Letter pubs.acs.org/NanoLett
Tuning the Spring Constant of Cantilever-Free Tip Arrays Daniel J. Eichelsdoerfer,†,‡ Keith A. Brown,†,‡ Radha Boya,‡,§ Wooyoung Shim,‡,§,∥ and Chad A. Mirkin*,†,‡,§ †
Department of Chemistry, ‡International Institute for Nanotechnology, and §Department of Materials Science and Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States ABSTRACT: A method to measure and tune the spring constant of tips in a cantilever-free array by adjusting the mechanical properties of the elastomeric layer on which it is based is reported. Using this technique, large-area silicon tip arrays are fabricated with spring constants tuned ranging from 7 to 150 N/m. To illustrate the benefit of utilizing a lower spring constant array, the ability to pattern on a delicate 50 nm silicon nitride substrate is explored.
KEYWORDS: Atomic force microscopy, scanning probe lithography, dip-pen nanolithography, spring constant, polydimethylsiloxane, hard-tip, soft-spring lithography
A
currently no method for customizing the mechanical properties of cantilever-free systems. While the stiffness of AFM cantilevers is determined by geometric parameters such as the cantilever width, length, and thickness,21,22 the pens in a cantilever-free array demand a different approach. In cantilever-free systems, the elastomeric backing layer serves as a spring (Figure 1a), and thus the spring constant could in principle be controlled by varying the mechanical properties of this layer. In order to determine the relationship between the mechanical properties of the substrate and the mechanics of tip motion, the displacement of a single silicon tip resting with a base diameter of 30 μm on a polydimethylsiloxane (PDMS) backing layer was calculated utilizing an axisymmetric finite element simulation in which the PDMS layer was modeled as a Mooney−Rivlin hyperelastic material.23 In a typical simulation, a force F = 100 μN was applied to the tip of the silicon probe, which displaced the tip into the backing layer (Figure 1b). We note that the simulation shows that even for a very high applied force, the deformed area beneath the tip extends only ∼50 μm beyond the edge of the tip, and thus mechanical coupling between tips should be minimal. The displacement d of the tip was measured for a series of applied forces, showing a linear relationship between F and d (Figure 1c). The observation that the F−d curve is linear over the entire range studied is important because a linear force−distance relationship is instrumental for many aspects of AFM. The slope of the F−d curve was used to calculate a spring constant from Hooke’s law, yielding k = 16 N/m for PDMS with a Young’s modulus E = 0.49 MPa (blue line in Figure 1c).
tomic force microscopy (AFM) has been widely adopted in the three decades since its invention1 and is currently used for a wide variety of applications, including the imaging of hard and soft materials,2,3 the measurement of electrical properties,4 and even the deposition of molecules and materials.5−9 The ability to sensitively measure and apply forces in such diverse situations is achieved by tailoring the mechanical properties of the cantilever on which AFM is based. For example, AFM probes with varying spring constants k have played a major role in molecular patterning with dip-pen nanolithography (DPN).6−8,10 Since its original conception, DPN has been used to pattern a wide variety of molecular inks, ranging from small-molecule self-assembled monolayers, a task best accomplished by a low-stiffness cantilever (k < 1 N/m),11−13 to proteins,5,6,14 a task which requires a higher stiffness cantilever (k > 1 N/m).14,15 While the successes of cantilever-based DPN revealed the promise of molecular printing as a nanofabrication technique, the complex processes16 required to fabricate these cantilever-based systems limit their widespread applicability. To address the cost and throughput issues in scanning probe lithography, we developed a cantilever-free architecture10,17−19 in which massively parallel arrays of tips are fabricated on an elastomeric backing layer, thereby dramatically reducing the complexity of array fabrication. This architecture, where the “spring”, conventionally provided by the cantilever, is replaced by a compliant backing layer, has been used to produce single17 and multicomponent20 elastomeric tips, as well as hard silicon tips.18 Of particular interest are the silicon tips utilized in hardtip, soft-spring lithography (HSL), which preserve the high resolution of DPN while drastically lowering the cost and increasing the throughput of tip-based nanofabrication. Despite these advantages over cantilever-based systems, there is © 2013 American Chemical Society
Received: November 19, 2012 Revised: December 20, 2012 Published: January 3, 2013 664
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moduli reported in the literature23,24 reflect the strong dependence of the mechanical properties of PDMS on curing conditions.26 All PDMS in this study was cured overnight in an oven at 80 °C. In order to test the hypothesis that the spring constant of cantilever-free scanning probes can be modulated, we fabricated arrays of silicon tips on PDMS backing layers of varying base/ cross-linker ratio (Figure 1d). Tip arrays were fabricated according to our previous method18 utilizing a 50 μm thick ⟨100⟩ Si wafer (Nova Electronic Materials) with an array of 120 μm edge length square masks, which is a fabrication process that results in pens with an average base diameter of ∼30 μm. In order to characterize the mechanical properties of individual tips in the resultant tip arrays, a tipless cantilever was used in a Bruker Dimension ICON AFM to record F−d curves on individual silicon tips (Figure 2a). In a typical experiment, a tipless cantilever (TL-NCL, Nanosensors) with a nominal spring constant of 30 N/m was calibrated by performing an F− d curve on a hard Si surface to measure the cantilever deflection sensitivity (blue curve, Figure 2a), and then the spring constant was determined by thermal tuning. After calibration, a silicon
Figure 1. Overview and simulations of the tip mechanics. (a) Geometry of the tip arrays used in this study, where the PDMS backing layer acts as a Hookian spring. (b) Finite element simulation showing the strain ε within the PDMS layer as a tip is deflected under a 100 μN force. (c) Example force−distance curves for tips on two different PDMS compositions, one with E = 0.49 MPa (blue), and one with E = 0.98 MPa (red). (d) Large area scanning electron micrograph showing an example silicon tip array fabricated on a PDMS backing. Inset shows a typical tip fabricated with this method. Scale bar in the inset is 5 μm.
Interestingly, when these calculations were repeated using material properties for higher modulus PDMS (E = 0.98 MPa, red line in Figure 1c), the resulting spring constant was 30 N/m. This suggests that one may be able to program the stiffness of the spring in a cantilever-free system simply by varying the modulus of the PDMS. Experimentally, one can vary the mechanical properties of an elastomer such as PDMS by exploiting the relationship between the cross-link density and the elastic modulus.23,24 This can be realized by varying the ratio of cross-linker to base in a commercially available PDMS elastomer (Sylgard 184, Dow Corning). To evaluate the ability of this process to generate films with controlled mechanical properties, we synthesized PDMS elastomer with base/cross-linker ratios of 50:1, 40:1, 30:1, 20:1, and 10:1 and measured the resulting reduced elastic moduli E* with nanoindentation. The indentation experiments were performed using a Hysitron 950 Triboindenter loaded with a Berkovic tip (100 nm radius of curvature). The results of this experiment demonstrate that the reduced modulus can be varied from 0.4 to 6.8 MPa.25 The variation in the values of
Figure 2. Experimental setup and results of spring constant measurements. (a) Schematic of the process used to measure the spring constant of a single silicon tip within an array. (b) Representative F−d curves for PDMS with varying base/cross-linker ratios. The blue line indicates the F−d curve taken on a bare silicon surface. (c) Distribution of spring constants found for 40 different tips on an array with a 30:1 PDMS backing layer. Note that the distribution is Gaussian. (d) Spring constant as a function of reduced modulus E*; the data are well fit by a linear function. 665
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fragile to pattern on using conventional HSL, as the tips would puncture the delicate window. A typical patterning experiment began by fabricating a tip array with a 50:1 base/cross-linker ratio (k = 7 ± 1 N/m) and dip-coating the array with a blockcopolymer based ink, following a previously established procedure.28 The ink for these experiments consisted of 0.5 wt % poly(ethylene oxide)-b-poly(2-vinylpyridine) in a 10 mM aqueous solution of fluorescein isothiocyanate (FITC) for fluorescence imaging. Once coated with ink, the tips were loaded into a customized AFM (Park Systems, XE-150) at 95− 100% relative humidity and pressed into contact with the surface in order to deposit dots of block copolymer. The resulting patterns were imaged by fluorescence microscopy and tapping mode AFM. To allow for visualization of the patterns in the fluorescence microscope, a long dwell time (500 ms) and high humidity (∼100%) were used, thus resulting in feature diameters greater than the pitch (500 nm) of the dot features. Figure 3 shows one such pattern, which was printed such that it
tip was selected at random, the cantilever was positioned over the tip, and three F−d curves were acquired at a scan rate of 1 Hz. This procedure was then repeated for ≥10 tips in each array. To match the calibration conditions, the cantilever was maneuvered such that the tip to be studied was as far down the cantilever as possible. We observed that reapproaching the same tip with varying tip/cantilever alignments did not produce an appreciable change in the measured properties. Figure 2b depicts representative F−d curves for each tip array, showing a clear dependence of the mechanical response of the tip on the backing layer cross-link density. Measurements of the displacement of individual tips in an array can provide an estimate of the spring constant k of the tips and therefore the average k of each array. Considering the mechanical system to be two springs in series (the first being the cantilever and the second being the PDMS substrate), the slope of each F−d curve can be used to the estimate the spring constant of the cantilever-free silicon tip. Considering an array prepared with 30:1 base/cross-linker, the distribution of spring constants measured for 40 tips shows a clear peak and is well fit to a Gaussian (Figure 2c). This shows that the arithmetic mean is an appropriate measure of the average spring constant with the standard deviation representing the spread in the spring constants in that array. Using this technique for measuring the average spring constant of the tips in a cantilever-free tip array, the relationship between the reduced modulus of the PDMS and the spring constant can be explored. Figure 2d shows that the average spring constants of five tip arrays prepared with base/crosslinker densities ranging from 50:1 to 10:1 exhibit a clear dependence on the modulus. Importantly, the spring constant of a given array was tuned between 150 and 7 N/m, demonstrating that this technique can generate tips that span the range from rigid to intermediate stiffness, thus covering most of the relevant range for scanning probe applications. The average spring constant fits very well to k = D (E* − E*0 ) with D = 22.6 ± 0.2 μm and E0* = 81 ± 34 kPa. The value of the slope D is in quantitative agreement with the value attained in simulation (D ≈ 23 μm). Furthermore, a model system of a cylindrical punch pressing on an elastic half-plane is expected to exhibit the same behavior with D equal to the punch diameter.27 We note here that due to the nonelastic behavior of PDMS the fitting parameter D is not a direct measurement of the tip diameter. An important implication of this is that the spring constant of a given pen depends linearly on the base width of the pen, which is in contrast to the cubic dependence of the spring constant of a cantilever on its length and thickness,21 suggesting that tip arrays made in this way can be very consistent and insensitive to variations in fabrication. We attribute the offset E0* to viscoelastic creep in the low cross-link density PDMS. More specifically, there was a ∼6% offset (compared to the total displacement distance) between the contact point in the trace and retrace F−d curves for the 50:1 sample, a ∼5% offset in the 40:1 traces, and no offset in the traces for the other samples. The agreement between these experimental results, simulations, and a simple model highlights the power of this method for tailoring the spring constant of cantilever-free arrays to a desired application. By making arrays with lower k, one can pattern on substrates that are too soft to pattern with conventional HSL. To test this hypothesis, patterns were written on a 50 nm thick Si3N4 transmission electron microscope (TEM) window in a 200 μm thick Si frame. It is important to note that this window is too
Figure 3. Pattern of block copolymer ink mixed with FITC demonstrating the ability to deposit materials on fragile substrates. (a) Fluorescence micrograph showing a pattern that spans the Si frame (left) and the flexible 50 nm thick Si3N4 window (right). (b) AFM (amplitude error channel) of the same pattern as shown in (a). Scale bars in both images are 5 μm.
spanned both the Si frame and the Si3N4 window. The continuity of such a pattern over a substrate with inhomogeneous stiffness demonstrates the ability of these arrays to deposit patterns onto fragile samples. In this work, we have shown that one can tune the stiffness of the backing layer, and therefore the spring constant, in cantilever-free tip arrays. Furthermore, the spring constant can be selected from a broad range encompassing the stiff and intermediate regimes of traditional AFM cantilevers. By using a tip array with a low k, polymers were deposited onto a substrate that is too flexible to pattern on using conventional HSL. Such arrays could be useful for a variety of applications such as highresolution patterning on flexible or inhomogeneous substrates. While PDMS was chosen here for its ubiquity in soft lithography, the widespread development of elastomers that span a greater range in elastic modulus, including butyl rubbers, neoprene and hydrogels, hints at the opportunity of this technique to fabricate tip arrays with sub-1 N/m spring constants. This is a major step forward for cantilever-free scanning probe systems as researchers can now customize the mechanical properties of a tip array for a specific application.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. 666
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Present Address
Spatz, J. P.; Watt, F. M.; Huck, W. T. S. Nat. Mater. 2012, 11 (7), 642−649. (25) Note that the reduced modulus (E*) as measured by nanonindentation relates to the Young’s modulus (E) through the following relation: 1/E* = (1 − νi2)/Ei + (1 − ν2)/E, where the subscript i is for the indenter material (here, diamond) and ν is Poisson’s ratio. (26) Eddington, D. T.; Crone, W. C.; Beebe, D. J. Development of process protocols to fine tune polydimethylsiloxane material properties. Proceedings of the 7th International Conference on Miniaturized Chemical and Biochemical Analysis Systems, Squaw Valley, California, October 5−9, 2003; pp 1089−1092. Available at: http://www.rsc.org/ binaries/loc/2003/Volume2/055-130.pdf. (27) Sneddon, I. N. Int. J. Eng. Sci. 1965, 3 (1), 47−57. (28) Chai, J. A.; Huo, F. W.; Zheng, Z. J.; Giam, L. R.; Shim, W.; Mirkin, C. A. Proc. Natl. Acad. Sci. U.S.A. 2010, 107 (47), 20202− 20206.
∥
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS C.A.M. acknowledges the U.S. Air Force Office of Scientific Research (AFOSR, Awards FA9550-12-1-0280 and FA9550-121-0141), the Defense Advanced Research Projects Agency (DARPA, Award N66001-08-1-2044) and the National Science Foundation (NSF, Award DBI-1152139) for support of this research. D.J.E. acknowledges the Department of Defense and AFOSR for a National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. K.A.B. gratefully acknowledges support from Northwestern University’s International Institute for Nanotechnology. R.B. acknowledges the Indo-US Science & Technology Forum (IUSSTF) for a postdoctoral fellowship.
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