University of Groningen Contact mode Casimir and capillary force measurements Zwol, Pieter Jan van IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2011 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Zwol, P. J. V. (2011). Contact mode Casimir and capillary force measurements Groningen: s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 18-06-2017 2 Electrostatic calibration procedure for force measurements with AFM 2.1 AFM force measurements The atomic force microscope or AFM (fig. 2.1 and 2.2) is an instrument capable of imaging specimen surfaces with a horizontal and vertical resolution down to a fraction of a nanometer. The instrument works by measuring the deflection produced by a sharp tip on a micron-sized cantilever as it scans across the surface of the specimen. However, the AFM is not only a tool to image the topography of solid surfaces at high resolution, but it can also be used to measure force-versus-distance curves [1]. It enables measurements in a short time span with a high spatial resolution, and also allows for nontransparent materials to be investigated. Force curves can provide valuable information on local material properties such as elasticity, hardness, adhesion, van-der-Waals and Casimir forces, and surface charge densities. For this reason the measurement of force curves has become essential in different fields of research such as surface science and engineering, and even biology [2-6]. During force measurements with an AFM, the cantilever, having spring constant k, bends under the load of a force and as a consequence of Hooke’s law it obeys F=kx, if the bending x is much smaller than the length of the lever. Nowadays pico-Newton sensitivity is well in reach of commercial AFMs. In this chapter we describe the calibration procedure for our AFM system used for the force measurements. It is worth noting that besides the AFM, there exists an historically important machine called the surface force apparatus (SFA) [2]. The SFA employs only surfaces of known geometry, thus leading to precise surface force measurements. The main difference between the two is the scale of the interacting surfaces or probes, which for the SFA are much larger, giving it higher force sensitivity and lower spatial resolution. To increase the force sensitivity of an AFM one can attach a microsphere to the end of the lever (see also chapter 3). Such a probe is used for the measurements presented here. 2.2 The PicoForce system The Picoforce system from VEECO is a multimode AFM specifically designed for force measurements. It includes a low-noise AFM head that achieves thermally limited pico-Newton scale performance. In addition it can perform any form of force or contact or tapping mode surface morphology analysis. 9 The closed loop Z scanner is separated from the X and Y scanners and has a noise level of <0.5 nm. Furthermore Piezo creep and hysteresis are reduced to 0.1%. The Piezo is positioned under the sample instead of on the cantilever. So the cantilever does not move with respect to the deflection sensor and the laser. Below (fig 2.1) the Picoforce AFM is shown. AFM Angler Figure 2.1: A typical Veeco Picoforce AFM. The angler tool allows ‘feeling’ of contact forces and enables precise manual nano-positioning of the cantilever. 2.3 Stiffer or softer cantilevers? A soft cantilever is more sensitive to weak forces since the force to noise ratio increases with lowering k. Besides that applied coatings (for electrical contact) result in unwanted bending (see §2.5.5), soft levers also jump to contact more easily. Therefore, the maximum force that can be measured with a soft cantilever will naturally be lower. If Casimir force measurements at small separations are to be performed (i.e. strong forces), a stiffer cantilever is needed. Stiff cantilevers will bend less, resulting in a lower force to noise ratio. A proper way to increase the force to noise ratio without changing the measurement range is to use bigger spheres with stiffer cantilevers. For example a 5 times stiffer cantilever with a 5 times larger sphere will result in a √5 increase in the force to noise ratio. Or one can just increase the amount of statistics if time allows this. 2.4 Thermal noise and drift Two important sources of error in force measurements are thermal noise and drift. However the obvious solutions to these two are mutually exclusive. A longer integration time reduces Brownian noise but increases the drift problem and vice versa. In our setup for one force curve, drift is not a serious problem, since it is measured within 1 second. However, drift is observed when one is 10 measuring multiple times to average noise. The point of contact, i.e. when the cantilever hits the surface, (lowest point in the curves shown in figure 2.3) does not remain at the same place but drifts somewhat horizontally, typically a few nm over time. This drift can be easily corrected by shifting the point of contact of all curves to the same place. Vertical drift seen in a graph is probably related to cantilever, laser, mirror, and photodiode, since all these parts may drift somewhat. This drift can be corrected by adding a fitting constant to the equation that is fitted to the data. Note that for old AFMs piezo hysteresis and creep can be a big problem, which is reduced with the advent of the closed loop scanner. It is also advisable to wait a few hours before starting the measurement with a typical AFM in order thermally stabilize the system, because the laser generates heat. 2.5 Electrostatic calibration of the AFM for force measurements In a typical AFM, sensing of cantilever bending due to a force can be performed with an interferometer or the deflection of a laser beam as shown in fig. 2.2. The latter method is used in the Multimode Picoforce AFM. The reflected laser goes into a photodiode which generates a voltage. Thus we still do not know the actual force. Therefore a calibration is needed. For this the electrostatic force is used. We will discuss the calibration procedure for our force measurement setup with a sphere (Duke Scientific 100±1.5 micron Au coated polystyrene) attached on the cantilever (450 µm long, k=0.2 N/m, and Au coated). The setup and calibration parameters are shown in fig. 2.2. For the plates we use Si wafers with Au coatings of thicknesses 100 -1600 nm. The thicker the evaporated gold film (deposited at room temperature and 10-6 mbar), the rougher it becomes. The sphere is first plasma sputtered with gold for good electrical contact, and then an 100 nm Au layer was evaporated resulting in a roughness of 3.5 nm RMS (see also chapter 3). The detailed description of the various calibration parameters depicted in fig. 2.2 is presented in the following. 2.5.1 Deflection sensitivity and deflection correction The deflection sensitivity ‘m’ relates the voltage of the photodiode to cantilever deflection. It can be measured when the cantilever is in contact with the surface as shown in figure 2.3, or by varying the force strength and fitting through the contact points of different curves (the latter method is more susceptible to drift). The piezo will continue to move while the cantilever bends as it is in contact with the surface resulting in a voltage change. The distance correction due to cantilever deflection should be added to the piezo movement in a typical force measurement. Veeco states that the typical 11 uncertainty in m is 3 percent [8]. Note that a variation in ‘m’ from measurement to measurement will result in a variation in the calibrated stiffness of the cantilever, and the force measurement, due to an uncertainty in distance from lever-bending. Figure 2.2: Sphere, cantilever and laser movement are indicated with thick arrows. Calibration parameters are also indicated in italic with question marks. 0 Deflection (nm) −100 −200 −300 −400 −500 −600 −700 1200 1400 1600 1800 2000 Piezo (nm) Figure 2.3: Here from left to right means that the sphere is moved closer to the surface, and at some point contact is made. Once in contact with the surface the piezo still moves and the cantilever will therefore further bend. In this linear regime, between the vertical dashed lines, one can relate the voltage of the diode to the linear piezo movement and obtain the deflection sensitivity. The fit through the contact point of different curves (thick black lines) with different forces (for example due to different applied voltages between sphere and plate) should give the same slope as in the contact (linear) region. (Negative deflection means that the lever bends towards the surface) 12 2.5.2 Cantilever spring constant The cantilever spring constant k can be measured using thermal tuning [7,8]. However, this method is only accurate within 10%, and one requires that the sphere is much smaller than the length of the lever. Using the electrostatic force one can determine k within roughly a few percent, but obviously that does not work for insulating samples. The equation for the electrostatic force Fe between a sphere and a plate is given by [9] F e = 2πε (V1 − V0 ) 2 [∑ csc −1 ( nα )(coth α − n. coth nα )] (2.1) n where α=cosh[1+(d+d0)/R], d the distance between sphere-plate, R the sphere radius, Vo the contact potential, and V1 the applied voltage between sphere and plate. This equation is not particularly easy to fit. Interpolating this equation with polynomials increases fitting speed. Measured electrostatic force curves (applied voltage of a few volts) are fitted at separations above a few microns, where the Casimir force is negligible (fig 2.4). In this case also the uncertainty in distance due to unknown contact point (§2.5.4) will be small. However from the roughness scans we obtain a rough estimate for the separation upon contact. Also there will be no roughness effect on the electrostatic force since the roughness (in the order of ≤10nm RMS) is negligible compared to the distance d. The deflection correction m must be applied to the curves before fitting. Since the electrostatic force scales with separation distance d as Fe~1/d, an error for example of 30 nm in d will result in only 1% error in the cantilever spring constant k. From roughness scans of sphere and plate one can estimate the separation upon contact (d0). If ‘m’ is known then measuring k is rather straightforward. This fitting process was found to be reproducible within a few percent for different voltages and separations. The value can be double checked with that obtained from the tuning method. (having the cantilever much larger than the sphere radius in this case). Electrostatic calibration of the cantilever spring constant is depicted with details in figure 2.4. The data is fitted at large separations by a vector function for +V and –V (in the order of a few Volt). In this manner the k constant and contact potential can be obtained simultaneously. Standard deviations can be obtained by using multiple curves and repeating the procedure. Typical calibration curves for different films show a small variation of the contact potential as will be shown in the next section. In fig. 2.4 inset, at separations d>3000 nm, for the weakest electrostatic forces, drift effects become more visible (larger difference between +V and –V curves). For smaller separations, and larger potentials, the difference becomes smaller (large force compared to drift). When correcting for this ‘drift offset’ by fitting, 13 the obtained contact potentials were constant with separation distance and applied voltage, within 5 mV (standard deviation) in the range 500-7000 nm. Fitting the data in the range 700-1500 or 2000-7000nm did not yield differences in k beyond 1% or V0 beyond 5mV. At the smaller plate-sphere separations the relative uncertainty in distance due to roughness becomes larger. Below 400nm, the cantilever jumps to contact (sharp change in scaling) due to the strong attractive force. 4 mV 1 Deflection (nm) −10 10 mV 2 −10 −−−− +V −−−− −V 2 −10 3 10 1000 2000 3000 4000 5000 6000 7000 Separation (nm) Figure 2.4: Electrostatic calibration of the cantilever spring constant on a semilog scale. Fit in the range 500-8000nm. Horizontal error is shown by grey lines. The data (dotted line) is fitted (solid line) at large separations by a vector function for +V and –V (in the order of a few Volt) since in this way the stiffness and contact potential can be obtained simultaneously, contact potentials are indicated. The inset shows another sample (10mV contact potential) on log-log scale. 2.5.3 Contact potential An electrostatic potential Vo exists between samples of two dissimilar electrically conductive materials (with different electron work functions) that have been brought into thermal equilibrium with each other, usually through a physical contact. Although Vo is normally measured between two surfaces that are not in contact, this potential is called the contact potential difference. A contact potential Vo is probably always present since the Au coatings on sphere and plate can have slightly different work functions (even when both surfaces are grounded). The contact potential Vo may not be small if badly conducting materials are used where contributions due to trapped charges can exist. Even in the case of Au surfaces it may be a few mV (Large potentials between Au surfaces may indicate bad grounding however). Actually, the parameters m, k and V0 can be measured with the same 14 electrostatic force curves. For this purpose we used eight curves with positive and negative voltages. First m is measured and applied to the curves, and then a vector function is fitted to two measurement curves with +V and –V (at a separation d it gives as output the vector [V-V0, -V-V0]). In this way k and Vo can be obtained simultaneously. For different voltages, k and Vo must of course be the same. The latter was confirmed for k within 2 % error and for Vo within 5 mV upon repeating the procedure (see table 2.1). If V0 became large >100mV the procedure was somewhat less accurate upon repeating. However, it was found to be quite robust and flexible for different cantilever spring constants k and contact potentials V0. Note that, if V0 is large enough to produce significant electrostatic force with respect to the Casimir force, then the effect of Vo cannot be subtracted from the Casimir force curves, due to an interfering signal of laser-surface scattered light which also has to be filtered out at larger separations (§2.5.5). Thus the effect of Vo should be removed while performing the force measurement by applying a compensating voltage. V0 calibration for different fit ranges (mV) Electrostatic Scaling Parameter Au Film Thickness (nm) 100 700-1500nm 2000-7000nm 700-2500 700-5000nm 1000-7500 29(2) 24(4) 1.01(0.01) 1.015(0.003) 1.017(0.003) 200 400 11(2) 27(2) 11(4) 26(6) 1.00(0.01) 1.00(0.01) 1.007(0.004) 0.999(0.004) 1.014(0.004) 1.009(0.003) 800 1600 3(2) 0(1) 5(1) -4(2) 0.99(0.01) 0.96(0.01) 0.985(0.004) 0.980(0.005) 0.996(0.004) 0.997(0.006) Table 2.1. The contact potential and the scaling parameter are shown for different fit ranges; see description in the main text. In table 2.1 the contact potential Vo is shown for different fit ranges, and it appears to be stable within 5 mV standard deviation. The electrostatic scaling with distance d has the form Fel~V2/dn with an expected n=1. If we define n as a free parameter in the fitting procedure we obtain n=0.99±0.02. This indicates that there are no large patch potentials or impurities present on either sphere or plates [10]. A small change of the contact potential with distance of a few mV cannot be ruled out. However this effect does not significantly affect the Casimir force measurements presented in this thesis at distances below 200nm. 2.5.4 Distance upon contact due to surface roughness Although we can measure pico-Newton forces, if the distance between sphere and plane is not known we will not reach high measurement accuracy [10]. The plate-sphere separation, which is measured with respect to the point of contact with the surface, is given by 15 d =d piezo +d o - d defl . (2.2) dpiezo is the piezo movement, do is the distance on contact due to substrate and sphere roughness, and ddefl=mFpd is the cantilever deflection correction. Fpd is the photodiode difference signal and m the deflection coefficient. The problem related to the measurement of d is surface roughness as it is manifested via do. Nowadays the smoothest surfaces have in many cases only a few nm top to bottom roughness. But even such a small roughness may lead to large errors in the force measurement. We will discuss this topic in relation to our Casimir force measurements. If one realizes that the Casimir force, taking into account the finite conductivity, scales with one over the distance squared to cubed, F∼dc (c=2-3), then to reach a 1% error in the force measurement one requires a 0.33-0.5% error in determining the distance. This can be understood if we consider the relative error ∆F/F=c(∆d/d). Therefore, by simple calculation one obtains that the separation distance d must be known to within 1 Å for example at d=30 nm. This is a difficult requirement and a technical challenge. The value of d0 can also be found electrostatically (fig. 2.5). Since k m, and V0 are known, we can determine d0 by fitting electrostatic curves, using potentials of a few hundreds of milliVolts and plate-sphere separations of up to a few hundreds of nanometers. Since the roughness of the deposited Au films is random (typical during deposition under conditions far from equilibrium) there is variety in local peaks. Unfortunately the spheres typically used in AFM measurements are also not smooth. Any applied gold coating will result in at least ~10 nm top to bottom. The typical error in d0 is therefore of the order of a nanometer depending on the surface roughness (tables 2.2 and 2.3). When fitting electrostatic force curves to obtain d0 (figs. 2.5-2.7, tables 2.2, 2.3), one must first shift all curves with contact points to zero and then substract the zero voltage or Casimir force curve from the curve with applied potential. Now eq.(2.1) can be fitted to the data with two free parameters; one is an offset to the force in eq.(2.1) and the other is d0. The offset parameter is necessary to correct for any vertical drift in the data. Notably more time is needed for the measurement of 60 electrostatic curves for the determination of d0 (measurement time~2-3 minutes) than for the measurement of the actual Casimir force (where 30 curves were used, measurement time < 1 minute). No drift in the calibrated value of d0 is visible in the time frame in which we perform our measurements (it appears more or less random). 16 Deflection (nm) 0 −5 −10 Casimir force Electrostatic force Fit −15 −20 0 100 200 300 400 500 Separation (nm) Figure 2.5: Determination of d0 by electrostatic calibration. The Casimir force and an eventual (close to) linear signal should be subtracted from the electrostatic curves prior to fitting. By comparison, the measured height profiles of the surfaces match with the point of contact do found from the electrostatic calibration (figs. 2.52.7 and tables 2.2 and 2.3). In practice if the topography distribution is symmetric one can estimate do by adding the top to bottom roughness and divide it by two (Note that this is only a rough estimate, since the roughness is random and the RMS roughness adds up squared). The topography distribution for the thicker films becomes more and more skewed (more high peaks). Then, one should estimate do from the mean and the distribution on the right side (fig. 2.7) of the mean (corresponding to the peaks, while the left side corresponds to the valleys). Vapplied (mV) V0 (mV) 3000 27.45 3500 21.90 4000 28.107 4500 20.32 K (N/m) 0.245301 0.24397 0.24195 0.242837 Applied voltage, and contact points do found from electrostatic fit of 60 curves 250 300 350 400 450 500 16.6004 17.9023 16.6795 15.8400 16.8534 16.8947 18.2507 16.8545 15.9478 17.2073 15.9018 17.0145 17.7187 18.0503 18.8961 17.6095 17.5917 18.5418 18.5290 17.2613 17.6723 17.5362 17.3446 18.3995 16.4955 17.8540 17.8284 17.4679 17.0206 16.8928 16.5543 18.4878 17.4599 17.4061 17.4984 17.3774 16.2645 17.5568 16.7768 17.5256 17.2500 17.0839 17.9401 17.2010 16.1211 17.9758 18.0913 17.1202 17.8019 17.7299 18.5228 18.8480 18.6787 18.3178 18.4538 18.2278 19.0830 17.9972 18.6736 17.7129 Vo=24±4mV, k=0.243±0.0014N/m, do=17.6±0.8nm Table 2.2: Typical values for the spring constant, contact potential and distance calibration. In this case the sphere had ~25-30 nm top to bottom roughness, and the plate ∼8 nm. The calibrated value for the contact distance do is in agreement with the roughness scans. 17 d0 values for different fit ranges d0 + (nm) Au film 100 20-400nm 17.9(0.8) 17.8(0.8) 19.4(1.3) 20.1(0.8) 23.7(0.7) 23.8(0.7) 33.6(1.6) 33.2(1.6) 50.5(1.0) 50.7(0.8) 200 400 800 1600 40-400 17.7(1.1) 18.1(0.9) 20.2(1.2) 20.8(0.9) 23.0(0.9) 23.6(0.7) 34.5(1.7) 33.9(1.5) 50.8(1.3) 50.9(0.9) 60-600 17.3(1.9) 18.3(1.0) 21.0(1.8) 22.0(1.1) 22.9(1.6) 24.4(0.7) 36.1(2.4) 34.9(1.7) 51.7(1.6) 51.5(1.0) 100-1000 16.9(3.7) 18.5(1.2) 24.0(3.2) 25.4(1.8) 25.6(3.4) 28.0(1.5) 38.3(3.0) 38.7(2.5) 53.5(3.2) 52.5(1.8) Table 2.3: Obtained values (with standard deviation) for the contact distance do when fitting electrostatic force curves in different ranges. Two values are shown in each cell. The first is performed with all 60 curves, and the second with 40 curves for higher applied potentials to improve force sensitivity. 16 12 100nm film Number of events 1600nm film 800nm film 14 12 10 12 10 8 10 8 6 8 6 6 4 4 4 2 2 0 14 16 18 20 22 0 30 2 32 34 36 0 50 52 54 Electrostatically callibrated distance upon contact d0 (nm) Figure 2.6: Values found for d0 for different rough films (shown in figure 2.8). The normal distribution calculated from the standard deviation and the mean found is also shown. Errors in the determination of the contact point do range between 0.8 and 1.6nm. Figure 2.7: AFM topography scans and height distribution of the Au coated sphere, and the Au coated Si plates. The measured height profiles match with the point of contact found from the electrostatic calibration (figs. 2.6, 2.7 and tables 2.1 and 2.2). 2.5.5 The non-linear signal A non-linear signal is present when performing force measurements with an AFM due to additional backscattering of laser light from the approaching surface into the photodiode. The non-linearity is not large but it cannot be 18 neglected at large separation range. If the measurement range is only a few hundreds of nm, then this signal is approximately linear. At first glance one might think that it completely spoils the force measurement. However, besides that it is relatively small, in case of fitting any electrostatic curve for calibration purposes it can be simply filtered out (by fitting with zero voltage and subtracting the fitted result from the electrostatic curve, see fig. 2.8) together with the Casimir force. When the Casimir force is measured, one can approximate the signal by fitting a linear function at larger separations, where the Casimir force is small or negligible. This is valid since the non-linearity is only visible in the range of a few microns and above. It is thus approximately linear at small ranges up to several hundreds of nanometers (see fig 2.5). 2 Data Fit Deflection (nm) 0 −2 −4 −6 −8 −6000 −4000 −2000 0 2000 Z−Piezo (nm) Figure 2.8: Non linear signal during force measurements with an AFM due to additional backscattering of light from the approaching surface into the photo diode. There are several factors causing the non-linear signal. For uncoated levers this signal was not observable. However, when a coating was applied we did see this effect of non-linearity (depending on the cantilever stiffness and coating thickness). A cantilever usually makes an angle of a few degrees with the substrate. But due to induced bending (from stress in the coating, i.e. due to elevated deposition temperatures and different material expansion coefficients) this may not be the case anymore. As a result any reflective surface, which may now be more parallel to the cantilever, may scatter light into the diode as well. A solution to this problem is to use cantilevers with high width (100 um) or large k constant (depending on the aimed force resolution) or one can use thinner coatings. Therefore, stiffer cantilevers, thinner coatings, and lower temperatures when evaporating or sputtering, may reduce this signal. Coatings on both sides of the cantilever can also help. 19 2.6 Conclusion We have outlined in detail the electrostatic calibration procedure for a cantilever with a metal coated sphere and a metal plate. Several cross checks for the calibration method were made, yielding consistent results. This electrostatic calibration procedure is used throughout chapters 5-7. References [1] R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy, Cambridge Universtiy Press, Cambridge (1994) [2] J. Israelachvili, Intermolecular and Surface Forces (Academic, New York, 1992), Vol. 2, p. 330. [3] A. Ata, Y.I. Rabinovich, R. K. Singh, J. Adhesion Sci. Technol. 16, 337 (2002) [4] H.J. Butt, B. Capella, M. Kappl, Surf. Sci. Rep. 59 (2005) [5] B. W. Harris, F. Chen, U. Mohideen, Phys. Rev. A. 62, 052109 (2000) [6] M. Bordag, U. Mohideen, V. M. Mostepanenko, Phys. Rep. 353 (2001) [7] J. L. Hutter, J. Bechhoefer, Rev. Sci. Instrum. 64 1868 (1993) [8] Practical Advice on the Determinaton of Cantilever Spring Constants (AN94) http://www.veeco.com/library/appnotes.php?page=application&id=15; For rough surfaces this contact method may not work. In this case due to friction the sphere cannot move laterally on the surface. Then the deflection sensitivity may not be correct. We calibrated the deflection sensitivity only once for the smoothest surface. From the contact points, and the linear contact regime the values we found appear similar (Fig. 3.3 left). Any systematic error in the deflection sensitivity would be the same for all our measurements on different rough films. The difference in slope from the 2 methods in figure 3 is 4%. [9] W. R. Smythe, “Electrostatics and Electrodynamics” (McGraw-Hill, New York 1950) [10] W. Kim, M. Brown-Hayes, D. Dalvit, J. Brownell, R. Onofrio, Phys. Rev. A 78, 020101(R) (2008) 20
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