Switchable tribology of ferroelectrics

Switchable tribological properties of ferroelectrics offer an alternative route to visualize and control ferroelectric domains. Here, we observe the switchable friction and wear behavior of ferroelectrics using a nanoscale scanning probe—down domains have lower friction coefficients and show slower wear rates than up domains and can be used as smart masks. This asymmetry is enabled by flexoelectrically coupled polarization in the up and down domains under a sufficiently high contact force. Moreover, we determine that this polarization-sensitive tribological asymmetry is widely applicable across various ferroelectrics with different chemical compositions and crystalline symmetry. Finally, using this switchable tribology and multi-pass patterning with a domain-based dynamic smart mask, we demonstrate three-dimensional nanostructuring exploiting the asymmetric wear rates of up and down domains, which can, furthermore, be scaled up to technologically relevant (mm–cm) size. These findings demonstrate that ferroelectrics are electrically tunable tribological materials at the nanoscale for versatile applications.

Abstract: Artificially induced asymmetric tribological properties of ferroelectrics offer an alternative route to visualize and control ferroelectric domains. Here, we observe the switchable friction and wear behavior of ferroelectrics using a nanoscale scanning probe where down domains having lower friction coefficient than up domains can be used as smart masks as they show slower wear rate than up domains. This asymmetry is enabled by flexoelectrically coupled polarization in the up and down domains under a sufficiently high contact force. Moreover, we determine that this polarization-sensitive tribological asymmetry is universal across ferroelectrics with different chemical composition and crystalline symmetry. Finally, using this switchable tribology and multi-pass patterning with a domain-based dynamic smart mask, we demonstrate three-dimensional nanostructuring exploiting the asymmetric wear rates of up and down domains, which can, furthermore, be scaled up to technologically relevant (mm-cm) size. These findings establish that ferroelectrics are electrically tunable tribological materials at the nanoscale for versatile applications.
Ferroelectrics, in which the switchable electric polarization is coupled with mechanical deformation, have been extensively studied in view of their technological applications as sensors, actuators, energy harvesters, and memory devices (1-4).
Fundamentally, these materials exhibit electromechanically coupled properties including piezoelectricity (1), flexoelectricity (5), and electrostriction (6), whose interplay can enrich critical opportunities in the field of condensed matter physics and functional materials engineering, but is only now beginning to be understood and controlled (7)(8)(9). In addition, oppositely polarized ferroelectric surfaces present different mechanical responses under inhomogeneous deformation as a consequence of the interaction between flexoelectricity and piezoelectricity (10), which could be harnessed for the mechanical reading of ferroelectric polarization (11). As we shall show in this article, increasing this flexoelectric contribution under highly inhomogeneous stress also has emergent consequences for coupled tribological properties-in particular, friction and wear coefficients-which in turn can be exploited for direct visualization of ferroelectric domains and extremely fine physical lithography without the need for masks or chemical reagents.
Precise control of ferroelectric surfaces as well as domain structures is essential for numerous applications such as data storage (3,4) and electro-optic devices (12). However, there are no previous studies on simultaneous or continuous control of both ferroelectric domains and the surface morphology nanostructure. During the nanostructuring of materials, including ferroelectrics, patterns with desired size, shape, and periodicity are transferred to the target substrate, generally via an intermediate bridging process using masking, resist, imprint or local thermochemical interactions (13)(14)(15)(16). In contrast, intrinsic properties of the substrate such as ferroelectric polarization are rarely employed as a marker for patterning, although we note the demonstration of selective deposition of functionalized nanoparticles (17) and chemical reaction rate difference (18) depending on the surface chemistry of ferroelectric domains. Nevertheless, there are no reports in which the ferroelectric polarization is used as a smart mask for nanoscale patterning based on differential and locally switchable mechanical, as opposed to chemical, etch rates.
In this study, we establish that such switchable, polarization-dependent mechanical etching is in fact possible. We demonstrate that the local friction and wear behavior of ferroelectrics is asymmetric and independent of surface chemistry under large strain gradient, and that this inherent tribological asymmetry enables facile and reversible control of friction and wear properties, which can be exploited for nano-lithographic patterning by simply "rubbing" the surface of a voltage-written ferroelectric. To prove our idea, we start from uniaxial ferroelectric LiNbO3 single crystals as a simple and accessible model system, already widely used in electro-optic applications (19). We discover polarization-dependent asymmetric friction and surface wear in these materials by applying a sufficiently high mechanical force using a diamond atomic force microscopy (AFM) probe at the nanoscale or silica particles at the bulk scale. Furthermore, we confirm that this asymmetry does not originate from either electrostatic effects, or inhomogeneous defect distribution, but is linked to the competing vs. synergistic interplay of flexoelectric and ferroelectric polarization in oppositely oriented domains, which moreover leads to an anomalous, positive correlation between the hardness of the materials and its wear rate. Switching the ferroelectric domains by local electric field application should thus allow simultaneous and reversible control of the tribological responses (friction and wear) of the material, which in turn can be used to dynamically manipulate surface morphology nanostructures. We extend our findings to LiNbO3 and PbTiO3 thin films to establish the universality of the observed tribological asymmetry, allowing for more precise polarization-derived friction microscopy and lithography, including single-lattice wear of ferroelectrics with atomic terrace edge features.
Finally, we demonstrate this approach as a top-down, chemical-free and resist/mask-less lithography technique, which can be potentially applied to the fabrication of threedimensional (3D) and monolithic nanostructures when multi-pass switching and milling of the ferroelectric surface is implemented.
The experiments were performed on commercially available periodically poled LiNbO3 (PPLN) single crystals, composed of alternating out-of-plane polarization domains, further described in fig. S1. We observed polarization-dependent tribology of the sample surface using single-crystalline conductive diamond probes (NM-TC, Adama Innovations), selected for their extreme hardness and stiffness, with relatively high contact loading force (5 μN) and scan rate (4.88 Hz, equivalently 146.48 μm/s). The down domains oriented into the sample plane are less heavily etched than the up domains oriented out of the sample plane, resulting in strongly asymmetric milling after multiple scans, as shown schematically in Fig.   1A.
Accompanying this wear asymmetry, even though the pristine surface presents a flat morphology (Fig. 1B), we observed a polarization-dependent friction contrast (Fig. 1C) during the milling scans, with higher friction in the up-oriented domains. After the 50 th milling scan by the diamond probe, the surface clearly shows the height difference between up and down domains (Fig. 1D); however, as demonstrated by subsequent piezoresponse force microscopy (PFM) imaging (Fig. 1E) using the same probe, this asymmetric milling process does not affect the domain polarity, which remains stable throughout the millings.
The 3D surface plot in Fig. 1F also shows a clearly visible height difference after 50 milling scans, as does the line profile across the domains during the last milling scan in Fig. 1G, demonstrating strong height and friction difference between up and down domains. The height and friction differences signals (Fig. 1H) oscillate because of the contact geometry difference between frame-up (scan from below to above) and frame-down (scan from above to below) during the continuous, repeated milling scans, but we note that height (down-up) and friction (up-down) differences are always positive. The height and friction differences are clearly correlated with increasing scan number and show three distinct regimes. In region 1, the height difference slightly increases with relatively stable friction difference. In region 2, it drastically increases with higher friction difference, and the slope of height difference (etch rate) approaches a maximum value with maximum friction difference. In region 3, the height difference finally starts to saturate with constant lower friction difference. The etch depth compared with the pristine background region is approximately 4.56 nm for up domain Crucially, we find that the polarization-dependent asymmetric mechanical wear varies significantly as a function of the loading force (figs. S6-8). As detailed in fig S6, below a threshold loading force (less than 5 μN), no significant etching is observed, whereas when the force is too high (20 μN), surface deterioration and material fracture rather than steady asymmetric etching can dominate the resulting topography (20,21). At the optimum loading force range (5-10 μN), we observed asymmetric etching of domains with some deterioration of the friction contrast and wear rate with continuous milling because of wear debris attachment of the tip, as further discussed in figs. S10 and S11. However, increasing or decreasing the scan rate during milling has insignificant effects on the tribological asymmetry (fig. S12).
Beyond micro/nano-scale wear of ferroelectric single crystals using an AFM probe, we also demonstrate scalability of this process to technologically relevant large-scale patterning by simply polishing the whole crystal using silica nanoparticles that effectively act as millions of mobile AFM tips (Fig. 1I). Fig. 1J shows the digital photograph of the crystal after such polishing and the optical microscope (Fig. 1K) and SEM (Fig. 1L) images exhibit the periodic boundaries of asymmetrically etched surfaces at large scale. As long as the nanoparticles were comparable in size to a typical AFM probe, giving rise to similar strain gradients under applied force, we could clearly see that up domains were preferably etched, resulting in nanoscale trench structures over 9-millimeter square area of the sample as seen in the height and PFM phase (Fig. 1, M and N), which is consistent with wear results observed using diamond probes. We believe that combining a bulk poling process with nanoscale silica bead polishing will enable us to realize bulk scale chemical-free/maskless lithography.
To understand the fundamental microscopic mechanisms behind our observations, we need to consider the possible interplay between friction-the resistance to relative motion between two surfaces-and mechanical wear-the removal of surface atoms after rubbing two surfaces-which can be strongly correlated if the loading force is sufficiently high, so that the probe indents the crystal during scanning. Friction and wear are complex tribological phenomena in which contributions of several possible micro/nanoscopic mechanisms could lead to the observed asymmetry of these responses in ferroelectrics (22). Previous studies have already reported on the asymmetric lateral force microscopy signals of ferroelectric single crystals (23,24), but at a few tens of nN loading force such asymmetry might come from the effects of screening charges or adsorbates on the surface. However, if the friction properties are indeed governed by screening charges (electrons or holes) or adsorbates (especially chemisorbed species), the asymmetry should disappear with continuous milling scans, as any surface species or asymmetric skin layers are gradually removed. This is not the case in our results. Rather we find that the asymmetry persists throughout the full cycle of continuous etching.
Beyond the surface electrochemistry mechanism described above, another possibility is that the asymmetry emerges as a result of the different mechanical properties of up and down domains induced by the flexoelectric field, generated by the non-uniform strain applied via the AFM tip. Although the ferroelectric remanent polarization is itself symmetric, the additional flexoelectrically driven contribution leads to a different effective polarization in the up and down domains. This strain-gradient induced polarization has been shown to produce asymmetric mechanical responses (10,25,26). At the same loading force in up and down domains, we should therefore expect a difference in contact area during the etching scan, as schematically illustrated in Fig. 2A. Because friction strongly depends on the real contact area (27), as does the mechanical wear rate, we consequently expect higher friction and wear in up domains than down domains (Fig. 2, B and C). Alternatively, in the second possible mechanism shown schematically in Fig. 2D, tribological asymmetry can arise electrostatically if the loading force is sufficiently high (around a few micronewtons) to enable screening charges to be scraped off the ferroelectric surface (20,28). The unscreened ferroelectric surface of up vs. down domains has opposite electrostatic potential and field, which would lead to an asymmetric electrostatic force between the tip and sample (29). Further, charge transfer during sliding of the tip across the opposite polarization surface could possibly induce asymmetric friction (30).  S19). Experimentally, we do not have access to contact area measurements. However, if we assume a linear relation between contact area and friction, as predicted by single asperity friction models (34), the ratio of contact areas between up and down domains should be equal to the ratio of their friction, which is an experimental observable. From the simulation, this ratio is found to be independent of the indentation force Moreover, to further investigate the role of surface electrostatics from the other extreme, we tested electrostatic effects on the friction and wear of PPLN when applying an electric field. If the observed asymmetric friction and wear arise from the electrostatic asymmetry of the surface, we would expect high voltage application during milling to significantly change the results. However, when we applied such high voltage, varying from -150 V to 150 V to the tip during etching scans, we observed no notable change in either the magnitude of the friction signal, or the contrast between the up and down domains during milling (Fig. 2, K and L). Furthermore, the resulting topography following 10 scans performed with the same varying applied bias shows no significant height change, as can be seen in Fig. 2M. We do, however, observe ferroelectric switching from up to down domain orientation occurring just as the voltage was varied between -150 V and 150 V, as shown in Fig. 2N. We note that these switched regions are slightly higher in topography than the unswitched up domain (Fig. 2M), further indicating the switchable nature of the wear asymmetry. We therefore exclude the electrostatic effects as a dominant contribution to the observed asymmetric nanotribological response.   Fig. 4E in which the distinct 3D structure can be discerned. We note that the use of a nanoscale probe allows us to create complex structures of nanoscale ferroelectric domains, and therefore, the resulting mechanical lithography shows significant technological promise. Although many previous studies on scanning probe lithography successfully carried out sample structuring, with a height difference obtained via mechanical, thermal or chemical etching (15,16,39), the present work is the first to demonstrate scanning probe nanostructuring using the tribological asymmetry between domains with different polarization orientations.
To summarize, our work reveals the asymmetric friction and wear of ferroelectrics, which opens up an alternative way towards probing and manipulating ferroelectric domains based on the switchable tuning of their tribological properties. We determine that the higher friction and thus faster wear rate in up domains originate from the strain-gradient driven flexoelectric response which either competes with or enhances the ferroelectric polarization in oppositely oriented domains, resulting in higher friction in up domains than down domains. Furthermore, our findings enable us to propose a simple methodology for patterning a desired 3D structure with arbitrary complexity by alternating electrical switching and mechanical milling steps. Finally, we establish the universal nature of tribological asymmetry independently of chemical composition or crystal structure, and demonstrate single-lattice scale wear in epitaxially grown ferroelectric thin films. We envision that this top-down, chemical/resist-free and maskless lithography technique can be scalably applied in the fabrication of ferroelectric nano/microstructures.

Estimation of friction force
To quantitatively compare the simulated asymmetry in the indentation depth to that observed experimentally in the friction, we assumed a linear relation between the friction force and contact area (34, 45,46). Consequently, the ratio between contact areas in up and down domains, should be equal to that of their friction. For a conical indenter, we can write   =   =       +   where   is the friction force,  is the shear strength,   is the contact area,   is the contact radius and  is the indentation depth. The ratio   is given in Table S2 for different values of flexocoupling coefficient. the resulting topography is dominated by etching with material fracture rather than asymmetric etching. Therefore, the loading force should be higher than the force required to initiate the etching but lower than the material fracture regime for asymmetric etching.
Figs. S7 and S8 also depict the effects of increasing and decreasing loading force on friction asymmetry and wear behavior. With a pristine diamond probe, each region was milled four times with a loading force starting from 1 to 10 µN in 10 different regions with the same polarity (Fig. S7A). We observe no significant etching in the regions milled at 1 to 3 µN, but do observe asymmetric etching in regions milled from 4 to 10 µN. Fig. S7B shows the height image obtained in an analogous manner but this time decreasing the loading force from 10 to 1 µN using the same tip, and we observe asymmetric etching between 10 and 7 µN. Fig. S7C shows the PFM phase in the region in Fig. S7B before millings, and it indicates alternating up and down domains. We believe that the origin of this hysteretic behavior is the probe degradation, which is further described in Figs. S10 and S11. and S8D indicate friction signals versus scan numbers with height during specific scans. As can be seen in the height images in Fig. S8C, the asymmetric etching starts during the 2 nd scan at 4 µN. We observe the friction signals jump up from 2 nd scan at 4 µN because of higher resistance to the AFM tip motion during etching. In Fig. S8D, the asymmetric etching starts from the 3 rd scan at 7 µN, and the friction signals also rapidly increase at the 3 rd scan at 7 µN, which implies a strong correlation between friction and asymmetric etching behavior.
Further, no transient flexoelectric switching occurred during the high force application as can be seen in Fig. S9. We simultaneously visualized ferroelectric domains with increasing loading forces from 200 nN to 20 µN, but we observe no flexoelectric switching from up to down domain even with loading forces (e.g., 15 and 20 µN) in material fracture regime.

Degradation of friction and wear
The asymmetric friction and wear rate show degradation with continuous milling scans, as can be seen in Fig. S10. Fig. S10A shows the PFM phase image before milling scans. First, the scan rate is increased from 1.26 to 9.77 Hz in four regions with a loading force of 5 μN, as can be seen in Fig. S12A. The wear depth decreases with increasing scan rate.
However, using the same probe immediately after the experiment in Fig. S12A, with decreasing scan rate from 9.77 to 1.26 Hz at the loading force of 5 μN, we observe drastically reduced wear depth rather than the effect of scan rate on the wear depth. We then increased the loading force from 5 to 8 μN with decreasing order of scan rate from 9.77 to 1. 26  S12A and S12C, respectively. The wear depth again decreases with scan order, not with the scan rate change.

Computational model
We follow the linear continuum model of piezoelectricity augmented with flexoelectricity (44). The electromechanical enthalpy density of a dielectric solid exhibiting piezoelectricity and flexoelectricity considered here, in terms of the strain , the strain gradient Ñ, and the electric field , is given by where  is the fourth-rank elasticity tensor,  is the third-rank piezoelectricity tensor,  is the fourth-rank flexoelectricity tensor,  is the second-rank dielectricity tensor and  is the sixth-rank strain gradient elasticity tensor. The strain gradient elasticity term is required to guarantee the thermodynamic stability of the model in the presence of flexoelectricity (48)(49)(50). Note that following (32), strain , and thus the polarization , are taken relative to the remanent state of the solid,   ,   .
The associated free enthalpy of the system is given by where     = − ,    −      +  ,   −         ,  is the boundary of the domain,   is the set of all edges (corners in 2D) of the boundary, and n is the unitary exterior normal vector.
The superscripts L and R respectively refer to the first and second surfaces sharing the edge, and where the strain, strain gradient and electric field in axisymmetric notation (, , ) are defined element-wise as (52,53)   =    , In addition, the following conditions ensure a well-posed saddle point problem: Finally, the weak form of the problem is given by (S18)

Contact model
The Signorini-Hertz-Moreau model (54,55) for a pair of points in contact (;   ) as where n is the normal vector to the contact boundary Γ  and   is the gap function described as We verify the model against the classical conical contact model in (56), for the case of an elastic solid with vanishing piezoelectricity , flexoelectricity , dielectricity , and strain gradient elasticity  (Eq. (S1)). We perform simulations for different vertical positions of the tip and compute the magnitude of the contact force and the contact radius. The relation between the indentation depth  and the contact radius   is given by where  = 42.5° corresponds to the nominal value provided by the manufacturer. The geometrical parameters of the simulation are shown in Fig. S14. The relation between the applied force  and the contact radius is given by where  * =    , with  = 164 GPa and  = 0.3 in this simulation. We have considered a rectangular elastic solid of length  = 100 nm and height  = 50 nm in Fig. S14. We find perfect agreement between the theoretical model and the computational one as shown in Fig. S15.

I-V curve measurements
To select a probe with negligible conductivity for the mechanism study of asymmetric tribology, we performed I-V curve measurements on a highly ordered pyrolytic graphite sample using six different types of probes: a Pt/Ir-coated Si probe (EFM, NanoWorld), diamond coated Si probes  Fig. S20C shows that D300 has the most negligible conductivity. D300 shows this insulating characteristic because the single crystalline diamond is attached to the cantilever with non-conductive glue. The probe selection for the asymmetric etching of PPLN is summarized with more detail in Table. S1. We successfully demonstrated asymmetric etching with five diamond probes, but not with the Pt/Ir-coated Si probe.

Asymmetric friction and wear in stoichiometric LiNbO3
A third possible mechanism is that the asymmetry is defect mediated, at the origin of the asymmetric tribology response. Asymmetric friction can originate from the defect concentration difference between up and down domains as in p-n junctions, which show varying friction because of charge depletion and accumulation (58). The congruent PPLN used in this study is known to have relatively high densities of defects (59). To evaluate their possible contribution, we and S21H. Therefore, we conclude that the presence of defects is not responsible for the observed asymmetry.

Tomographical studies of LiNbO3 nano pillars
We note that up domains are visible in the core of the pillars after prolonged etching of around 60 milling scans (see Supplementary Fig. 23E). This feature observed in LiNbO3 nanodomain structures is a product of the electrostatic boundary conditions at the tip of the growing domain during initial switching, resulting in incomplete polarization reversal through the single crystal (60)(61)(62). This core domain places a limit on the pillar height which can be achieved by nanodomain patterning. As seen in Fig. 3E, while the pillars are still fully capped by a down domain (first 30 millings), their height increases with milling in a linear fashion, similar to what we observed for the wide periodic domains fully penetrating the PPLN single crystal. However, as this cap is gradually worn through, and the up polarized core is revealed, the wear rate of the pillar increases, and becomes comparable to that of the up-oriented background state in Supplementary Fig. 23E.
Ferroelectric polarization-derived nanostructuring of LiNbO3 using wear asymmetry We found that our polarization-determined structuring could be demonstrated in reduced dimensions such as 100 nm of LiNbO3 thin film (NanoLN). To allow easily controllable domain patterning, we used a thinner LiNbO3 fabricated by the ion slicing method. The pristine domain configuration is upward. Fig. S24 shows that facile fabrication without any chemicals or photomask is realized after the artificial decoration of the thin film with the text "FERRO" with down domains, and "LITHO" with up domains before etching. We used a Pt-coated Si probe (HQ:DPER-XSC11, MikroMasch) to switch the domain, and then changed to single-crystalline diamond probe (NM-TC, Adama Innovations, Lot number: 009-013) to prevent tip contamination.
Multiple mechanical milling scans using a diamond probe create a height difference between up and down domains. As shown in Fig. S24D, the friction in the up domain is still higher than down domain during the milling scan at the loading force of 12.5 μN, with a friction ratio close to the simulation values in Fig. 2G. Fig. 3F-I shows the nanostructures shown in Fig. S24 with a pristine background region, which clearly indicates the height difference between etched up and down domains and pristine surface. Fig. S27 shows the 3D fabrication procedure for ferroelectric LiNbO3 by repeated switching and milling. The loading force is gradually increased from 5 to 25 μN to maintain the wear efficiency at a scan speed of 4.88 Hz. Fig. S28 shows the evolution of the topography in the 3D nanostructuring in Fig. S27.            The end of the probe has a dull shape covered by debris from the sharp cone shape. The debris coverage on the diamond probe is correlated with the degradation of the friction and etch depth during the continuous milling.          The friction of switched domains is lower than that up domains, and the resulting topography is also higher in the switched domains. All scans are measured at 20°C and 20% relative humidity.  Fig. S23E shows the existence of up domain at the core of the pillar, maybe because of the insufficient bias to switch the crystal, and it can be correlated with the saturation of the pillar growth. The z-scale of the 3D image is identical to the 2D height image.
All scans are measured at 20°C and 20% relative humidity.      V are based on experimental values in (25).