1. Introduction

Even with the recent emergence of new and important applications of photonic bandgap crystals (PBCs), the search continues for improved architectures and fabrication methods for these artificial optical media with the ability to localize light and modify photon emission [1,2]. In particular, the practical fabrication of PBCs with complete, three-dimensional bandgaps has traditionally been very difficult (as in the case of the yablonovite [3] or woodpile [4] PBC architectures), or yielded rather small or leaky 3D bandgaps (such as in the inverse opal [5] and 2D slab [6] PBC structures, respectively).

A new 3D PBC architecture proposed by Toader and John in 2001 offers an opportunity to address some of the shortcomings of previous PBC blueprints. Their proposed ‘square spiral’ architecture consists of a tetragonal array of spirals with a square outline (as seen along the spiral central axis), with the corners of the spirals nearly connecting lattice points in the diamond lattice [7]. According to numerical simulations, this PBC structure not only provides some of the largest bandgaps for any known 3D PBC architecture (as large as 16% for a direct structure of dielectric in air, or 24% for an inverse structure of air in dielectric), but the bandgaps are also remarkably robust to structural disorder and imperfections [8]. Even more important, periodically arranged square spirals are readily amenable to fabrication over large areas using a thin film fabrication method known as glancing angle deposition (GLAD), in which evaporation or sputtering onto tilted, rotating substrates delivers highly porous thin films with unique, columnar microstructures [9–11].

Kennedy et al. demonstrated the first fabrication of square spiral PBC thin film structures using GLAD [12], and subsequently provided optical characterization of the structures [13]. Based on reflectance spectra, they found evidence of a photonic bandgap centered at 2.7 µm in a silicon GLAD thin film of square spirals arranged in a square array with a period of 1.0 µm. Yet, the optical data did not confirm the presence of a complete bandgap in all three dimensions, and the bandgap was smaller than expected due to structural disorder. Seet et. al. recently presented the fabrication of precise square spiral PBC structures in SU-8 resist using two-photon laser writing, and provided optical results indicating stop bands at mid infrared frequencies. However, although this technique is flexible and permits the incorporation of various crystal defects, the approach is time consuming and yields only small-scale crystals on the order of tens of micrometers. Furthermore, the use of two-photon laser writing restricts the crystal material to photoresists with low refractive indices, thus reducing the potential bandgap effect and limiting the range of achievable stop band frequencies [14].

In this paper we present methods to improve the microstructure and uniformity of GLAD-based PBCs, and demonstrate new optical measurements that deliver the most conclusive evidence yet of a complete, 3D bandgap in the square spiral architecture, at a higher frequency and with a larger bandgap than previously reported.

2. Fabrication

The GLAD thin film deposition method works by collinear vapor impingement at highly oblique angles relative to the substrate normal (typically greater than 75°). In the absence of substrate heating, geometrical shadowing becomes the dominant film growth mechanism and leads to extremely voided film structures with mean densities below 40% of bulk values [15,16]. Furthermore, the lack of significant surface or bulk diffusion causes the initial substrate nuclei to evolve into a columnar microstructure. Through computer controlled substrate rotation, the basic columns can be engineered into a variety of unique shapes, including square spirals.

To obtain the periodic spiral arrangement necessary for a photonic crystal, a topography of vapor intercepting seeds must first be prepared on the substrate to enforce nucleation at predetermined sites. We have employed direct write lithography to obtain complete design freedom for easy fabrication of various prototype substrate topographies, while maintaining sub micrometer resolution. Our best results were obtained with a Heidelberg DWL 200 laser direct write lithography system, where careful optimization of the krypton-ion laser and beam optics enabled us to produce highly uniform arrays of substrate seeds in Clariant AZ-1518 resist with resolutions better than 250 nm over areas as large as 40 mm² [17].

Following substrate topography preparation, the only other step in the fabrication of a square spiral PBC structure is the GLAD process itself. For all the PBC structures described here we used a CHA Instruments e-beam evaporator fitted with a motorized dual axis substrate holder for adjustment of the required substrate tilt and rotation. All PBC structures were deposited using silicon, whose low absorption and high dielectric constant are well suited for PBC purposes. Typical deposition pressures were 0.4 mPa, with deposition rates on the order of 1 to 2 nm/s.

Traditionally, square spiral GLAD films have been deposited by simply rotating the substrate 90° at regular intervals, with four such turns constituting one complete winding of the square spiral [12]. However, this approach implies aligning the unit vectors of the tetragonal lattice of substrate surface seeds with the incidence direction of the collimated vapor. Since the GLAD process relies solely on geometrical shadowing, and such shadowing occurs only in the plane spanned by the vapor incidence direction and the substrate normal, there is then no control over the film microstructure perpendicular to the vapor incidence direction. The result is broadening of the spiral arms, distortion of the arm cross-section, and bifurcation of the spirals at the square spiral corners, which degrade the optical characteristics of the PBC structure [13].

In order to eliminate these growth effects we developed two new substrate motion algorithms for GLAD square spiral film deposition. The so-called PhiSweep algorithm –previously described in ref. [18] –works by oscillating the substrate from side to side about a central axis, thus decoupling the spiral growth direction (the central oscillation axis) from the vapor incidence direction. This approach significantly suppresses spiral arm broadening and cross-sectional distortion, thus yielding a much more uniform PBC structure.

Even better film microstructures were obtained by the second new substrate motion algorithm, in which the substrate is rotated to introduce a slight but permanent misalignment between the vapor incidence angle and the substrate seed lattice. Although this misalignment represents a minor distortion of the ideal square spiral PBC architecture, it also breaks the shadowing anisotropy within the growing GLAD film and hence eliminates almost all of the aforementioned growth problems. Figure 1 shows examples of the resulting film structures, in this case for silicon GLAD films deposited at a vapor incidence angle of 85° onto soda lime glass substrates with a 0.74 µm period tetragonal lattice of seeds. The morphology of these GLAD films is very close to the ideal square spiral PBC architecture described by Toader and John [7,8].

 

Fig. 1. Scanning electron micrographs of silicon square spiral thin films deposited using the GLAD technique. The tetragonal arrangement required for the square spiral PBC architecture is achieved by preparing the substrates with a periodic topography of small seeds prior to deposition.

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3. Optical characteristics

In the wavelength range of a photonic bandgap, an otherwise transparent material must feature simultaneous high reflectance and low transmittance. However, transmittance measurements have not been performed in any previously published reports on GLAD-based square spiral PBCs. We therefore examined the photonic bandgap response of the improved square spiral GLAD films using a Thermo Nicolet Nexus 670 Fourier transform infrared (FTIR) spectrometer, with a resolution of 1 nm and a beam spot size of approximately 1 mm. A typical transmittance spectrum is shown in Fig. 2. This spectrum was obtained at normal light incidence on the film previously shown in Fig. 1(a), and was corrected for losses in the soda lime glass substrate. The GLAD film was 10.5 µm thick, and had a volume fill factor of 0.21. A band of low transmittance is clearly observed for the wavelength range 1.4 µm to 2.1 µm. Since the GLAD films still contain minor imperfections relative to the ideal square spiral PBC structure, random scattering over the spot size leads to some transmission inside the stop band, as well as to tapering of the high wavelength band edge. The small fringes at the bottom of the stop band are caused by interference in the GLAD film, with the fringe separation given by the film thickness and the effective dielectric constant of the film (taking the high porosity and slight silicon dioxide content of the film into account).

 

Fig. 2. Transmittance spectrum of the periodic square spiral GLAD film previously shown in Fig. 1(a). The low-transmittance band from 1.4 µm to 2.1 µm overlaps with the high-reflectance bands shown in Fig. 3, and is indicative of the presence of a photonic bandgap.

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For the same GLAD PBC sample, Fig. 3 shows a series of FTIR reflectance spectra with external angles of incidence from 30 to 60°. (With the instrument used here, reflectance measurements at 0° could not be performed.) Each reflectance measurement was performed against a matching reference sample of aperiodic silicon GLAD square spirals. This method was preferred over absolute measurements against an “ideal” reference (such as a polished gold surface), since absolute measurements would blend the intrinsic spectral features of the high porosity silicon GLAD film with the spectral response attributable to the 3D periodic structure of square spirals, and hence prevent isolation of the photonic bandgap characteristics. In consequence, the obtained PBC spectra are relative rather than absolute, and may exhibit reflectance values larger than 100% (the reflectance of the reference samples was 60–70 %). At every incidence angle in Fig. 3, a distinct high-reflectance band is observed. These bands overlap each other as well as the transmission stop band in Fig. 2, and they maintain their position even as the angle of incidence is altered. Indeed, the high frequency bandgap edges for the 45 and 60° spectra coincide perfectly with the normal incidence transmittance spectrum for the same PBC in Fig. 2. Meanwhile, the more blurred low frequency edge of the transmittance spectrum, caused by increased scattering in this measurement setup, may misleadingly indicate a lower frequency bandgap center than is true.

 

Fig. 3. Reflectance spectra for the same square spiral GLAD PBC as examined in Fig. 2, for various external light incidence angles. The photonic bandgap position remains constant, indicating that the bandgap is complete with respect to crystal direction.

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The simultaneous high reflectance and low transmittance, and the invariance of the stop band frequencies with respect to the light incidence direction, are fundamental and required evidence in support of GLAD square spiral PBCs having complete, three-dimensional photonic bandgaps.

Since the crystal directions probed here correspond to the Γ-Z-R-X plane in the irreducible Brillouin zone of the tetragonal square spiral PBC, it is likely that the pinched high frequency edge of the 30° reflectance spectrum shown in Fig. 3 results from the similar high frequency pinch in the theoretical PBC dispersion relation in the Γ-R crystal direction [12]. We also probed the azimuthal dependence of the reflectance, in the Γ-Z-A-M plane (spectra not included here), and still found the photonic bandgap maintained, but now with the bandgap center tending slightly toward a higher frequency location (in continued accordance with theory [12]).

Finally, in order for a photonic bandgap to be complete, the bandgap must be maintained for all polarizations of the impinging light. Figure 4 shows reflectance spectra for different polarizations for the previously discussed GLAD square spiral PBC, at an external light incidence angle of 30°. A high reflectance region is maintained for both s and p and the intermediate polarization directions (although for p polarized light the reflectance is abnormally low due to the measurement setup), and the position of this stop band is invariant to the polarization direction. The impact of light polarization was also investigated at other angles of light incidence, with the bandgap location still found to remain constant irrespective of the polarization direction. This shows that a complete bandgap exists for all polarizations, and is the first experimental verification of a GLAD square spiral photonic bandgap being complete. It also emphasizes the advantage of 3D PBCs over 2D PBCs, with the latter in many cases yielding bandgaps for only one polarization.

 

Fig. 4. Reflectance spectra for a square spiral GLAD PBC for different linear polarizations of the impinging light (s, p, and intermediate polarizations). The measurements were performed at an external light incidence angle of 30°. The photonic bandgap remains in place for all polarizations, indicating that it is a complete bandgap.

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We also sought to confirm that the spectral features indeed derive from the tetragonal arrangement of square spirals, and not just from some inherent artifact of the substrate, the substrate seed topography, or the material making up the GLAD sample. We thus analyzed each of the sample constituents, and investigated the response of an identical GLAD sample without the substrate seed topography, consisting of randomly arranged silicon square spirals. For both reflectance and transmittance measurements we found that no individual or composite part of the GLAD square spiral sample system was able to account for the spectral stop band observations. That is, coinciding high reflectance and low transmittance bands were found only for the periodic, tetragonally arranged square spiral GLAD films. This validates that the observed spectral features – such as the opacity demonstrated by the spectrum in Fig. 2 – are those of photonic bandgaps introduced by the square spiral film structure.

Using a ‘full width, half maximum’ approach, the complete bandgap for the GLAD square spiral PBC examined here was found to be centered at 1.65 µm and have a bandgap width of 180 nm (or a relative width of 10.9%). When taking the volume fill factor of 0.21 of the GLAD film into account, the location of the experimental bandgap is in good agreement with the theoretical band calculations for similar square spiral PBCs previously performed by Toader and John [7,8]. Furthermore, the bandgap width is near the theoretically predicted, optimized bandgap width of 12.4% for this particular square spiral structure [8]. However, a more detailed, quantitative comparison of the experimental data with theoretical reflectivity predictions will require dedicated numerical modeling of the new GLAD square spiral structures.

When the same ‘full width half maximum’ method is applied to the best previously published optical data for a square spiral GLAD PBC [13], a partial bandgap of 6.4% centered at 2.7 µm is found. The GLAD square spiral PBC fabricated and analyzed here thus represents a large increase in the available bandgap width, and a center frequency that is significantly higher than previously reported as well as close to the third telecommunications window at 1.55 µm.

The improved photonic bandgap properties derive from the better square spiral film structure achieved using the new GLAD substrate motion algorithms discussed above. In particular, the greater uniformity in the shape and dimensions of the spirals throughout the films reduces disorder and hence scattering in the films, and the greater control over the film microstructure makes it easier to approach the theoretically ideal square spiral PBC architecture. There is still room for enhancement of the optical quality of GLAD square spiral PBCs, however, as evidenced by the lack of complete extinction of transmission inside bandgaps and the gradually tapering rather than vertical bandgap edges.

With arbitrary substrate topographies achievable using direct write lithography, and the ability of the new GLAD substrate motion algorithms to provide greater control over the exact dimensions of the square spirals, the work presented here enables engineering of the bandgap location and width of GLAD based square spiral PBCs. We have thus successfully fabricated and analyzed a number of other GLAD square spiral films with photonic bandgaps centered from 1.7 µm to 3.2 µm. Crucially, this bandgap engineering capability is achieved simply by changing the substrate seed lattice and the deposition settings, while maintaining a fabrication approach that is much easier than any other 3D PBC technology, even for large scale crystals.

4. Conclusions

Through the development of new substrate motion algorithms, we have shown that the GLAD thin film deposition technique is capable of fabricating uniform tetragonal square spiral PBC structures. We have found evidence of complete, three-dimensional photonic bandgaps in the GLAD square spiral films, with improved bandgap widths close to the theoretical maximum. Higher bandgap frequencies than previously reported have also been achieved, approaching the near infrared telecommunications range. When taking the film volume fill factor into account, the measured bandgap center corresponds to theoretical predictions.

Beyond the optical characteristics of GLAD square spiral PBCs, their key advantage in comparison with other 3D PBC architectures is the relative ease of fabrication. With only one surface topography fabrication step and one thin film deposition step, GLAD PBC fabrication relies on well-established semiconductor technologies. Furthermore, the GLAD process offers unique possibilities for defect engineering, as required for subsequent functionalization of the PBCs. Numerical modeling has shown that GLAD based PBCs yield superior light localization for waveguiding [19], and methods for the introduction of intentional defects in GLAD PBCs without the need for post deposition processing have already been published [20]. GLAD square spiral PBCs thus constitute a promising approach to the eventual realization of full 3D PBC devices.