1. Introduction

In recent years, optical microcavities have gained considerable interest because of their applications in optoelectronics and integrated optics. A variety of cavity resonator geometries, including Fabry-Pérot resonators, photonic crystal resonators and whispering-gallery mode (WGM) resonances, has been fabricated [1,2]. Optical microcavities of different materials have been investigated in the forms of microdisks [3], microspheres [4,5], or micropillars [6]. Compared to other resonators, WGM exhibits much lower threshold and fairly high quality factor laser [7]. A new type of optical cavities, with the use of rolled-up micro- and nanotubes, have been developed, which are formed when a coherently strained epitaxial heterostructure is selectively released from the host substrate. Photons are strongly confined around the periphery of the tube, and the resulting near-perfect overlap between the maximum optical field intensity and the active region can lead to an extremely large modal gain. Optical coherent and stimulated emission have been observed in microtubes formed by GaInAsP material system as well as oxide material system [8–13]. It has also been demonstrated that their emission characteristics, including the mode profiles, emission direction, and output coupling efficiency, can be controlled by varying the tube diameters, wall thicknesses, as well as the surface geometry using standard photolithography process from Si and GaAs platform [14–17]. Yet there has been no investigation on the microtube optical resonators using III-Nitride semiconductor material, which have been of great interest both for basic research and for a wide range of applications in optoelectronics [18,19], integrated optics [20], electronics [21], micro fluidics [22], and biology [23]. Lasing behavior has been studied in GaN based micro rod, pillar, and disk by several groups, and observation of stimulated emission under optical pumping has been reported [24–27]. However, general problems inhibited in these structures include relative insufficient optical confinement factor, quality factor, and non-controllable lasing mode, all of which are essential to the realization of highly efficient visible light emission micro lasers. To target these problems, we present a novel microtubular structure laser with high confinement factor based on InGaN quantum wells (QWs) material system.

2. Experiments

The microtube structures are made from strained layers grown by Metal Organic Vapor Phase Epitaxy (MOVPE) on c-plane sapphire substrate. Starting from the substrate, first a 2 μm undoped GaN buffer layer is grown to increase epitaxial quality. Then 2 μm n-GaN (doping concentration of 3 × 10¹⁸) and a 150 nm highly doped n⁺-GaN layer (3 × 10¹⁹) was grown sequentially. The n-GaN layer serves as the current spreading function during electrochemical etching process during which the highly doped n⁺-GaN sacrificial layer was etched away. Then it was followed by a layer sequence which rolled up during selective removal of the sacrificial layer in HNO₃. The layer sequence consists of a 3 nm GaN bottom barrier, a single 3 nm InGaN QW, 20 nm GaN capping barrier and a 20 nm AlGaN top layer. For comparison, another multiple quantum wells (MQWs) microtube consisting 3 pairs of QW(InGaN)/QB(GaN) as the core layer were used. In the MQWs microtube, the GaN capping barrier and AlGaN top layer are reduced accordingly to keep the total thickness of the membrane to be around 50 nm, same as the Single QW (SQW) microtube. A regular photolithographic patterning followed by inductive coupled plasma (ICP) etching was used to transfer a rectangular (50 × 25 μm²) pattern down to the highly doped n⁺-GaN layer. Due to the chemical inertness of III-nitride compound semiconductors, it is difficult to undercut etch and for a free-standing nanomembrane. Here we adopted method based on a recent discovery of conductivity-selective electrochemical (EC) etching of GaN to remove the highly doped n⁺-GaN sacrificial layer [28,29]. Once the patterns were defined and all four sides of the sacrificial layer were exposed, a timed etching using 1:5 HNO₃: H₂O was used to laterally remove n⁺-GaN sacrificial layer and release the QWs structure from the substrate for strain induced self-rolling. Such method provides a fine microtube with smooth surface morphology that is critical for achieving high quality factor and gain. The optical properties of the rolled-up InGaN/GaN QWs microtubes were characterized by micro-photoluminescence (PL) spectroscopy at room temperature using a pulsed 337-nm laser excitation. The emitted light was collected by the same objective lens (20X) and then dispersed by a 500-cm spectrometer with 2400 lines/mm grating. The spectral resolution of the instrument is 0.02 nm.

3. Results and discussion

3.1 Three-dimensional structure of a rolled-up InGaN/GaN QWs microtube

The geometry of microtubes can be controlled in the fabrication process. The microtube was rolled-up from square-shaped nanomembrane with side length of 50 × 25 μm². The diameter is about 5-6 μm predetermined by the strain of the pseudomorphic InGaN layer and the subsequently grown GaN/AlGaN heterostructure. The top-left part of Fig. 1 shows an optical microscope image of an ordered array of rolled-up InGaN/GaN QWs microtubular structures. The bottom-left part shows SEM images of the rolled-up microtube from different viewing angles, demonstrating a nicely circular shape. The image on the right shows a schematic cross section of the microtube. The number of rotations is calculated to be about 1.3 for diameter of 6 μm microtube. Since the rolled-up microtube systems have spiral symmetry, there are two notches, i.e., asymmetry in the structure.

 

Fig. 1 Optical microscope image of an ordered array of rolled-up microtube (top-left); bird’s-eye/cross-sectional view SEM images (bottom-left) and three-dimensional schematic diagram (right) of a rolled-up microtube (not drawn to scale).

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3.2 Optical properties of single QW and multiple QWs microtube

Figure 2 shows PL spectra from a SQW microtube excited at a pump power density of ~445 kW/cm² (0.46I_th) and ~1880 kW/cm² (1.79I_th), respectively. At low pumping power density, the PL spectrum is dominated by the spontaneous emission from the active region. It shows a broad QW emission band (FWHM∼36 nm) superimposed by a periodic oscillation, which has been identified later as cavity modes. The dominant resonant mode rested near the peak wavelength side of the background luminescence (∼435 nm). The optical modes separation was measured to be around 26.8 meV (~3.6 nm), which is assigned to WGM in this special type of optical resonator based on the periodic boundary condition n_effL = λm, with the tube circumference L, the vacuum wavelength of the propagating light λ, and the azimuthal mode number m. Observation of optical oscillation in microtube at excitation well below the threshold indicates good quality of microcavity. The Eigen frequencies are characterized by a set of three mode numbers m, l corresponding to the azimuthal, and radial degrees of freedom, respectively. Unlike the microdisk, which sustains multiple radial modes at location of different distance from the disc center, only the basic radial mode (l = 1) can be supported by the thin-wall microtube. Different azimuthal mode correspond to resonance emission at wavelength of 420.86, 423.96, 427.72, 431.50, 434.98, and so on, which satisfy the phase matching for resonance around the microtube circumference.

 

Fig. 2 PL spectrum of InGaN/GaN SQW microtube measured at an excitation power density of 0.46I_th and 1.79I_th, respectively. Inset shows the distribution of the simulated optical resonance mode approximately at 423.96 nm by the FDTD method.

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With increasing pump power the background luminescence blue-shifts to near 425 nm. This is partially due to the band filling effects, more electron-hole pairs generated by intensive optical pumping leads to a blue shift of the emission patterns. The screening of the quantum confined stark effect (QCSE) of the strained thin QW layers by the intense exciting photons density was also one reason to induce the blue-shift in wavelength. As a result, modes at longer wavelengths are no longer supported by the gain medium from QWs. Modes with shorter wavelengths located within the new PL background range were instead supported such as mode at 420.86 nm 423.96 nm and 427.72 nm. Increasing the excitation power caused a distinctive transition to occur in which some WGM abruptly became dominant and linewidth became much narrower, then achieved amplified emission. Similar to J. Sélles et al.’s results [30], the WGM(s) at 423.96 nm and 427.72 nm, located near the peak wavelength (425 nm), get higher chance to lasing, beyond which other mode are suppressed. No significant enhancement was found for mode at 420.86 nm. This may partially due to larger wavelength different from the PL peak wavelength and thus lower initial PL intensity compared to the other two amplified modes emission. Another possibility is that the shorter wavelength WGMs are likely to be reabsorbed before efficient coupling outside [31,32]. Small changes of the wall geometry along tube axis have been reported to induce the light confinement along the tube axial direction [33]. In order to further verify the existence of effective-refractive index non-uniformly induced lateral confinement and the Fabry-Pérot oscillation that might be generated from end facets of the microtube, the length of the microtube was varied in a wide range (50 μm/100 μm/150 μm) and the pump laser spot was also adjusted into different size. It is found that the mode spacing of the previous oscillation remains roughly the same regardless the cavity length (not shown). Thus it's verified that no effective lateral confinement along the tube axis nor Fabry-Pérot oscillation and the collected WGM signals were mainly from radial emission from the excited ring cavities. The inset in Fig. 2 shows the electrical field profile of the azimuthal mode at 423.96 nm. The electrical field is well confined in a rolled-up microtube with a 6 µm diameter and 50 nm-thick membrane. The simulated electric field profile at the inside and outside notch locations were illustrated in the inset. Electric-field fluctuation was observed especially at the inside notch part, which may have a significant effect on the quality factor and threshold of the microtube. The discontinuous in material index and tube radius from the inside/outside notches has been proved to induce two nondegenerate modes sometimes and decrease the quality factor because of the diffraction losses [34], the notches may also be useful for realization of controlled directional emission [33]. But no obvious degeneracy was observed in our measurement.

Figure 3(a) shows the integrated PL intensity of the emission peak at 427.72 nm versus the pumping power density in a log-log plot for the SQW microtube. Below threshold (the first change of slope) it shows a linear increase of the output intensity as a function of the pump power. At threshold I_th around 1 MW/cm² a superlinear increase of the output intensity takes place as expected. A rather smooth transition from linear to superlinear behavior at threshold indicates a relative high β factor representing spontaneous coupling efficiency. The curve shows a soft kink between the excitation power values 1 and 10 MW/cm², noted by the change in the slope. Such a soft transition from spontaneous to stimulated emission is characteristic of high β lasers [35]. Fitting the data in Fig. 3(a) yields the β factor of 0.12. Figure 3(b) shows such transition in linear scale around threshold. When the threshold is approached, the cavity linewidth quickly decreases strongly from 3.81 nm with increasing pump power down to a value of 0.18 nm. A similar decrease of the emission linewidth was observed for microdisk lasers and interpreted in terms of an increase of temporal coherence [36]. The transition of the spectral linewidth is in excellent agreement with the slope change of PL intensity characteristics, clearly confirming the achievement of lasing phenomenon. Multiple microtubes were selected, measured and the quality factor Q range was estimated using λ/Δλ below and above the threshold. By fitting the peaks one receives an average λ/Δλ value range from 112 to 267 below threshold and 2376 above threshold for the modes at 427.72 nm. Such numbers are much smaller than the general theoretical Q value of tube-cavity [7]. The difference can be attributed to the imperfect measurement and the defects in the material or to the imperfection of rotational geometry highly depending on the fabrication method. The inset of Fig. 3(b) shows CCD-captured optical images of a SQW microtube being excited below and above the lasing threshold. Above threshold, a periodical pattern along the microtube boundary as well as bright speckles within the microtube can be observed, both of which are signs of coherent light emission. Figures 3(c) and 3(d) show the log-log and linear plot of PL intensity versus the pumping power density for the MQWs microtube. The inset clearly shows the optical image under spontaneous and stimulated emission separately. It is noticed that the MQWs microtube has a threshold as low as 415 kW/cm², much lower than that of the SQW microtube. The fitted β factor of 0.46 is higher than that of the SQW microtube. The lower threshold and higher β factor indicate that MQWs are necessary to supply sufficient gain to compensate losses.

 

Fig. 3 Log-log plot of PL intensity as a function of optical pumping power density at RT for (a) SQW and (c) MQWs microtube; Linear plot of PL intensity for (b) SQW and (d) MQWs microtube. In (b) also shown the corresponding spectrum linewidth vs. the pumping power density for SQW microtube. CCD-captured optical images of a SQW and MQWs microtube pumped below and above the lasing threshold are shown in its inset (scale bar 5 μm).

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The polarization property of the coherent emission was further investigated. The polarization measurements were performed by inserting a linear polarizer in the optical beam path. For photons circulating around the periphery of the tube, electric fields of the TM and TE modes are defined to be parallel and normal to the tube axial direction, respectively [13,33]. The microtube and polarizer were carefully aligned such that 0° and 90° correspond to TM and TE polarizations, respectively. The peak intensity was then recorded by varying the polarization angle. Figure 4(a) reveals that by rotating the polarization axis with respect to the tube axis one can enhance (upper spectrum) or completely suppress (lower spectrum) the modes, confirming that the stimulated emission is primarily TM polarized(electrical field parallel to the wall sheet and a magnetic field perpendicular to the wall). Plotted in Fig. 4(b) is the intensity of the lasing mode as a function of the polarization angle at excitation density above threshold. It further illustrates that optical resonant modes observed in the PL spectra are almost TM polarized. This is caused by repetitive total reflection of the light at the tube walls. This observation is also consistent with recent theoretical and experimental studies that dominant TM optical modes, with an electric field parallel to the microtube axis, can be supported by a rolled-up microtube ring resonator with a relatively thin wall [37]. Transverse-electric TE modes having an electric field normal to the wall surface result in a great loss due to diffraction [34].

 

Fig. 4 PL measurement at RT of a freestanding SQW microtube for different polarization configuration (a) PL spectrum polarized parallel (upper spectrum) and perpendicular (lower Spectrum) to the tube axis at excitation density above threshold. (b) Average PL peak-to-valley ratio as a function of the polarization angle with respect to the tube axis. Zero degree represents polarization parallel the tube axis.

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3.3 Purcell effect and spontaneous emission factor evaluation

Conventional ridge type waveguide cavity shows a much smaller β value on the order of 10⁻¹~10⁻³ [35,38]. Even compared with some microdisk cavity, the microtube presented here has a higher β value. To explain this, the confinement factor was investigated using FDTD simulation. With a low refractive index contrast (∆n~0.05) in the conventional AlGaN based ridge type cavity laser, the confinement factor does not exceed 3% [39,40]. In the microtube, a significant ∆n~2.5 was achieved using natural ambient air as one of the confinement layers. Based on our calculation the confinement factor can be enhanced up to 25.1% for MQWs microtube. Such strong mode confinement introduce a high β value in microtube [41]. Purcell Effect is used as a figure of merit to describe the ability of the cavity for spontaneous control [42], and it takes the form of F = 3λ³Q/4π²n³V_mode where λ is the operation wavelength, n is the refractive index. V_mode is the mode volume of the cavity, which can be calculated by the total electric field energy divided by the maximum electric filed energy density [43]. Assuming a perfect cylindrical structure, the V_mode was calculated to be ~0.1 μm³ by FDTD simulation. Using the measured Q value, a calculated range for Purcell factor is 0.40 (Q = 112) to 0.93 (Q = 267), for MQWs microtube. On the other hand, an approximate relation between Purcell factor and β is given by F = β/(1−β). Applying the measured β, Purcell factor is calculated to be 0.85, roughly close to value calculated by previous method. Obviously, the low value of Q is one of the main issue for achieving higher Purcell factor. Further optimization of geometrical design and fabrication process could be a solution.

4. Conclusion

In summary, the fabrication of high-quality InGaN/GaN QWs microtubes with thickness of 50 nm on sapphire substrate is demonstrated. Optically pumped lasing near 425 nm at RT has been observed and attributed to WGM. Such thin wall membrane eliminates high radial mode from WGM and the emission due to Fabry-Pérot by confining the photon within the thin wall. Even though the relatively small Q factor was measured before stimulated emission, a reasonably high spontaneous emission factor β of 0.46 and low threshold of 415 kW/cm² were demonstrated in MQWs microtube. This is probably due to the high cavity confinement factor of 25.1% achieved by large refractive index contrast between the film and the ambient air. Our results suggest promising and practical pathways for achieving novel microcavities lasing with III-Nitride material system for on-chip application.