NANO LETTERS
Nanoscale Shape-Memory Function in Highly Cross-Linked Polymers
2008 Vol. 8, No. 12 4398-4403
T. Altebaeumer,† B. Gotsmann, H. Pozidis, A. Knoll, and U. Duerig* IBM Research GmbH, Zurich Research Laboratory, 8803 Ru¨schlikon, Switzerland Received July 28, 2008; Revised Manuscript Received October 23, 2008
ABSTRACT Topographic engraving of structures in polymer surfaces attracts widespread interest for application in imprint lithography and data storage. We study the nonlinear interaction of nanoindents written in close proximity, 20-100 nm, to one another in a highly cross-linked polystyrene matrix. The indents are created thermomechanically by applying heat and force stimuli of 10 µs duration to a tip, thereby raising the polymer temperature to 250 °C and exerting contact pressures of up to 1 GPa. We show that on the nanoscale plastic deformation is highly reversible providing outstanding shape-memory functionality of the material.
Polymeric materials can be tailored to exhibit remarkable shape memory functionality.1 The materials are capable of adopting a strained metastable conformation, which can be relaxed to the initial unstrained state by applying an appropriate thermal2,3 or optical4 stimulus. One of the virtues of polymeric materials is their ability to accommodate extremely high strains with values as high as 400% having been reported.5 The shape memory property is facilitated if some degree of cross-linking for stabilizing the polymer network exists. However, polymers will lose the capability of accommodating large strains without fracturing as the amount of cross-linking increases. Here, we show that highly cross-linked polymers still exhibit excellent shape memory properties on the nanoscale, albeit under conditions that differ radically from those used in bulk studies. Specifically, we investigate the shape recovery of indents written with a hot tip. The indents have a depth and diameter varying between 1 and 5 nm and 10 and 20 nm, respectively. Thus, the material is highly nonuniformly strained at the surface. In addition, the material is locally subjected to extreme stresses on the order of up to 1 GPa during the formation of the indents, which would inevitably lead to failure on the macroscopic scale. Finally, the formation of the metastable strained state and the recovery of the unstrained relaxed state happen on a 10 µs time scale, which is more than 6 orders of magnitude faster than in typical bulk shape memory samples. The work presented in this article bears strongly on IBM’s thermomechanical data storage project.6 The principle of operation is based on the massively parallel operation of scanning probes that can be resistively heated. A thin * To whom correspondence should be addressed. E-mail: drg@zurich. ibm.com. † Present address: Sharp Laboratories of Europe LTD, Oxford, U.K. 10.1021/nl8022737 CCC: $40.75 Published on Web 11/04/2008
2008 American Chemical Society
polymer film serves as storage medium, and data is stored as nanoscale imprints created by applying short force pulses to the heated probe tip.6–8 Using single probes, it has been shown9 that data can be recorded at a density of 641 Gb/in2 and read back with raw error rates better than 10-4. Moreover, a feasibility study has demonstrated that densities of 4 Tb/in2 can be achieved.10 It has been also shown that it is possible to revert indents by writing a second indent in close proximity,6 a process that forms the basis for the erasing of thermo-mechanically written data. While the ability to erase data is an important feature for data storage applications, it also demonstrates surprising shape memory properties of polymers in general. The purpose of this paper is to elucidate the erasing mechanism in detail by showing (1) that the recovery of the indent obeys a simple scaling law, (2) that the original surface can be recovered with subnanometer accuracy, and (3) that it is possible to erase the same area more than 10 000 times without manifest degradation of the polymer film. Thereby we show that highly crosslinked polymers can be plastically deformed on the nanoscale in a reversible fashion without noticeable fatigue over thousands of cycles. The polymer films of this study were prepared by means of spin coating from a random copolymer of 70% styrene and 30% benzo-cyclo-butene with the latter providing crosslinking between the polystyrene chains.11 The films had a thickness of 120 nm and were deposited on a Si substrate. Indents were written by pushing a heated indenter tip in to the polymer surface (see Supporting Information for details). Figure 1a shows the typical shape of a thermomechanically formed indent. It consists of a trough, the actual indent, which is surrounded by a characteristic rim. As a rule, the indents are not perfectly cylindrically symmetric owing to offsets of the indenter axis with respect to the surface normal. Their
accumulated in the polymer are varied. Thus a wide range of the indentation parameter space is probed. The experiment is repeated for different indenter tips having cone apertures of 40, 50, 73, 95, and 115°, respectively, thereby further expanding the parameter space by the indenter geometry. Figure 1b illustrates the experimental procedure. For a given set of parameters, a 5 × 16 array of indent pairs is written, whereby indents in a column are written with the same pitch, p, whereas the pitch is decreased from the right to the left along the rows. The nominal shape parameters of the undistorted indents are determined from indents that are located far apart, that is, from those in columns 14-16 counting from left to right in Figure 1b, such that any interference can be excluded. Also shown in Figure 1b are the cross-section profiles of the nine left-most indent pairs, which are written with a pitch varying from 18 to 98 nm. The indent profiles are averages over the corresponding five indent pairs of one column in order to reduce medium-related and electronic noise. The dashed red line indicates the position at which the first indent is written. The dashed blue lines indicate the positions of the second indent. In addition, the plastic radius, c ) 48 ( 3 nm, and the indent radius, a ) 20 ( 2 nm, are indicated by green and blue arrows, respectively, to help the visualization of the characteristic regimes to be discussed below. Figure 1. (a) Indent profile, left panel, measured along the dashed white line of the topographic image, right panel. (b) Top panel: 5 × 16 array of indent pairs written with a pitch increasing in steps of 10 nm from left to right from 18 to 168 nm (cone aperture of indenter ) 73°, indentation force ) 190 nN, heater temperature ) 395 °C, depth of undistorted indents ) 10 ( 0.5 nm). Bottom panel: line profiles averaged over five indent pairs in one column. Dashed red line: nominal position of the indent written first. Dashed blue lines: nominal position of the subsequently written indent. Dashed green line: position of the satellite trough. Green and blue arrows indicate the plastic radius c and the indent radius a, respectively. Partial erasing, β ) d1/d, is defined as the ratio of the depth of the profile at the nominal position of the first indent divided by the depth of an isolated indent.
geometry is described by four parameters: the indent depth d, the rim height h, the indent radius a, and the plastic radius c defined as the outer radius of the rim. The last three parameters represent the arithmetic mean of the respective values averaged over the distorted indent profile. It has been shown that a linear scaling law treating d and c as separable variables applies, where the lateral dimensions scale with respect to c and the vertical dimensions with respect to d.12 It is speculated that erasing is also governed by a simple scaling law based on the renormalization of the distance between adjacent indents. The proposition is put to an experimental test by writing pairs of indents using identical writing conditions but varying the distance between them. The indent pairs are subsequently imaged and their shapes are analyzed. The experiment is iterated for different values of the writing force and heater temperature. By adjusting the force/temperature combination, the depth and size of the indents as well as the stress that is Nano Lett., Vol. 8, No. 12, 2008
Depending on the pitch p, we can distinguish three regions: (1) with p > 1.5c, (2) with a < p e a + c, and (3) with p e a. In region (1), comprising the four topmost line traces down to a pitch of 68 nm, the depth and the trough profile of the first indent written are not affected by the presence of the second indent. The only interference that is seen is the merging of the rims into one single hump between the two troughs. Region (2), which starts at a pitch of 58 nm, corresponds to the situation when the rim of the second indent penetrates into the trough of the first indent. Now, the depth of the first indent written starts to “fade” and its apparent position is shifted to the left. At a pitch of 38 nm, the residual depth of the first indent measured at its original position (dashed red line in Figure 1b), amounts to only 20% of its initial value. Yet, a pronounced minimum to the left of the nominal indent position, indicated by the dashed green line, still persists. This “satellite” trough results from the inhomogeneous erase activity, which is highest in the overlap region indicated by the green arrow, and low outside. In fact, up to this point, the line profile to the left of the green line has not changed markedly. At a pitch of 28 nm, the plastic radius penetrates almost completely through the trough profile of the first indent. As a result of the associated high erase activity, the satellite trough is substantially reduced. Finally, at a pitch of 18 nm, regime (3) sets in. The satellite trough has vanished and the line profile to the left of the green line is almost flat. Interestingly, the original indent seems to reappear. This feature is caused by the onset of the overlap of the second indent with the trough profile, which causes a reversal of the relaxation direction. This interference with the trough of the second indent also limits the erase efficiency. In fact, the depth of the profile at the nominal 4399
Figure 2. Partial erasing β as a function of indent pitch p renormalized by the plastic radius c measured for five different tips with a cone aperture R varying from 40 to 115°. Data points obtained for four different writing conditions, marked as circles, squares, diamonds, and triangles, are superimposed in each panel. Heater temperature and force used for writing the indents and the depth d of the corresponding undistorted indents are indicated in the table at the top. Solid lines: fit to the data using the function β(x) defined by eq 1. The fit parameters are indicated in each panel.
position of the first indent is lowest for p ) 28 nm and then increases again for smaller pitch values. The characteristics described above are generically observed irrespective of the indent depth, writing conditions, and cone aperture of the tip. Specifically, if the indents are spaced at a distance that is closer than ∼1.5 times the plastic radius, the depth of the first indent written will be reduced, whereas the indent written next in essence retains the same shape as that of the reference indent. Henceforth we will use the term partial erasing to describe this nonlinear interference between indent pairs.13 To put the observations on a quantitative basis, we define a partial erase parameter β ) d1/d as the ratio of the depth of the profile at the nominal position of the first indent, d1, that is, the distance between the baseline and the interception of the dashed red line with the profile, see Figure 1(b), to the depth of an isolated indent, d. The five panels in Figure 2 show plots of β versus the indent pitch normalized by the plastic radius c using data measured for the five different tips. Irrespective of the depth of the indents and the writing conditions, viz. hot tip and low force or cold tip and high force, the data points fall on top of one another. We thus confirm our conjecture that partial erasing follows a universal law by renormalizing (1) the residual depth of the indent by the nominal depth of the unperturbed indent and (2) the indent pitch by the plastic radius. We fit the data (black solid lines in Figure 2) using a heuristic expression for an S-shaped partial-erase function 1 β(x) ) (1 + tanh(2sx0 log(x ⁄ x0))) 2
(1)
where x ) p/c. The function is defined by two parameters: The stretch factor x0 is given by β(x0) ) 1/2, and s denotes the slope of the β-function at x ) x0. The function provides a good fit to the data except for small values of x, which are typically less than 0.5. Here, the data points are systemati4400
cally higher than predicted because of the interference with the trough of the second indent, which limits the degree of erasing that can be achieved (see above). Besides the fact that partial erasing is independent of the bit depth, that is, deep bits erase just as well as shallow bits do, we also find no systematic dependence of the fit parameters on the cone aperture of the tip, see Figure 2. The respective values determined from the data are x0 ) 0.81 ( 0.06 and s ) 1.48 ( 0.16. This remarkable universality renders partial erasing a robust process requiring no delicate parameter fine-tuning to work, which is of paramount importance for practical applications as will be shown below. Partial erasing limits the minimum pitch with which indents can be written into a polymer and thus is one of the major factors determining the indent density. The maximum remnant indent depth is achieved for a partial-erase ratio of 0.8-0.6, depending on the size of the plastic radius for small indents (see Supporting Information for details). If one attempts to write deeper indents, partial erasing crushes the net depth gain, whereas less partial erasing can only be realized with shallower indents. The universal nature of the partial-erase function allows one to make accurate predictions of the storage density that can be achieved. The predictions were recently experimentally confirmed in a high-densityrecording study.10 The upside of partial erasing is the fact that its effect can be cumulated to achieve complete erasing of written indents. In Figure 1b, one sees that by writing the second indent at an erase pitch, pe, on the order of the indent radius a (bottommost curve), an almost perfectly flat topography is recovered in the region where the first indent overlaps with the rim of the second indent. The second indent is erased by writing a third indent displaced by the same pitch of pe with respect to the second one. The process is repeated in a linewise fashion, and as a result the indents in a line are erased with the exception of just one indent, namely, the one written last at the end of the line. Erasing is further assisted by the aggregate action of shape recovery mediated across closely spaced lines written with a line pitch pe. In practice, erasing is performed using an indent and line pitch of pe ) 1/2 to 1/3 of the indent pitch used for writing the data. The effectiveness of erasing is demonstrated in Figure 3. The sample was prepared using a replica technique (see Supporting Information and ref 14) in order to achieve an extremely low surface roughness of less than 30 pmrms measured over a wavelength range from 5 to 100 nm (see Supporting Information). The topographic image of the sample prepared in this way is shown in Figure 3, top panel. In the next step, a data pattern is written using a minimum indent and line pitch of 36 nm (center panel). The pattern consists of a preamble of 20 indents written at the minimum pitch followed by a pattern generated by random data. The indents have a depth of 1 + 0.5/-0.2 nm. The inset in Figure 3 is a close-up view demonstrating the quality of the indents. In the last step, the data is erased by writing lines of indents at an indent and line pitch of 12 nm, viz. 1/3 of the pitch used for writing the data. As can be seen from Figure 3, bottom panel, the pattern of indents representing the data has been completely erased. Furthermore, the overall surface Nano Lett., Vol. 8, No. 12, 2008
Figure 3. Top panel: topographic image of the virgin polystyrene sample prepared by means of a replica technique which yields a surface with a roughness of 30 pmrms measured over a wavelength range from 5 to 100 nm. Center panel: indent pattern representing a preamble of 20 consecutive 1’s followed by random data. The indents were written using a force of 375 nN and a heater temperature of 350 °C The line pitch and the minimum indent pitch are 36 nm; the depth of the indents is 1 nm. Bottom panel: erased surface obtained by writing lines of all 1’s with a line and indent pitch of 12 nm.
topography has not changed. Only slight residuals of the line traces can be discerned. In addition, one clearly recognizes a bright and a dark stripe at the beginning (left-hand side) and at the end of the erase field (right-hand side), respectively. The bright stripe is due to the remnants of the rim of the first indent written in each line, and the dark stripe corresponds to the trough of the last indent written. A spectral analysis (Supporting Information) reveals that residual roughness after erasing amounts to 100 pmrms measured over a wavelength range from 5 to 100 nm. In other words, the residual short wavelength corrugation of the erased surface is on the order of atomic dimensions, and it is significantly lower than the thermal equilibrium corrugation expected for a free polymer surface. Furthermore long-wavelength corrugations have perfectly recovered to their initial state after erasing. Both observations evince the extraordinary perfection with which the indents can be erased, and they demonstrate the stability of the polymer network, which is able to revert to the initial configuration state with subnanometer precision. While the above experiment demonstrates high-precision erasing, data-storage applications are less demanding in this respect. Here the feature of prime importance is that erasing and rewriting can be performed many thousands of times, and that the new data written after each erasing step can be read with a sufficiently low error rate, typically on the order of 10-4.9 A standard spin coated polymer sample with an intrinsic surface roughness of 0.3 nmrms (see Supporting Information) is used for the demonstration. The indent pattern written on the virgin area of the polymer comprises 2700 data symbols. The minimum indent pitch and the line pitch are both equal to 41 nm, yielding a 4.5 µm long and 0.5 µm wide written field (12 lines with 225 symbols each). The typical depth of an indent is 4 nm. The data pattern is then Nano Lett., Vol. 8, No. 12, 2008
Figure 4. Top panel: topographic image of indents representing data consisting of a preamble and random data written on a virgin polystyrene sample prepared by means of spin-coating. The indents which have a depth of 4 nm were written using a force of 100 nN and a heater temperature of 400 °C. Line and indent pitch are 41 nm. The data pattern is subsequently erased by writing lines of all 1’s with a line and indent pitch of 20.5 nm using the same parameters as for writing the data pattern. Then the original data pattern is rewritten and read back. The full cycle, erase/write/read, takes about one minute for completion. Center panel: topographic image of the erased surface after 2000 erase/write/read cycles. Bottom panel: topographic image of the indent pattern after 15 000 erase/write/read cycles.
read back using the same probe as for writing, and the error rate is measured. The top panel in Figure 4 shows the first 3 µm of the written field. Subsequently, the data pattern is erased by writing lines of indents (corresponding to all 1’s) at an indent and line pitch of 20.5 nm, that is, half of the writing pitch. Then the original data pattern is rewritten on the erased surface. Because of thermal drift, the position of written data blocks differs slightly between successive write cycles. By periodically recalibrating the position, the overall drift is kept below 50 nm throughout the experiment. This ensures that approximately the same polymer area is reused. The topography of an erased field after 2000 write/read/erase cycles is shown in the center panel in Figure 4. One can barely discern the periodic structure of the preamble in the erased field. The quality of erasing is also reflected in the PSD which is practically indistinguishable from the PSD of the virgin sample (see Supporting Information). The bottom panel in Figure 4 shows again the first 3 µm of the written field after 15 000 erase/write/read cycles, which corresponds to 10 days of continuous operation of the experiment and a total of 108 written indents. Visually one cannot discern any deterioration of the quality of the indent pattern. As a stringent quantitative test, the raw bit detection error rate is measured. Because the size of the pattern is small, error-rate statistics are aggregated every 1000 write/read/ erase cycles, corresponding to 2.7 million symbols. The evolution of the error rate in blocks of 1000 erase cycles is shown in Figure 5. The raw error rate stays below the 10-4 level at all times as is required for error-free data retrieval using standard error-correction schemes.9 Furthermore, the total error rate, calculated over the entire 15 000 erase cycles, amounts to 3.7 × 10-5, another proof of the quality of the thermomechanical erasing scheme. From a fundamental point 4401
Figure 5. Bit-error-rate statistics aggregated over blocks of 1000 erase/write/read cycles. Note that the error rate is always below the 10-4 level. No errors were detected in the aggregated data sets for 2000, 3000, and 4000 cycles, and hence the corresponding data points were omitted in the graph.
of view, the experiment also demonstrates that the mechanical integrity of the polymer surface remains unaltered even after many thousand repetitions of harsh indentations involving local strains on the order 25% (indent depth divided by indent diameter), local pressures on the order of Gigapascal (writing force divided by indent area), and polymer temperatures of ∼200 °C (corresponding to a heater temperature of 400 °C,15 see Supporting Information). The remarkable reversibility observed suggests that the indents are formed by a process that bears similarity to rubbery deformation, whereas irreversible processes such as crude breaking of chemical bonds or viscous flow of entire polymer strands contribute only marginallysif at all. It has been argued that the plastic deformation is mediated by the activation of backbone flips of the polymer chains,6,12 henceforth termed R-transitions.16 The R-transitions act as memory elements switching the polymer between a high compliance state if activated and a low compliance state if frozen in. Activation of the R-transitions is effected by thermal energy. Above the glass transition temperature, Tg, the polymer chains are fully flexible and the polymer behaves like a soft elastic material. Below Tg, the R-transition activity is suppressed because the associated energy barrier Ea, also referred to as activation barrier,17,18 is much larger than the thermal energy kT. However, mechanical stress eases the activation of R-transitions by reducing the effective barrier E ) Ea - Ωaσ which is modeled in terms of a linear coupling to the stress σ via a so-called activation volume Ωa.17,18 Therefore, applying sufficiently high stress during indentation expands the motional degrees of freedom of the polymer in a similar way as heating above Tg does and thus enables the formation of an indent also at temperatures substantially below Tg. In this respect, nanoindentation below Tg bears close similarity to creep, albeit at much faster time scales. During the indentation, the hot tip is pushed into the polymer, which in turn is heated locally via thermal conduction, and stress is accumulated, which is highest underneath the tip apex.19 Hence the R-transition activity is drastically enhanced in the hot, highly stressed polymer volume beneath the tip. Most of the deformation strain is accumulated in this highly 4402
compliant volume, termed yielded volume. The strain at the boundary of the yielded volume must be elastically accommodated by the surrounding polymer that is in the low compliance state, giving rise to a secondary “plastic” response which manifests itself, for example, in the form of the rim. At the end of the indentation, the heater is turned off, and the polymer temperature reverts to room temperature virtually instantaneously.20 Furthermore, the indenter load is removed, giving rise to partial elastic recovery to establish force balance at the surface. However, the polymer is now uniformly in the low-compliance state because the R-transition activity is low. Therefore the strain in the yielded volume is mostly preserved, but the volume is under a significant restoring stress due to the secondary response in the surrounding material. Relaxation of the stressed indents can be effected solely by thermal annealing, that is, by elevating the sample temperature. Note that thermal annealing acts globally on the entire hot sample. Experiments show that thermal annealing only reduces the depth of the indents but does not change their width,21 which is a clear sign that diffusive mass transport does not take place in the process. Instead, the indents recover as expected for an elastically deformed material, which is crucial for the local indent by indent erasing scheme to work. During indentation with a hot tip, the polymer temperature at the previously written neighboring indent is raised. The temperature rise is substantially lower than at the tip apex, and the distribution is highly nonuniform. Therefore, the thermal energy is not sufficient to drive the relaxation on the 10 µs scale. As a new element one also has to consider the effect of the mechanical stress. Relaxation sets in as soon as the stress field of the rim of the second indent overlaps with the yield volume, viz. the trough region, of the first indent, where it constructively interferes with the restoring stress. The stress- and temperature-induced accelerations are on the order of exp(Ωa∆σ/ kT) and exp(Ea∆T/kT2), respectively, which translates to approximately 1 order of magnitude for a stress increment of ∆σ ) 2 MPa or a temperature increment of ∆T ) 10 °C, assuming Ωa ∼ 3.5 nm3 22,23 and Ea ∼ 1.8 eV.24 Hence, raising the stress by 20 MPa or the polymer temperature by 100 °C is sufficient to reduce the relaxation time scale from years to the time scale of 10 µs of the experiment. In short, one can visualize the indent as a compressed spring which is locked by a dashpot.12 In order to relax the spring, viz. erase, the dashpot merely needs to be activated by applying suitable force and temperature stimuli. Cross-linking is crucial for achieving a high degree of reversibility and cyclability of local erasing. Wear experiments revealed that the rate at which permanent wear patterns emerge at the surface decreases in proportion to Mc4 if the mean molecular weight between cross-links, Mc, is below a critical threshold of Mc ∼ 2000 Da.25 This suggests that the number of available local equilibrium states of the glassy system is quenched by coupling the polymer chains more tightly together. Thus, the accessible configuration space of the glassy polymer network is constrained, which increases the likelihood that the indentation path is followed in a time Nano Lett., Vol. 8, No. 12, 2008
reversed fashion during relaxation. In fact, we observe that the characteristics of local erasing correlate well with the measured wear rate dependence on Mc. Local erasing was virtually impossible without inducing irreversible wear patterns on the polymer surface in lightly cross-linked samples with Mc > 2000 Da (corresponding to a BCB content of
