a -SiO x <Er> active photonic crystal resonator membrane fabricated by focused Ga + ion beam

: We have fabricated thin erbium-doped amorphous silicon sub-oxide ( a -SiO x <Er>) photonic crystal membrane using focused gallium ion beam (FIB). The photonic crystal is composed of a hexagonal lattice with a H1 defect supporting two quasi-doubly degenerate second order dipole states. 2-D simulation was used for the design of the structure and full 3-D FDTD (Finite-Difference Time-Domain) numerical simulations were performed for a complete analysis of the structure. The simulation predicted a quality factor for the structure of Q = 350 with a spontaneous emission enhancement of 7. Micro photoluminescence measurements showed an integrated emission intensity enhancement of ~2 times with a Q = 130. We show that the discrepancy between simulation and measurement is due to the conical shape of the photonic crystal holes and the optical losses induced by FIB milling.


Introduction
Erbium-doped silicon-based materials have been recognized as attractive and promising for the realization of all-silicon optoelectronics and integrated photonics -of particular interest for telecom [1]. This is mainly due to the luminescence originated from the transition between the Er 3+ two lowest spin-orbit levels 4 I 13/2 → 4 I 15/2 that occurs at 1540 nm, near the center of the C-band for optical fiber communication [2,3]. Also, because in principle one can obtain optical gain in these materials without the use of hybrid structures employing III-V compounds [4]. A promising approach to telecom applications is combining the Er doped layers with a photonic crystal cavity. The use of resonant cavities based on Photonics Crystals (PC), with a photonic trap, i.e., a defect in the lattice, has been the subject of intense investigation due to their capability of providing very high photonic confinement with enhanced interaction between photon and matter [5]. Particularly in this area, several works have been reported where an Er-doped silicon rich nitride (SRN) layer is coupled to photonic crystals. Makarova et. al. demonstrated high quality factor (Q-factor) in 2-D PC based on SNR/Si suspended membranes [6]. Gong et al. observed linewidth narrowing and Purcell factor enhancement both in 2-D PC´s and in microresonators [7]. Moreover, they also reported the observation of transparency in photonic nanobeam cavities made with this same material [8]. It is interesting to notice that high Q-factors are obtained for these structures even though they all have low index contrast. In this regard, several authors have also reported on the design of high Q-factor, low index PC cavities with a variety of indices of refraction (from 1.4 to 2.5), using one dimensional nanobeam cavities and two dimensional planar cavities [9][10][11][12][13][14]. Furthermore, perturbation to PC´s near the photonic trap has lead to great enhancement of the Q-factor [15,16].
A considerable drawback of using these Er based materials is that their light emission efficiency is very low when compared to other semiconductor active materials such as III-V. We have recently shown that a multilayer structure based on Er-doped amorphous silicon suboxide, silicon dioxide and silicon can enhance up to 4.2 times the emission at 1540 nm. This was accomplished using a multilayer structure that provides the optimum overlap between the electromagnetic field and the active material. Also important in that work is optimized thermal annealing of the active material [17,18]. Our challenge in this present work is to combine a high luminescent multilayer structure with the optical confinement provided by a photonic crystal. We expected that while the photonic bandgap enables the in-plane confinement, the multilayer structure allows the best vertical overlap with the active material and, thus, both can enhance the light emission.
In this work we report an active photonic crystal resonator H1 type (H1-PBG) [19] based on amorphous silicon sub-oxide doped with erbium as gain media. We designed a multilayer structure with a-SiO x <Er>/SiO 2 /Si(substrate) for post photonic crystal fabrication. 2-D simulations were performed to obtain the air holes dimensions and periods that support a resonance at the photonic bandgap of the structure. For a rapid and single step fabrication approach we used a Focused Ion Beam (FIB) milling as an alternative method for conventional etching techniques. FIB milling has been frequently used for the fabrication of devices in hard materials such as diamond [20,21], but has also been employed for the fabrication of devices based on III-V compounds and silicon [22][23][24]. In our design, FIB milling was used to create the PC air holes and an air layer in the Si substrate right below the SiO 2 layer. This new layer creates an active media suspended in air, which brings possibilities of applications in active photonic devices and optomechanical systems [25,26]. Notice that this layer has to be designed such that it does not affect the multilayer enhancement of the luminescence. The use of etching of an underneath layer for the fabrication of high performance 2-D photonic crystal lasers using III-V compounds has been demonstrated [27][28][29]. These works rely on wafer bonding, AlAs oxidation, and/or InP/InGaAsP selective wet chemical etching which in general are not as easily implemented on silicon-based materials such as a-SiO x <Er>. Moreover, if FIB can be used for a single step fabrication of high Qfactor structures on silicon based material that can also provide gain at wavelengths of interest for telecom; our approach is of great relevance. A challenge with our design is the fact that the utilized material has a much lower refraction index contrast, which will intrinsically provide lower Q-factor than III-V materials. Although it was aforementioned the possibility to design high Q-factor resonators with low index contrast materials, we are still investigating the possibility of obtaining a design which provides high Q´s using our highly efficient multi-layer structure [18]. A second challenge is that FIB milling is known to produce conical holes due the Gaussian profile of the beam cross-section, as well as damages induced by ion implantation, for instance, that can seriously affect device performance [20,21,23,24]. In spite of this, the results showed an enhancement of photoluminescence intensity as well as a reduction in emission linewidth. Using a full 3D simulation we were able to show the effects of the conical holes in the photonic bandgap and predict the measured enhancement and to pinpoint the most important causes for performance deterioration. Particularly, we show that the conical holes geometry shifts the as-designed bandgap center and reduces its width. More importantly, we show that optical losses induced by FIB milling are majorly responsible for a drastic reduction in the cavity Q-factor.

Design of the photonic bandgap structure
The proposed device shown in Fig. 1 is an air-bridge photonic crystal slab with 3-D confinement [27]. The slab is made of a-SiO x <Er>/SiO 2 /Si multilayer separated by an air layer from the silicon substrate. The multilayer structure without the air layer is already optimized for high luminescence. Therefore, our task here is to define an air gap thickness that maintains the enhancement. The thicknesses of the layers, including the air gap are chosen to provide the largest overlap of the optical mode (electromagnetic field) and the Er 3+ doped material at the wavelength of 1540 nm. The design essentially optimizes the integral [17,18]  SiO 0 where E air and E SiO2 are the counter-propagating waves calculated at 1540 nm after a single reflection at the a-SiO x <Er>/air and the a-SiO x <Er>/SiO 2 interfaces, respectively. The average integral is performed in the perpendicular direction (z direction) for all points within the a-SiO x <Er> layer. L is the a-SiO x <Er> layer thickness as shown in Fig. 1. A simple transfer matrix method was used to design the multilayer structure [30]. According to the simulation, the thicknesses are: 600 nm of a-SiO x <Er>, 530 nm of SiO 2 , 114 nm of Si and 1550 nm of air. Refraction index of 2.6, 1.44, 3.4 and 1 were used for the layers, respectively. A H1-defect hexagonal photonic crystal was designed to provide the confinement, as well as small effective volume, of guided modes within the slab. The initial design was based on a 2-D approach using the effective refraction index of a first order guided electromagnetic field in the a-SiO x <Er> layer. To carry out this simulation we used the BandSOLVE module of the Rsoft photonics simulation tool, employing the plane-wave expansion (PWE) method [31]. We considered an effective medium with refraction index of n eff = 2.4. The lattice dimensions are 11 x 13 air holes of 240 nm of radii and period (center-to-center) of 600 nm. The total area of the device is 5676 nm x 7980 nm. Although the resulting band structures obtained with this method include multiple folding of the real band diagram, its simplicity and short computation time results in an efficient tool for the initial design. Also, quasi-TM and quasi-TE modes can be easily separated. Moreover, it is possible to include the H1-defect in the unit cell such that localized states in the planar direction can be found. In summary, the initial design includes a 2-D simulation plus a simple analytical discussion about the expected confined modes. Further in this paper, we perform a full 3-D hybrid TE-TM simulation for the band structure and the resonant modes. Using this full 3-D simulation we validate our initial approach and can proceed to evaluate the effects of fabrication limitations to the final result of our structure.
The band diagrams for the transverse electric like (TE-like) and the transverse magnetic like (TM-like) polarizations are shown in Fig. 2. TE-like and TM-like are defined such that TE-like (TM-like) has no electric (magnetic) field along the direction perpendicular to the membrane. We have used the normalized frequency / 2 c / a a ω = ω π = λ in this plot, where ω is the free space angular frequency, a is the lattice period, c is the phase velocity of light and λ the free space wavelength. Figure 2(a) shows that there is no photonic bandgap for TM-like polarization. On the other hand, there is a photonic bandgap between 0.343 and 0.466 with photonic resonances near ω = 0.385 for the TE-like polarization, as shown in Fig. 2(b). This corresponds to a photonic bandgap between 1290 nm and 1750 nm with resonances near 1555 nm. The latter value is very close to the intrinsic Er 3+ 4f shell emission ( 4 I 13/2 → 4 I 15/2 : 1540 nm).  Figure 3 exhibits the electric field energy distribution on the slab calculated for the resonance within the photonic bandgap for TE-like polarization (electric field in-plane). We observe two quasi-doubly-degenerate second order dipole modes as also described by Tang et al [32]. In fact, the calculated resonances are doublets with a typical split of ∆ω ~0.00025.
We call this mode quasi-doubly-degenerate because there is an asymmetry in the 11 x 13 air holes finite lattice. The fact that only the second order modes are observed can be explained qualitatively. Since the photonic bandgap is centered at the K point of the first Brillouin zone of the hexagonal lattice, the normalized angular frequency of the bandgap center (a/λ) gap can be written as: where n is the area average refraction index between material with the effective index n eff and air holes of radii r. We can also obtain a simple expression for the resonance normalized angular frequency (a/λ) res assuming the center defect as a Fabry-Perot cavity with a length equal to 2(ar) and refractive index n eff : where M is an integer number. In our case, r/a = 0.4 and n eff = 2.4; as a result (a/λ) gap ~0.4 and (a/λ) res ~0.17M, therefore, M = 2 (second order) is required for the resonance to fit within the photonic bandgap. Figure 4 shows the TE-like bandgap opening and the resonances as a function of r/a (r fixed at 240 nm) simulated by the BandSOLVE. Also, Fig. 4 displays the expected values for the bandgap center and the first and second order resonances as obtained by Eqs. (2) and (3), respectively, showing that a first-order resonance does not occur inside the photonic bandgap.

Fabrication of the structure
A 530 nm SiO 2 layer on n-type Si (100) wafer was grown by wet-oxidation at 1000 °C for ~100 minutes in a flux of 1.0 l/min of O 2 and water vapor. A refractive index of 1.44 was measured by spectroscopic ellipsometry at 1540 nm. Subsequently, a 600 nm thick a-SiO x <Er> film was deposited on SiO 2 /Si(substrate) by reactive co-sputtering method [33]. The base pressure of the vacuum chamber was 2x10 −6 mbar and the sputtering was carried out in RF mode with the bias fixed at 1kV from circular sources in an atmosphere of 8x10 −3 mbar of argon and 5.5x10 −5 mbar of oxygen. The oxygen pressure, and the consequent oxygen composition of the a-SiO x <Er> layer, was determined after extensive optimization of the photoluminescence at ~1540 nm [34]. A Si wafer mixed with metallic erbium pieces (~2 mm 2 ) was used as the source target for the sputtering deposition. The substrate temperature was maintained at 240 °C and the deposition rate was roughly 1.5 Å/s. This technique is a direct form to obtain simultaneously a-SiO x film doped with Er 3+ , unlike other reported methods requiring plasma deposition followed by Er implantation [35,36]. Rutherford Backscattering Spectrometry (RBS) indicated an Er concentration of ~5.5x10 18 atom/cm 3 , that corresponds to ~0.01 at.% [Er/Si]. The refraction index of the as-deposited material, measured at 1540 nm was about 2.6. This is a relatively high index value, very suitable for light confinement between a-SiO x <Er> and air, and agrees with literature for the same material obtained by different deposition techniques [37,38]. After co-deposition, the sample was thermally annealed in a N 2 atmosphere (3.0 l/min flux) at 400°C for 1 hour. This temperature was the best annealing condition obtained for the optimization of the emission efficiency in the wavelength range between 1500 -1600 nm (region of Er 3+ 4 I 13/2 -4 I 15/2 transition). Further increase in temperature tends to heal the dangling bonds and inhibit the Er emission [18]. A photoluminescence intensity enhancement of over 4.2 times after the thermal treatment was observed. Next step involved the fabrication of the photonic crystal membrane on the multilayer structure. This step was completely done by FIB using a Dual Beam FIB/SEM New 200 model from FEI Company. Gallium was used as the ion source. This technique has been shown to be an extraordinary tool for quick prototyping of devices with very good morphology [39]. Moreover, it is also very suitable for the fabrication of the photonic crystals because it allows the placement of the membrane anywhere in the sample, facilitating their monolithic integration with other optoelectronic devices. For the fabrication of the PC on the a-SiO x <Er> layer, FIB milling was performed to create air holes in this layer. The milling was done with an emission current of 50 pA and a voltage of 30 kV. The low current provides high resolution (20 nm) for this process with a total milling time of 30 minutes. Subsequently, a second milling was performed to obtain the air bridge. For this last step, the sample was rotated by 90° and a rectangular hole was milled using the following conditions: emission current of 0.5 nA, voltage of 30 kV and milling time of 16 minutes. Figure 5(a) shows a high resolution scanning electron microscopy (SEM) image of the air-bridge photonic crystal fully fabricated with the FIB. The central region is depicted in details in Fig. 5(b). Figure 5(c) shows a cross section image of the milled holes filled with platinum to enhance contrast. One observes that the holes have a tilt angle of about 6°. This occurs due to the Gaussian profile of the Ga + ion beam [21,24].

Results and Analysis
Micro-photoluminescence (µ-PL) measurements were carried out at room temperature. We used a 532 nm line of a Solid State Laser (Spectra Physics) as the optical pumping source. The pump laser was focused on the sample surface by a microscope objective lens (Mitutoyo NIR HR 50x, numerical aperture = 0.65) and positioned by piezo-electric nanopositioners. The spot diameter was about 2 µm. The luminescence from the sample was collected by the same objective lens and dispersed by a single-grating monochromator (SPEX 0.5m focal length with 600 grooves/mm grating and 1.6 nm spectral resolution and ± 0.5 nm accuracy). The collected light was measured by a liquid-N 2 cooled Ge p-i-n photodiode in the 1400 -1700 nm wavelength range and standard lock-in technique was used to improve the signal to noise ratio. Figure 6(a) shows the µ-PL spectra obtained at the H1 photonic defect region and out of the PC structure. Figure 6(a) also shows a circle corresponding to the pumping laser spot area. Clearly, one can selectively excite areas inside and outside the photonic crystal membrane. These measurements were performed with an estimated excitation power of 5 mW (measured on the sample). The spectrum outside the PC shows a peak (highest-intensity at ~1537 nm) corresponding to the 4 I 13/2 -4 I 15/2 transition and a smaller peak at ~1547 nm caused by the Stark effect [40]. The spectrum at the PC shows a main peak at 1535 nm and the Stark peak at the same position as the spectrum outside the PC. A lorentzian fit to each main emission peak is performed in the range from 1490 -1540 nm to ensure the Stark shoulder is not included. A reconstruction of the peaks after the fitting is shown on Fig. 6(b). We observed a small shift in the main emission peak by 1.8 nm, approximately 4 times larger than the spectrometer accuracy. The small shift and the absence of major cavity features in the emission spectrum at the photonic crystal is a result of the small Q-factor of the structure and, therefore, the large overlap between the optical resonance and the Er emission spectra. In addition, the emission from the photonic crystal membrane certainly has some contribution from scattered light from defects. Moreover, it is important to observe that no shift is observed for the Stark peak. Also, the emission spectrum at the photonic crystal shows an enhancement in the integrated PL intensity and a linewidth reduction with respect to the outside measurement. The total emission in the 1500 -1575 nm wavelength range is enhanced by a factor of 2, while the full width at half maximum (FWHM) reduces from 18.1 nm to 11.8 nm (measured outside and on the PC, respectively). The 6.3 nm reduction in linewidth is almost 8 times larger than the FWHM determination error. Therefore, it is reasonable to assume that the photonic crystal is narrowing the linewidth. In what follows, we will provide further evidence that indeed this enhancement is caused by the photonic crystal membrane. Further work with different designs and passive cavities should be performed to better tune our design and clarify this point. The enhancement in the integrated emission and the observed reduction in FWHM, are expected to be related to the presence of resonances in the photonic crystal. However, there is a ~20 nm disagreement between the peak position of the emission spectrum and the calculated resonances. For a more realistic description of the resonances in the structure, we performed a three dimensional band structure simulation and a three dimensional confined mode analysis using the full 3-D FDTD (Finite-Difference Time-Domain) method -FullWave module of the R-soft photonics simulation tools [31]. The multilayer structure and the exact device geometry were implemented in the simulation. The spatial domain used in the calculations was limited by a photonic crystal identical to the designed (11 x 13 air holes lattice around the central defect in the x-y plane).
We first proceed to calculate the band structure using the full 3-D simulation. Figure 7 shows the band structure considering hybrid polarization and even parity in the vertical direction. Figure 7(a) is the calculation for a structure fabricated exactly as designed, and, therefore, with cylindrical holes. A clear gap appears in the same region predicted for the quasi-TE band obtained by the 2-D simulation. Therefore, we observe that indeed the gap remains open even when the entire structure is considered. We also notice the presence of narrow high vertical order bandgaps that the layer can support. Before we proceed to the actual confined mode calculation it is important to investigate the band structure for the real device with the 6° conical holes. Figure 7(b) shows the calculation of the hybrid polarization, even vertical parity, band structure. One observes a narrowing of the bandgap and a shift of the bandgap center to shorter frequencies. Indeed, these effects have to be considered for the proper design of photonic bandgap structures. Nevertheless, considering the gap remains open for the real 3-D structure, we can proceed to search for confined resonant modes. The resonant modes were obtained as described in the following. First, matched layers (PML) were used as spatial boundaries in the crystal, acting as a non-absorbing reflective layer. A short electromagnetic field pulse is used to excite the cavity modes, and therefore, excite a large frequency range. The spatial distribution of this pulse is Gaussian and its wavelength range is between 500 -3000 nm, centered at 1550 nm. The simulation calculates the field components decay with time in the middle of the a-SiO x <Er> layer at the center of the H1 defect in the photonic crystal. A Fourier transform of the time decay of the field components provides a rough determination of the resonances. To refine the calculations, a new simulation is done with a pulse centered at the estimated resonance wavelength and with the spatial dependence of the mode obtained in the first iteration. More iterations are performed until the calculation converges.
Initially the perfect 3-D structure was simulated. To evaluate the differences between inplane and out-of-plane Q-factors, a perfect 2-D structure was also considered with an effective refractive index adjusted to provide the same resonance wavelength as the perfect 3-D. It was observed that only TE-like (electric field in-plane) polarization generates resonances -in agreement with the results shown in Fig. 2. Finally, a realistic simulation of the 3-D structure with the 6° conical holes was performed. Figure 8 shows the electric field energy decay obtained by each simulation. The resonance wavelength for the perfect 2-D and 3-D structure were found at 1557 nm, in very good agreement with the value obtained by the PWE method ( Fig. 2(b)). We estimated a Q of 638 and 350 for the perfect 2-D and the 3-D structure, respectively, from the time decay of the TE-like energy distribution. For the 3-D structure with conical holes it was found a resonance at 1533 nm and a Q diminished to 300a 14% reduction in the quality factor. This resonance wavelength calculated with the conical holes matches perfectly with the wavelength measured by µ-PL detection. Figure 8 also shows the TE-like mode spatial profiles (square of the in-plane electric field amplitude) provided by the three simulations. One clearly observes second order dipole modes for the calculated 3-D resonances -as predicted by the simpler treatment depicted in Fig. 3. The calculated 2-D resonance shows some delocalization and a mixture of first and second order dipole modes. It is still not clear why our simulation does not converge to a pure confined dipole mode in this 2-D case. Assuming that the measured Q-factor is the ratio between wavelength and the FWHM of the emission detected by µ-PL measurement at the PC defect, one obtains a Q ~130, and which is less than half the value obtained by simulation of the 3-D structure with conical holes. With the calculated spatial distribution of the mode we obtain an effective modal volume of V eff = 0.36 (λ/n) 3 and hence, an spontaneous emission enhancement for the two doubly degenerate modes of approximately 15 [41]. A simple rate equation analysis leads to a steady state photon density inside the resonator given by p = QR sp /ω, where ω is the photon frequency and R sp is the spontaneous emission rate. The rate of photons emitted on the vertical direction can be given by: where Q V is the vertical Q-factor. The vertical quality factor can be estimated as Q V ≈(Q || Q Total )/(Q || -Q Total ) = 775, where Q || = 638 is the value obtained with the perfect 2-D simulation. The enhancement of measured output power emission for light collected vertically from the structure should be directly proportional to the Purcell factor, but also it is directly proportional to the ratio between vertical and total Q-factor. Therefore, it is expected an enhancement of approximately 6 (15x300/775) for the PBG with the conical holes. The expected enhancement for the perfect 3-D structure (perfect air holes) is ~7, therefore the effect of the tilted hole profile in the emission enhancement is relatively small. Its effect is much more pronounced in the resonance wavelength position. In any case, our PL measurement shows only a factor 2 of increase. However, if we consider the same ratio between vertical and total Q, and assume the measured Q-factor instead of the simulated value, an enhancement of 2.5 is obtained, with a much better agreement with the experimental value.
Although the simulation appears to be consistent, one needs to understand the causes for the reduction in Q-factor from 300 to 130. One element that has not been included in the simulation is the possible residual loss induced by the Ga + ion implantation during the FIB milling. It is known that FIB milling leaves a 30 nm skin of heavily implanted gallium ions (up to 10 21 /cm 3 ) in all etched surfaces. One of the main effects of the implantation is an increase in optical scattering losses [24]. To evaluate the induced optical losses we simulated the same device adding optical absorption to a 30 nm skin of all FIB etched surface of the membrane. The calculated absorption constant that leads to a reduction in quality factor from Q = 300 to the measured value of 130 is approximately 3300 cm −1 . The time decay of the TElike energy distribution obtained for this simulation is shown by the dash-dotted red line in Fig. 8. This is indeed a large value that probably is over estimated, but nevertheless indicates that severe optical losses may be caused exactly at the edges and sidewalls of the holes. One needs to develop techniques to either heal or avoid this kind of damage in order to FIB to become a useful tool for nano-photonic fabrication.

Conclusion
We have fabricated active thin erbium-doped amorphous silicon sub-oxide (a-SiO x <Er>) photonic crystal membrane using focused gallium ion beam (FIB) for emission near 1550 nm. Integrated photoluminescence intensity enhancement of 2 times with linewidth reduction of 53.4% was observed with the photonic crystal structure. Full 3-D band structure and FDTD (Finite-Difference Time-Domain) simulations were performed for the analysis of the real structure including the conical shape of the air holes in the photonic crystal. The emission enhancement and the linewidth decrease agrees with the calculated Purcell and quality factors if the conical shape of the air holes is included in the simulation as well as a 30 nm thin absorption layer is added to all FIB milled surface. We estimated optical absorption losses of up to 3300 cm −1 by the FIB process, probably due to heavy implantation of gallium species.