Glancing angle deposition (GLAD) can grow tetragonal square-spiral photonic crystals — a diamond-lattice-derived architecture predicted by Toader and John to sustain a complete three-dimensional photonic band gap of up to 15% of the gap center frequency for silicon spirals in air and 24% for the inverse structure — in a single thin-film deposition step. The first GLAD demonstration (Kennedy, Brett, Toader and John, 2001/2002) produced only a nonoptimized four-turn specimen with a computed 9.3% gap and no optical measurement, and identified a linked set of unresolved directions: deposition-protocol optimization (e.g. spin-and-pause substrate motion) toward idealized cross sections, suppression of surface roughness including post-deposition annealing, fabrication and spectroscopic verification of optimized multi-turn crystals, mapping of reproducible GLAD process windows, and introduction of functional defects (waveguides, microcavities). Later work delivered improved motion algorithms, ion-assisted tilt control, visible-scale nanoimprint seeding, and measured infrared and visible stop gaps, but no fabricated square-spiral crystal has yet demonstrated an accepted complete omnidirectional photonic band gap (the single 2005 claim of complete gaps, by Jensen and Brett, is contradicted by the later assessments of Seet et al. 2008 and Krabbe et al. 2012), and no functional defect mode in such a crystal has been optically demonstrated. The problem remains open: fabricate GLAD square-spiral photonic crystals of sufficient structural fidelity and optically establish the predicted complete three-dimensional band gap, including the reproducible process windows and defect functionality that make the material useful.

Background

A photonic crystal is a periodic arrangement of dielectric materials whose 'photonic band gap' (PBG) — a frequency interval in which electromagnetic propagation is forbidden — can be used to inhibit spontaneous emission, trap light, and guide it sharply, in the way a semiconductor band gap manipulates electrons. Because Maxwell's equations are linear and source-free in dielectrics, a structure with lattice constant aa has a gap that scales simply with aa, so the same design can be shifted between the visible, near-infrared, and infrared by changing the length scale.

The diamond lattice of high-index dielectric is the classic template for a large three-dimensional PBG, but it is hard to microfabricate directly. Various approximations to it exist, such as woodpile stacks, criss-crossing pores, and spiral-post lattices. Toader and John (Science, 2001) proposed the tetragonal square spiral: a two-dimensional array of posts on a square (tetragonal) lattice, each post growing as a stepped square spiral whose 90° turns place its 'elbows' on a distorted diamond lattice. Unlike earlier circular-spiral proposals, adjacent posts require no phase shift, making microfabrication realistic. Band-structure computations predict a complete PBG between the fourth and fifth photonic bands of up to 15% of the center frequency for silicon posts in air (direct structure) and about 24% for the inverse structure (spiral air voids in silicon), robust to moderate parameter disorder (Toader and John 2001; Toader and John 2002).

Glancing angle deposition (GLAD) is a physical vapor deposition technique in which vapor arrives at the substrate at a highly oblique incidence angle (typically 80–90° from the substrate normal). Self-shadowing confines growth to the tallest nucleation sites; computer-controlled rotation of the substrate about its normal then 'sculpts' the growing columns. On a substrate pre-patterned (seeded) with a square array of relief dots, growth is restricted to the seed positions, and rotating the substrate by 90° at quarter-pitch intervals produces exactly the stepped square-spiral posts of the Toader–John design. The tunable parameters are the seed spacing (lattice constant aa), the helical pitch cc, the horizontal arm length LL (set through the growth angle, which Tait's rule — the empirical relation between the vapor incidence angle and the resulting column tilt — limits to roughly 55–60° from the substrate normal at these incidence angles), and the post cross section. Electron-beam evaporation of silicon at a rate of a few Å/s yields, in one step, a periodic three-dimensional crystal over large areas.

Kennedy, Brett, Toader and John (Nano Letters, 2001/2002) demonstrated this fabrication route for the first time: a silicon film with a=1000a=1000 nm, four helical turns, square post cross sections (side e=0.44ae=0.44a), and parameters [L,c,e]=[0.7,1.3,0.44]a[L,c,e]=[0.7,1.3,0.44]a, for which the computed relative gap is 9.3%. No optical measurement of the gap was reported. The paper explicitly identifies the outstanding work: adapting the process (including 'spin-and-pause' advanced substrate motion) to obtain idealized, symmetric circular cross sections instead of square ones; eliminating microscopic surface roughness (noting that post-deposition annealing of GLAD films changes surface properties and improves crystallinity); growing optimized crystals with more turns and optically verifying the computed gap; exploiting the stability of the predicted gap over large regions of parameter space, mapped through GLAD process control; and introducing controlled defects — waveguides and microcavities — by pre-deposition seed modification or by intermediate processing steps.

Subsequent work measured infrared stop gaps in such films (Kennedy et al. 2003: Fourier-transform infrared (FTIR) reflectance with band edges at 2.50–2.75 µm, a relative gap of about 10%), improved the deposition algorithms (Kennedy and Brett 2004: slow-corner and variable-angle-post methods; ion-assisted GLAD raising column tilt toward the optimum), demonstrated visible-scale structures (grown on nanoimprint-lithography seed lattices, i.e. seed arrays stamped mechanically into a resist by a master mold) and a visible pseudo-gap in titanium dioxide spirals (Krabbe et al. 2012), and replicated square spirals in silicon through polymer-template double inversion (Seet et al. 2008). However, in every case the measured features are directional stop gaps or pseudo-gaps rather than a demonstrated complete omnidirectional gap, and the theoretical 15–24% gap sizes have not been recovered experimentally.

Problem Statement

Can the tetragonal square-spiral photonic crystal architecture be fabricated by glancing angle deposition with sufficient structural fidelity that its predicted complete three-dimensional photonic band gap — up to 15% of the gap center frequency for silicon spirals in air and about 24% for the inverse structure — is experimentally realized and optically verified? The single objective spans five linked sub-goals: (1) optimize the GLAD deposition protocol (including spin-and-pause advanced substrate motion and refined timing control) so that the spiral cross sections, arm swing, pitch, and growth angle approach the idealized geometry that maximizes the band gap, over an increased number of helical turns; (2) reduce or eliminate microscopic surface roughness through process control and post-deposition annealing protocols that modify surface properties and crystallinity without distorting the lattice, so that the theoretical gap is not degraded by scattering and defect states; (3) fabricate optimized structures tuned within the mapped parameter space and measure their optical spectra (e.g. angle-resolved reflectance or transmission) to verify the presence, bandwidth, and spectral position of the complete photonic band gap against the computed band structure — establishing a genuine omnidirectional gap rather than directional stop gaps; (4) determine the reproducible windows of the GLAD parameter space (seed spacing, incidence angle, pitch, cross-section size, number of turns) within which large complete gaps survive growth disorder and competition; and (5) introduce controlled defects — waveguides and microcavities — by predeposition seed modification (removing or tying together seeds) or by intermediate processing (changing deposition parameters mid-growth, or backfilling and regrowing), and demonstrate their optical functionality. These five sub-goals are linked directions of one research program. The objective concerns the directly deposited crystal — silicon spirals in air, predicted gap up to about 15% of the gap center frequency — fabricated with sufficient structural fidelity through the process control of (1)-(2) and optically shown to possess a complete omnidirectional photonic band gap (3), not merely directional stop gaps or pseudo-gaps. The roughly 24% gap predicted for the inverse structure (spiral air voids in silicon) instead requires the multi-step inverse route — template conversion, backfilling and template removal. The reproducible process-window mapping (4) and the defect functionality (5) are additional directions of the wider program. No fabricated square-spiral crystal has yet demonstrated the complete omnidirectional gap, so the full objective, in its original generality, remains open.

References

  1. Scott R. Kennedy, Michael J. Brett, Ovidiu Toader, Sajeev John, 'Fabrication of Tetragonal Square Spiral Photonic Crystals', Nano Letters 2(1), 59-62 (published on web 2001-11-06; issue 2002), DOI 10.1021/nl015635q, https://doi.org/10.1021/nl015635q.
  2. Ovidiu Toader, Sajeev John, 'Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals', Science 292(5519), 1133-1135 (2001), DOI 10.1126/science.1059479, https://doi.org/10.1126/science.1059479
  3. Ovidiu Toader, Sajeev John, 'Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps', Physical Review E 66, 016610 (2002), DOI 10.1103/PhysRevE.66.016610, https://doi.org/10.1103/PhysRevE.66.016610
  4. Scott R. Kennedy, Michael J. Brett, Hernan Miguez, Ovidiu Toader, Sajeev John, 'Optical properties of a three-dimensional silicon square spiral photonic crystal', Photonics and Nanostructures - Fundamentals and Applications 1(1), 37-42 (2003), DOI 10.1016/S1569-4410(03)00005-1, https://doi.org/10.1016/s1569-4410(03)00005-1.
  5. S. R. Kennedy, M. J. Brett, 'Advanced techniques for the fabrication of square spiral photonic crystals by glancing angle deposition', Journal of Vacuum Science & Technology B 22(3), 1184-1190 (2004), DOI 10.1116/1.1752903, https://doi.org/10.1116/1.1752903
  6. Martin O. Jensen, Michael J. Brett, 'Square spiral 3D photonic bandgap crystals at telecommunications frequencies', Optics Express 13(9), 3348 (2005), DOI 10.1364/OPEX.13.003348, https://doi.org/10.1364/opex.13.003348.
  7. Martin O. Jensen, Michael J. Brett, 'Defect and bandgap engineering in square spiral photonic crystals', Proceedings of SPIE 5360, 91 (2004), DOI 10.1117/12.528463, https://doi.org/10.1117/12.528463.
  8. D. Ye, Z. Yang, A. Chang, J. Bur, S.-Y. Lin, T.-M. Lu, R. Z. Wang, S. John, 'Experimental realization of a well-controlled 3D silicon spiral photonic crystal', Journal of Physics D: Applied Physics 40(9), 2624-2628 (2007), DOI 10.1088/0022-3727/40/9/S02, https://doi.org/10.1088/0022-3727/40/9/S02.
  9. Jason Sorge, Mark Summers, Michael Fleischauer, Kyrylo Tabunshchyk, Andriy Kovalenko, Michael Brett, 'Ion Beam Assisted Square Spiral Photonic Crystal Fabrication', MRS Proceedings 1014 (2007), DOI 10.1557/PROC-1014-AA07-26, https://doi.org/10.1557/proc-1014-aa07-26.
  10. Michael D. Fleischauer, Jason B. Sorge, Robert A. Joseph, Michael J. Brett, 'Enhanced Control of Porous Thin Film Morphology via Ion Bombardment', MRS Proceedings 960 (2006), DOI 10.1557/PROC-0960-N01-03, https://doi.org/10.1557/proc-0960-n01-03.
  11. Mark Alan Summers, Michael J. Brett, 'Oxidation of Structured Silicon Thin Films for Inverse Silicon Square Spiral Photonic Crystal Fabrication', MRS Proceedings 934 (2006), DOI 10.1557/PROC-0934-I09-14, https://doi.org/10.1557/proc-0934-i09-14.
  12. M. A. Summers, M. J. Brett, 'Thermal oxidation of periodically aligned silicon square-spirals', Microelectronic Engineering 85(5-6), 1222-1224 (2008), DOI 10.1016/j.mee.2008.01.050, https://doi.org/10.1016/j.mee.2008.01.050
  13. M. A. Summers, M. J. Brett, 'Optimization of periodic column growth in glancing angle deposition for photonic crystal fabrication', Nanotechnology 19, 415203 (2008), DOI 10.1088/0957-4484/19/41/415203, https://doi.org/10.1088/0957-4484/19/41/415203
  14. M. Summers, K. Tabunshchyk, A. Kovalenko, M. Brett, 'Fabrication of 2D-3D photonic crystal heterostructures by glancing angle deposition', Photonics and Nanostructures - Fundamentals and Applications 7(2), 76-84 (2009), DOI 10.1016/j.photonics.2008.12.001, https://doi.org/10.1016/j.photonics.2008.12.001
  15. Kock Khuen Seet, Vygantas Mizeikis, Kenta Kannari, Saulius Juodkazis, Hiroaki Misawa, Nicolas Tetreault, Sajeev John, 'Templating and Replication of Spiral Photonic Crystals for Silicon Photonics', IEEE Journal of Selected Topics in Quantum Electronics 14(4), 1064-1073 (2008), DOI 10.1109/JSTQE.2008.922909, https://doi.org/10.1109/JSTQE.2008.922909.
  16. Joshua D. Krabbe, Viktor Leontyev, Michael T. Taschuk, Andriy Kovalenko, Michael J. Brett, 'Square spiral photonic crystal with visible bandgap', Journal of Applied Physics 111(6), 064314 (2012), DOI 10.1063/1.3695388, https://doi.org/10.1063/1.3695388.
  17. D. A. Gish, M. A. Summers, M. J. Brett, 'Morphology of periodic nanostructures for photonic crystals grown by glancing angle deposition', Photonics and Nanostructures - Fundamentals and Applications 4(1), 23-29 (2006), DOI 10.1016/j.photonics.2005.11.003, https://doi.org/10.1016/j.photonics.2005.11.003.
  18. Rong-Juan Liu, Sajeev John, Zhi-Yuan Li, 'Waveguide-mode polarization gaps in square spiral photonic crystals', EPL 111(5), 54001 (2015), DOI 10.1209/0295-5075/111/54001, https://doi.org/10.1209/0295-5075/111/54001
  19. Matthew M. Hawkeye, Michael J. Brett, 'Glancing angle deposition: Fabrication, properties, and applications of micro- and nanostructured thin films', Journal of Vacuum Science & Technology A 25(5), 1317-1335 (2007), DOI 10.1116/1.2764082, https://doi.org/10.1116/1.2764082
  20. P. V. Braun, S. A. Rinne, F. Garcia-Santamaria, 'Introducing Defects in 3D Photonic Crystals: State of the Art', Advanced Materials 18(20), 2665-2678 (2006), DOI 10.1002/adma.200600769, https://doi.org/10.1002/adma.200600769