Atomic imprinting in the absence of an intrinsic length scale

Nanostructured and nanopatterned surfaces are an integral component in many nanotechnological applications. Since nanoimprinting offers an avenue to economically produce related products,^1,2 its suitability has been explored related to a wide range of uses, including high-density data storage,³ photonic devices,^4–6 holograms,⁷ bio-nanofluidic chips,⁸ sensing,^9,10 manipulation of cellular response,^11,12 water filtration,¹³ and electrodes in fuel cells.¹⁴ In order to assess the method’s suitability for a specific application, one ought to know the size of the smallest reproducible structural features and the smoothness of the exposed surfaces obtainable with given combinations of materials used for molds and replicas. For certain material combinations, there are intrinsic length scale-related limitations, which have spurred worldwide research efforts into atomic-scale imprinting.^{1,11,13,15,16} While progress has been made in the past, so far, only one idealized case demonstrated sub-angstrom replication fidelity.¹⁷ To establish a universally applicable approach, this paper explores the fundamental limits of nanoimprinting to accurately reproduce a given mold’s surface.

Among the different approaches to nanoimprinting, the use of glassy materials as replica materials is particularly promising since they enjoy outstanding processability through thermoplastic forming (TPF) as they soften when heated above their glass transition temperature T_g.⁷ From a microscopic perspective, it has been suggested that the room temperature plastic flow that occurs in glassy materials due to externally applied pressure originates from the shear movement of flow units, which are typically referred to as “shear transformation zones” (STZs).^18–24 When the mold feature size decreases and is eventually smaller than that of a flow unit, one would assume an increase in flow resistance to occur during molding. This ultimately makes the replication of features much smaller than the typical flow unit size of the material more challenging.²⁵ 

For a deeper insight into the mechanisms governing replication fidelity, let us look at a specific example. Despite a room temperature flow unit volume of 123 nm³ and a chain radius of 0.29 nm,^26,27 polymethyl methacrylate (PMMA), a prototypical glassy polymer, can replicate atomic steps on sapphire through TPF.^15,28 This is possible since at the increased temperatures at which TPF takes place, flow units are much smaller than at room temperature; depending on the temperature at which TPF takes place, they could ideally be as small as individual chains flowing “on their own”—an atomistic picture that is, among other evidence, inspired by the fact that a polymer’s viscosity drops above T_g by orders of magnitude. In addition, even if at the temperature where TPF is being performed, there were still flow units with sizes larger than individual chains, these reduced-size flow units (if compared to room temperature) may also more readily alter their shape when exposed to pressure due to the availability of additional thermal energy, shorter relaxation times, and the extra free volume created through thermal expansion, further reducing flow resistance and improving the material’s adaptability to confinement.

However, even though the combination of all these factors allows PMMA and other polymers to succeed in replicating features at least two orders of magnitude smaller than both their room temperature flow unit size and their chain length,¹⁶ replication using such materials did not produce any more intricate smaller-scale patterns other than mostly straight steps and the surface terraces on the replica exhibited a roughness noticeably larger than on the mold.^15,16 This remaining limitation likely arises from an entanglement of polymer chains that naturally restricts them how efficiently they flow and pack, thereby effectively preventing “truly homogeneous” flow at the atomic scale. Finally, in the case of PMMA replicating a sapphire surface, overall fidelity was lacking as imprinted step heights were smaller than on the sapphire due to what was assumed to be thermal shrinkage and viscoelastic relaxation.²⁸ 

When looking for a material class likely to overcome such limitations, bulk metallic glasses (BMGs) appear well positioned as room temperature volumes of STZs for BMGs are only a fraction of a nm³ to several nm³,²⁹ i.e., much smaller than for polymers.³⁰ In addition, the relative atomic structure of BMGs can be flexibly rearranged with the size and packing density of the atoms themselves as the only limiting factors. At temperatures sufficiently above T_g, this may result in an ideally homogeneous flow that allows the material to adapt to any externally imposed confinement. For proof of concept, a Pt_57.5Cu_14.7Ni_5.3P_22.5 BMG alloy has been used that exhibits excellent ductility, plasticity, and thermoplastic formability as well as a conveniently long processing window without suffering from excessive oxidation or premature crystallization at conditioning temperatures.³¹ Thermoplastically pressing this BMG onto strontium titanate (SrTiO₃) replicated the crystal’s step edges with atomic precision and high fidelity while preserving the smoothness of its terraces with a ≈0.060 nm root mean square (rms) roughness¹⁷ even though the size of an STZ at room temperature of Pt-BMG was reported to be approximately several nm³, which contains several hundreds of atoms.²⁹ 

Returning to the original question of maximum imprinting accuracy, the success of this proof-of-concept suggests that the limit of replication fidelity that can be achieved by TPF with BMGs can go beyond the scale of their flow unit size, which ultimately may be the size of a single atom. In the above case, however, the step height between terraces of SrTiO₃(100) is 0.3905 nm,³² a value that diverges less than 0.2% from the lattice constant of the BMG’s majority chemical compound, platinum, of 0.3912 nm.³³ Thus, it is valid concern to wonder whether or not the precise replication of SrTiO₃(100) using an Pt_57.5Cu_14.7Ni_5.3P_22.5 alloy may simply be owed (or at least facilitated) to the coincidental quasi-match of the mold’s lattice constant with the one of platinum.

In this research, it is shown that atomic imprinting via TPF can be generalized to the replication of surfaces with different characteristic dimensions. For this case study, we use the (100), (110), and (111) surfaces of lanthanum aluminate (LaAlO₃), all of which offer different step heights and surface features such as screw dislocations that despite their complexity can be reproduced without loss of resolution. From these results, we infer that bulk metallic glasses may indeed not possess an apparent intrinsic length scale limiting the accuracy of atomic feature replication through TPF, thereby providing an ideal platform for advancing research in the fundamental study of structure, deformation, and phase transitions of glasses^34,35 as well as enabling novel applications in fields that make use of surface functionalization through topography.^25,36

LaAlO₃ (100), (110), and (111) single crystals with one side polished were bought from MTI Corporation (Richmond, CA, USA). The surfaces were cleaned by wet etching in dilute HCl with the pH value near 4.5 for 30 s. The crystalline surface was then annealed at 1050 °C in air for 10 h.³⁷ Thermoplastic forming was conducted using an Instron 5569 mechanical testing machine with custom heating plates as follows: A cylindrical ingot of an amorphous Pt_57.5Cu_14.7Ni_5.3P_22.5 alloy (“Pt-BMG”)³¹ ∼2 mm in length and 1 mm in diameter that was produced by casting was thermoplastically formed onto LaAlO₃ substrates at constant force and temperature. After a thermal equilibrium at a temperature of 270 °C was achieved, the force was ramped up to a maximum value of 1 kN (≈10 MPa) that was maintained for about 3 min. The sample was then air cooled to ambient temperature. Details of the TPF procedure can be found in previous publications.^17,38

The surfaces of the LaAlO₃ molds and Pt-BMG replicas were characterized with atomic force microscopy (AFM) using a Bruker Multimode AFM with Nanoscope III electronics and Bruker RTESPAW-300 cantilevers with driving frequencies around 300 kHz in tapping mode. Following a protocol developed previously,¹⁷ the original AFM images of as-imprinted Pt-BMG were mirrored along the y–z plane followed by inverting the image’s z-scale in order to facilitate direct comparison between the surface morphologies of mold and replica.

At room temperature, single crystalline LaAlO₃ has a rhombohedral structure, which can be simplified as a pseudo-cubic structure with a = b = c = 0.3787 nm and α = 90.066°.^39,40 Thus, step heights between individual terraces on LaAlO₃ (100), (110), and (111) are integer multiples of ≈0.38 nm, ≈0.27 nm, and ≈0.22 nm, respectively. Similar to other perovskite oxides, LaAlO₃ surfaces exhibit under ultra-high vacuum conditions a variety of surface reconstructions.^41,42 The combined effects of orientation, miscut, and preparation-dependent surface termination led to surface patterns that are, at least for the samples investigated in this study, distinct for LaAlO₃ (100), (110), and (111) surfaces: while the (100) surface [Fig. 1(a)] shows terraces with relatively sharp corners, the step edges separating individual terraces on LaAlO₃(110) [Fig. 1(b)] tend to be more rounded. There are also more island-like and pit-like features on the (110) surface, which may be a consequence of this particular crystal’s lower miscut compared to the one of Fig. 1(a). In contrast, the surface of the LaAlO₃(111) single crystal is not only exhibiting the largest miscut of the three samples, but it was also prone to degradation. Thus, rather than observing a more fine-structured pattern with step edges exhibiting frequent kinks, only continuous and dense steps were observed that separated terraces showing significantly higher roughness than on the other two samples [Fig. 1(c)]. Nevertheless, the step heights between terraces matched the theoretical values for all three samples.

Moving forward, the distinctively different surface patterns exposed by the crystals combined with their well-defined step heights provide ideal references for assessing the fidelity of feature replication through thermoplastic forming when using them as comparative molds. Without loss of generality, Figs. 1(d)–1(f) present AFM images of the morphology of the respective nanoimprinted surfaces using Pt-BMG after mirroring and z-inversion, where all three expose the same signature features and step heights found on the corresponding LaAlO₃ molds. Despite the above-mentioned increased on-terrace roughness, the replication of the LaAlO₃(111) surface demonstrates the capability to fabricate feature sizes down to 0.22 nm using Pt-BMG.

To highlight an exemplary case in more detail, we quantified the replication quality through surface roughness analysis and comparison of line profiles across terraces using LaAlO₃(110). Toward this end, Fig. 2(a) shows the mold LaAlO₃(110) surface after thermoplastic forming, while Fig. 2(b) was taken at the corresponding location on the imprinted Pt-BMG. After mirroring and z-inversion, we can easily see that it indeed shows the exact same features as the mold. For the roughness analysis, we use the areas within the squares shown in Figs. 2(a) and 2(b), which are 150 × 150 nm² in size each. Computing the root mean square (rms) roughness results in values of 0.065 nm and 0.055 nm, respectively, with the slight difference possibly being due to the probing tips exposing differently sharp apexes. In any event, the observed surface roughness matches previously reported results on SrTiO₃, indicating that Pt-BMG also has favorable wetting properties toward the LaAlO₃ surface.¹⁷ The line profiles in Fig. 2(c) then demonstrate the accurate replication of the 0.27 nm height of the step edges. As a result, we conclude that nanoimprinting Pt-BMG onto LaAlO₃ crystals achieves the same quality as obtained when using SrTiO₃ as molds.

Compared to the LaAlO₃ (100) and (111) surface terminations, the (110)-terminated LaAlO₃ crystal was exhibiting more complex atomic-scale features originating from defects such as screw dislocations, which can provide additional insight when evaluating the scale limit of atomic imprinting. For example, the surface area presented in Fig. 3(a) exposes two screw dislocations terminating at the surface, which are highlighted by two dashed lines with arrows; Fig. 3(b) reflects the corresponding structure in the Pt-BMG replica. Following the dashed lines along the direction of the arrow, one can seamlessly move from a lower terrace to a higher one, while the step edge emerges from the point where the screw dislocation line intersects with the surface. Since the nature and appearance of screw dislocations at surfaces have been investigated in detail elsewhere,⁴³ we only note here that the successful replication of such a continuously changing feature corroborates again that there is likely no intrinsic scale limit to the accuracy of thermoplastically replicating the height of surface features with suitable BMGs even at the atomic scale.

More generally, TPF is found to be capable of replicating most or all features that are resolvable by AFM, which is sub-angstrom in the z direction and, due to the finite radius of the probing tip, a couple of nanometers laterally during ambient air imaging. As a result, it provides an ideal platform to study local glass transition kinetics at the nanometer scale. For example, previous research has shown that the change in surface morphology during sequential annealing of imprinted Pt-BMG replica using SrTiO₃(100) as mold results from the competition between surface relaxation and crystallization.³⁵ Thereby, the smoothening of the steps is due to the surface relaxation, while the roughening on the terraces is because of the onset of crystallization starting first near the surface. Through the purposeful selection of surfaces employed as molds, we can generate BMG replicas with different step heights. Subsequently, we could get an estimation of the time scale for surface and bulk relaxation by pinpointing the temperatures and annealing times at which steps with different heights flatten out.

In this research, we demonstrated the nanoimprinting of Pt-BMG by LaAlO₃ surfaces with atomic-scale replication fidelity through TPF. Particular emphasis was given to the reproduction of patterns with clearly defined but different characteristic dimensions, which was achieved through the use of LaAlO₃ single crystals with three different crystallographic surface orientations. Surfaces on these crystals then expose terraces separated by distinct but different step heights, all of which were replicated with sub-angstrom precision. Together with the impeccable replication of screw dislocations on LaAlO₃(110), which feature continuously changing terrace heights near the point where the dislocation line hits the surface, the results indicate that there may indeed not be an intrinsic scale limiting the ability of BMGs to accurately replicate the heights of surface features on molds by TPF. This presumed “ultimate” imprinting capability of TPF with BMGs not only broadens the application of TPF in atomic imprinting and precision nanofabrication but also offers a material system that allows us to continuously tune the size of surface features for fundamental high-resolution and local studies of glass properties and behavior.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Helpful discussions with Omur Dagdeviren are gratefully acknowledged. The authors thank Todd Schwendemann for sharing laboratory resources and equipment and the National Science Foundation for funding through Grant No. NSF CMMI-1901959. Work carried out before January 6, 2019 was supported by the Department of Energy (Grant No. DE-SC0016179).