Fabrication and optical characterization of GaN micro-disk cavities undercut by laser-assisted photo-electrochemical etching

For the fabrication of GaN micro-disk cavities, we used the substrate shown in Fig. 1(a) where a GaN buffer layer, InGaN/GaN SL, a GaN layer including an InGaN QW are sequentially grown on a c-plane sapphire by metal-organic chemical vapor deposition. The thicknesses of the layers are 1 μm, 300 nm, and 120 nm, respectively. In the SL, the respective thicknesses of InGaN and GaN are approximately 3 nm and 6 nm each. Figure 1(b) is a macro-PL spectrum measured for the substrate under the excitation by a CW He-Cd laser at room temperature. PL from the single QW is located at around 390 nm wavelength whilst that from the SL is around 430 nm. Circular disk patterns of diameter D are formed by reactive ion etching using Cl₂ and BCl₃ gas through a SiO₂ hard mask defined by EB-lithography. Then, the sample is immersed in 25 percent tetramethylammonium hydroxide (TMAH) aqueous solution for 10 min at 80 °C. For PEC undercut etching, we used the setup in Fig. 1(c). The sample and a Pt electrode are soaked in a HCl aqueous solution of 0.006 M concentration under a bias voltage of 0.1 V. Laser light at 405 nm wavelength pulsed by a chopper is irradiated to the sample. The pulse width, peak power, and repetition rate are 50 μs, 5 mW, and 10 kHz, respectively. The laser, of which wavelength is longer than the light emission of the QW, but shorter than that of the SL, is bandgap-selectively absorbed in the SL. Thus, highly selective undercut etching is expected.

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Optical characterization is performed by μ-PL spectroscopy using CW He-Cd laser at room temperature. The excitation laser is focused on the top of the micro-disk cavities with an objective lens of 20 times magnification and 0.45 numerical aperture. The PL signal is collected by the same objective lens and measured by a spectrometer equipped with a cooled CCD array. We measured PL spectra with different resolutions. The groove density of the grating used for the low-resolution measurement is 1200mm⁻¹ and 2400mm⁻¹ for the high resolution.

For calculation of free spectral range (FSR) and modal distribution for WGMs in GaN micro-disk cavities in Sect. 3.3, we used a three-dimensional finite-difference time-domain (3D-FDTD) method. ⁵¹⁾ The spatial mesh size is 0.01 μm × 0.01 μm × 0.01 μm. The micro-disk of D = 2.6 μm is simulated as a 120 nm thick-cylindrical disk made of GaN in air. Although the SL layer around the center of the micro-disk is left un-etched by PEC etching, it is not taken into account in our simulations. The refractive index of the GaN disk is set to 2.6. The influence of material dispersion and InGaN QW is not included.

Figures 2(a) and 2(b) are top and side-view SEM images of an undercut GaN micro-disk for D ∼ 3 μm. The PEC etching is conducted for 30 min for this sample. From the side view, you can find that the PEC etching occurs only at the layer underneath the GaN micro-disk, which indicates the selective removal of the SL layer under the GaN disk. The edge of the GaN micro-disk has high verticality because of the TMAH process before the PEC etching. The thickness of the disk is estimated to be approximately 120 nm. In the top view image, the undercut region is bright, while the darker region around the center of the disk indicates where the SL still remains. The high-level circularity of the bright region suggests that the PEC etching proceeds homogeneously in lateral directions. The length of the PEC etching in the lateral direction is approximately 1 μm. This corresponds to the etching rate of 33 nm min⁻¹ which is almost the same as that reported in Ref. 40 where a Xe lamp is used as the light source. The selective etching of relatively thick sacrificial layers of more than 100 nm is important for strong light confinement in GaN micro-disks. ⁵²⁾ These results indicate that the undercut etching of the GaN micro-disk is accomplished by our laser-assisted PEC etching.

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The red curve in Fig. 3(a) shows a measured low-resolution μ-PL spectrum for an undercut GaN micro-disk of D ∼ 3.0 μm. The spectrum for the unprocessed substrate is also shown in black. The excitation power is 4.6 μW for these measurements. Two distinct peaks are observed around 380 nm and 430 nm wavelengths for the unprocessed substrate. Through comparison with the micro-PL spectrum in Fig. 1(b), these peaks can be attributed to light emission from the QW in the micro-disk and that from the SL. In the measured spectrum for the GaN micro-disk, the PL intensity from the SL decreases due to undercutting etching of a part of the SL. Several sharp peaks are also observed in wavelengths longer than the QW emission peak. For detailed investigation, the spectral region of the peaks is magnified in Fig. 3(b). We can confirm that a few peaks periodically appear at a wavelength interval of Δλ ∼ 5.6 nm. This wavelength interval is considered the FSR of WGMs in the GaN micro-disk cavity. For the estimation of a theoretical value of the FSR, we calculate the value of the equation Δλ = λ²/(πDn_g), where n_g is the group refractive index. This leads to Δλ ∼ 5.7 nm under the assumption of n_g = 3, ²¹⁾ which coincides well with the experimental one. This result indicates that the observed peaks originate from WGMs in the GaN micro-disk cavity.

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The PL spectrum for D ∼ 3.0 μm in Fig. 3(b) also exhibits several peaks within the FSR. This result suggests that higher-order modes also exist in this cavity. For a more detailed investigation, we measured μ-PL spectra for different Ds. Blue and green curves in Fig. 3(b) show the spectra for D ∼ 2.6 μm and D ∼ 3.4 μm, respectively. As D increases from 2.6 μm to 3.4 μm, the number of peaks significantly increases. On the other hand, the theoretical FSR only varies from 6.5 nm to 5.0 nm. Thus, the increased number of peaks can mainly be due to the increase in higher-order modes.

For quantitative evaluation of the GaN micro-disk cavity, we estimate the quality factors of the WGMs by measuring the Lorentz line widths of cavity mode spectra. We observed high-quality factors for the GaN micro-disk cavity with D ∼ 2.6 μm. A measured high-resolution cavity mode spectrum is shown in Fig. 3(c). Two resonant peaks are observed at 396.2 nm and 396.6 nm wavelengths in this spectrum. Note that the background is subtracted by polynomial fitting. The fitted Lorentz function for these peaks is shown in black. The extracted line widths are 0.0589 nm and 0.0593 nm, corresponding to Q ∼ 6730 and Q ∼ 6690. These values are comparable to the highest Q-factor reported for GaN micro-disk cavities undercut by PEC etching. ¹⁹⁾ This result suggests that undercutting by laser-assisted PEC etching can form a smooth surface at the backside of GaN micro-disk cavities. The measured line widths in Fig. 3(c) are currently limited by the resolution of our optical setup. Spectroscopy evaluation at higher resolution may result in higher Q-factors.

Although some WGMs in our GaN micro-disk cavities can exhibit high Q-factors, the characteristic mode index for these WGMs is still unclear. As discussed in Sect. 3.2, a large number of higher-order modes are included in the PL spectra observed. In the case of our thin micro-disk cavities, the observed higher order modes can be mainly attributed to WGMs of higher radial mode indices rs. In order to identify the r for high-Q WGMs, we evaluated another GaN micro-disk cavity with a shorter undercut length of L_uc ∼ 0.4 μm. In our substrate, the QW light emission wavelength is shorter than that of the SL [see Fig. 1(b)]. Thus, an insufficient undercut (short L_uc) can result in a large absorption loss for WGMs. However, in the case of L_uc ∼ 0.4 μm, the absorption loss could be large only for r > 1 due to the difference in their spatial field distribution. In Fig. 4(a), a planar distribution of electric field energy density U_E calculated for the middle of thickness is shown for a WGM of r = 1 and r = 2. The U_E is strongly localized around the disk edge for r = 1. For r = 2, on the other hand, the U_E is also distributed apart from the disk edge. At 0.4 μm from the disk edge, the U_E for r = 1 becomes almost zero while the value is finite for r = 2 as shown in Fig. 4(b), where U_E is plotted as a function of position along the radial direction. Thus, we can expect that only the fundamental WGMs are observed from the micro-disk cavity of L_uc ∼ 0.4 μm.

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Figure 5 shows PL spectra measured for micro-disk cavities of D ∼ 2.6 μm with different L_ucs. The black curve is the spectrum for L_uc ∼ 0.4 μm and the blue is for L_uc ∼ 1 μm. For L_uc ∼ 0.4 μm, we observed six resonant peaks which are labeled with numbers 1 to 6 in Fig. 5. Because of the reason discussed above, these peaks can be attributed to the fundamental (r = 1) WGMs. The wavelength interval between the peaks is 4.7 nm for modes 1 and 3, and 5.1 nm for modes 3 and 5. These values are close to the theoretical FSR in Sect. 3.2. The wavelength dependence of the FSR is likely due to the material dispersion of GaN and InGaN QW. ^53,54) We also observe another resonant peak within the wavelength range of each FSR, namely the modes 2, 4, and 6 in Fig. 5. These modes appear with an FSR few percent larger than modes 1, 3 and 5. A 3D-FDTD simulation indicates that the fundamental WGMs with different polarizations exist in our micro-disk cavities. A calculated FSR for TE-like modes (dominant electric field is parallel to the disk plane) is approximately 10% larger than that of TM-like ones. Thus, the WGMs observed with slightly different FSR would be the fundamental WGMs of different polarizations. Although the polarization dependence of the FSR is slightly different between the simulation and experiment, it is likely due to the polarization dependence of InGaN QW absorption which can be stronger for TE mode than TM mode. ⁵⁵⁾ By comparing this result of L_uc ∼ 0.4 μm with the spectrum for L_uc ∼ 1 μm (blue curve in Fig. 5), the peak wavelengths of the fundamental WGMs for L_uc ∼ 0.4 μm reasonably match with some of the peaks for L_uc ∼ 1 μm. These modes can be considered as fundamental WGMs and labeled by the numbers 1' to 6' in Fig. 5. The high Q modes shown in Sect. 3.2 correspond to the modes 3' and 4', suggesting that these modes are the fundamental WGMs with different polarizations.

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