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Abstract
We experimentally investigate a new class of quasi-aperiodic structures for improving the emission pattern in nanowire arrays. Efficient normal emission, as well as lasing, can be obtained from III-nitride photonic crystal (PhC) nanowire arrays that utilize slow group velocity modes near the Γ-point in reciprocal space. However, due to symmetry considerations, the emitted far-field pattern of such modes are often ‘donut’-like. Many applications, including lighting for displays or lasers, require a more uniform beam profile in the far-field. Previous work has improved far-field beam uniformity of uncoupled modes by changing the shape of the emitting structure. However, in nanowire systems, the shape of nanowires cannot always be arbitrarily changed due to growth or etch considerations. Here, we investigate breaking symmetry by instead changing the position of emitters. Using a quasi-aperiodic geometry, which changes the emitter position within a photonic crystal supercell (2x2), we are able to linearize the photonic bandstructure near the Γ-point and greatly improve emitted far-field uniformity. We realize the III-nitride nanowires structures using a top-down fabrication procedure that produces nanowires with smooth, vertical sidewalls. Comparison of room-temperature micro-photoluminescence (µ-PL) measurements between periodic and quasi-aperiodic nanowire arrays reveal resonances in each structure, with the simple periodic structure producing a donut beam in the emitted far-field and the quasi-aperiodic structure producing a uniform Gaussian-like beam. We investigate the input pump power vs. output intensity in both systems and observe the simple periodic array exhibiting a non-linear relationship, indicative of lasing. We believe that the quasi-aperiodic approach studied here provides an alternate and promising strategy for shaping the emission pattern of nanoemitter systems.
© 2017 Optical Society of America
1. Introduction
Photonic structure plays a significant role in tailoring emission in nanoemitter systems [1–12]. For instance, concentrating high electric field near active regions can enhance the radiative recombination rate [13–16]. Improving the radiative recombination rate is essential for systems inhibited by nonradiative processes, such as surface recombination. Moreover, aligning the emitter frequency with an optical mode above the light cone can drastically increase light extraction [15–17]. Interestingly, however, optical modes can exist above the light cone that are forbidden by symmetry to couple into the radiation continuum [18]. Such uncoupled modes have found extensive use in photonic crystal surface emitting lasers (PCSELs) owing to their high quality factors (Qs) and low lasing thresholds [19,20]. However, uncoupled modes also yield cylindrical far-field patterns referred to as donut beams, which are often undesirable in lasing and lighting applications. Previous work has improved the far-field uniformity of uncoupled modes by breaking the symmetry of the emitting structure [19,20]. Specifically, a square array of circular holes in a photonic crystal slab was tailored into a square array of triangular holes [19,20].
Recently, much nanoemitter work has turned its attention to III-nitride material systems [12,21,22]. One attractive feature of III-nitride devices is their wavelength tunability, which extends throughout the visible spectrum [23]. Both bottom-up and top-down fabrication strategies have been used to produce highly anisotropic nanowire arrays in III-nitride material systems [12,21,22]. However, these fabrication methods make it difficult to arbitrarily change the shapes of nanowires due to growth considerations and etch-plane competition. Consequently, new methods for improving the far-field uniformity of uncoupled modes in III-nitride nanowire systems are of interest to a variety of lighting and lasing applications.
In previous work, we theoretically investigated quasi-aperiodic nanowire arrays in a III-nitride emitter system [16]. In quasi-aperiodic arrays, symmetry is broken by introducing asymmetry on a small scale and repeating the small-scale asymmetry on a larger scale. In our theoretical work, we predicted that quasi-aperiodic arrays could be leveraged to improve vertical light extraction without sacrificing broad band emission [16]. In the present work, we experimentally demonstrate the tailoring of emission using quasi-aperiodic nanowire arrays. We fabricate the quasi-aperiodic nanowire arrays using a top-down approach, beginning with a III-nitride epitaxial structure. We also fabricate simple periodic arrays, consisting of a square array of cylindrical nanowires, in order to compare its optical behavior with the quasi-aperiodic array. The two structures are characterized using room-temperature micro-photoluminescence (µ-PL) measurements. Both structures exhibit optical resonances in predicted theoretical windows. The resonance associated with the simple periodic array is shown to be much sharper than the quasi-aperiodic array, but it also produces a donut beam in the emitted far-field. Alternatively, the resonance associated with the quasi-aperiodic array is much broader, but produces a more uniform far-field emission pattern. We then study the relation between input pump power vs. output intensity in each system and find that the simple periodic array exhibits a non-linear dependence, indicative of lasing. We analyze the optical behavior of each structure using the finite-difference time-domain (FDTD) method and perform photonic bandstructure calculations. We discuss the potential for reducing distributed in-plane feedback using quasi-aperiodic structures, which is a quantity critical to large-area photonic crystal surface emitting lasers (PCSELs). We believe quasi-aperiodic arrays offer a promising platform for beam-shaping and decreasing in-plane distributedfeedback in nanoemitter systems.
2. Device design and fabrication
We begin by considering the III-nitride system of a simple periodic array shown in Fig. 1(a). Each nanowire is composed of GaN (green) and contains five axial InGaN quantum wells (black). The lattice spacing is a, the rod height is h, and the nanowire radius is r. For the structures studied here, we choose a = 240 nm – 280 nm, r/a = 0.167 - 0.25 and h = 600 nm. The selection of these lattice parameters aligns a series of uncoupled, guided resonance modes within the emission bandwidth of our III-nitride system. Figure 1(b) shows a quasi-aperiodic array wherein the dashed white lines indicate the boundaries of four complex unit cells (or supercells), each containing four nanowires. Each complex unit cell in the quasi-aperiodic array is asymmetric, but the overall structure remains periodic on a larger scale. The nanowire height and radius are the same as for the simple periodic array, and the lattice constant of the complex unit cell is double that of the simple periodic array.
Fig. 1 Schematics of (a) simple periodic and (b) quasi-aperiodic arrays. In the figures light green shading indicates GaN, while dark green shading indicates the position of five axial InGaN QWs. The dashed white lines indicate the boundaries of the irreducible unit cells in each structure (in (b), a* = 2a). Electric field intensity (gray scale) and in-plane electric field vectors (green arrows) of resonant modes for the (c) simple periodic and (d) quasi-aperiodic complex unit-cells. Solid green lines indicate nanowire boundaries while white dashed lines indicate cross-sectional planes. Emitted far-field patterns for the (e) simple periodic and (f) quasi-aperiodic resonances as a function of direction cosines. The intensities depicted are in arbitrary units.
The epitaxial structures used in this work were grown on c-plane GaN/Al2O3 using metal-organic vapor phase epitaxy (MOVPE). The wafer consists of a nominally 4.7 μm thick n-GaN buffer layer grown on an Al2O3 substrate. The thick n-GaN growth is followed with a 185 nm thick In0.04Ga0.96N underlayer, five 2.7 nm thick In0.15Ga0.85N/GaN QW layers and, finally, a 200 nm cap of n-GaN. Device fabrication is illustrated in Fig. 2 and follows a top-down recipe developed at Sandia National Labs [12].
Fig. 2 Device fabrication procedure: (a) EBL patterning of PMMA followed by MIBK:IPA development (b) Ni deposition followed by liftoff (c) Cl-based dry etch (d) KOH-based wet etch followed by H2SO4–based Ni removal. Green indicates GaN, blue indicates PMMA, silver indicates Ni, and black lines indicate axial InGaN QWs.
We begin device fabrication by spinning polymethyl methacrylate (PMMA) resist onto our sample and patterning an array of holes using electron beam lithography (EBL) [Fig. 2(a)]. Following development, the patterned holes are filled with Ni in an electron beam evaporator. Next, Ni islands are formed via lift-off in an acetone bath [Fig. 2(b)]. Lift-off is followed with an inductively coupled plasma (ICP) etch, utilizing a Cl2/BCl3-based etch chemistry. The Ni islands function as a hard mask during the dry etch, leading to the formation of tapered nanowires [Fig. 2(c)]. To improve nanowire anisotropy, the devices are immersed in a KOH-based solution (1:6 KOH: DI H2O) at a temperature of nearly 65 ̊ C. Finally, the remaining Ni is removed using H2SO4, producing an array of anisotropic nanowires [Fig. 2(d)]. Fig. 3(a) and 3(b) show scanning electron micrographs (SEMs) for fabricated simple periodic and quasi-aperiodic nanowire arrays. Insets show overhead views of each array and contain the same number of nanowires in equal cross-sectional areas. Black scale bars represent a physical length of 500 nm. Typical device size was 20 μm x 20 μm. The combination of a dry etch followed by a wet etch results in near atomically smooth sidewalls effectively lowering non-radiative recombination [12]. However, since this process results inetch termination at atomic planes [12], it is inherently difficult to arbitrarily change the shape of nanowires using this method. Consequently, in order to break field symmetry, it grows important to instead change the position of the nanowires using a supercell, as shown in the inset of Fig. 3(b).
Fig. 3 SEMs for a (a) simple periodic and (b) quasi-aperiodic device. Insets show cross-sectional views of each structure. Black markers indicate a physical length of 500 nm. Black arrows indicate areas where nanowire bases are connected in the quasi-aperiodic array
3. Device characterization
Fabricated devices were optically characterized at room-temperature using an ultraviolet micro-photoluminescence (µ-PL) setup. Our excitation source was a quadrupled Nd:YAG laser with a peak emission wavelength of 266 nm, a 10 kHz repetition rate and pulse lengths of ~500 ps. The laser’s peak power density was adjusted using a tunable neutral density filter. A 50X Mitutoyo deep-UV objective focused the laser to a spot size of nearly 5 µm onto the sample. Device photoluminescence was collected using the same objective, and divided into two separate paths using a 50/50 beamsplitter. The first path was used to image the fabricated devices while the second path was directed into a 300 mm spectrometer and liquid N2 cooled CCD camera for spectrum analysis.
Figure 4 shows the optical response of a simple periodic (black) and a quasi-aperiodic (purple) array. In order to better visually compare the two resonances, the integration time associated with the quasi-aperiodic array was approximately six-times longer. As seen in the figure, the simple periodic structure exhibits a resonance at λ ~385 nm, corresponding to the gain window of the InGaN underlayer, and exhibits a quality factor (Q) of 385. On the other hand, the quasi-aperiodic resonance is red-shifted towards peak MQW emission (λ ~440 nm) and is broader with a much lower quality factor (Q ~ 40). The emission wavelength of the simple periodic array corresponds to a reduced frequency of a/λ = 0.623 (assuming a = 240 nm). Similarly, the emission wavelength of the quasi-aperiodic resonance corresponds to a reduced frequency of a/λ = 0.545 (assuming a = 240 nm, where a* = 2a = 480 nm). Please note that the correspondence between normalized frequency and wavelength for this lattice constant are also presented graphically in Fig. 6.
Fig. 4 (Left) Room-temperature PL for a simple periodic (black) and quasi-aperiodic (purple) device. Dashed lines indicate the center of a resonance in each device. (Right) Emitted far-field patterns of the simple periodic (top) and quasi-aperiodic (bottom) resonances.
The significant difference in quality factors arises from the symmetries of the optical modes supported in each structure. The simple periodic structure supports a resonance which is forbidden by symmetry to escape as normal radiation, and thus lends itself to smaller losses and a higher quality factor. To illustrate this point, we calculated the electric fields and far-field distributions of modes supported in each structure using the finite-difference time-domain (FDTD) method (Lumerical FDTD Solutions). The electric field intensity and in-plane electric field vector for a low-order mode supported in the simple periodic array is illustrated in Fig. 1(c). Such modes are commonly referred to as uncoupled modes, and manifest themselves as donut beams in the emitted far-field, as evidenced from inspection of Fig. 1(e). The short range aperiodicity in the quasi-aperiodic structure, however, breaks the mirror symmetry present in the original geometry. Breaking the mirror symmetry also breaks the optical mode symmetry [Fig. 1(d)], similar to changing emitter shape [19,20]. Breaking the mirror symmetry enables vertical light to escape more easily, thereby reducing the resonance’s Q. Figure 1(f) confirms these details and shows, by comparison, a much more uniform far-field distribution.
We further evaluate our theoretical predictions by measuring the emitted far-field distributions produced by each resonance. The right inset of Fig. 4 shows the measured far-field patterns produced by both the simple periodic and quasi-aperiodic resonances. As theoretically predicted, the higher Q, simple periodic resonance (top right) emits a donut-like beam while the lower Q, quasi-aperiodic resonance (bottom right) emits a more uniform beam. While donut beams have found extensive use in a variety of applications [24], they are often not ideal beam profiles for lasing and lighting applications [20]. Using a quasi-aperiodic array, however, it is possible to significantly improve light extraction along the normal direction and reshape the emitted beam profile.
Next, we study the evolution of the optical output intensity of each resonance as a function of input pump power [Fig. 5]. For the simple periodic case [Fig. 5(a)], the output intensity of the resonance begins to linearly increase as the input power steadily increases. Near an input power density of 120 kW/cm2, however, the input power-output intensity relation turns non-linear. For the quasi-aperiodic array [Fig. 5(b)], the input power-output intensity remains linear through an input power density up to 1200 kW/cm2. A further increase of the input power resulted in a total loss of the quasi-aperiodic resonance, likely due to optically destroying the nanowires. Not observing a nonlinear input power-output intensity relationship for the quasi-aperiodic resonance is likely attributed to its low Q. To examine this further, we theoretically calculated Qs in each structure using FDTD. Our theoretical calculations predicted Qs of 442 and 129 for the simple periodic and the quasi-aperiodic arrays, respectively. While the theoretical Q for the simple periodic resonance is close to its measured value, this is not the case for the quasi-aperiodic resonance. The discrepancy between theoretical and measured Qs likely arises from the close nanowire proximity in the quasi-aperiodic array and resulting fluctuation in nanowire heights. During the KOH-based wet etch, close nanowire proximity results in a large degree of etch-plane competition near nanowire bases, effectively altering the heights of neighboring nanowires; this effect can be seen in Fig. 3(b) and is indicated by two black arrows. However, this fluctuation in nanowire height could potentially be mitigated using a two stage dry etch / wet etch process. Further, incorporating organic sulfide passivation techniques into the process may increase the device’s quantum efficiency [25]. However, such an approach involves increased fabrication complexity. Consequently, another alternative for addressing nanowire height uncertainties and device passivation might, instead, involve bottom-up, selective-area growth techniques such as molecular beam epitaxy (MBE) or metal-organic vapor phase epitaxy (MOVPE) [22, 26–28].
Fig. 5 Input power-output intensity relations for a resonance in a (a) simple periodic array and (b) quasi-aperiodic array. Projected scale bars mark the peak amplitude of each device resonance at varying pump powers.
4. Photonic bandstructure calculations
To gain further insight into the optical behavior of each system we theoretically examine their photonic bandstructure. Figure 6(a) and Fig. 6(b) show calculated photonic bandstructures for both the simple periodic and quasi-aperiodic arrays taking r = 65 nm, h = 200 nm, a = 240 nm and a* = 2a = 480 nm. Here, we assume emission is predominantly tangential to the quantum well plane, and thus calculate the transverse electric (TE) band structure, or even-symmetric modes [13]. Moreover, we have used a smaller nanowire height to more clearly show band dispersion. We note that increasing nanowire height increases the effective index, pushing photonic bands lower in frequency (or longer in wavelength). For the present study, the bands of interest are shown in red, and extend along the Γ-X direction in reciprocal space. The simple periodic array, shown in Fig. 6(a), supports a band which is highly quadratic. Near the Γ-point, the group velocity (υg = dω/dk) of the red band approaches zero, dramatically increasing the density of states at this frequency. Such slow light, band-edge modes have proven to be of great use in nanoemitter design [12,15,19,20]. Aligning the emission frequency with slow light modes has been shown to significantly improve the spontaneous emission rate [12,15]. However, slow light modes can also pose a problem to large area PCSEL design due to distributed in-plane feedback, a quantity inversely proportional to the group velocity of light. Distributed in-plane feedback, if too large, can create separate areas of coherence, or multiple lasing regions within a single device. Solutions have recently been proposed to decrease distributed in-plane feedback by using specialized photonic lattices that produce highly linear bands [29,30].
Fig. 6 Calculated TE photonic bandstructures for (a) simple periodic and (b) quasi-aperiodic arrays composed of GaN nanorods in air. Here, r = 65 nm, h = 200 nm, a = 240 nm and a* = 2a = 480 nm. Insets within each figure represent unit cell cross-sections.
Figure 6(b) shows the band dispersion for the transverse electric modes in the quasi-aperiodic array. In the figure bands of interest are outlined in red. As compared to the simple periodic structure [Fig. 6(a)], the dispersion of the quasi-aperiodic array’s modes (lower of the two red colored band) is much more linear at the Γ-point. The lower Q of the emission would suggest it corresponds to the lower red band. Such bands could also potentially be of interest for reduction of distributed in-plane feedback strength [29,30]. We note that tailoring photonic bandstructure dispersion in this manner is not limited to a 2x2 complex unit cell, nor to a square lattice and, and thus, provides many degrees of design flexibility.
5. Summary
In summary, we have experimentally demonstrated a new method for tailoring emission in nanophotonic systems composed of III-nitride nanowire arrays. We fabricated a quasi-aperiodic photonic crystal array using a top-down fabrication procedure. The quasi-aperiodic structure was obtained from a square lattice by adjusting the position of nanowires within 2x2 supercells. The introduction of small scale asymmetry effectively broke the field symmetry present in the original, simple periodic array, thereby leading to a great improvement in far-field uniformity. Further, a theoretical analysis of photonic bandstructures showed that quasi-aperiodic arrays can be leveraged to decrease distributed in-plane feedback. We believe quasi-aperiodic arrays offer a promising new topology for increasing far-field uniformity and decreasing the in-plane feedback strength of future nanoemitter systems.
Funding
U.S. Department of Energy’s National Nuclear Security Administration (DE-NA-0003525).
Acknowledgments
This work was completed in part at the Center for Integrated Technologies. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525. The authors thank Arthur J. Fischer, George T. Wang, John Nogan, Anthony R. James, Anthony J. Coley, Michael Smith and Olga Blum Spahn for helpful discussions.
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