallel to the xy (sample) plane yield estimated tip diameters (ETD) for the two heights shown in Fig. 5. Normally, the two heights are selected as 5 and 10 nm, respectively and as displayed in Fig. 6. While ETD representation of tip shape is convenient and straightforward, we were concerned that a single peak traversal (as shown in the rightside diagram of Fig. 5) could dominate the tip shape determination. Such sharp peaks could be due to temporary mechanical/electronic drift under environmental stimulation. A statistical
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Height2 Height1
1.5
µm
Fig. 5. Schematics showing the tip qualification process. Top left: a sharp tip and rounded surface feature produce a similar trace to that from a dull tip and a sharp surface feature. Bottom left: actual image with the local maxima marked. Right: topographic data in the neighborhoods of the local maxima are superimposed, aligning the peaks. The inner envelope of the traces, projected through the summit point, is taken as the tip shape. The ETDs are the average tip cross-section diameters at height1 and height2 above the tip apex.
treatment of the data is therefore preferred. Note that simply performing a fast Fourier transform (FFT) to view the components in k-space is insufficient because even a blunt tip may yield a very sharp minimum and an FFT does not differentiate maxima from minima, so it could produce a misleading spectrum instead. The ‘‘innermost’’ data subset of the maxima is no longer necessarily continuous, therefore, performing an FFT on it becomes nontrivial. To simplify the data analysis, we generated a histogram of peak traversal neighborhood data subsets each characterized by its calculated radius of curvature. The number of image peaks measured at each radius of curvature, within a 4 nm bin size, is plotted as a function of radius in Fig. 7. The distribution curves shift systematically to higher calculated radii with increasing ETD value, implying that ETD serves as a valid representation of tip shape. Theoretically, the area under each of the three curves is identical irrespective of the associated tip radius change. However, sample drift may result in different sample areas and therefore a different total number of local maxima. Also, severe tip shape change may result in totally
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different topographic data and a changed total number of maxima. Sample drift and abrupt tip degradation may explain the lack of area conservation beneath the curves of Fig. 7. With confidence established in the data analysis algorithm, a group of tips were used to wear on the same surface but at different relative set points. Fig. 8 illustrates the progression of ETD with tip wear under different set points. The initial tips were chosen from the same batch. However, the first frames show a slightly smaller diameter as the set point is reduced. This tendency may reflect how well a tip tracks a surface. After a few frames of scanning (512 scan lines), the dependence of tip wear on set point becomes clear. The shapes of the curves of ETD as a function of relative set points (Fig. 8) generally resemble the shapes of the curves in Fig. 2 and also follow the calculation of Anzykowski et al. and Toyama et al. There is one abrupt drop point in ETD for set point Rs ¼ 0:38 at the 20th frame that may be due to hitting the surface so hard that the tip fractured. Similar measurements were also performed on a surface with polysilicon grains. Rs values within the range 0.4–0.5 were again found to be the most damaging imaging conditions. The most visible effect of tapping force was seen when imaging silver nanocrystals with a height of 3–20 nm, deposited at low temperature under UHV [10]. The particles are weakly bound to the underlying Si(1 1 1) surface. Imaging must proceed with great care to avoid moving them [11]. Fig. 9 shows, for the same probe, the difference between imaging silver nanocrystals at a very low set point, Rs ¼ 0:1; where their spherical shape is clearly distinguishable (Fig. 9a), and at a medium set point of Rs ¼ 0:5; where the particles are no longer stationary. In Fig. 9b, the tip is pushing nanocrystals along the slow scan direction, as indicated by the arrows. Note that nearly all the features in Fig. 9b are distorted along fast scan direction as well.
5. Discussion We have demonstrated that hard tapping (at a low relative set point) is the operating condition
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Fig. 6. An example of ETD determination. Top left: original data with local maxima identified. Bottom left: data measured. Top right: cross section (white area and the most inner circle) at height1. Bottom right: cross section (gray area and the innermost circle) at height2.
Fig. 7. Histograms of tip radii. Bin size for all curves: 4 nm. All data are from the same tip scanned at the relative set point of 0.5 (initial free amplitude approximately 44 nm). Curves 1–3: first frame, third frame and sixth frame. The legend shows ETD calculated for each set of data.
which best preserves the tip. The advantage of tapping at low relative set point is the potential for faster amplitude growth. The focus of an AFM control system is error growth around the set point. If the tip hits a higher feature than at the previous scan location, the surface can always stop the tip oscillation and generate error at a rate faster than the cantilever dynamics. On the other hand, when the tip reaches a new scan location that is lower than the previous one, the amplitude growth is determined by the cantilever dynamics. The growth rate is shown in Fig. 10, where the rate was measured by sudden withdrawal of the sample surface during tapping. This figure clearly shows that operating at lower set point results in much quicker error growth, therefore allowing the feedback loop to run at higher bandwidth,
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corresponding to higher P and I gains. The combination of greater bandwidth and higher gains allows a tip to track a surface while scanning faster. The drawback of the low set point operation is that it may turn into contact mode. Given a tapping amplitude of 200 mV pp, as in our case, if the feedback control error is more than 100 mV,
the tip will be on the surface with zero amplitude, scanning in contact mode before the feedback loop can respond to the error. In all our experiments, the scan rate was kept at 0.3 Hz to assure negligible control error. A much higher scan rate is desirable as a practical matter, and we have now learned that the cantilever dynamics is capable of
Fig. 8. ETD at 5 nm (height1) as a function of set point after tips were tested with the same amount of tapping on Ti surfaces. Each relative set point uses a different tip and tip wear proceeds as the number of scanned frames increases. Curves 1–6: ETD calculated from data sampled at the first, second, third, fifth, 10th and 20th frames.
Fig. 10. Amplitude error growth rate measured by sudden withdrawal of the surface when the tip is tapping, at different set points. Measurements were taken with an MESP type cantilever (resonant frequency approximately 87 kHz and Q approximately 270).
Fig. 9. Tapping mode imaging of silver nanocrystals on Si(1 1 1) surface. The free oscillation amplitude is the same for both cases shown. The scanning size is 500 nm 500 nm (a) Relative set point of 0.1, (b) relative set point of 0.5.
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providing much faster response at lower set points, most importantly, without sacrificing the tip in hard tapping. The bottleneck then becomes the feedback loop itself. Fortunately, Minne et al. developed a nested feedback loop [12], which was implemented by Digital Instruments in the Nanoscope IV Controller [13]. The combined system can lower the feedback control error by a factor of 20, greatly reducing the risk of tip degradation while running surface scans at a low set point. As for the wear mechanism, the similarity between the curves in Figs. 2 and 8 suggests that the wear process is dominated by momentum exchange between tip and surface. The residual speed of the tip hitting the surface determines the rate of tip wear. One more aspect worth noting: in practical operation, the tip should be engaged with low tapping amplitude and the cantilever drive increased after the feedback loop achieves set point control. Failing to do this may result in the tip going through the maxima in both Figs. 2 and 9 and tip damage may occur.
6. Conclusion We have proved experimentally the correlation between residual tip speed before impacting a surface and tip wear for the relatively hard samples used in this investigation. It is demonstrated that lower set point is not harmful to tips for those samples under our experimental conditions. On the other hand, the potential amplitude growth rate is greatly increased by running the microscope at lower set points, rendering faster scanning possible.
Acknowledgements The authors are indebted to Michael Serry of Digital Instruments, Veeco Metrology for his initial experimental work. We also appreciate enlightening discussion with Dr. R. Garcia and careful editing work by Alan Rice.
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