Curved display based on programming origami tessellations

Curved electronics and displays are desirable for aesthetics and function across wearables, optics, smart appliances, and robotics. Conventional flexible (but non-stretchable) displays, such as OLEDs and organic TFT-based LCDs, cannot conform to nondevelopable surfaces because Gaussian curvature is preserved under isometry (Gauss’s Theorema Egregium). Stretchable display approaches—either embedding devices in elastomers or connecting rigid islands by serpentine interconnects—can conform to nonzero Gaussian curvature but suffer from drawbacks including low stiffness and fatigue life of elastomers (e.g., PDMS, Eco-flex, PEDOT), complex processes, cost, and limited yield. Origami offers an alternative by localizing strain at creases and keeping facets nearly rigid, which is compatible with mounting rigid components. Prior Miura-ori-based strategies either require additional diagonal creases (incompatible with rigid components) or produce inhomogeneous facet sizes. This work addresses the research question of how to design and fabricate nondevelopable curved displays without stretchable materials by programming Miura-like tessellations that fold into target geometries while minimizing facet deformation and remaining compatible with scalable microfabrication and assembly. The authors propose a structure–mechanics-inspired functional optimization that minimizes facet pseudo-strain energy and demonstrate spherical and saddle-shaped LED displays fabricated and folded via mold guidance.

The paper surveys: (1) Flexible, non-stretchable displays (e.g., OLEDs on flexible substrates, organic TFT LCDs) that can form only developable shapes (tubes, cones) due to curvature constraints. (2) Stretchable displays using elastomeric matrices and embedded emitters (e.g., AC-driven capacitive displays with ZnS phosphors in Eco-flex) and active-matrix stretchable systems with elastic conductors, organic transistors, and OLEDs that can wrap spheres; these face mechanical durability issues and material limitations. (3) Island–serpentine architectures (e.g., μ-ILED arrays on pre-stretched PDMS with pop-up bridges; AMLED matrices with horseshoe interconnects) that still rely on soft substrates and complex processing, limiting yield and scalability. (4) Origami-based approaches (Miura-ori) previously applied to stretchable devices; mathematical designs that realize prescribed curvature require added diagonal creases and lead to inhomogeneous facet sizes, hindering compatibility with rigid components and manufacturability. This context motivates an origami approach that preserves rigid facets, avoids added creases, and yields manufacturable, uniform tessellations.

Design and optimization:

• A Miura-like origami tessellation is programmatically designed to approximate target nondevelopable surfaces (spherical and saddle). The optimization minimizes the pseudo-strain energy associated with facet distortion during folding. Vertices are granted extra degrees of freedom, and a weak-form functional extremum in classical differential geometry is computed via a special finite element scheme to find vertex positions that minimize total potential energy. The algorithm preserves near-constant center-to-center spacing between neighboring facets to ease LED placement and improve display uniformity and is tuned to favor origami-dominated folding over global buckling.

Device stack and microfabrication:

• Substrate: parylene-C multilayer (10 μm bottom, 5 μm blocking, 5 μm top).
• Electrodes: two copper layers (0.5 μm each) forming row/column address lines.
• Stiffeners: SU-8 (100 μm) covering most of each facet; a central rounded-square aperture houses the LED chip. SU-8 footprints are smaller than facets, leaving ~400 μm clearance along crease lines to ensure safe bending.
• Crease and vertex preparation: reactive ion etching (RIE) opens vias to Cu for LED bonding and removes vertex areas between SU-8 quadrilaterals to reduce local stiffness.
• Emitters: LED chips (~150 μm thick) are placed via pick-and-place and soldered in the center of each SU-8 stiffener aperture. Encapsulation uses epoxy resin; YAG/resin is used with the LED packages as indicated.
• Overall sheet thickness ~200 μm, with crease regions thinned to ~20–30 μm to accommodate folding.

Electrical and control:

• Passive-matrix addressing; line-scan control at 100 Hz to drive individual pixels.

Planar device prototypes:

• Spherical-target sheet: 4.8 cm × 6 cm with 16 × 20 LED array; 3 mm pixel pitch (flat).
• Saddle-target sheet: 6 cm × 6 cm with 20 × 20 LED array; 3 mm pixel pitch (flat).
• Yield >95% after soldering.

Mold-guided folding process:

• 3D-printed molds: hemisphere radius 5 cm (Gaussian curvature K ≈ 0.04 cm^-2); saddle (hyperbolic paraboloid) with 5 cm radius of curvature at saddle point (K ≈ −0.048 cm^-2). Positive/negative mold pairs embody the optimized tessellation state prior to final bending to the target surface.
• Step 1 (crease inscription): The flat display is aligned using a corner pixel, sandwiched between partially folded mold halves. Mountain and valley creases are formed row-by-row by pressing the molds together.
• Step 2 (forming to target): Lateral squeezing forces and bending moments are applied to further bend and fix the sheet onto the curved surface; the SU-8-free gaps and mold compliance accommodate dynamic misalignments.
• Folding level: facets folded ~45° from flat (≈30% nominal biaxial strain from the initial flat configuration). Pixel pitch reduces to ~2 mm after folding.
• Alignment tolerance characterization: maximum crease centerline torsion ≈ 8°; end offsets ≈ 200 μm.

Design modifications for robust folding:

• SU-8 stiffeners tuned to promote origami-dominated deformation and suppress global buckling in Miura-Ori under compression.
• The optimization maintains near-uniform facet dimensions compatible with high-throughput pick-and-place assembly and consistent optical pixel geometry.

Demonstrations:

• Devices are shown operating in both flat and curved states, including rendering letters (e.g., HK, UST; spherical display “TK2U” pattern) and full-field illumination.

• Demonstrated nondevelopable curved LED displays using origami-programmed tessellations without stretchable substrates or serpentine interconnects, achieving spherical (R = 5 cm, K ≈ 0.04 cm^-2) and saddle (K ≈ −0.048 cm^-2) geometries.
• Fabricated thin, foldable 2D display sheets (overall thickness ~200 μm; crease regions 20–30 μm) with SU-8 stiffened facets and Cu interconnects on parylene-C, compatible with standard microfabrication and pick-and-place assembly.
• Planar arrays: 16×20 LEDs (4.8×6 cm) and 20×20 LEDs (6×6 cm) at 3 mm pitch; post-folding pixel pitch ~2 mm.
• Electrical performance: passive-matrix line-scan at 100 Hz; >95% pixel yield after soldering; stable operation in flat and curved configurations, including dynamic bending in the flat state.
• Folding mechanics and tolerances: facets folded ~45° (≈30% nominal biaxial strain referenced to the original flat sheet), with measured maximum crease centerline torsion ~8° and end offset ~200 μm; process robust to misalignments due to mold flexibility and 400 μm SU-8-free crease gaps.
• Optimization algorithm minimized facet pseudo-strain energy, maintained near-uniform facet spacing, and favored origami-dominated deformation over global buckling, enabling reliable folding and compatibility with rigid LED chips.
• Visual output: full-field illumination on curved surfaces; alphanumeric patterns displayed on both spherical and saddle configurations (some image distortion noted).

The study shows that nondevelopable curved displays can be realized by programming origami tessellations that localize deformation to creases, maintaining rigid facets suitable for mounting conventional LED chips. This approach addresses the geometric limitations of non-stretchable flexible displays and avoids the material and reliability challenges of elastomeric stretchable systems and serpentine interconnects. By minimizing facet pseudo-strain energy and carefully tailoring stiffener geometry, the folding process remains origami-dominated, reducing in-facet bending that would otherwise damage devices. Mold-guided, two-step folding provides a scalable, alignment-tolerant method to achieve prescribed curvature with acceptable misalignment tolerances. The results confirm functional operation on spherical and saddle surfaces and indicate feasibility for mass production using established microfabrication and pick-and-place workflows. Slight image distortion and measured alignment errors suggest room for further refinement of tessellation design, mold precision, and assembly to enhance optical uniformity and registration on curved surfaces.

This work introduces a structure–mechanics-inspired optimization strategy to design Miura-like origami tessellations that fold flat, microfabricated LED arrays into prescribed nondevelopable geometries while minimizing facet deformation. Integrating parylene-C/Cu circuitry, SU-8 stiffeners, pick-and-place LED assembly, and mold-guided folding, the authors demonstrate functional spherical and saddle-shaped displays with high pixel yield and robust operation. The method advances curved display manufacturing by leveraging rigid-foldable architectures compatible with high-throughput processes. Potential future directions include: increasing pixel density and array size; integrating active-matrix drivers for finer control; refining optimization and mold tooling to reduce misalignment and optical distortion; extending to additional surface geometries and device types (e.g., multicolor or emissive technologies beyond discrete LEDs); and automating folding/lamination steps for improved throughput and yield.

• Some pixels were damaged during the soldering process (yield >95% but not 100%).
• Slight image distortion was observed in the curved configurations.
• Folding introduces measurable misalignments (crease centerline torsion up to ~8°, end offsets ~200 μm), which may affect registration and uniformity.
• Demonstrations use passive-matrix driving and discrete LEDs at modest resolution; scalability to higher-resolution or fully integrated active-matrix systems is not shown.
• The approach relies on accurate molds and optimized tessellations; generalization to arbitrary geometries and automated high-volume assembly may require further process control and tooling refinement.