Uniform and bright light emission from a 3D organic light-emitting device fabricated on a bi-convex lens by a vortex-flow-assisted solution-coating method

We herein present the results of a study on the novel fabrication process of uniform and homogeneous semiconducting polymer layers, in this case hole-injecting and fluorescent light-emitting layers that were produced by a simple solution-coating process for 3D conformal organic light-emitting diodes (3D OLEDs) on curvilinear surfaces. The solution-coating process used was a newly developed method of vortex-flow-assisted solution-coating with the support of spinning of the coating solution. It is shown that the vortex-flow-assisted spin-coating process can produce high-quality thin films at nanoscale thicknesses by controlling the liquid surface of the coating solutions, which can easily be adjusted by changing the spinning speed, even on complex curvilinear surfaces, i.e., a quasi-omnidirectional coating. This excellent film-forming ability without any serious film defects is mainly due to the reduction of line tension among the solution, air, and the substrate at the contact line due to vortex flows of the coating solution on the substrate during the vortex-spin-coating process. As a proof of concept, we present vortex-spin-coated 3D OLEDs fabricated on bi-convex lens substrates which exhibit excellent device performance with high brightness and current efficiency levels comparable to those of a conventional spin-coated 2D planar OLED on a flat substrate. It is also shown that the EL emission from the 3D OLED on the bi-convex lens substrate exhibits a diffusive Lambertian radiation pattern. The results here demonstrate that the vortex-flow-assisted spin-coating process is a promising approach for producing efficient and reliable next-generation OLEDs for 3D conformal opto-electronics.


Reference configuration of the system
. Reference configuration of a liquid in a rotating truncated cone with inner top radius R1, inner bottom radius R2, and height H with a slant angle of α and slant height of L with the relationship = sin . The inner radius, height, and slant height of the liquid before its rise and without the capillary effects are R, h and l, respectively.
Supplementary Fig. S1 shows a reference configuration of the system, just at the point of the removal of the external torque which put the system into a rotating state. The reference configuration is virtual in the sense that it is assumed that the liquid has not yet begun to rise from its still level (h) state and that the capillary effects are frozen. The mass of the liquid is = 0 , where is its density. The moment of inertia of the liquid in this state is 0 = 3 10 , the moment of inertia of the rigid truncated conical container is • , and 0 = ℋ( 0 + • ) is the angular speed corresponding to the given angular momentum ℋ . The volume of the liquid is 0 = 1 3 ( 2 + • 2 + 2 2 ) • ℎ and the surface area of the side wall of the truncated cone is π( + 2 ) • , where R, h, and l are the internal radius, height, and slant height ( = ℎ sin = ℎ csc ) of the liquid, respectively.

S-3
The internal energy 0 associated with the reference liquid configuration, up to a constant term, is then expressed as (S1.1) Here, the solid/vapour, liquid/vapour, and solid/liquid surface energies are denoted by , , and , respectively, and is the line tension along the triple solid/liquid/vapor contact line.
The centre of mass of the liquid ℎ is ℎ = ( + 2 ) • ℎ. The slant height of the truncated cone is L and = • is the specific weight of the liquid, where is the acceleration of the gravity. The density of the surrounding gas is assumed to be much lower than the density of the liquid ( ≪ ). It is assumed that the angular velocity 0 is sufficiently small such that the surface of the liquid does not reach the bottom of the truncated conical container, causing the interface energy . Assuming that the shape of the liquid surface is axisymmetric and can be described by a single-valued function = (r), the internal energy of the system is We neglect the small effect of gravity and the angular speed on the surface energy . The corresponding kinetic energy of the liquid is The area in Eq. (S2.1) is the surface area of the liquid/vapour interface, whose profile is ( ). The expressions of the surface area S and the volume V can be expressed as Here and the kinetic energy is With regard to the actual dewetting, the surface energy * is * = � − � with the surface energies � and � at bottom, which are different from the surface energies and at the lateral wall surface. The line tension along the triple contact line at the bottom surface is * . If the liquid withdraws from the bottom surface of the container by leaving a thin film behind, the surface energy * is equal to . It is assumed that the film is sufficiently thick such that its lower face, which is in contact with the solid, can still be assigned surface energy , while its upper face is assigned surface energy . In this case, * = 0, as the liquid elevates from the film smoothly and without contact with a solid surface of the container.
The surface elements at the points of the contact circles = 0 and = must also be stretched in the direction tangential to the surface to preserve the liquid contact with the bottom of the container and with its lateral wall. Thus, the total area change of the surface can be written as The variation of the potential function becomes (S3.5) The stationary condition = 0 leads to that is, the liquid elevates from a deposited film with a vanishing slope, i.e., ′( 0 ) = 0. (S3.14)