Room temperature molding of amorphous dielectrics via van der Waals anisotropy at the nanoscale

Abstract

Mechanical instabilities produce periodic out-of-plane deformations, but applications remain limited by the need for elastic substrates and weak controllability. Here, we induce coherent, instability-driven buckling in both van der Waals (vdW) layers and underlying amorphous silica at room temperature, achieving precise spatial control and deterministic orientation. Electron-beam builds crystal-axis-dependent stress in α-MoO₃, while simultaneously facilitating viscous flow in silica, producing sinusoidal wrinkles at subwavelength whose dimension are tunable by α-MoO₃ thickness and electron dose. These wrinkles diffract light as on-chip optical gratings. We show coherent buckling across vdW heterostructures and peel off α-MoO₃ post-buckling, leaving imprinted silica. Similar crystal-aligned wrinkles appear on amorphous Al₂O₃ and SiN_x. By removing reliance on elastic substrates, this work extends the scope of instability-driven, lithography-free subwavelength patterning to CMOS-relevant dielectrics.

The authors show that crystal anisotropy can guide nanoscale wrinkles on rigid chip substrates at room temperature, turning hard dielectrics into tunable, aligned patterns that diffract light and could support future on-chip photonic devices.

Introduction

Thin films subjected to compressive stress often develop surface undulations (wrinkles) via buckling due to mechanical instabilities, phenomena exploited in stretchable electronics^1–3, photonics^4,5, microfabrication^6,7, and fundamental studies^8,9. Van der Waals (vdW) layered materials are excellent platforms for mechanical instabilities due to their unique combination of high in-plane stiffness and ultralow out-of-plane stiffness^10–13. In practice, however, periodic wrinkles are usually achieved on compliant elastomers^7,14–16, whereas thin films on rigid substrates, typical of real-world devices, tend to delaminate or form irregular blisters and cracks, limiting device applications^17–19. Moreover, because compressive stresses are typically introduced globally, by physically compressing or stretching the underlying elastic substrate, the precise spatial control of buckling required for on-chip applications remains challenging.

The vdW layered oxide α-MoO₃ has recently drawn considerable attention due to its intriguing physical properties stemming primarily from its strong in-plane anisotropy^20–24. This anisotropy arises from its orthorhombic crystal structure, characterized by distinct bond angles and lengths along the [100] and [001] crystallographic directions. Notably, α-MoO₃ exhibits opposite signs of permittivity along its in-plane axes, giving rise to hyperbolic phonon polaritons that enable confined, directional light-matter interactions^25–27. Beyond these optical characteristics, α-MoO₃ possesses anisotropic in-plane thermal expansion coefficients with opposite signs along in-plane axes^23,28, as well as a pronounced anisotropy in Young’s modulus^20,22. Collectively, these properties make α-MoO₃ an appealing platform for studying how atomic-scale crystallographic anisotropy translates into physical responses across different length scales.

Here, we present mechanical instability-driven buckling in α-MoO₃ thin film on rigid, amorphous SiO₂ substrate at room temperature. Under electron-beam irradiation, α-MoO₃ and SiO₂ buckle in couple, producing localized array of sinusoidal wrinkles at the subwavelength scale with an orientation precisely aligned with the a-axis of α-MoO₃ crystal. Electron-beam locally induces viscous flow in SiO₂ and builds anisotropic compressive stress in α-MoO₃; consequently, the α-MoO₃ film molds the underlying SiO₂. The resulting wrinkle period and amplitude can be controlled, with the period increasing with α-MoO₃ thickness, while the amplitude scales with electron dose. We experimentally verify that these wrinkles effectively diffract light, functioning as on-chip gratings. Beyond SiO₂/α-MoO₃, buckling also occurs with additional vdW layers and α-MoO₃ can be peeled off after buckling, leaving the wrinkles imprinted in SiO₂. Moreover, similar crystal-aligned wrinkles appear on other amorphous dielectrics, including Al₂O₃ and SiN_x, suggesting broader applicability across amorphous dielectrics. This single-step, on-chip technique offers a scalable and precise route to engineering subwavelength structures in CMOS-relevant dielectrics and vdW heterostructures for advanced photonic and optoelectronic technologies.

Results

Coupled buckling under electron-beam irradiation

Thin α-MoO₃ flakes were mechanically exfoliated onto Si/SiO₂ substrates. Due to the orthorhombic crystal structure, flakes typically present rectangular morphologies with edges along the principal in-plane crystallographic axes (Supplementary Fig. 1)²¹. High-current electron-beam exposures (5 kV, 13 nA, dwell 300 ms per pixel, 200 nm scan spacing), far exceeding typical scanning electron microscopy (SEM) imaging conditions, are applied to selected regions (Fig. 1a–c). Within the exposed areas, outlined by yellow dashed lines in Fig. 1b, c, parallel wrinkles emerge in α-MoO₃. Atomic force microscope (AFM) measurements further confirm the morphological changes. The AFM map and the corresponding height profile (Fig. 1d, e) show that the α-MoO₃ thin film deforms locally into sinusoidal wrinkles with a ~ 30 nm amplitude and a ~500 nm period. We note that all crests and troughs in the deformed region are equally irradiated, distinguishing this process from conventional electron-beam etching²⁹. Moreover, the deformation is permanent after the beam is off and stable during subsequent ex-situ tests.

Fig. 1. Coupled buckling of α-MoO₃ on a Si/SiO₂ substrate.

a Schematics of the wrinkle formation under electron-beam irradiation. SEM secondary electron (SE) images of the α-MoO₃ crystal exfoliated on a Si/SiO₂ substrate before (b) and after (c) high-current electron-beam exposure. Yellow dashed boundaries mark the irradiated regions. d AFM map of the resulting wrinkles. e Height profile along the red arrow in (d), indicating an average amplitude of ~30 nm and a period of ~500 nm. f Cross-sectional HAADF-STEM image, showing coherent sinusoidal deformation of both α-MoO₃ and SiO₂. Carbon and Pt on top of α-MoO₃ were deposited during the focused ion beam process. The inset shows an EDS map of the region indicated by the dashed box, with Mo in blue and Si in yellow. g Magnified HAADF-STEM image of the dashed box in (f), highlighting an interfacial void between α-MoO₃ and SiO₂. Source data of (e) are provided as a Source Data file.

To elucidate the wrinkle morphology in detail, we performed high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) imaging on a cross-sectional sample. Figure 1f reveals the periodic sinusoidal deformation not only in the α-MoO₃ film but also in the underlying SiO₂ layer, demonstrating a coupled deformation. Energy-dispersive X-ray spectroscopy (EDS) mapping corroborates a well-defined coherent interface between the two layers. This observation is particularly noteworthy because amorphous SiO₂ (a-SiO₂) is typically regarded as brittle, requiring high temperature close to its glass-transition temperature (1373 K) to deform^30,31. In our case, however, the high-current electron-beam enables local Si-O bond rearrangement (bond breaking/rotating/reformation) in a-SiO₂ that produces viscous, plastic flow in a-SiO₂^32–34. This bond rearrangement is observed in amorphous oxides and ceramics where viscous flow proceeds through the motion of point defects facilitated by electron-beam irradiation^35–37. When α-MoO₃ deforms significantly, interfacial voids appear (Fig. 1g), indicating local delamination once the film stress exceeds the interfacial cohesive force, confirmed by EDS mapping (Supplementary Fig. 2) to be empty of any material. This suggests the α-MoO₃ film is the stress source, as further confirmed by Fig. 2. Control experiments (Supplementary Fig. 3) further support this conclusion; the blank Si/SiO₂ chip without α-MoO₃ under identical exposure shows no discernible topographical change, excluding electron-beam-induced deformation of SiO₂ alone. α-MoO₃ on Si without SiO₂ shows no comparable deformation, because there is no ductile underlayer (like a-SiO₂) to accommodate stress generated in α-MoO₃. Also, graphite and hexagonal boron nitride (hBN) flakes on Si/ SiO₂ show no changes in surface topography under the identical electron-beam irradiation (Supplementary Fig. 4). Collectively, stress in the α-MoO₃ film molds the underlying electron-beam softened a-SiO₂, driving the coupled buckling.

Fig. 2. Deterministic wrinkle orientation set by α-MoO₃ crystal structure.

a SEM SE image of the wrinkles formed in a single α-MoO₃ flake with electron-beam scans at 0°, 45°and 90° relative to the a-axis. The red arrows show the fast-scan direction. The discontinuity of wrinkles in the second irradiated region from the top is likely due to the defect in α-MoO₃ or electron-beam drift. b AFM map of localized deformations produced by stationary beam exposure in a 4$\times$4 array with 1$\mathrm{\mu }\mathrm{m}$ spacing. c Enlarged view of the dashed box in (b). The inset shows the height profile along the dashed line. d Schematics of crystal structure of the α-MoO₃ and compressive stress along the c-axis responsible for buckling. e AFM topography image and f KPFM potential mapping of the patterned wrinkles. g Corresponding height profile (top) and potential profile (bottom) extracted from the dashed arrows in (e) and (f), respectively. The in-plane α-MoO₃ crystal axes (a- and c-axes) are indicated by white arrows in (a), (b) and (e). Source data of (c, g) are provided as a Source Data file.

Buckling aligned with α-MoO₃ crystal axes

To identify the origin and direction of the driving stress developed in α-MoO₃, we first examined how buckling and the resulting wrinkles depend on the electron-beam scan direction. Figure 2a demonstrates wrinkles formed in a single α-MoO₃ crystal when the fast-scan direction of the electron-beam is rotated. In the first two regions, the fast-scan direction is set parallel (0°) to the a-axis ([100]) and is then rotated by 45° and by 90° relative to the a-axis. In all cases, the wrinkle ridges remain parallel to the a-axis (i.e., the wrinkle wavevectors point along the c-axis [001]), independent of scan direction. We then held the electron-beam stationary (dwell 300 ms per pixel) at discrete points arranged in a 4×4 array with 1 $\mathrm{\mu }\mathrm{m}$ spacing (Fig. 2b). Each exposure produces a localized deformation with smaller amplitude and width than under continuous scanning (Supplementary Fig. 5). Even with a circular, isotropic beam, the response remains highly anisotropic and aligned with the a-axis (Fig. 2c), and the affected area at each spot exceeds the nominal beam size. As the deformation consistently follows the α-MoO₃ crystallographic axes, we can conclude that the electron-beam generates anisotropic, lattice-directed stress in α-MoO₃, which is transferred to electron-beam-softened a-SiO₂.

Given that the wrinkle geometry indicates that the electron-beam locally generates compressive residual stress along the c-axis in α-MoO₃ (Fig. 2d), we propose two potential stress sources and a two-stage wrinkle evolution model (Supplementary Notes I-II). First, anisotropic thermoelasticity: α-MoO₃ has anisotropic in-plane thermal expansion, with a positive coefficient along the a-axis and a negative one along the c-axis^23,28. The mismatch between the negative thermal expansion in α-MoO₃ and the positive thermal expansion in the SiO₂ substrate induces the compressive stress along the c-axis under the high-current electron-beam exposure. Based on the estimated temperature increase under irradiation, the thermal elastic stress can be calculated to be ~0.10 GPa, corresponding to a compressive strain of 0.11% (Supplementary Note I-(1)). We note that laser heating does not induce this deformation (Supplementary Fig. 6), indicating that heating alone is insufficient without the concurrent electron-beam-induced viscous flow in SiO₂. Second, defect-induced compressive strain: electron-beam irradiation is known to generate oxygen vacancies in α-MoO₃^38–40, consistent with our experimental Kelvin probe force microscopy (KPFM) map (Fig. 2e–g), X-ray photoelectron spectroscopy (XPS) (Supplementary Fig. 7), and Raman spectroscopy (Supplementary Fig. 8). Figure 2f shows that the entire buckled region exhibits a ~ 180 mV increase in contact potential difference (CPD) relative to the adjacent unirradiated flat region. This corresponds to a 180 meV decrease in work function, consistent with reduction due to oxygen vacancy formation^41,42. In α-MoO₃, because Mo-O octahedra share edges and corners differently along the a- and c-axes, vacancy formation relaxes anisotropically, producing greater contraction along the c-axis when oxygens are removed^43,44. When constrained in-plane, this anisotropic shrinkage manifests as an effective compressive stress along the c-axis. The Raman peak shifts observed under irradiation correspond to a compressive residual strain of 1.06% along the c-axis (Supplementary Fig. 9, Note I-(2))⁴⁵. Since the estimated thermal elastic strain is ~10% of the residual strain, we suggest that oxygen defect-induced compressive strain is the dominant mechanism driving wrinkle formation.

Control of wrinkle dimensions

Next, we investigate how wrinkle dimensions – period and amplitude – depend on key parameters such as α-MoO₃ thickness and electron-beam conditions. Figure 3a, b compares three α-MoO₃ flakes of 11, 22, and 37 nm thicknesses irradiated under identical conditions in one session to minimize beam-related uncertainties. The wrinkle period increases with thickness, as indicated by the yellow arrows that mark the fourth crest in each profile. This behavior reflects the thickness scaling of the wrinkle period predicted by the following equation derived from the compressive-residual-stress driven instability: ${\lambda }_{\mathrm{c}}=\pi h\sqrt{\frac{\overline{E_{\mathrm{c}}}}{3∣{\sigma }_{\mathrm{c}}∣}}$, where ${\lambda }_{\mathrm{c}}$ is the critical period, $h$ is the flake thickness, $\overline{E_{\mathrm{c}}}$ is the effective Young’s modulus of α-MoO₃ along c-axis, and ${\sigma }_{\mathrm{c}}$ is the critical compressive residual stress (Supplementary Note II)^46,47. To quantify this relationship, Fig. 3c summarizes results over a broader thickness range and shows a near-linear correlation between period and thickness as predicted. From the linear fit, ${\sigma }_{\mathrm{c}}$ can be extracted from the slope, yielding an estimate critical strain of 1.43%, comparable to the values estimated from Raman (Supplementary Notes I-(2)), further validating the mechanical model. Under our electron-beam conditions, periods from ~245 nm to ~540 nm are accessible simply by adjusting film thickness, demonstrating fine control of the period. Notably, flakes thicker than 60 nm do not exhibit similar wrinkles under the exposure (Supplementary Fig. 10), presumably because their increased bending rigidity suppresses wrinkling and the substrate remains stiff due to reduced electron-beam interaction. Conversely, flakes thinner than 15 nm often exhibit less regular wrinkles, likely due to elevated sensitivity to minor thickness variations or non-uniform beam effect. In addition to the wrinkle period, thickness affects the wrinkle amplitude (Supplementary Figs. 11 and 12). Further details are discussed in the Supplementary Note III-(1).

Fig. 3. Modulation of wrinkle dimensions.

a AFM maps of wrinkles formed in the α-MoO₃ flakes with different thicknesses. b Height profiles with periods of 356, 457, and 654 nm for flakes 11, 22, and 37 nm thick, respectively. The scan spacing is 100 nm. c Wrinkle period as a function of flake thickness. The dashed line is a linear fit. The blue-shaded region denotes the 95% confidence interval (CI) of the linear fit. Periods were measured on 18 wrinkles prepared on 12 flakes with distinguished thicknesses. d–i Modulation of wrinkle amplitude. AFM maps of wrinkles formed under varying d electron-beam dwell time and g current on a single flake (~ 24 nm thick). (i–iv) Dwell time per pixel increases from 50 to 300 ms, (iv–vi) Beam current decreases from 13 to 3.2 nA. Height profiles corresponding to (i–iv) and (iv–vi) in (d, g). In e, the amplitudes are 5.7, 25.4, 36.3, and 39.3 nm for dwell times of 50, 100, 200, and 300 ms, respectively. In h, the amplitudes are 4.2, 27.2, and 39.3 nm for 3.2, 6.4, and 13 nA, respectively. Wrinkle amplitude as a function of f dwell time and i current, showing sublinear behaviors. The wrinkle amplitudes in (f, i) are measured from flakes with similar thicknesses of ~ 30 nm. Scale bars in (a, d, g): 1 $\mathrm{\mu }\mathrm{m}$. Profiles in (b, e, h) are aligned at the first crest, indicated by the dashed lines. The fourth crests in (b, e, h) are highlighted by yellow arrows for comparison. Data points in (c, f, i) are presented as mean values. The error bars in (c, f, i) denote one standard deviation (1 SD). Source data of (b, c, e, f, h, i) are provided as a Source Data file.

After establishing the wrinkle period and thickness relationship, we examine the role of electron-beam conditions in tuning the wrinkle dimensions at fixed thickness. Here, we primarily demonstrate modulation of the winkle amplitudes with electron-beam dwell time and current (Fig. 3d–i). By systematically varying the dwell time, we observe that the wrinkle amplitude grows with prolonged irradiation, from a few nanometers at 50 ms to nearly 50 nm at 500 ms (Fig. 3d–f), while the periods exhibit a systematic but relatively small increase (Supplementary Fig. 13). Similarly, increasing beam current increases the amplitudes from a few nanometers at 3.2 nA to approximately 40 nm at 13 nA (Fig. 3g–i), with a small increase in the periods (Supplementary Fig. 14). The behavior of the wrinkle amplitude is consistent with the classical buckling theory (Supplementary Note II-(2))^7,15, where the amplitudes increase with higher applied compressive stress and lower critical strain for a fixed film thickness. Longer irradiation or higher beam current induces greater compressive stress in the film, primarily through increased defect generation, and lowers critical strain through substrate softening. More details about the wrinkle dimension control mechanisms and the quantitative approximation are provided in Supplementary Note II-(2) and (3). Parameters such as scan spacing (Supplementary Fig. 15) and accelerating voltage (Supplementary Figs. 17–19) can also modulate wrinkle dimensions, primarily by changing the effective dose density and the electron-beam interaction volume, respectively (Supplementary Notes II-(2) and (4)). Overall, we show that the wrinkle period can be more efficiently modulated by α-MoO₃ thickness, while the amplitude can be primarily modulated by electron-beam conditions. This provides tunability for customizable nanoscale patterns in advanced photonic and optoelectronic applications.

Diffraction from wrinkles as optical gratings

Having established the mechanism and tunability of the wrinkles, we experimentally verify their function as diffraction gratings using the experimental setup in Fig. 4a⁴⁸. According to the light diffraction equation: $m\lambda =d\left(\sin \alpha +\sin \beta \right)$, where $m$ denotes the diffraction order, $\lambda$ is the wavelength of the incident laser, $d$ is the grating period, $\alpha$ and $\beta$ represent the angles of incidence and diffraction relative to the normal of the sample plane, respectively. For a representative set of α-MoO₃ wrinkles with a period of $d\approx 600\mathrm{nm}$ and an incident laser wavelength $\lambda =660\mathrm{nm}$, an incident angle $\alpha =60^{\circ }$ would be associated with a diffraction angle $\beta \approx 15^{\circ }$ for the $m=-1$ diffraction order. This allows us to detect the −1^st order diffracted light using a feasible experimental configuration (Supplementary Figs. 20 and 21).

Fig. 4. Diffraction measurements of the wrinkles on α-MoO₃ flakes for optical gratings.

a Experimental setup used for the diffraction measurements. LP: linear polarizer; HWP: half wave plate. b Blue dots: measured signal intensity as a function of the incident laser polarization angle, Δθ. Red curve: fitting using the equation described in the main text. Data points are presented as mean values. The error bars denote 1 SD. c Histogram of the light intensity detected by the CMOS camera at two different rotational angles Δθ = 20⁰ (blue, top) and Δθ = 70° (orange, bottom). The corresponding data points in (b) are marked by arrows. Source data of (b, c) are provided as a Source Data file.

To measure the light diffracted by the buckling, a collimated laser beam was directed onto wrinkles in the α-MoO₃ flake. The diffracted light, along with scattered light and other backgrounds, was detected by a CMOS camera. To isolate the diffracted component, two key considerations were incorporated into the measurement procedure. First, the size of the collimated laser beam was reduced to approximately 100 µm using a pinhole placed in the excitation path. This effectively focuses the laser illumination onto the wrinkles (~ 20 ×20 µm²) (Supplementary Fig. 20) without compromising its collimation. Second, a linear polarizer was introduced into the excitation path. While the diffracted light is highly dependent on the incident light’s polarization, the scattered and other background signals are insensitive to this factor, as confirmed by our control measurements (Supplementary Fig. 22). Measurement as a function of polarization thus allows us to estimate the contributions of diffracted light to the overall signal.

Figure 4c shows representative photon count histograms recorded by the CMOS camera for polarization angles of $\mathrm{\Delta }\theta =20^{\circ }$ and $70^{\circ }$. The blue data points in Fig. 4b represent integrated intensities at different $\mathrm{\Delta }\theta$, where a clear polarization dependence is observed. Fitting the data to the equation: $I=I_0+I_{\mathrm{ac}}*\cos \left(\frac{\mathrm{\Delta }\theta +{\theta }_0}{T}\right)$, where $I_0$ represents the background intensity that does not change with the polarization angle, $I_{\mathrm{ac}}$ is the amplitude of the diffracted light, Δθ is the rotational angle of the half-wave plate (HWP), $T$ is the rotation period, and ${\theta }_0$ is the offset angle, we obtain a fitted periodicity of T = 88.3°. This value is in good agreement with the expected rotation period of 90° (Supplementary Note IV). These results confirm that the polarization-dependent signal originates from diffraction by the wrinkles, thereby establishing that the wrinkles in α-MoO₃ function as optical gratings.

Integration and broader applicability

Finally, we broaden the scope of our approach by leveraging the advantages of vdW materials. Their dangling-bond-free interfaces enable vdW heterostructure assembly with good shear transfer and peeling off without damage. Beyond the Si/SiO₂/α-MoO₃ stack, we integrate α-MoO₃ with thin graphite and hexagonal boron nitride (hBN) placed either beneath or above the α-MoO₃ to form vdW heterostructures (Fig. 5a and Supplementary Fig. 23). Figure 5b shows optical and SEM images after local electron-beam irradiation. Wrinkles form coherently across the heterostructures and remain aligned with the α-MoO₃ crystal axes. The crystal orientation of graphite and hBN is random, indicating that they do not affect the wrinkle direction. The wrinkle period scales with the total thickness of the vdW heterostructures, rather than α-MoO₃ thickness alone, and approximately follows the thickness dependence in Fig. 3c. These results show that our method induces periodic out-of-plane deformations with deterministic orientation across diverse vdW heterostructures.

Fig. 5. Integration and removal of the vdW layers.

a Schematic of coherent buckling of α-MoO₃ (blue) and additional vdW layers (hBN or graphite (Gr)) (purple) on a SiO₂ substrate (yellow). vdW layers can be transferred onto α-MoO₃ (left) or covered by α-MoO₃ (right). b Optical microscopy images of SiO₂/α-MoO₃/hBN (top left), SiO₂/α-MoO₃/graphite (bottom left), SiO₂/hBN/α-MoO₃ (top right) and SiO₂/graphite/α-MoO₃ (bottom right) wrinkles. Dashed lines mark the boundaries of hBN or graphite. Insets show corresponding SEM SE images of the vdW heterostructure wrinkles. The scale bars in SEM images are 1 µm. c Schematic of peeling off the α-MoO₃ mold from the SiO₂ substrate. Wrinkles remain in SiO₂ after α-MoO₃ removal. d AFM topography images of SiO₂/α-MoO₃ wrinkles before α-MoO₃ removal (top left) and bare SiO₂ after α-MoO₃ removal (top right). The bottom plots show the height profiles before and after removal extracted from the AFM topography images. Source data of (d) are provided as a Source Data file.

Because α-MoO₃ is bonded to the SiO₂ substrate via vdW forces, we can physically remove α-MoO₃ after irradiation (Fig. 5c and Supplementary Fig. 24). We peel it off using a polymer support; after coating the chip and immersing it in water, capillary action drives water into the SiO₂/α-MoO₃ interface and separates the layers. As shown in Fig. 5d, the AFM map measured directly on SiO₂ shows the same height profile as before removal of α-MoO₃, confirming coherent buckling. Pits in the AFM map correspond to interfacial voids formed by delamination. The α-MoO₃ layer therefore serves as a removable mold that patterns SiO₂ at room temperature without resists and etchants.

To test the generality of this approach, we repeat the process on amorphous Al₂O₃ and SiN_x, which are reported to undergo bond switching under irradiation similar to a-SiO₂^35–37. α-MoO₃ thin films exfoliated on these dielectrics show crystal-aligned wrinkles after electron-beam irradiation. (Supplementary Figs. 25–27) The period and amplitude differ from those on a-SiO₂ because of the distinct mechanical properties of dielectrics under electron-beam irradiation, and the wrinkles are less homogeneous, likely reflecting high roughness and potential impurities of the as-prepared Al₂O₃ and SiN_x substrates (Supplementary Fig. 28). Therefore, our approach is not specific to silica and extends to common CMOS-relevant dielectrics.

Discussion

This work provides a complementary route to other periodic surface patterning techniques with comparable scales. Recent studies that create wrinkles by pre-loading¹⁶, laser^49,50, or thermal scanning probe⁵¹ generally require compliant, soft materials, whereas our method directly shapes solid-state vdW layers and rigid dielectric substrates without the need for mask. Unlike conventional lithography^29,52, ion beam⁵³, and laser irradiation^54,55-induced surface nanostructures, our patterned topography arises from crystal orientation-dependent compressive stress and mechanical instability. This distinction is important because it enables highly aligned, dimension-tunable structures with high spatial selectivity. The resulting sinusoidal-like profiles approximate optical Fourier surfaces and thus offer additional flexibility for light manipulation, while similar wavy geometries can be produced by greyscale lithography, often at the cost of spatial resolution and depth control^50,51. Given that periodic photonic structures with similar dimensions have been used as Fourier surfaces^50,51 and optical gratings⁵⁶, the wrinkles demonstrated here have the potential for broader practical photonic applications. We note that the wrinkle fabrication speed is approximately 7.5 s/µm², which can be further reduced by increasing the beam current and voltage, or by decreasing the dwell time and scan spacing.

In summary, we introduce a single-step method that couples the crystallographic anisotropy of α-MoO₃ with electron-beam-softened amorphous silica to produce localized, crystal-aligned wrinkles on conventionally rigid substrates at room temperature. Wrinkle geometry is tunable, with the period scaling with α-MoO₃ thickness and the amplitude increasing with electron dose. The resulting wrinkles function as on-chip diffraction elements, with wrinkle periods spanning the subwavelength to visible light range. Owing to vdW interfaces, we show that coherent buckling extends to vdW heterostructures and that α-MoO₃ can be peeled off after buckling as a removable mold. Comparable orientation-locked patterns are observed in amorphous Al₂O₃ and SiN_x, underscoring broader applicability among dielectrics. This approach provides a maskless, lithography-free pathway to deterministic subwavelength patterning on CMOS-relevant dielectrics, bridging crystallographic anisotropy in a vdW film to programmable subwavelength scale structures for photonics and optoelectronic integration.

Methods

Materials and sample preparation

The α-MoO₃ flakes were exfoliated from the bulk crystals (2D Semiconductors) and deposited onto Si/SiO₂ (Nova Electronic Materials), Si/SiN_x, or Si/Al₂O₃ wafers. About 200 nm thick SiN_x or Al₂O₃ was deposited on the Si wafer (Nova Electronic Materials) by PECVD or Sputterer, respectively. Al₂O₃ thin films were deposited using an AJA ATC Orion sputtering system equipped with a high-purity (99.99%) Al₂O₃ ceramic target. Deposition was carried out under an argon flow of 30 sccm with an applied RF power of 200 W for 100 min. SiN_x thin films were prepared using a Plasma-Therm Versaline system. A gas mixture of silane (SiH₄, 200 sccm) and ammonia (NH₃, 7 sccm), with nitrogen (N₂, 550 sccm) as the carrier gas, was introduced into the chamber. Plasma was sustained by an RF power of 65 W, with a deposition time of 13 min. The hBN (NIMS, Japan) and graphite thin flakes (NGS) were exfoliated from their bulk crystals and deposited onto Si/SiO₂ wafers. The vdW heterostructures were prepared by transferring the top layer onto the bottom layer via polypropylene (PPC) polymer-assisted dry transfer. The α-MoO₃ flakes with wrinkles can be removed from Si/SiO₂ wafers with the assistance of cellulose acetate butyrate (CAB) polymer sheet in water.

Characterizations

SEM images were taken by the Apreo SEM (Thermo Scientific). High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and energy-dispersive X-ray spectroscopy (EDS) mapping were conducted using a FEI Titan Themis G3 scanning/transmission electron microscope equipped with double aberration correctors at 300 kV accelerating voltage with a convergence angle of 25 mrad. The TEM sample was prepared using FEI Helios 660 focused ion beam (FIB). During the thinning process, the accelerating voltage of the Ga ion beam gradually decreased from 30 kV to 2 kV to mitigate beam-induced amorphization of the specimen surface. AFM was performed by Park AFM NX20 microscope using the tip AR10-NCHR (NANOSENSORS). KPFM measurements were conducted by SmartSPM (AIST, Horiba) with 3 V and 1042 Hz bias, using the tip ACCESS-SNC-GG (AppNano). The Si layer in the Si/SiO₂ layer was grounded with indium metal. Raman spectra were collected by a Reinshaw inVia confocal Raman microscope with 532 nm laser excitation. XPS spectra were collected by Nexsa G2 X-ray Photoelectron Spectrometer (Thermo Scientific). The X-ray spot size was set as 10 µm, smaller than the size of the measured grating (15 ×15 µm²).

Wrinkle formation

The nano-wrinkles were fabricated using electron-beam irradiation in the SEM. A typical electron-beam condition was set to 5 kV accelerating voltage, 13 nA current, and a dwell time of 300 ms per 200 nm size pixel (scan spacing). The magnification was kept at 5000 times. The electron-beam current and accelerating voltage were controlled by the SEM software. The dwell time, scan spacing, and the spatial selection were controlled by the Odemis software for the cathodoluminescence system (Delmic). The wrinkles formed under other conditions were noted in the main text and supplementary information.

Light diffraction experiments

Laser beams from a 660 nm continuous wave laser were passed through a 100 μm pinhole and directed onto the wrinkles on the α-MoO₃ thin films. The laser power onto the wrinkle structure on the sample surface was estimated to be 100 nW. A linear polarizer and a half-wave plate were used to tune the polarization angle of the incident beam. Signals from the sample surfaces were collected by a CMOS camera using the layout in Fig. 4a. Histograms of photon counts from the camera were integrated and used to construct the polarization angle-dependent results. The photon counts were then transferred to diffracted light power with careful calibration results.

Author contributions

H.Y.L. and Y.L. conceived the idea; Y.L., A.C. and T.L. prepared the samples; Y.L. designed, fabricated, and characterized the wrinkles; Z.H. performed the light diffraction measurement on gratings, supervised by X.M.; X.L. performed TEM, supervised by Y.H.; C.L. grew the SiNx and Al₂O₃ films, supervised by J.L.; K.W. and T.T. provided hBN crystals; Y.G. provided the mechanical models for wrinkle formation. The manuscript was written through contributions of all authors, and all authors have given approval to the final version of the manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

Additional methods and data are provided in the Supplementary Information. All data are available within the paper and its Supplementary Information. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-73078-0.