Tuning of the Effective Refractive Index of Crystalline Si Thin Films with Controlled Modification of Nanohole Dimensions By Dry-Etching
Authors: Zayouna Sarah , Kjellberg Mikko Erik , Abeyratne Nevan , Schröder Stephan , Anand Srinivasan 
Published: February 2024

Silicon thin films with holes are composite materials with noteworthy optical properties that can be controllably fabricated by state-of-the-art Si process technologies. For light with wavelengths larger than the hole sizes and spacing, typically by a factor of 10, the perforated Si thin films behave like an effective (refractive index) medium. Under these conditions, the optical properties of the films can be modelled by the effective medium approximation (EMA). By manipulating the volumetric air fraction (holes) of such films, the refractive index can be modified accordingly. Such a property can be exploited to tune the index contrast in various photonic devices such as filters and waveguides.
This work presents a novel scalable method that combines charged sphere colloidal lithography (CSCL) and dry-etching to pattern Si thin films. We demonstrate controlled tuning of the effective refractive index by controlled lateral dry-etching of the holes. The fabricated nanoholes are spatially disordered in a 220 nm thick crystalline Si film. CSCL is performed using polystyrene particles of 60 (P60) and 100 (P100) nm diameter. The CSCL step results in a disordered arrangement of the particles with average spatial separations of 2-4 times their diameter. Using Cr as a mask, cylindrical holes are etched into Si by inductively coupled plasma-reactive ion-etching (ICP-RIE) using a pseudo-Bosch process. An additional isotropic ICP-RIE dry-etch step is introduced to widen the holes in a controlled manner, utilizing CF4 and O2 gas mixture. Importantly, this hole-widening step is time-controlled to ensure that the holes do not overlap laterally. Finally, the Cr mask is removed by wet-etching.
By analyzing scanning electron microscopic (SEM) images, we estimate the lateral etch rates for the P60 and P100 samples are approximately 0.76 nm/s and 0.52 nm/s, respectively. Using this process, the average hole diameter can be increased systematically up to circa 68-97%, compared to their original diameters, while avoiding overlap. The effective refractive index of the perforated Si thin films is determined using the optical air fill factor obtained from modelling the spectroscopic ellipsometry data with Bruggeman effective medium approximation. The determined optical air fill factor varies from circa 20% to 50% with hole widening. The ellipsometry data provides the true air fill factor of the samples directly; SEM analysis could also be used, however, it is complex and cannot determine the actual porosity of the films. The ellipsometry results show that the determined refractive index is constant in the 1500 - 4000 nm wavelength range. The refractive index decreases from 3.42 for unstructured Si film to 2.9 and 2.7 for the as-etched perforated Si films of P60 and P100 samples, respectively. With controlled lateral etching of the holes, the effective refractive index systematically decreases further to approximately 2.1 for the P60 and P100 samples, which is a 39% reduction compared to Si refractive index. The determined effective indices represent averaged values accounting for possible structural birefringence, which can be used as a guideline to design photonic devices such as filters.
The presented findings indicate that the effective refractive index of perforated Si thin films can be engineered by controlling the lateral dimensions of holes. While this conclusion relates specifically to crystalline Si thin films, the same concept may also be applied to other perforated dielectric thin films.

Figure 1