1. Introduction

Large-scale three-dimensional (3-D) micro-fabrication of photonic crystals using standard semiconductor lithographic technology remain tedious and costly [1,2], prompting development of lower-cost and simpler fabrication approaches. Laser holographic lithography (HL) is one such promising approach first introduced in 2000 by Campbell et al. [3] that generates photonic crystal templates by interference of multiple laser beams inside photosensitive media. Such low index media can be infiltrated [4] with high refractive index materials to form a complete photonic bandgap device. In this way, 3-D HL is the critical processing step offering advantages of rapid parallel 3-D imprinting, control of filling fraction, and flexible shaping of motif by means of tuning the relative beam intensities, polarizations, intercepting angles, and light source wavelength [3,5,6]. However, multi-beam HL requires stable and vibration-free alignment of multiple beam-splitting and steering optical components during the exposure. A diffractive optical element (DOE) is a promising alternative device for 3-D HL where one DOE creates multiple laser beams in various diffraction orders that are inherently phase-locked and stable for reproducible creation of 3-D interference patterns from a single laser beam. Rogers and coworkers [7] demonstrated the formation of various 3-D periodic nanostructures in thick photoresist using conformal phasemask DOEs. Our group was first to extend DOEs to the fabrication of 3-D photonic crystal templates, creating “Woodpile”-type structures in SU-8 photoresist by two sequential exposures of orthogonal one-dimensional DOEs (1D-DOE) with an Ar-ion laser [8, 9]. In this DOE approach, control parameters such as grating period, duty cycle and laser wavelength determine the periodic crystal structure while etch depth, laser intensity, polarization and photoresist threshold define the filling fraction and motif that together enables a wide variety of 3-D photonic crystal structures to be formed.

The present paper builds on this sequential DOE-exposure method [8,9] by improving the fabrication precision of “Woodpile”-type photonic crystal templates and, for the first time, spectroscopically characterizing the templates to verify their 3-D structure against energy band models. Section 2 provides a theoretical guideline for fabricating “Woodpile”-type photonic crystal templates by sequential DOE laser exposures. Detail DOE design criteria are presented, for the first time, for creating templates that will support a complete stopband after inversion with high index media. Section 3 describes the formation of 3-D templates in SU-8 photoresist with telecom-quality 1D-DOEs. Thick, large-area periodic nano-structures are confirmed to have “Woodpile”-type structure closely matching the computed optical interference iso-intensity surfaces. In Section 4, spectroscopic characterization of the templates reveals numerous low and high energy stopbands along preferential crystallographic directions that are consistent with calculated band dispersion curves for the low-index media. The results demonstrate good structural uniformity through a relatively large resist thickness and over large exposure area.

2. DOE design criteria

In this section a general theoretical guideline for fabricating “Woodpile”-type photonic crystal templates by the double-exposure 1D-DOE method is presented. Laser exposure conditions and DOE design parameters are outlined for creating stable 3-D photonic crystal templates with wide bandgaps.

2.1. DOE-generated interference patterns

 

Fig. 1. Formation of multiple diffracted beams from a single laser beam by a 1-D DOE and arrangement for photoresist exposure.

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Figure 1 shows the separation of an incident laser beam into m=+1^st, 0^th, and -1^st diffraction orders after passing through a 1D-DOE of period, Λ. In the overlap volume immediately below the DOE, the diffracted beams interfere to create a 2-D log-pile type interference pattern as shown in Fig. 2(a). After solving interference equations it can be shown that the lateral and vertical periodicities of this structure are

respectively, where λ_d is the free-space laser wavelength illuminating the DOE, and n _r is the refractive index of the photoresist medium in which the interference occurs as shown in Fig. 1. Note that the refractive index of the DOE, n _d, and the incidence medium, n _i, do not affect the periodicity of the interference pattern. The 2-D periodic interference pattern can be accurately captured with a thick (≫c) negative photoresist placed in the beam overlap region of Fig. 1 and by applying a laser exposure that just exceeds the photo-polymerization threshold of the photoresist. Post exposure development then solidifies the polymerized volume and dissolves the under-exposed volume to replicate the interference pattern. A positive photoresist will generate an inverted structure to that shown in Fig. 2(a).

To create a 3-D periodic structure, the first 1D-DOE exposure [Fig. 2(a)] is followed by a second exposure with an identical but orthogonal 1D-DOE, creating the rotated 2-D log-pile intensity pattern show in Fig. 2(b). The combination of two sequential exposures then yields an intensity pattern approximately described by the interlaced 3-D “Woodpile”-type structure as shown in Fig. 2(c). Although the figure depicts uniform elliptical-like cross-sections with asymmetric radii, R _x and R _z, as defined, the sum of two interference patterns are more complex than shown. A more precise representation of the intensity distribution can be easily generated with numerical computations that account for laser polarization together with the diffraction efficiencies and angles that depend on the groove depth and DOE period. The final structure of the photoresist is further governed by complex relations between laser exposure dose, photoresist exposure threshold, shrinkage and chemical diffusion.

 

Fig. 2. Periodic interference laser patterns created by (a) a single exposure with a 1D-DOE, (b) a single exposure with a similar 1D-DOE rotated by 90°, and (c) the resulting interlaced 3-D “Woodpile”-type structure due to combination of the two exposures in (a) and (b).

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2.2. Interlacing of log-pile structures

To form a stable interconnected “Woodpile”-type structure [Fig. 2(c)] that does not collapse on development, the two log patterns in Figs. 2(a) and 2(b) must be physically offset with displacement, S, while also having sufficient axial cross-section, R _z, defined in Fig. 2(c), that conservatively satisfy:

While R _z is defined by the laser exposure, the S offset requires precise alignment stages to vary the resist-to-DOE gap, d (see Fig. 1), used in each of the orthogonal DOE exposures. R _z=c/8 defines the lowest exposure threshold at which Eq. (2) demands an exact quarter period offset of S=c/4, while any offset value is acceptable for R _z>c/4.

2.3. Controlling structure dimensions

A complete photonic bandgap in “Woodpile”-type structures is available only in a narrow range of axial-to-transverse periodicity ratios, c/a, that further depends on the refractive index of dielectric medium and the filling fraction [10, 11]. For example, a “Woodpile”-type structure made with dielectric material n=3.45 will provide a complete photonic bandgap only for the range 0.6<c/a<2.1 for a given filling fraction of 26% [10, 11]. DOEs provide wide latitude here for varying the c/a ratio and thereby optimizing the bandgap properties. According to Eq. (1), c/a depends principally on the DOE period, refractive index of the photoresist, and laser wavelength, and is plotted in Fig. 3 as a function of the normalized wavelength, λ _d/Λ, for SU-8 photoresist (n _r=1.6). To produce a template offering a wide bandgap (after inversion), near-symmetric periodic structures with near unity c/a ratio are required. According to Fig. 2, this can be achieved with a small period DOE such that Λ~λ _d. However, this condition yields high diffraction angles for the first order beams that will only propagate inside the DOE substrate for periods larger than the optical wavelength, Λ>λ _d/n _d. Total internal reflection at either of the DOE-incidence medium or the incidence medium-resist interfaces (Fig. 1) impose additional constraints of Λ>λ _d/n _i and Λ>λ _d/n _r, respectively, that together limit the valid range of the c/a data in Fig. 3 to a minimum value defined by the normalized wavelength

By substituting this limit into Eq. (1), one obtains the minimum c/a value, for example, identified by the X-marks in Fig. 3, for different incidence media and assuming n _d>n _i. For air (n _i=1), one can generate a minimum c/a ratio of only 2.85. Alternatively, in the limit of using an index matching fluid with n _i=n _r=1.6, one obtains a symmetric periodic structure (c/a=1).

 

Fig. 3. Variation of c/a ratio in SU-8 photoresist (n _r=1.6) with normalized wavelength,λ _d/Λ, for different refractive index values of the incidence medium (n _i).

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To access the full c/a range of 1≤c/a≤∞, the refractive index of DOE (n _d) and the incidence medium (n _i) must exceed the refractive index of the photoresist and this has been expressed in Eq. (4).

Larger n _i and n _r values are attractive to reduce Fresnel losses, but c/a=1 is the minimum ratio available by this DOE method for any value of n_r.

2.4. Bandgap optimization

From the ongoing development, it is evident that with suitable selection of optical materials and DOE design, a stable interconnected 3-D “Woodpile”-type structure can be fabricated by double-exposure based 1D-DOE holographic lithography. While such “Woodpile”-type structures can be classified as face centered cubic (FCC) or tetragonal (TTR) lattice symmetry [12, 11], the TTR irreducible Brillouin zone is known to be more appropriate symmetry [12, 11] for “Woodpile”-type structures and hence we base our band dispersion calculations on TTR symmetry. To determine the band positions, band dispersion curves were calculated for DOE-HL structured templates using the plane wave expansion (PWE) method as previously described in [13]. Calculations were carried out over a wide range of c/a ratios (1<c/a<3) and laser exposure levels (filling fractions of 10%<f <90%) to identify the experimental exposure parameters that provide the widest bandgap for silicon inverted structures. The filling fraction could be controlled by varying any combination of laser intensity, exposure time, and photoresist threshold. Unlike the c/a ratio, the filling fraction has no closed form expression to produce a desired structure and required an iterative method of optimization.

The c/a range was restricted by the λ _d/Λ ratio as defined in Eq. (3) (Fig. 3) by our choice of n _r=1.6 for the refractive index of SU-8 resist, n _i=1.9 for an incidence medium, and n _d=1.9 for the DOE substrate. The relative intensity of diffraction orders is controllable by the DOE etch depth and values of 30%, 30% and 30% were assumed for the -1^st, 0^th and 1^st orders respectively. The laser polarization was slightly elliptical in both exposure orientations.

The 3-D intensity pattern was calculated for two equal intensity DOE exposures and then set to a threshold intensity that finally yielded an iso-intensity surface defining the 3-D structure of the resist. This numerical calculation yielded an irregularly shaped motif, from which numerical band calculations [13] provided energy dispersion curves.

A direct band calculation of the polymer structure with c/a=1.2 and f ≈ 25% is shown in Fig. 4(a). Values of S=c/4 and R _z=c/8 were selected to satisfy interlacing conditions [Eq. (2)]. This polymer structure provides an 8.1% bandgap along the Γ-Z direction—indicated by the hatching—but does not provide a complete photonic bandgap due to a low refractive index contrast of n _r - n _air=0.6. However, if we double invert this structure using know procedures [4] to create a silicon log structure with an air background, a similar calculation yields the band dispersion curves of Fig. 4(b) where a complete bandgap of Δω/ω=18.5% is identified by the hatched area.

 

Fig. 4. Band dispersion diagram (a) for 3-D “Woodpile”-type structure in photoresist for values of n=1.6, c/a=1.2, and f≈25% and b) modified dispersion diagram with the same structure after double inversion to a silicon “Woodpile” with n=3.45, c/a=1.2, and f≈25%.

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The spectral width of the bandgap strongly depends on the c/a ratio, which, in turn, is easily controlled [Eq. (1)] by the ratio of laser wavelength to DOE periodicity (λ _d/Λ). Figure 5 shows the dependence of complete bandgap width for double-inverted silicon structures with λ _d/Λ ratio for a constant filling fraction of f≈25%. The top axis shows the corresponding variation with c/a ratio. The maximum bandgap is noted at λ _d/Λ≈1.57 just before the cut off for total internal reflection at λ _d/Λ=1.6. The energy dispersion curve in Fig. 4(b) is plotted for this maximum bandgap condition.

 

Fig. 5. Variation of the complete bandgap with λ _d/Λ ratio for silicon inverted structures of silicon logs in air background (f≈25%).

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This section shows that double-exposure 1-D DOE HL can provide stable, interconnected “Woodpile”-type photonic crystal templates. DOE design criteria were presented for creating templates that will support a full stopband after inversion with high index media.

3. Fabrication of 3-D “Woodpile”-type structures

Three-dimensional “Woodpile”-type templates were patterned into photoresist by two sequential exposures of a cw argon ion (Ar+) laser (Coherent, Innova Sabre MotoFred) at 488-nm wavelength through two orthogonal 1D-DOEs (fused silica, n _d=1.46), each a linear phasemask with Λ=1.066 µm period and 265-nm groove depth. The measured diffraction efficiencies of 0^th and 1^st order beams were η ₀=53% and η ₁=η _-1=19%, respectively, for elliptically polarized light having 95% intensity polarized parallel to the grating grooves. Due to very low diffraction efficiencies of <2%, higher order diffracted beams (m≥2) were ignored in the calculations. Because SU-8 (MicroChem, SU-8, n _r=1.6) was optimized for i-line exposure (~350 nm), photo-initiator (Spectra Group, HNU470) was added (0.1 wt %) to improve SU-8 response at 488 nm. A uniform 15-µm thick resist layer was spun onto glass substrates. Periodic structures of a=1.066 µm and c=7.29 µm were expected inside the negative photoresist according to Eq. (1). To avoid surface damage, an ~0.2-mm air gap was maintained between the DOE and the photoresist during alignment and exposure. Two consecutive 1D-DOE exposures produced interlaced orthogonal log patterns to create the “Woodpile”-type structure as predicted by Fig. 2(c). The interlacing offset, S, was difficult to control to c/4=1.82 µm precision across the full surface area of the resist using our present alignment stages. However, a slight non-parallel alignment (<10 mrad) was introduced between the two DOE surfaces to slowly varying the S offset across the 3-mm diameter (full-width half maximum, FWHM) laser exposure area. A 5-second exposure was applied through each 1D-DOE at 650-mW power, and followed by two steps of post-exposure baking (65°C and 95°C) of the resist to complete the polymerization process after laser exposure.

Figure 6 shows the scanning electron beam microscope (SEM, Hitachi S-5200) images of the top view (a) and cross-sectional view (b) of the photoresist after two orthogonal DOE exposures and development. A “Woodpile”-type 3-D photonic crystal structure is clearly evident with lateral periodicity of a≈1.05 µm and axial periodicity of c≈6.27 um.

 

Fig. 6. Top SEM view (a) of the DOE fabricated 3-D photonic crystal template together with cross-sectional view (b), showing 5 layers in the SU-8 photoresist. Inset ii) shows magnified version of cross-section and inset i) and inset iii) shows calculated isointensity surfaces.

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Because the photoresist is bonded at the glass substrate, there is little lateral shrinkage (~1%) of the resist as the observed lateral period (a≈1.05 µm) closely matches the Λ=1.066-µm grating period as predicted by Eq. (1). On the other hand, the axial period (c=6.27 µm) is 14% smaller than the expected c=7.29-µm value, which is attributed to resist shrinkage during development, an unfortunately common problem with thick SU-8 photoresist [14]. The cross-sectional view in Fig. 6(b) shows uniform structure formation across the full 13-µm thickness of the developed photoresist, supporting our assertion that the DOE method can produce thick photonic crystal templates in photosensitive materials. A 3-D periodic structure extended fully across the ~2000-µm diameter exposure area.

Isointensity surface calculations were carried out as briefly described in Section 2 to match the observed SEM structure and are shown overlaid as inset (i) and (iii) in Fig. 6. Resist shrinkage was taken into account in the simulation by anisotropic scaling by a 14% axial shrinkage factor. The SEM observations are accurately replicated by the isointensity calculations over a large sample area. The SEM in Fig. 6(b-ii) provides values of R _x=0.23 µm, R _z=1.45 µm≈c/4.32 and S=0.85 µm≈c/7.38. These values satisfy the interlacing conditions of Eq. (2) for formation of a stable, interconnected 3-D structure. The SEM images provide an estimated filling fraction of f ≈ 69%, which closely corresponds with the f ≈ 64% value used to optimize the iso-intensity profile matching in Fig. 6. The fabricated 3-D structure was found to be smooth over large sample area (~2000 µm diameter) with minimum resolvable feature size of ≤200nm. The surface morphology is relatively smooth with roughness of ~10 nm that suggest low optical scattering loss. The slight tilting of the structure [Fig. 6(b)] has been attributed to lateral shrinkage of the top layer relative to a bonded (non-shrinking) bottom layer.

With the present DOEs, various filling fractions could be reproducibly created by varying the exposure time (3 to 15 seconds) and laser power. The DOE-HL fabrication arrangement was robust and simple to align unlike multi-beam holography. 3-D photonic crystal templates were consistently fabricated over large sample area (~2000 µm diameter) and through large 10–15 µm thickness on a non-floating optical table. The rapid exposure time (~5 s) and small number of process steps shows promise for scaling to very large volume fabrication, dramatically improving the throughput, quality and structural uniformity of 3-D photonic crystals, especially over that provided by tedious and costly semiconductor processing technology [1, 2]. Even a flexible fabrication approach like 3-D laser direct write becomes unacceptably timely when processing sample sizes of only 100 microns [4, 15]. In contrast, DOE-HL is a parallel processing method that is easily scalable to generating centimeter-scale 3-D photonic crystals in several seconds when using high power lasers and beam scanning exposure techniques.

4. Optical characterization

Although the refractive index of the photoresist (n _r=1.6) is too small to create a wide photonic bandgap, the quality of the 3-D structure could be examined optically along several crystallographic directions where stopbands are predicted. The sample shown in Fig. 6 was probed along the Γ-Z direction (c axis in Fig. 6(b) for TTR symmetry) with a Fourier transform infrared (FTIR) spectrometer (Bruker, Tensor 27) in the 1.4-µm to 5-µm spectral range. All spectral recordings were normalization against a reference spectrum recorded through an identical substrate coated with a fully developed solid resist coated to 13-µm thickness. The normalized transmission spectrum of the structure is shown in Fig. 7(b). A strong absorption trough from 2.6 to 3.6 µm has been attributed to intrinsic material absorption by the SU-8 film. Outside this band, a moderately strong stopband is noted at 4.45-µm wavelength that we attribute to a Γ-Z direction stopband, together with several higher-order bands near 2 to 3 µm. Diffraction losses due to the a=1.05 µm periodic planar structure are only possible for λ<1.45 µm. A narrow ~45-nm (FWHM) bandwidth indicates that all 5 half-periods seen in Fig. 6(b) are acting coherently. Hence, the DOE method of laser interference appears robust in replicating identical multi-layer periodic structures deeply throughout the resist.

The band dispersion relation for this structure was calculated from the iso-intensity surface of Fig. 6 and is shown in Fig. 7(a). This iso-intensity surface had been computed iteratively to match the SEM contours, the periodicity, and the ratio c/a=6.27/1.05=5.97 observed in the fabricated structure. The computed filling fraction of f=64% corresponds well with the approximate f ≈ 69% value estimated from the SEM cross-sections. The observed stop band at 4.45-µm closely matches the predicted stopband at 4.62-µm (a/λ=0.2273) in the Γ-Z direction of the energy dispersion curve as identified by the two horizontal lines crossing both figures. The predicted bandwidth of ~58-nm slightly exceeds the observed ~45-nm (FWHM) bandwidth.

 

Fig. 7. Band calculation a) for 1D-DOE formed “Woodpile” template (f=64%, c/a=5.97, n _r=1.6) shown in Fig. 6 and b) infrared spectral recording along Γ-Z direction.

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These mismatches can be readily attributed to uncertainties in estimating the structural shrinkage, the filling fraction, the motif, and the refractive index of SU-8 (n _r=1.6). The spectral response of the stopband was nearly invariant over relatively large sample area (~2000 µm diameter) confirming the good structural uniformity of the photonic crystal over the large exposure area. Figure 7(a) further reveals several narrow higher order bandgaps are also predicted in the band calculation, which however we could not definitively assign to the spectroscopic observations in Fig. 7(b) at the present time.

We further performed spectral characterization of stop bands at multiple angles of incidence from normal incidence (Γ-Z) up to close to ~70 degree from surface normal in the azimuthal plane at lower wavelength range of 1.2–1.6 µm to probe higher order bands. Transmission spectra were recorded on a fiber-to-fiber U-bench using a broadband light source (Agilent, 83437A) collimated to 500-µm diameter (1/e² intensity), a rotating mount for the sample holder, and an optical spectrum analyzer (Ando, AQ6317B). A reference transmission spectrum was recorded for a solid photoresist-coated (~13-µm thick) glass substrate for various angles between ±70 degree and used to normalize the transmission spectra of the “Woodpile” samples. Aside from differences in Fresnel losses, no angular dependence effects were observed in the reference sample spectra. The normalized transmission spectra of the “Woodpile”-type structure are plotted in Fig. 8 for various incident angles between 0° and 24°. High transmission with relatively flat spectral response was noted for all angles from 0 to 16°. Three strong attenuation troughs started to appear around 16° angle of incidence at ~1280 nm, 1397 nm and 1541 nm with spectral spacing of 117 nm and 144 nm, respectively. The spectral attenuation increases monotonically with angle from the approximate -1-dB baseline at 16° to a peak value of approximately -22 dB at ~21°. With further increase in angle of incidence, the attenuation diminishes and a flat high transmission spectrum is found again at ~25°, which continues to remain high up to angle 70°. As expected due to the crystal symmetry, the spectra follow similar angular dependence at negative angles of incidence as well. The spectral resonances are not due to Fabry-Perot resonances which would generate a much smaller free-spectral range for 13-µm thick photoresist on 1-mm thick glass substrates.

 

Fig. 8. Infrared transmission spectra through a “Woodpile” template (Fig. 6) for various angles of incidence (degree) from the sample normal.

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It is interesting to observe that these stopgaps are present only for a narrow angular range. Given the a≈1.05-µm lattice constant and λ=1.2–1.6 µm probing range, the range of a/λ ≈ 0.84–0.65 correspond to higher order bands. However, small uncertainties in the physical structure prevent sufficiently precise energy band calculations to permit definitive band assignments to these higher energy stop bands which remain open for such narrow range of angle. Nevertheless, the narrow angular resonances in Fig. 9 confirm the formation of a highly uniform 3-D “Woodpile”-type structure throughout the thick resist (13 µm) and over large area (2 mm diameter), which would otherwise be washed out by minor lattice distortions for such high-order bands. Such narrow angle spectral sensitivity can be exploited for various sensor applications. We are presently developing DOE methods that will reduce the c/a ratio and provide complete photonic bandgap when inverted with high refractive index materials.

5. Summary

This paper provides a design guideline for fabricating “Woodpile”-type photonic crystal templates by sequential 1D-DOE laser exposure. With suitable DOE parameters, a complete stopband was shown to be possible after inversion with high index media. Long-period DOEs (Λ=1.066 µm) provided 3-D templates in SU-8 photoresist that confirm formation of thick, large area periodic nano-structures with “Woodpile”-type structure closely matched to optical interference iso-intensity predictions. Spectroscopic characterization of the templates revealed numerous low and high energy stopbands along preferential crystallographic directions that were consistent with calculated band dispersion curves for the low-index media. The SEM and spectral observations show good structural uniformity through a relatively large resist thickness and over large exposure area that promise 3-D photonic crystal devices with high optical quality.