Nanomolding of topological nanowires

Topological materials possess symmetry-protected surface states with unique electronic properties that make them potentially transformative for fields such as catalysis,¹ optoelectronics,² microelectronics,^3,4 and quantum computing.⁵ Since the first experimental demonstration of topological materials,⁶ there has been great interest in discovering new topological material classes and compounds. Theoretical calculations of inorganic crystals predict ∼27% of all known compounds are topological;⁷ yet, experimental studies have focused on only a handful of model systems, representing a tiny fraction of predicted topological materials. Investigating potential topological compounds could lead to new fundamental discoveries of topological states, such as topological crystalline insulators with rotational symmetry-protected states⁸ or new intrinsic topological superconductors,⁹ as well as new material candidates for functional devices that exploit these attractive electronic properties.

The huge gap between the number of predicted and experimentally realized topological materials is largely a consequence of the inefficiency of both fabricating and testing materials rapidly. Currently, topologically protected surface states are mostly studied via angle resolved photoemission spectroscopy (ARPES) using bulk single crystals.¹⁰ While there are several bulk crystal growth techniques,¹¹ considerable optimization of experimental conditions is needed for each specific composition, which makes fabrication of high quality single crystals at a rapid pace impractical. Also, ARPES is typically done at synchrotron facilities; thus, it is not a widely available or scalable characterization technique.¹⁰ Furthermore, ARPES can only confirm the presence and band structure of topological surface states but does not provide transport properties, which are relevant for device applications.

To this end, nanostructures are a viable alternative for the experimental study of the topological surface states and transport measurements.^12,13 Given their nanoscale dimensions that minimize the number of bulk electrons and maximize the surface area, a variety of magneto-transport signatures, such as Aharonov–Bohm oscillations, Shubnikov–de Haas oscillations, and various quantum Hall states, can be used to experimentally probe topological surface states, as evidenced by transport studies of topological insulator nanoribbons, topological crystalline insulator nanowires, and topological semimetal nanobelts.^12,14–17 When compared to ARPES on bulk crystals, these aforementioned transport measurements can be performed using equipment that is available in many laboratories and university facilities. More importantly, transport measurements are directly relevant for microelectronic applications, such as topological semimetals for interconnects.^3,4,18 However, if bulk crystal growth is deemed slow and labor-intensive, synthesis of high quality nanostructures, and subsequent transport measurements, is crushingly slow and painstaking.

The bottleneck for using nanostructures to study topological materials is synthesis. To synthesize nanostructures, numerous bottom-up and top-down strategies have been developed over the last 3 decades. However, most of these strategies suffer from a lack of controlled structure, morphology, and defect density and require extensive trial and error to achieve optimal conditions for each composition.¹² Bottom-up techniques, such as molecular beam epitaxy (MBE) or chemical vapor deposition (CVD), have been used to grow several topological nanowires, such as Bi₂Se₃,^13,19 SnTe,^20,21 and Cd₃As₂.^22,23 MBE-grown nanowires generally have controlled morphology and few extended defects, but extensive parameter optimization is necessary for each material grown using MBE and the technique is not high throughput. CVD techniques, such as metal catalyzed vapor–liquid–solid (VLS) growth, have rapid growth conditions and can explore a much wider compositional space of inorganic compounds than MBE, but there is limited control over the morphology of the nanowires and the final nanowires can have a sizeable level of defects, which can mask surface state properties in electron transport. Another bottom-up strategy is colloidal synthesis, a rapid and scalable method that provides great control of shape and defect-free crystals.²⁴ However, to stabilize nanowires in solution, colloidal synthesis requires surface ligands, which are undesirable and must be stripped away from nanowires to make good electrical contact to the nanowires. Alternative to bottom-up syntheses, top-down approaches have borrowed techniques used in semiconductor fabrication, such as extreme ultraviolet (EUV) or electron lithography, to fabricate nanowires with diameters <100 nm.²⁵ While lithography is a well-established technique, limited material choice, uncontrollable defect formation, and multiple processing steps limit the ability to fabricate topological nanowires in a high throughput manner.

Given the vast potential library of topological materials, screening nanowires for topological states using current fabrication approaches will thus take too long. If we assume an individual researcher can successfully synthesize and experimentally measure one topological material nanowire per year, it would take 1000 man-years to experimentally examine 1000 topological compounds,²⁶ a tiny fraction of the 27% of all known inorganic compounds. This number does not include modifying other extremely relevant parameters, such as doping concentrations to tune Fermi levels or fabricating advanced nanowire architectures, such as core–shell.

To overcome both fabrication and characterization limitations, new experimental approaches are needed to screen topological material candidates in a high throughput matter. In this Perspective, we introduce thermomechanical nanomolding (Fig. 1), whereby a bulk feedstock material is pressed into a mold with nanoscale features at an elevated temperature (≈0.5T_m, where T_m denotes melting temperature) and pressure (>100 MPa), as a new fabrication method for defect-free single crystal topological nanowires in a high throughput, material agnostic manner.²⁷ Originally developed by Liu et al. at Yale University, one critical advantage of nanomolding over other nanowire synthesis techniques is the ability to use polycrystalline samples as the bulk feedstock. Unlike bulk single crystal growth, polycrystalline samples can be made using simple, cheap, and rapid fabrication methods, such as arc melting, induction melting, or spark plasma sintering. Once cut and polished, a single polycrystalline disk is pressed into a mold to make vertically standing nanowires. Currently, the most common mold used is anodized aluminum oxide (AAO),²⁷ which forms periodic arrays of size-tunable one-dimensional (1D) pores. Aluminum oxide is an inert high modulus material with a high melting temperature, making it resistant to deformation during nanomolding. In addition, AAO can be etched away using KOH,²⁷ which is nonreactive with most metals and ordered phases. The final free standing nanowires can be detached from the surface via sonication for material characterization or electrical transport measurements.

The original studies of nanomolding focused on viscous, amorphous materials, such as polymers or metallic glasses. In these materials, nanomolding at high temperatures above the glass transition temperature decreases viscosity by up to 9 orders of magnitude, enabling easy viscous flow through an appropriate mold.²⁸ By controlling pressure, temperature, and time, amorphous nanowires of the desired length can be formed without crystallization or oxidation. When nanomolding was performed on crystalline metals, surprisingly, nanowire formation still occurred.²⁹ Crystalline nanowires can have extremely large aspect ratios >1000 and do not contain any noticeable 1D or 2D defects, such as dislocations or grain boundaries. Interestingly, the fabricated nanowires are all single crystals with similar orientation, regardless of the bulk feedstock’s polycrystallinity.²⁹ For example, nanomolding of polycrystalline fcc metals leads to the formation of single-crystal 〈110〉-oriented nanowires. From transmission electron microscopy (TEM), it is observed that nanowire orientation occurs via grain rotation near the base of the nanowire. It is believed that grain rotation is driven by surface energy minimization of the nanowire during molding, i.e., (111) surfaces for fcc 〈110〉-nanowires.²⁹ If the crystal orientation of the bulk feedstock is aligned to the nanowire growth direction, grain rotation does not occur.³⁰ 

The growth process for crystalline nanowires into a mold is temperature and size dependent.^31,32 For small wires (diameter < 100 nm) or high temperatures (>0.4 T_m), nanomolding occurs via interfacial diffusion driven by the pressure gradient in the pore. Unlike bulk diffusion, which is size independent, interfacial diffusion scales inversely with the diameter, $L∼d−12$⁠.³¹ Thus, smaller diameter molds require less pressure or time to form similar length nanowires. In addition to changing mold pore size, the choice of the mold material can greatly modify interfacial diffusion and chemistry to promote wire formation. For example, the formation of Au nanowires was greatly enhanced by using a Si mold rather than an AAO mold as Au diffusivity on a Si surface is much larger than on aluminum oxide.³³ For large wires (diameter > 100 nm) or low temperatures (<0.4 T_m), nanomolding occurs via dislocation nucleation and motion. Under these conditions, atomic diffusion via bulk or interface is greatly inhibited. Instead, edge dislocation loops nucleate near the base of the nanowire and are punched into the mold. For dislocation-driven nanomolding, the nanowire length scales linearly with diameter, i.e., L ∼ d.³¹ Because of the high energetic cost in nucleating dislocation loops, nanowires with high aspect ratios have not been fabricated for large diameter wires and it is unclear whether the dislocation loops remain in the nanowire after etching of the AAO mold or annihilate at the free surface due to image stresses.³⁴ At 0.5T_m, the transition between dislocation-mediated and interfacial diffusion growth is ∼100 nm for fcc metals.^29,31

For ordered phase materials, which include the most known topological materials, the size-dependent diffusion mechanism during nanomolding matches those seen in pure metals discussed previously. Surprisingly, there is no chemical composition change along the length or radius of the nanowire, as evidenced in topological crystalline insulator SnTe nanowires (Fig. 2).³⁵ This uniform chemical composition is thought to be related to the narrow Gibb’s free energy range that most ordered phases exist in Ref. 35. Any slight deviations from the narrow composition range would require a large energetic cost that cannot be overcome by nanowire growth. In contrast, nanomolding of solid solutions where atoms are randomly mixed in a lattice leads to a composition gradient along the nanowire length dictated by the diffusivity of each constituent atom, such as the Au–Cu nanowire formed by the nanomolding [Fig. 2(b)].³⁵ 

Exploration of nanomolding for topological materials is nascent. Given the low defect density, small nanowire diameters achievable, and single crystalline structure, topological nanowires formed via nanomolding is an exciting and scalable approach to enhance surface states and measure transport properties. Currently known topological materials that have been successfully nanomolded include BiSb, In₂Bi, Ge₂Sb₂Te₅, SnTe, and Sb₂Te₃.³⁵ We provide a list of experimentally confirmed topological materials that we think are suitable for nanomolding in Table I. All materials listed in Table I have T_m < 2000 °C, which suggests nanomolding is experimentally achievable, and are ordered phases. To our knowledge, many of these compounds do not have alternative nanowire fabrication approaches. Of the compounds listed in Table I, Sb₂Te₃,³⁶ Ge₂Sb₂Te₅,³⁷ and SnTe²⁰ have been made into nanowires using CVD, while the other compounds have not been made into nanowires. A comprehensive list of topological materials that have been made into nanostructures can be found in the 2019 review by Liu et al.¹² 

Although nanomolding can be performed on a wide variety of material compositions, certain limitations on material choices do exist. Strongly covalent materials, such as C or Si, have low diffusivity, high melting points, and high dislocation nucleation energies, which prevent nanowire formation. It is currently unknown whether topological borides and phosphides, such as MoP³ or WP₂⁴⁷, can form nanowires by nanomolding due to their high strength and covalent bonding nature.⁴⁸ Similarly, nanomolding is unlikely to work well with 2D layered structures as diffusivity out of a plane is negligible. Finally, topological alloys, such as Bi_x Sb_1−x, will not maintain a consistent composition along the nanowire length due to the different diffusivities of constituent atoms. Whether alloyed topological ordered phases such as Pb_1−xSn_xTe and Pb_1−xSn_xSe will maintain a consistent composition along the length is unknown.

To showcase the high throughput capabilities and advantages of nanomolding to examine topological nanowires, we propose an example fabrication route for a candidate topological material, Ca₂Sb. The Ca₂As crystal family, which includes Ca₂Sb and Sr₂Sb, has been proposed as topological crystalline insulators protected by rotational and mirror symmetry.³⁹ To date, there is no experimental verification of topological states in Ca₂Sb using either single crystal or nanoscale samples. Ca₂Sb is chosen because it is a thermodynamically stable phase, unlike Ca₂As, and has a low melting temperature of 827 °C.⁴⁹ Initially, a polycrystalline Ca₂Sb rod can be fabricated via induction melting in an argon environment.⁵⁰ The rod can then be sliced into 1 mm thick disks and mirror-polished. An AAO mold will then be placed on top of the Ca₂Sb disk, and the entire sample can be pressed together at 200 MPa at 350 °C (0.56 T_m) for one hour. To enhance transport properties of the surface states and to enable TEM characterization, AAO pore sizes below 100 nm are recommended. The nanowire length can be modified by changing the temperature or pressure. Upon fabrication, the AAO mold can be etched away using KOH and the nanomolded sample can be placed in water and sonicated to detach the nanowires from the unmolded region of the disk. The detached nanowires can be used to fabricate devices for magneto-transport measurements to verify the predicted topological states.¹⁴ Figure 1 schematically illustrates the whole process.

For the integration of the nanomolded topological nanowires into functional devices, new mold geometries and materials are necessary to generate desired size, shape, and length. Currently, the mold materials have been restricted to AAO and Si due to ease of fabrication.^27,33 New mold architectures could lead to the fabrication of 2D structures, such as nanoplates or nanoribbons, that can enhance different aspects of the topological properties.¹² Hierarchical architectures have been successfully made for single metal and metallic glass samples through sequential molding steps, which could prove beneficial for optical devices.^31,51,52 Changing the mold material must be done carefully to prevent unintended reactions at high temperatures. For example, using Si molds can lead to silicide formation depending on nanowire composition.³³ While protective barriers or coatings can prevent diffusion, altering interfacial properties can affect nanomolding kinetics and must be accounted for.

In addition to new mold geometries, more complex nanowire architectures can be fabricated through modification of mold material, elemental diffusivities, and molding steps. Heterostructure/hybrid nanowires, such as topological superconductor-semiconductor nanowires, are excellent candidates to probe Majorana bound states (MBS).⁵³ At present, disorder, defects, and oxide formation at the interface between the superconductor and semiconductor greatly affect experimental measurements of MBS.⁵³ Currently, intrinsic topological superconductors are not used to probe MBS due to both a lack of viable candidates and difficulty in fabrication. Using nanomolding, a hybrid device can be made by sequential nanomolding of a semiconductor and a topological superconductor, e.g., InSb and UTe₂, from opposite ends of a freestanding AAO mold. Commercially available freestanding AAO molds can be bought with thicknesses as small as 20 μm. Using the aforementioned materials, UTe₂ would be initially nanomolded at 650 °C and 200 MPa followed by InSb, which has been previously nanomolded at 450 °C and 400 MPa.³⁵ Since UTe₂ has a higher melting temperature, 1180 °C, compared to InSb, 530 °C, interdiffusion should be minimal by sequential nanomolding. In addition, the enthalpy of formation of UTe_2, −317 kJ/mol,⁵⁴ is significantly lower than USb₂, −174 kJ/mol,⁵⁴ or InTe, −71.2 kJ/mol.⁵⁵ The large difference in enthalpy of formation between the compounds should prevent the formation of any new phases at the interface. Core–shell architectures could also be made by a selection of mold materials. For example, an Ag–Au alloy should form a core–shell nanowire when using a Si mold, as Au has a greater affinity to bind with Si than Ag.³³ A similar approach could be considered with alloyed topological ordered phases, such as Pb_1−xSn_xTe, where a radial gradient in Pb or Sn could be observed depending on binding energies to the mold material.

In summary, nanomolding is a promising new addition to the fabrication toolbox for topological materials. As a high throughput fabrication method, we envision nanomolding as a viable approach to screen candidate topological materials via transport measurements before integration into functional devices, thereby saving considerable time. With further development, new geometries, heterostructures, and material compositions can be realized, expanding the applicability to a diverse array of fields and new fundamental physics experiments.

M.T.K. acknowledges support from NSF Grant No. DMR 2103730, and J.J.C. acknowledges support from the Betty & Gordon Moore Foundation under the EPiQS Synthesis Investigator award.