Extending ion-sheath-controlled double-angled deep etching to thicker, scalable three-dimensional photonic crystals in silicon

A 2009 Nature Materials paper introduced a top-down route to three-dimensional (3D) photonic crystals: a metal 'ion-sheath control plate' placed on the wafer reshapes the plasma sheath into electrostatic lenses so that reactive-ion etching (RIE) proceeds at controlled oblique angles, and two (or more) such angled etches create a woodpile-type 3D photonic crystal with a complete bandgap in a single-crystalline silicon wafer. The demonstration was limited to roughly two vertical lattice periods of etch depth, and the paper and its supplementary material left open four linked fabrication issues: sidewall degradation with etch depth, unquantified ion reflection and angular dispersion at the plate walls, unproven portability of the plate method to other RIE reactors, and the lack of process windows combining depth, low angular dispersion, low damage, and device-scale area. This task asks for the resolution of that cluster: a validated deep multi-directional angled-etch process that reaches at least three vertical lattice periods with preserved sidewall geometry, with the ion-optical and cross-reactor issues quantified. Later work by the same group (2014–2015) simplified the process to a single-step multi-directional etch but the deepest reported crystals remain two periods thick, with depth-dependent hole tapering identified as the dominant performance limiter; the group then pivoted to wafer-bonding/stacking for large-area crystals. Sheath-engineered angled etching has been generalized by other groups (Faraday-cage, glass-pad, magnetic-field, and field-modulation methods) but only at other scales and for other structures, leaving the stated deep-crystal questions open.

Background

A photonic crystal is a dielectric material with a periodic refractive-index modulation at the wavelength scale of light; a complete (omnidirectional, all-polarization) photonic bandgap forbids light propagation in every direction, enabling ultimate control of spontaneous emission and light guiding (Yablonovitch, 1987). In three dimensions (3D), the most studied complete-gap architecture is the 'woodpile' lattice — stacked, alternating orthogonal rods — and the archetypal top-down route has been to stack many patterned 2D layers by wafer fusion, as in the first near-infrared 3D bandgap crystals (Noda et al., Science, 2000). Bottom-up self-assembly (opals) and pick-and-place stacking suffer uncontrolled defects, small crystal size, or long process times, which motivated single-wafer top-down alternatives. Reactive-ion etching (RIE) is a standard plasma process in which ions accelerated across a thin boundary layer — the ion sheath, a space-charge region that forms parallel to the wafer surface — bombard a masked substrate and etch it vertically; this sheath geometry normally forces etching perpendicular to the wafer, so deep etching at a controlled oblique angle, needed for angled woodpile architectures, cannot be obtained by simply tilting the wafer. In 2006 the Kyoto group combined angled etching with wafer fusion (Takahashi et al., Appl. Phys. Lett. 89, 123106), and in 2009 they solved the angle-control problem by placing a metal 'ion-sheath control plate' with oblique holes (wall angle determining the etch angle; wall interval $d$ and wall height $h$ chosen comparable to or larger than the sheath thickness) directly on the wafer: the sheath deforms into the plate holes, acting as electrostatic lenses that deflect ions onto the wafer at a controlled oblique angle, and reversing the plate by 180 degrees gives the opposite angle (Takahashi et al., Nature Materials 8, 721–725, 2009). Using an inductively coupled $\mathrm{SF}_6+\mathrm{O}_2$ plasma at cryogenic wafer temperature with a thin aluminium mask, whose silicon-oxyfluoride ($\mathrm{SiO_xF_y}$) passivation suppresses lateral etching, they produced silicon woodpile crystals with sub-micron periods ($a_x=0.83\,\mu\mathrm{m}$), measured vertical depth of only about two vertical lattice periods ($\sim 2a_z$, where $a_z$ is the lattice period along the vertical direction), and a strong complete bandgap signature (>20 dB attenuation in all measured directions, >14% estimated gap width). Related ion-optics approaches exist in parallel: a Faraday cage around the sample forces the plasma sheath to lie normal to the cage faces so that ions etch at the cage angle (Lee et al., 2009; Cho et al., 2014; Latawiec et al., 2016), which has become a standard tool for angled etching of bulk dielectrics such as diamond. The 2009 paper and its supplementary material explicitly identified the method's own remaining fabrication and scalability problems, which form the open fabrication problems addressed here: (i) increasing the number of vertical lattice periods beyond $\sim 2a_z$ is limited by degradation of the etched sidewalls as depth grows; (ii) ions can be reflected at, or collide with, the control-plate walls, broadening the angular distribution of incident ions and destabilizing the etched profiles, an effect that was neither measured nor modeled; (iii) although the plate dimensions $d$ and $h$ should track the sheath thickness and the method was claimed applicable to many RIE systems and facilities, cross-reactor reproducibility and calibration were never established; and (iv) process windows simultaneously achieving deeper etches, minimal angular dispersion, low surface damage, and areas and layer counts sufficient for practical devices remained to be demonstrated.

Problem Statement

For the ion-sheath-control-plate method of double- and multi-directional deep reactive-ion etching — the single-wafer top-down route by which woodpile-type 3D photonic crystals with a complete bandgap were directly created in single-crystalline silicon — specify, with quantified ion-optical modeling, a fabrication process that goes substantially beyond the demonstrated vertical depth of about two lattice periods $a_z$ (a target of at least $3a_z$ is the natural next step, consistent with the originators' own analysis) while preserving the etched sidewall geometry, and state the requirements for its scalability and transferability. Concretely, the linked questions to be answered are: (1) by what combination of etch chemistry, mask design, and ion-trajectory control can angled deep etching reach the target depth stated above without the depth-dependent broadening or tapering of the etched features that the same group later measured at the $\pm 1^\circ$ sidewall-angle level and identified as the dominant limiter of the photonic band-gap strength (their simulations indicate the tapering magnitude must be held below about $0.5^\circ$)? (2) How do ion reflections at, and collisions with, the walls of the ion-sheath control plate — treated in existing self-consistent sheath models only by the assumption that incident ions are absorbed — contribute to the angular dispersion of ions reaching the wafer, and how should the plate-sidewall geometry and surface properties be designed or modified to minimize this dispersion and the resulting degradation of the etched profiles? (3) Can the method be reproducibly transferred to other RIE reactors and plasma conditions, and what calibration procedure and reproducibility data are required? (4) What process windows simultaneously achieve the target depth stated above, an ion angular dispersion small enough to hold the depth-dependent sidewall-angle deviation below about $0.5^\circ$, surface damage low enough to preserve the etched sidewall geometry, and crystal area and layer count sufficient to reproduce the demonstrated complete bandgap (attenuation above 20 dB in all measured directions and an estimated gap width above 14%), verified by geometric metrology (e.g. cross-sectional electron microscopy of the etched profiles) and optical band-gap characterization (e.g. omnidirectional attenuation and reflectance spectra)? These four questions share one scientific objective — making the sheath-engineered angled deep-etching route yield thick 3D photonic crystals meeting the quantitative depth, sidewall-fidelity, and band-gap thresholds stated above — and are to be answered together for that route; they are not a request to survey the alternative fabrication routes (stacking, direct writing) by which others have made 3D band-gap crystals.

References

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