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Molecular Scale Modeling of Polymer Imprint Nanolithography Michael Chandross* and Gary S. Grest Sandia National Laboratories, Albuquerque, New Mexico 87185, United States ABSTRACT: We present the results of large-scale molecular dynamics simulations of two different nanolithographic processes, step-flash imprint lithography (SFIL), and hot embossing. We insert rigid stamps into an entangled beadspring polymer melt above the glass transition temperature. After equilibration, the polymer is then hardened in one of two ways, depending on the specific process to be modeled. For SFIL, we cross-link the polymer chains by introducing bonds between neighboring beads. To model hot embossing, we instead cool the melt to below the glass transition temperature. We then study the ability of these methods to retain features by removing the stamps, both with a zero-stress removal process in which stamp atoms are instantaneously deleted from the system as well as a more physical process in which the stamp is pulled from the hardened polymer at fixed velocity. We find that it is necessary to coat the stamp with an antifriction coating to achieve clean removal of the stamp. We further find that a high density of cross-links is necessary for good feature retention in the SFIL process. The hot embossing process results in good feature retention at all length scales studied as long as coated, low surface energy stamps are used.
I. INTRODUCTION Nanomanufacturing has the potential to impact nearly every sector of traditional manufacturing, especially in the areas of technology where increasingly high demands for bit density and data transfer stress the applicability of current generation materials. In order for a nanomanufacturing process to truly be practical, it must have high throughput, which implies that it can work with large areas or volumes. One of the major barriers to success in accessing large areas or volumes with nanomanufacturing techniques is the predictions of defects over large areas, particularly with respect to the understanding of long-range order in systems. This aspect is crucial for commercialization of devices, as labscale processing is often shown to be viable on small scales, but the connection to machine scale is difficult. Several alternative approaches toward nanostructure fabrication have been developed recently. These techniques include microcontact printing or soft lithography,17 nanoimprint lithography,810 and dip-pen lithography.11 A good overview of several of these various techniques can be found in ref 12. Here we are interested in modeling nanoimprint lithography in which hardening of the polymer is achieved by either cooling a thermoplastic polymer melt below Tg or cross-linking the polymer using UV light. The former is often referred to as hot embossing while the latter is known as step-flash imprint lithography (SFIL).13,14 Nanoimprint lithography can achieve feature sizes in the sub50 nm range in polymer films that are generally much thicker than the desired imprint height. SFIL and hot embossing are both multistep processes in which a liquid-based polymer solution is dispensed onto a substrate, the solid mold/template pressed into the liquid and filled, the polymer cured, and the template removed. The main difference between the two is in the curing process. For hot embossing, a thermoplastic polymer such as poly(methyl methacrylate) which has a glass transition temperature Tg above room temperature is first r 2011 American Chemical Society
heated above Tg prior to the mold being pressed into the polymer. The temperature is then reduced below Tg. For SFIL, the polymer is a UV-curable resin, and the mold chosen so that it is transparent to ultraviolet light. One advantage of the SFIL process is that it can be carried out at room temperature. While the SFIL process is quite cost-effective (109 dots of liquid can currently be dispensed for less than $1.00), the two barriers to commercialization beyond a few niche applications are elusive long-range order without defects, as discussed above, and the rate-limiting steps of spreading the UV-curable resin and the curing process, which can take between 3 and 40 s per imprint/ release process depending on the template type.15 While a number of corporations have commercial machines that perform these types of nanolithographic processes, there has been little in the way of modeling. One exception is the recent work of Carrillo and Dobrynin,16 who modeled nanoimprinting of hemispherical particles. They found the quality of the replication process is an optimization of the surface energy of the moldliquid interface and the elastic energy of the polymeric mold, echoing results found in previously by Yu-Su et al.17 from both experiments and explicit calculations. A related study is that of Van Workum and de Pablo, in which the mechanical properties of amorphous polymer nanostructures, as might be formed after nanoimprint lithography, were investigated by numerical simulations.18 In this paper we will discuss the results of largescale molecular dynamics (MD) simulations aimed at understanding the imprint and release steps, with particular emphasis on feature retention. First we investigate the nanoscale details of the SFIL process with fully 3D models that can access a much wider phase space than experimental studies. Our work centers Received: September 19, 2011 Revised: November 3, 2011 Published: November 08, 2011 1049
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on rigid stamps impressed into a melt of entangled polymer chains which is then cured (cross-linked) in order to study the basic dynamics and to understand the complicated release process. In the next section, we provide a brief description of the model used for the polymer matrix and the stamp, together with a description of the simulation methodology. In section III, we present our results for the stamp insertion process. In section IV we present simulations for the SFIL process, while in section IV we present results for hot embossing. In section V, we summarize our results.
II. SIMULATION DETAILS We use a beadspring model to simulate the polymer melt.19 The polymers are treated as freely jointed beadspring chains of N monomers, or beads, of diameter σ and mass m which interact through the standard Lennard-Jones 612 potential cutoff at rc = 2.5σ UðrÞ ¼ 4ε11 ððσ=rÞ12 ðσ=rÞ6 Þ
Figure 1. Contact angle between polymer and rigid stamp for T = 0.7ε/kB as a function of polymerstamp interaction ε12.
ð1Þ
Here ε = ε11 is the interaction strength between polymer monomers. Beads in a chain are connected by an additional finite extensible nonlinear elastic (FENE) potential20 with a spring constant k = 30ε/σ2 and maximum extent R0 = 1.5σ. The polymer films were constructed following the methodology of Auhl et al.21 The polymer films were initially equilibrated between two repulsive featureless walls in which the interaction between a polymer monomer and the wall is modeled as Uwall ðzÞ ¼ εw ð2=15ðσ=zÞ9 ðσ=zÞ3 Þ
ð2Þ
where z is the distance of a polymer monomer normal to the wall. Periodic boundary conditions were applied in the x- and y-directions with Lx = 180σ and Ly = 40σ. The top wall was then removed and the polymer was allowed to equilibrate prior to the introduction of the stamp. The interaction of the polymer with the lower wall was increased to εw = 4.0ε, and the range of the interaction extended to zc = 2.5σ to avoid debonding of the polymer from the substrate when the stamp was removed. For weaker εw failure occurred at the substrate which is not of interest here. The equations of motion were integrated using a velocityVerlet algorithm with a time step δt = 0.01τ, where τ = σ(m/ε)1/2. The temperature was held constant at the desired temperature by a Langevin thermostat20 with damping constant Γ = 0.5τ1. For SFIL, random-cross-linking22 is carried out by instantaneously adding FENE bonds between randomly chosen pairs of beads separated by less than the reaction distance of 1.3σ. For hot embossing, after imprinting the polymer we lowered the temperature below the glass transition, which for a polymer melt of long chains for this model is Tg ∼ 0.5 ε/kB, where kB is the Boltzmann constant.23 The stamp was made of a rigid fcc block of atoms of the same diameter σ. The polymer monomers and atoms in the stamp also interacted with a Lennard-Jones interaction, eq 1, with an interaction strength ε12. The polymer chain length of N = 500 is above the entanglement length Ne = 85 ( 7.24 The number of chains for all simulations was 1200 while the number of atoms in the stamp varied from 298 925 to 379 250 depending on the number of stamps. In all cases, the stamps were continuous across the periodic boundary conditions in the y-direction, i.e., perpendicular to both the features and the insertion/removal directions. This results in stamps that are effectively infinitely
Figure 2. Snapshot of simulation after insertion of stamp (yellow) into polymer (blue). The system has been equilibrated at T = 0.7ε/kB in (a) and then cooled to T = 0.3ε/kB in (b). The interaction strength between the stamp and polymer monomers is ε12 = 0.5ε.
long in one dimension and reduces the size of the phase space from fully three-dimensional stamps. As the interaction strength ε12 between the polymer and the stamp is typically known only indirectly through the contact angle between a polymer and the stamp, we carried out a series of simulations in which a solid stamp is inserted into bulk polymer solution and equilibrated at fixed temperature. Results for the contact angle as a function of polymerstamp interaction for T = 0.7ε/kB are shown in Figure 1. In the simulations presented here we set ε12 = 0.3ε or 0.6ε, to model systems in which the stamp walls are either weakly interacting (coated) or strongly interacting (uncoated). While cross-linking the polymer for SFIL has little effect on the contact angle, the change in temperature 1050
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Figure 3. Density of the polymer melt as a function of temperature. Initial and final simulation temperatures are labeled on the plot.
for hot embossing has a strong effect on the contact angle as shown in Figure 2. Here we show a snapshot for the single stamp after cooling from T = 0.7ε/kB to T = 0.3ε/kB or about 0.6Tg. The contact angle, which was initially ∼90°, is now much lower, and the polymer partially wets the stamp. This is likely a real effect that occurs in the manufacturing process and should be considered when making a choice of monomer solutions.
III. STAMP INSERTION The stamp is inserted into the polymer melt at T = 0.7ε/kB or 1.4Tg, at a fixed velocity vz = 0.005σ/τ, until the mold is completely filled. In order to determine when the mold is completely filled, it is necessary to monitor the density of the polymer film deep below the stamp during the insertion process. It is also important to know at what density the process should be stopped. For SFIL we stopped the compression when there was a slight over pressure and the density of the polymer F = 1.0σ3. However, we also performed simulations in which the molds were compressed to densities as high as F = 1.3σ3 and found little effect on the final structures. For the hot emboss process, it is important to consider that the polymer density increases upon cooling. Figure 3 shows the density of a bulk polymer melt from a separate simulation of 500 chains of length 500 in a periodic simulation cell as a function of temperature with the initial (Ti) and final (Tf) temperature of the hot embossing studies indicated. The system is cooled in an NPT ensemble at rate of 104ε/kB/τ. Therefore, for this case we use the density of the polymer at T = 0.3ε/kB, F = 1.064σ3, as the target density, so that upon cooling the polymer does not pull away from the stamp. Note that the SFIL simulations are all performed at Ti; only the hot emboss simulations are cooled to Tf. We chose systems with 3, 4, or 5 total stamps in the simulation box, although, as discussed above, periodic boundary conditions effectively make these all infinitely long stamps. Snapshots during a simulation showing insertion of a system with three stamps are shown during filling (Figure 4a) and when the mold is filled (Figure 4c). The peaks in the polymer melt between the posts in Figure 4a are likely due to the high insertion speed in our simulations and relax to the appropriate contact angle after equilibration as shown in Figure 4b. These snapshots are representative of the setup of a typical simulation. The size of the stamp posts themselves are not varied, so that by using more stamps the pitch of the remaining features (i.e., after stamp removal) will be changed. Using σ ∼ 1 nm for the bead size,20 the stamps are ∼18 nm across, leading to resulting feature sizes of 42, 27, and 18 nm for the 3, 4, and 5 stamp systems, respectively. The height of the stamp posts is set to be approximately half the height of the polymer melt. This allows us to insert the stamp
Figure 4. Snapshots of simulations with three stamps (a) during insertion (b) after 30 000τ of equilibration and (c) after full insertion. Polymer atoms are colored turquoise, and stamp atoms are yellow.
fully while still monitoring the pressure and density of the polymer melt far from the tops of the posts. To calculate the density, we use a region of the polymer that is 40σ high over the full cross-sectional area of the simulation cell. The density in this region during insertion is shown in Figure 5 for the three systems. As the posts insert into the melt, there is a slight linear increase in density, but the melt is able to accommodate the posts. When the melt reaches the top plate of the stamps, there is an abrupt increase in density as indicated by the knees in the density curves. At this point the density increases slightly sublinearly. We have examined the density in the polymer as a function of the strength of the polymer/stamp interactions and found that there is no effect, as expected. 1051
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Figure 5. Density in polymer melt during insertion of stamps with 3 (), 4 (O), and 5 (0) posts. The stamp/polymer interaction strength is ε12 = 0.3ε.
IV. STEP-FLASH IMPRINT LITHOGRAPHY For the SFIL process, after filling the mold, the polymer is cross-linked and then equilibrated for 4000τ in an NVT ensemble before the process is reversed and the stamp removed from the polymer film. Two methods to remove the stamp were examined. In the first, the stamp is removed instantaneously by deleting all stamp atoms from the simulation cell. This is effectively a zero-stress removal of the stamp, as it does not lead to any frictional or adhesive forces being placed on the hardened polymer, as would occur during a forced pull-out. We have performed such zero-stress stamp removals for systems after cross-linking with 100 000, 200 000, or 300 000 cross-links, corresponding to one cross-link for every 6, 3, or 2 monomers. After the stamp atoms were removed, the remaining polymer was equilibrated for 20 000τ. Snapshots of the resulting systems, which are stable and do not change with time, are shown in Figure 6. With 1 cross-link per 6 monomers (Figure 6a), feature retention is poor, with visible curvature at the tops of the features and weak definition of the remaining channels between them. Increasing the number of cross-links to 1 cross-link per 3 monomers (Figure 6b) results in very good feature retention, with only slight curvature at the sharpest corners. Some improvement is still seen upon increasing to 1 cross-link every 2 mononers in Figure 6c. For a more accurate depiction of the actual SFIL stamp removal process, we removed the stamp from the polymer at a fixed normal velocity and investigated the effects of the adhesive polymer/stamp interactions on the features. For a weak polymer/wall interaction (equal to the polymer/stamp interaction of ε12 = 0.6ε), we find complete detachment of the polymer from the lower flat wall upon “removal” of the stamp. This effect can be mitigated, however, by increasing the strength of the wall polymer interaction. An increase of this interaction by a factor of more than 3 (such that ε1w = 2.0) does not prevent adhesive failure at the wall in our simulations, but we find that an additional factor of 2 (i.e., ε1w = 4.0) is nearly effective. As shown in Figure 7b, upon removal of the stamp there is a small section of polymer that undergoes adhesive failure directly under the second stamp from the left. This, however, is not enough to prevent removal of the stamp from the polymer as is clear from the figure. The features above this area of wall-stamp failure, however, are slightly raised relative to the remaining features, where no failure has occurred. Experimental SFIL systems generally coat the stamps with an antiadhesion coating to lower the adhesion.25 We mimic these
Figure 6. Snapshots of simulations showing equilibrated features after zero-stress stamp removal for systems with (a) 6, (b) 3, and (c) 2 monomers/cross-link.
coatings by reducing the polymer/stamp interactions to ε12 = 0.3ε. Upon such reduction we find that the stamps removes cleanly from the polymer melt with no failures and excellent feature retention. An example of such a system after partial stamp removal is shown in Figure 7a. Changing the polymer/stamp interaction effectively corresponds to a change in the surface energy in the model presented in Yu-Su et al.17 In our case, this 1052
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Figure 7. Snapshots of simulations showing removal of stamp with interaction strength of (a) ε12 = 0.3ε or (b) ε12 = 0.6ε for 1 cross-link for every two monomers.
results in a crossover from a transfer condition at ε12 = 0.6ε to a molding condition at ε12 = 0.3ε.
V. HOT EMBOSSING Hot embossing is a nanomanufacturing technique that shares many steps with SFIL. In the hot embossing method, a rigid stamp is pressed into a polymer melt that is held above the glass transition temperature of the polymer, Tg. The entire system is then cooled below Tg to harden the polymer, and the stamp is then removed. As with the SFIL simulations, we begin with a zero-stress stamp removal in which we delete the stamp atoms from the simulation box and equilibrate the remaining polymer atoms at the lower temperature. In these cases we see excellent feature retention in all cases and have determined that stress from stamp removal is the dominant cause of defects in the hot emboss process. We therefore proceed to simulations in which the rigid stamps are removed from the cooled polymer at fixed velocity. For a weak polymer/wall interaction (ε1w = 0.6ε), attempts to remove the stamp result in adhesive failure at the polymer/wall interface. In this case, the stamp and polymer remain bonded to each other during and after separation from the fixed bottom wall. With an increased interaction (ε1w = 12.0ε), we find that the stamp is removed, but with cohesive failure within the polymer itself.
Figure 8. Snapshots of simulations of three stamps showing failures during removal after cooling to T = 0.3ε/kB ∼ 0.6Tg. Snapshots are at t = (a) 0, (b) 50 000τ, (c) 200 000τ, and (d) 400 000τ. 1053
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Figure 9. Pressure in the polymer during stamp removal for both a coated (+) and an uncoated ()) stamp. The failure can be seen in the uncoated stamp beginning at ∼3 105τ.
The specific mechanism of cohesive failure in the polymer is interesting to study in more detail. In all cases, separation of the stamp occurs at the tops of the posts first, since stresses are concentrated at the sharp corners. As the removal proceeds the polymer separates into alternating regions along the stamp posts, where the polymer either pulls away from the stamp completely or is compressed against the posts. The compressed regions remain in contact with the stamp throughout the removal process, which introduces frictional interactions as the stamp slides along the polymer. We show examples of the defects generated during removal of the three stamp system in Figure 8ad, where these alternating regions in the polymer can be seen. The polymer separates away from the middle post in Figure 8b,c, causing compression against the inner sides of the remaining two posts. Similarly, the polymer separates away from the outer portion of those two posts, leading to a compressed region between them. We again mimic coated stamps by reducing the polymer/ stamp interactions to ε12 = 0.3ε. Upon such reduction we find that the stamps removes cleanly from the polymer melt with no failures and excellent feature retention. This change in interaction results in a crossover from transfer to molding, as discussed in Yu-Su et al.17 In Figure 9, we show the calculated pressure in the polymer during removal for both a coated (ε12 = 0.3ε) and an uncoated (ε12 = 0.6ε) stamp. During the initial phase of the removal process, the pressure increases sharply to a value of approximately 0.1σ3/ε where it reaches a plateau value. The pressure in the system with the coated stamp increases slightly linearly as the stamp slides smoothly out of the glassy polymer. In the uncoated system, however, there is no initial change in the pressure in the polymer until failure begins to occur at approximately 3 105τ, where the pressure jumps sharply to a positive value before increasing linearly with time. The jump in the pressure in the uncoated system is coincident with the failure in the removal process, indicating that the remaining changes in the presure are due to the postfailure re-equilbration process.
VI. DISCUSSION During insertion for both the SFIL and hot embossing processes we find little evidence that defects are introduced, as long as the stamps are completely filled. However, unlike a large scale manufacturing process, it is quite easy for the stamps to be completely filled in our simulations because they are all of exactly equal heights and widths and have no existing gas pressure to cause filling resistance. These are all features that are likely barriers to filling in commerical systems and can be treated in a
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statistical fashion in larger-scale simulations to determine the ultimate effects. The fluid flow of the liquid polymer solution, including the frictional interactions with the stamp walls, could also be a major factor. Here we have focused predominantly on the release step for our simulations. In the SFIL simulations we find that the biggest barrier to defect-free removal is the interaction strength of the polymer with the bottom surface. If this is not large enough, the polymer debonds from the wall, leading to adhesive failure rather than stamp removal. With an increased interaction strength, we find that the stamp is generally pulled free without a major effect on the resulting features. However, this is due in part to the excessive number of crosslinks we found were necessary to maintain feature stability. With fewer cross-links we found that features became rounded rather than retaining sharp corners on the time scale simulated. It is indeed possible that lower numbers of cross-links could lead to failures in the stamp removal process as well. It is important to note that the feature sizes we are investigating, while somewhat variable due to our coarse-grained simulation technique, tend to be on the smaller size scale of experimental features. It is conceivable, then, that lower numbers of cross-links will lead to good feature retention for larger features, as curvature of sharp corners is less pronounced with larger surface areas. We found removal of the stamp from the hot emboss simulations, in which the polymer was cooled below Tg to be much more defect-prone. While the zero-stress removal led to excellent feature retention, the simulations in which the stamp was physically pulled from the polymer led to much more difficulty. With a stronger interaction between the stamp and the polymer (e.g., a contact angle near 90°), we found that, assuming the interaction with the bottom wall is strong enough to prevent adhesive failure, the polymer fails through stamp adhesion. Only by reducing the polymerstamp interaction to mimic a frictionreducing coating were we able to remove the stamp cleanly. The simulations we have presented are in essence twodimensional due to the periodic boundary condition in one direction. In this sense, our simulations are most applicable to systems in which features with high aspect ratios are necessary, such as for creating wiring-like electrical contacts in microprocessors. We note that while the third dimension adds complexity to the phase space of the potential simulations, this is primarily through the introduction of more corners where stresses can concentrate. The effects of these corners can already be seen in the work we have presented above. Other future directions to this work include variations in the feature heights, at both the tops and bottoms of the stamps. Finally, we mention that in both SFIL and hot emboss experiments, rather than pulling with a force that is purely normal to the surface, stamp removal is generally achieved by a peeling process. This has the benefit of introducing a crack tip to avoid some stress propagation through the polymer but likely also introduces additional stress patterns to the removal that we have not considered here. Our work, then, can be considered a first approach to understanding the defects introduced by the removal of the stamp. The peeling process is another interesting area of future work, where both the angle and velocity of the mold removal could be investigated to determine their effects on defect propagation.
’ ACKNOWLEDGMENT We thank P. R. Schunk for helpful discussions and critical reading of the manuscript. This work is supported by the Laboratory 1054
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Langmuir Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.
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