A combination of block copolymer (BCP) lithography and solid-phase epitaxy can be employed to form large areas, on the order of square centimeters, of a high density of epitaxial crystalline complex oxide nanostructures. We have used BCP lithography with a poly(styrene-block-methyl methacrylate) (PS-b-PMMA) copolymer to template a nanohole array either directly on an (001)-oriented SrTiO3 (STO) single crystal substrate or on a 20 nm-thick Si3N4 layer deposited on the STO substrate. BCPs with the selected compositions assembled in a cylindrical phase with 16 nm diameter PMMA cylinders and a cylinder-to-cylinder spacing of 32 nm. The substrate was modified with an energetically non-preferential polymer layer to allow for the vertical alignment of the cylinders. The PMMA cylinders were removed using a subtractive process, leaving an array of cylindrical holes. For BCPs assembled on Si3N4/STO, the pattern was transferred to the Si3N4 layer using reactive ion etching, exposing the underlying STO substrate in the nanoholes. An amorphous LaAlO3 (LAO) layer was deposited on the patterned Si3N4/STO at room temperature. The amorphous LAO epitaxially crystallized within the nanoscale-patterned holes with fully relaxed lattice parameters through solid phase epitaxy, resulting in the formation of nanoscale LAO/STO epitaxial heterostructures.

There is a significant and longstanding interest in the technological use of complex metal oxides in electronic, optical, and superconducting devices.1 The fabrication of epitaxial complex oxide nanostructures using lithography followed by subtractive patterning has proven to be highly challenging. The challenge arises in large part from difficulties in achieving precise chemical etching of complex oxides, including variations in the surface composition during etching.2 In addition, chemical and structural modifications induced by chemical, plasma, or ion-beam etching can lead to variations in the functional (e.g., ferroelectric) properties.3–5 A further challenge arises in the selection of materials and etching processes in the lithography of metal oxides because common processes can lead to the degradation of oxide thin films.6 There are many approaches that aim to circumvent or eliminate the drawbacks of previous complex oxide patterning techniques.7 Here, we show that many of the limitations of previous approaches can be overcome by reversing the order of the patterning and complex oxide synthesis processes, such that the oxide is deposited and crystallized in a pre-patterned substrate. Epitaxial crystallization templated by nanoscale patterns provides the means to expand the scope of epitaxial oxide thin films to new nanoscale geometries.

The patterning process is particularly important in epitaxial crystalline thin film heterostructures containing an interface between the perovskite complex oxides LaAlO3 (LAO) and SrTiO3 (STO). We focus here on a block-copolymer (BCP) lithography technique that, combined with solid-phase epitaxial growth (SPE), yields a patterned array of epitaxial LAO crystals on an STO substrate. LAO/STO quantum dots and arrays of quantum dots exhibit effects arising from quantum confinement and transport phenomena resulting from the overlap of wavefunctions on adjacent features.8 Solid-phase epitaxy has been previously applied in the crystallization of group-IV semiconductors, such as Si and Ge,9,10 unpatterned thin films of complex oxides,11–13 and in crystals seeded by nanosheets or nanocrystals.14,15 The present work extends these efforts by applying SPE in combination with nanoscale patterns to create epitaxial complex oxide nanostructures.

Nanopatterning by several methods can be used to create nanostructures in the LAO/STO system.16,17 The lithographic approaches for patterning LAO/STO heterostructures with nanoscale dimension include conventional photolithography or electron beam-lithography, ion beam irradiation, and surface modification through conductive atomic force microscopy (c-AFM) lithography.18–21 For example, an amorphous LAO layer patterned by ultraviolet (UV) and electron-beam lithography on STO has been used to define regions with widths as small as 200 nm in which crystalline LAO was grown epitaxially.18 Optical lithography has also been used to pattern an AlOx layer on STO and create a mask for subsequent LAO deposition.22,23 Using this method, crystalline LAO features down to 1 µm were fabricated. Conducting features in STO/LAO using a combination of ion beam irradiation with electron beam-lithography have also been fabricated.20 Using a c-AFM tip in contact with the top LAO surface, conductive features as small as 2 nm were achieved.21 These approaches to the nanoscale patterning of LAO/STO have limitations of low throughput and scalability, especially when smaller features are targeted.

Relatively large features with sizes of 300–700 nm have been fabricated via controlled pulsed-laser deposition (PLD) of perovskite materials on STO through a stencil mask fabricated by laser interference lithography.24–26 Clogging of the stencil at small mask dimensions effectively reduces the resolution and limits the achievable feature size.27 In a similar approach to the stencil technique, a hexagonal array of nano islands of complex oxides with lateral feature sizes of a few hundred nanometers were fabricated by nanosphere lithography combined with PLD.28–30 However, defects in the nanosphere layer, such as bilayer formation and discontinuity of the hexagonal packing, leads to variations in the size and shape of the features.

BCP lithography employs self-assembled BCP thin films to create periodic nanopatterns over large areas. BCP lithography provides features at the nanometer size scale with high throughput compared to other techniques we discussed above.31–33 BCPs are macromolecules consisting of two chemically distinct polymer chains covalently bonded to each other. If the blocks or chains are sufficiently incompatible, they will self-assemble into one of four possible morphologies (spheres, cylinders, gyroids, or lamellae), depending on the volume fraction (fi) of each block.34–36 The size of the ordered structures is dictated by the length or degree of polymerization (N) of the blocks and the degree of incompatibility quantified by the Flory–Huggins interaction parameter (χ); thus, the features can range from a few to 100 nm.

BCP lithography has been used extensively to pattern conventional oxides, such as silicon dioxide, graphene/SiO2, or highly oriented pyrolytic graphite/SiO2, for a range of applications from fin field effect transistors and bit-patterned media, to graphene plasmonics.37 Each substrate poses a unique set of challenges to deposit and self-assemble the BCP film for subsequent subtractive or additive processes. There have been two significant challenges in adapting BCP lithography to complex oxide materials. The first of these challenges has involved the development of oxide/polymer interfaces that guide the assembly of BCPs in selected morphologies. A second, separate, challenge arises in developing processing conditions to translate the BCP assembly to nanoscale patterns that can subsequently be used to guide epitaxial crystallization. In this work, we specifically demonstrate two complementary aspects of the development of BCP lithography methods applicable to complex oxides. In the first approach, we demonstrate a buffer layer compatible with STO that allows the subsequent assembly of BCP thin films. The chemical removal of one of the BCP blocks in the pattern assembled by this approach results in a nanohole array pattern that exposes regions of the underlying STO substrates. A second approach involves the assembly of a BCP thin film on a Si3N4/STO substrate and the subsequent pattern transfer into the Si3N4. The second approach is particularly valuable in the creation of nanoscale epitaxial complex oxides.

The nanoscale epitaxial crystallization of LAO in the patterns produced by BCP lithography employed SPE. SPE involves the crystallization of amorphous materials with an orientation templated by a crystalline substrate or seed.38 The SPE approach can be applied to amorphous layers in nanoscale geometries.14,15 We demonstrate nanoscale epitaxy through the deposition and epitaxy of LAO in the nanopatterned Si3N4/STO substrates.

For the first approach, BCP lithography using a cylinder-forming poly(styrene-b-methyl methacrylate) (PS-b-PMMA) was employed for the fabrication of nanohole arrays on 1.5 cm2 TiO2-terminated STO substrates following the procedure shown in Fig. 1(a). The STO substrates were cleaned before starting the BCP lithography process. Traditionally, this is achieved by dipping the substrates in a mixture of sulfuric acid and hydrogen peroxide known as piranha solution. Nonetheless, we observed that the initially clear piranha solution turned yellow after cleaning the STO substrates, indicating degradation of the substrates. For this reason, an alternate approach of exposure to oxygen plasma in the reactive ion etch (RIE) process, was used. The oxygen plasma removes organic contaminants by chemical degradation and/or physical ablation, and this process successfully cleaned the surface of the STO without unintended damage.

FIG. 1.

(a) Schematic of the fabrication of nanohole arrays of PS in STO substrates. (b) Top-view SEM, (c) AFM, and (d) GISAXS measurements of the STO substrates with the PS nanohole arrays.

FIG. 1.

(a) Schematic of the fabrication of nanohole arrays of PS in STO substrates. (b) Top-view SEM, (c) AFM, and (d) GISAXS measurements of the STO substrates with the PS nanohole arrays.

Close modal

As a first step for the BCP lithography process, a non-preferential surface is required to achieve the perpendicular orientation of the holes relative to the substrate. The orientation of the BCP microdomains in thin films is primarily dictated by the interaction of each block with the substrate and the free surface. In most cases, the difference in the interfacial energy between the blocks leads to the preferential wetting of one of the blocks with either the substrate or free surface, resulting in the parallel orientation of the microdomains.39,40 The interfacial interactions of the blocks with the substrate can be balanced by grafting a random copolymer of similar composition to the BCP onto the substrate to form an energetically non-preferential surface or a neutral layer on traditional oxides, such as silicon dioxide.39,41,42 Subsequent development of a substrate independent chemistry based on a self-cross-linking neutral layer, which is widely applicable to non-oxide substrates, further broadened the application of BCP lithography.43 We used a substrate-independent neutral layer in this study. Specifically, two random copolymers of varying compositions of styrene and methyl methacrylate (MMA) were developed and screened for three cylinder-forming poly(styrene-block-methyl methacrylate) (PS-b-PMMA) of similar molecular weights and feature size (cylinders of ∼16 nm diameter). The random copolymers also contained glycidyl methacrylate (GMA), a self-crosslinkable unit that can form a stable cross-linked thin-film at 160 °C.43 The styrene: MMA: GMA ratio in the random copolymers used in this work was varied from 70:26:4 to 74:24:2 to identify the composition that resulted in the formation of a neutral layer on the STO surface and, as a result, allowed perpendicular orientation of the cylindrical BCP domains with respect to the substrate. A random copolymer layer was assembled by spin coating a solution of 0.3 wt. % of the copolymer in toluene onto the STO substrates and annealing at 160 °C for 3 h in vacuum. Subsequently, the substrates were rinsed with toluene to remove uncrosslinked random copolymer, resulting in a ∼10 nm layer. A 1.7 wt. % solution of the BCP in toluene was then spin coated onto the neutral-layer coated STO substrate and annealed at 220 °C for 3 h in vacuum, resulting in a ∼45 nm thick self-assembled BCP layer. The nanoholes were then formed by selective degradation and removal of the PMMA cylinders by UV exposure and acetic acid wash, respectively, followed by O2 plasma etching to remove any residual PMMA and random copolymer from the neutral layer, leaving the PS nanohole template in place.

As shown in Fig. S1, even though the three commercial BCPs have similar compositions, the defects in their assembled thin films were quite sensitive to subtle variations in composition. Of the three BCPs, perpendicular orientation throughout the 1.5 cm2 substrate was achieved using a random copolymer with a ratio of 72:24:2 of styrene: MMA: GMA for an overlaying BCP (PS-b-PMMA 53-20 with a molecular weight of 53 and 20.5 kDa for the PS and PMMA blocks, respectively). The scanning electron microscopy (SEM), atomic force microscopy (AFM), and the grazing incidence small angle X-ray scattering (GISAXS) measurements shown in Figs. 1(b)1(d) confirm the fabrication of uniform nanohole arrays with ∼16 nm diameter and a center-to-center distance of ∼32 nm. This process provides a means of creating a nanohole array with a high areal density of ∼6 × 1010 cm−2, which can then be used for subsequent templating of nanomaterials on STO. Throughout the rest of this work, we used the combination of this optimized random copolymer and BCP for the fabrication of the nanohole arrays.

To study the epitaxy of nanoscale complex-oxide heterostructures, the BCP patterns were implemented on a Si3N4/STO substrate following the procedure shown in Fig. 2(a). The conditions required for the deposition and crystallization of the amorphous material, such as high temperatures, could potentially lead to the decomposition of the polymer and subsequent destruction of the BCP nanohole arrays. Hence, a nanopatterned Si3N4 layer was selected for this purpose because of its physical and chemical stability compared to the nanopatterned PS template. First, a Si3N4 layer (∼20 nm) was deposited onto the STO substrate by plasma enhanced chemical vapor deposition (PECVD). Subsequently, a PS nanohole mask was prepared following the procedure described in Sec. II A. Finally, the nanohole pattern was transferred onto the Si3N4 layer by RIE using the CF4 plasma. After pattern transfer, the remaining PS mask was removed using the O2 plasma, leaving a clean nanopatterned Si3N4/STO. The SEM images of the nanopatterned Si3N4/STO substrates shown in Figs. 2(b)2(d) confirm the formation of a uniform nanohole pattern throughout the 1.5 cm2 substrate.

FIG. 2.

(a) Schematic representation of the fabrication of the nanopatterned Si3N4/STO substrates using BCP lithography. (b) Top-view and (c) and (d) 45° tilt-view SEM images of the nanopatterned Si3N4/STO substrates.

FIG. 2.

(a) Schematic representation of the fabrication of the nanopatterned Si3N4/STO substrates using BCP lithography. (b) Top-view and (c) and (d) 45° tilt-view SEM images of the nanopatterned Si3N4/STO substrates.

Close modal

During pattern transfer with the CF4 plasma, the PS nanohole template was also etched. This means that a minimum thickness for the PS nanohole template and, thus the BCP layer, is required to avoid the etching of the Si3N4 layer in areas other than the nanoholes. The thickness of the BCP layer is dictated by the concentration of the solution and the parameters used for spin-coating. In general, increasing the concentration of the solution increases the thickness of the BCP layer. For example, by increasing the concentration of the BCP solution from 1.7 to 3.0 wt. %, an increase in the thickness of the BCP layer from 45 to 120 nm was achieved (Table S1 and Fig. S2). This makes the patterning of thicker Si3N4 layers using this approach a possibility. Previous studies by us and others have shown that the maximum thickness of a PS-b-PMMA BCP layer that can be assembled on the neutral layer without interrupting its perpendicular orientation is ∼300 nm, if the processing conditions, such as annealing temperature and time, can be tweaked to make the air/film interface non-preferential to either PS or PMMA blocks.44 Building on these studies, we first determined the etching rates for Si3N4 and PS in the CF4 plasma (Fig. 3). It was essential to optimize the breakthrough process from the PS template to Si3N4 and the exposure of the STO substrate in the holes. The procedure used to determine the etching rates is described in the supplementary material. We found that PS is etched at a rate of 0.81 nm s−1 with a thickness offset at zero etching time of −3.20 nm, while Si3N4 is etched at a rate of 0.92 nm s−1 with an offset of −3.84 nm. The etching rate shown in Fig. 3 is constant within the precision of our measurement and does not appear to be a function of the thickness of Si3N4 removed or the depth of the etching with respect to the Si3N4/SrTiO3 interface. The observed offset could be a result of a delay in the RIE instrument stabilizing the RF power and gas flow required during the etching process. Figure 3 shows that PS and Si3N4 etch at similar rates in the CF4 plasma. With this insight, we can predict that a Si3N4 layer with a maximum thickness of more than 300 nm can be patterned in the case where the thickness of the BCP layer is increased to the largest thickness reported44 so far, ∼300 nm.

FIG. 3.

Etching of PS and Si3N4 in the CF4 plasma. PS is etched at a rate of 0.81 nm s−1 with an offset of −3.20 nm, while Si3N4 is etched at a rate of 0.92 nm s−1 with a thickness offset at zero etching time of −3.84 nm.

FIG. 3.

Etching of PS and Si3N4 in the CF4 plasma. PS is etched at a rate of 0.81 nm s−1 with an offset of −3.20 nm, while Si3N4 is etched at a rate of 0.92 nm s−1 with a thickness offset at zero etching time of −3.84 nm.

Close modal

We targeted an aspect ratio of 1:1 by using a 20 nm thick Si3N4 layer and a BCP with feature size ∼20 nm. Nonetheless, the aspect ratio of the nanoholes can be modified by varying the feature size of the BCP and/or the thickness of the Si3N4 layer (Fig. 4 ). A wide range of commercially available BCPs that self-assemble into cylinders of different domain and feature sizes are accessible, although the composition of the neutral layer to obtain the perpendicular orientation of the self-assembled BCP thin film would need to be tuned. Thus, this approach can be useful to study how the dimensions and aspect ratio of the nanoholes affect the epitaxial growth and properties of the nanoscale complex-oxide heterostructures.

FIG. 4.

Different approaches to changing the aspect ratio of the Si3N4 nanoholes. The aspect ratio can be changed by using BCPs with different feature sizes or by changing the thickness of the Si3N4 layer.

FIG. 4.

Different approaches to changing the aspect ratio of the Si3N4 nanoholes. The aspect ratio can be changed by using BCPs with different feature sizes or by changing the thickness of the Si3N4 layer.

Close modal

Epitaxial LAO nanocrystals were fabricated using the series of steps shown in Fig. 5(a). A uniform 30 nm-thick amorphous LAO film was deposited at room temperature onto a Si3N4-patterned STO substrate using radio-frequency sputtering. An SEM image after the deposition of the amorphous LAO onto the patterned Si3N4/STO substrate is shown in Fig. 5(a). The surface morphology post-deposition follows that of the patterned Si3N4/STO substrate, suggesting conformal deposition on the nanoscale-patterned substrates.

FIG. 5.

SEM images of (a) amorphous LAO and (b) partially crystallized LAO on an STO substrate with the BCP-patterned Si3N4 layer. (c) XRD θ–2θ scan of epitaxial growth LAO on patterned Si3N4/STO.

FIG. 5.

SEM images of (a) amorphous LAO and (b) partially crystallized LAO on an STO substrate with the BCP-patterned Si3N4 layer. (c) XRD θ–2θ scan of epitaxial growth LAO on patterned Si3N4/STO.

Close modal

The crystallization process is shown schematically in Fig. 5(b). The structures were heated in air at 750 °C for 3 h to crystallize the LAO layer by SPE. The crystallization conditions of LAO on STO substrates followed those used for the recrystallization of amorphous LAO films formed by ion beam irradiation.45 The crystallization was nucleated at the interface between the crystalline STO substrate and amorphous LAO within the nanoscale holes in direct contact with the STO substrate. This contact facilitated the initial crystallization, transforming the amorphous material into a crystalline state, evidenced by the emergence of LAO reflections in the x-ray diffraction results shown in Fig. 5(c). The crystallization progressed and filled the nanoscale holes. The selected heating parameters were designed to partially crystallize the materials within the holes, focusing on selective nucleation at the interface between the exposed crystalline STO substrate and amorphous LAO. The SEM image in Fig. 5(b) displays the surface morphology after crystallization, confirming that the nanoscale geometries are preserved following crystallization.

The crystalline structure and epitaxial alignment were probed using x-ray diffraction. A θ–2θ scan along the surface normal direction of reciprocal space, shown in Fig. 5(c), exhibits x-ray reflections from the crystallized LAO and the STO substrate. The only LAO reflections shown in Fig. 5(c) arise from 00L planes of LAO. The x-ray diffraction results thus verify the epitaxial alignment of the LAO nanocrystals. The out of plane lattice parameter calculated from LAO reflection angles is 3.798 Å. The out of plane lattice parameter is close to the bulk lattice parameter of LAO, 3.792 Å, suggesting that the epitaxial film is relaxed.

This work lays out a high-throughput method for nanoscale epitaxial crystallization of complex oxides using SPE. The method involves using BCP lithography to create high density array of nanoholes on a Si3N4 mask on STO, which was then used for epitaxial crystallization of an overlying amorphous LAO film following a high temperature annealing process. The post-annealing XRD results show the epitaxial alignment of the LAO film along the STO (001) plane. Although the nanoholes fabricated in this work used a BCP patern with a feature size of ∼16 nm, the method developed is easily adaptable to length scales ranging from 10 to 100 nm by the appropriate choice of BCP as both the size and shape of the features is encoded in the BCP composition. The aspect ratio of the features can also be increased by an appropriate choice of the BCP and the Si3N4 film thickness. These findings not only demonstrate the successful nanoscale epitaxial growth of perovskite oxide but also highlight the potential of SPE in precisely engineering complex oxide structures on block copolymer-processed patterned substrates, such as STO. This advancement opens new avenues for exploring and fabricating nanostructured materials with tailored properties for diverse applications, particularly in nanopatterned quantum electronic materials and optical metamaterials.

See the supplementary material for details regarding materials, fabrication, and characterization.

This research was primarily supported by the NSF through the University of Wisconsin Materials Research Science and Engineering Center (Grant No. DMR-1720415). PG and MBP acknowledge partial support for this research by the University of Wisconsin-Madison, Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation. The authors acknowledge the use of facilities and instrumentation supported by the NSF through the University of Wisconsin Materials Research Science and Engineering Center (Grant No. DMR-2309000).

The authors have no conflicts to disclose.

M.A.B. and R.L contributed equally to this work.

Miguel A. Betancourt-Ponce: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Resources (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead). Rui Liu: Data curation (lead); Formal analysis (lead); Investigation (lead); Resources (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead). Jian Sun: Investigation (supporting); Resources (supporting). Paul G. Evans: Conceptualization (equal); Supervision (equal). Padma Gopalan: Conceptualization (equal); Supervision (equal).

The data that support the findings of this study are available within the article.

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Supplementary Material