Shot-filling effects in nanometer-scale electron-beam lithography

Photonic nanocavities achieve tight temporal and spatial confinement of light through the quality factor, Q, and the mode volume, V, respectively. This results in local enhancements of the electric field, E, which is central to a number of applications requiring enhanced light-matter interaction [1], such as nonlinearities [2] or efficient optical interconnects [3]. Previously, it was believed that the mode volume in dielectrics was bound by the diffraction limit [4], and therefore field enhancements were achieved by large quality factors [5]. With the recent discovery of dielectric bowtie cavities, however, mode volumes deep below the diffraction limit are possible in devices with nanometer-scale features [2,6]. Such features, in turn, pose challenges to the resolution of fabrication at the deep nanoscale.

Here we investigate the importance of precise pattern design and the effects of rasterization (shot-filling) in electron-beam lithography when pushing the resolution limit. We consider a novel nanocavity design obtained by inverse design using tolerance-constrained topology optimization [6] in which the local density of optical states (LDOS) is optimized at the very center of a silicon cavity to have Q = 1100, V = 0.08 (λ/2n)³, and λ = 1551 nm.

To illustrate the importance of shot-filling for high-resolution electron-beam lithography, we first consider the test structure shown in Fig. 1. The contours between material boundaries are used to define a set of polygons as shown in Fig. 1a. Individual patterns are well separated to be isolated from long-range proximity effects [7]. Figures 1b and d show the fracturing of the polygon as well as the discretization into individual shots separated by a pitch, p, and exposed with a uniform dose density, D. This means that the impinging charge dose of each shot (in coulomb) is q = p²D. Electron-scattering through the material broadens the point-like exposures along with the other process steps, here development and etching, to yield an effective deposited dose density, Deff, shown on the grayscale map in Figs. 1c and e [7-8]. The regions that receive an effective dose density greater than the dose to clear, D0, will be developed as indicated by the green contour. Figure 1c, shows visible line-edge roughness caused by the coarse discretization and poor dose uniformity, which, for a cavity, can cause substantial optical loss through scattering (reduction in Q) [5], while the finer discretization in Fig. 1e produces much smoother edges and a higher fidelity in the pattern transfer due to the finer discretization.

Figure 2 shows three nanocavities fabricated with the same process on the same chip where the current, and therefore pitch, is varied. Already when the pitch is increased from 1 nm to 3.5 nm, several of the small features cannot be resolved, and with p = 6 nm the central part becomes disconnected, thus charging up under SEM inspection. We will report on our latest progress towards realizing structures with extreme confinement of light.