There have been great research interests in gallium nitride material due to its promising applications in UV to blue optoelectronic devices. Conventionally, the devices are built in two-dimensional thin film structure, where emission sources are from the planar quantum wells. Recently, devices with one-dimensional nanostructure have gained substantial attention for their interesting properties and potential applications [36-38]. The one-dimensional structure can be fabricated by top-down patterned etching or bottom-up self assembled growth. The fabricated nanostructures have shown quantum confinement effect and interesting light emission properties [39-41]. Stimulated emission from single free standing lying nano wire and 2-D periodic nanorod arrays have been observed [42,43], where lasing modes are the Fabry-Perot modes of the wire end surfaces or photonic crystal band edge modes.
Recently, lasing action due to the feedback from the multiple scatterings of optically pumped disordered nanorods was also reported [44]. This phenomenon is called random lasing [45], which is often analyzed in terms of statistics.
The statistical nature of random lasing is interesting. However, it puts a limitation to device applications due to the lack of control on the lasing modes and
frequency locations from sample to sample. Recently, there are great interests in studying photonic quasicrystals, which may look random at first glance yet have well defined patterns. Their optical properties are fascinating and lie somewhere between those of periodic and random structures [46-49]. It therefore may provide a way to design a pseudo random laser with deterministic properties, which could be important for practical applications. Here we report the observation of lasing action from room temperature optically pumped GaN quasicrystal nanorod arrays.
The lasing phenomenon resembles that of a random laser. The quasicrystal nanorod array sample was fabricated from a GaN epitaxial wafer by nano-imprint patterned etch, followed by epitaxial regrowth. The imprint was a 12-fold symmetric quasicrystal pattern [46-49]. The regrowth formed hexagonal facets on the nanorod sidewalls and hexagonal pyramids on the top. The regrowth also grew InGaN/GaN MQWs on the sidewalls and pyramid facets. The use of MQWs allows us to investigate the optical properties of QPC at a designed wavelength. Under optical pumping, multiple lasing peaks were excited. The lasing was identified to be from the MQWs on the nanorod sidewalls. The peak distribution did not show obvious regularity and behaved like a random lasing action. The linewidth of laser peaks was in the range of 0.2-0.3 nm, indicating a strong resonant feedback oscillation. The lasing threshold pump intensity decreases with increasing pump area. The lasing mechanism is attributed to the feedback of close loop multiple scatterings among nanorods.
Here we report the observation of lasing action form room temperature optically pumped GaN nanorod arrays in a quasicrystal pattern. The imprint patterned etching created nanorod arrays in a 12-fold symmetric quasicrystal pattern. The epitaxial
regrowth formed { ̅ } m-plane facets on nanorod sidewalls and { ̅ } s-plane hexagonal pyramid on the top. Sample HT with the smooth sidewall surfaces was optically excited by a 355 nm tripled Nd:YAG pulse laser at room temperature. The pulse width was 0.5 ns and the pulse repetition rate was 1 KHz. The laser beam was focused on the sample surface in normal incident by a 15X UV microscope objective.
The pump spot at sample surface had a Gaussian intensity profile with 1/e2 diameter of 37 m, verified by a knife edge measurement. The photoluminescent (PL) from the broad emission background. The integrated power within the spectral range of these emission peaks versus pump intensity is shown in Figure 5-15 (a), which indicates an onset of lasing action at threshold pump intensity of ~5 MW/cm2. These emission peaks span from 450 to 470 nm, which corresponds to emission from the quantum wells located from middle to upper part of the nanorod columns as shown by CL images Figure 5.2 (b). The spacings among these lasing peaks do not show obvious regularity. It implies that the lasing modes are unlikely due to whispering gallery modes of individual nanorod. Not all lasing peaks always increase with the increase of pump power. Some of the peaks can decrease due to the increase of other emerging peaks, which indicates that there are lasing mode competitions. Given the rather irregular lasing peaks, what we have observed here is likely a random lasing action. In addition, no lasing action is observed in sample LT because the degraded sidewall surfaces with the low regrowth temperature of MQWs [45, 50].
A random laser is a lasing action in a disordered active media due the existence of scattering loops where the round trip losses are compensated by gain. The scattering loop serves as the function of optical feedback as the conventional laser cavity. There could also be multiple scattering loops returning to one starting point or overlapping, which can be viewed as randomly distributed feedback. The nanorods in our sample play the roles of scattering sites and providing gain. The lack of short range order of the quasicrystal pattern and the hexagonal nanorod facets together make the sample HT pseudodisordered media. One of the random laser characteristic is the lasing threshold pump intensity decreases with increasing pump spot area in a power law relation [45, 50, 51]. The reason in a simplified picture is because there are more multiple recurrent scattering loops that can create tighter confined modes in a larger gain area, which leads to a lower threshold pump intensity. We have measured the threshold pump intensity versus pump spot size. The experimental data points are shown in Figure 5-15 (b), along with a power law fitting function. The power law function fits well to the experimental data and gives a threshold pump intensity Ith ~ 1/A0.27 dependence.
We investigated the resonant modes of this pseudo random lasing by performing twodimensional (2D) finite difference time domain (FDTD) simulation. The 2D model was chosen for simplicity and believed to be a reasonable approximation because the gain was predominantly distributed in 2D direction perpendicular to nanorod axis. The lasing mode field would therefore mainly follow the gain in the 2D direction. The finite nanorod length in the vertical direction will certainly modify the mode frequency and profile, but we consider it as a secondary effect. The simplified model is meant to explain qualitatively the observed lasing behavior. Figure 5-16 (a) shows the quasicrystal model used for simulation. The nanorod and quasicrystal
pattern dimensions measured from SEM image were used to construct the model. The overall pattern size is about 6 μm across. The finite pattern size was used due to the limit of computation power and time. An optical pulse with a center wavelength at 470 nm and a linewidth of 30 nm was launched at a randomly chosen location near nanorod sidewall to simulate the emission from MQWs. The pulse spectral width was chosen according to the observed lasing spectral range. Both transverse electric and magnetic field were calculated. After a long enough propagation time, the shape of spectrum became steady. The spectrum contained distinct resonant peaks, which were the resonant modes excited by the broad-band pulse. The same calculation was repeated for different pulse launching locations. The quality factors of these modes are in the range of 500. The spectrum varied from location to location and had many or just a few resonant peaks. All these resonant peaks can be regarded as the potential lasing modes. For illustration purpose, three spectra were shown in Figure 5-16 (b)-(d). The corresponding launching locations are the points labeled (b), (c), and (d) in Figure 5-16 (a). Points (b) and (c) are deliberately at locations away from center.
Point (d) is at the center rod.
The calculated resonant spectra show irregular peak locations, similar to what was observed in the experiment. The calculated resonant peaks do not match to the observed spectrum in peak to peak locations. This can be attributed to the fact that the model used in simulation is an overly simplified approximation. The lasing peaks should be ideally deterministic and can be engineered by design since the QPC pattern is deterministic. This could be important in practical applications. We then calculated the resonant mode profiles. It was calculated by choosing one of the peaks in the resonant spectrum and launching it at the same location. After propagating for a reasonable long time, a distinctive pattern was developed. We regarded it as the mode
profile of the specific peak. Ideally, one can repeat the calculation for all the peaks to obtain all the mode profiles. We have calculated a few of them. The mode profiles could be rather irregular or have certain distinctive feature. For illustration purpose, the mode profiles of the resonant peaks labeled Figure 5-17 (a) and (b) in Figure 5-16 (b), and (c). Figure 5-16 (c) are shown in Figure 5-17 (a)-(c), respectively. The mode field in Figure 5-17 (a) shows that certain part of nanorods can couple together to provide guiding effect and form various propagation loops. Figure 5-17 (b) on the other hand shows a more scattering like coupling pattern. Figure 5-17 (c) is the field pattern for a source launched at the center rod. The mode field propagates outward and forms triangular shape resonant loops. These patterns show that the intricate property of quasicrystal structure has varieties of mode field patterns, which require a further investigation.
5.5 Summary
We have successfully fabricated core-shell MQW nanopillar arrays by patterned top-down etching and a subsequent epitaxial regrowth. The regrowth results in crystalline hexagonal pyramid nanopillars with { ̅ } nonpolar sidewalls and { ̅ } semipolar pyramid facets. The MQWs grown on these facets have large location dependent InN fraction variations. The emission has a broad spectrum covering from 420 to 520nm. The PL spectrum remains fairly stable over two orders of carrier density change due to the low polarization field of nonpolar and semipolar facets. The broad emission linewidth and low polarization field make the coreshell MQW pillar structure an attractive design for LED lighting applications.
In short, we have observed a red shift as the location moves from the bottom to
top portion of nanorods from the spatially resolved CL images. According to the APSYS modeling wavelength, CL images, the multiple peaks fitting from the PL spectrum, the internal electron field and its related indium content can be assigned to the location of core-shell nanorods. Furthermore, the IEF is found to be remarkably reduced by changing the growth planes from (0001) plane to { ̅ } and { ̅ } plane. Color temperature ~60,000 of sample HT is situated on the blue region of the CIE 1931 chromaticity diagram, whereas color temperature ~6,000 (a natural white light) of sample LT is situated on the white region. The tunable color temeprature is attainable by core-shell nanorods grew under a different regrowth temperature of MQWs.
From investigation of TDPL result, the IQEs of the green and blue color MQWs of HT-sample are 23.92% and 18.86%, respectively. The increasing of IQE due to the reducing the degree of localization, strain relax and suppressing the QCSE. In addition, the IQEs of the yellow and Green color MQWs of LT-sample are 11.12%
and 19.86%, respectively. In addition, the time-resolved photoluminescence (TRPL) measurement shows a much faster radiative recombination rate in 3-D core-shell semipolar (1-101) green and nonpolar (10-10) blue MQWs, indicating a lower polarization field. The peak emission energies of these samples monotonically decrease with increasing temperature without the typical red-blue-red shift observed in c-plane MQWs. This implies that there is no significant localized potentials due to inhomogeneous In distribution in MQWs grown on the 3-D core-shell MQWs facets [15-19]. The r of remains constant at low temperature below ~50 K, indicating the excitons are trapped in localized potentials due to inhomogeneous In composition in MQWs at low temperature. Above 180 K, r increases linearly as rising temperature. It is implied that thermal activated excitons are excited out of the traps
and become free excitons in the 2D MQWs, resulting in approximately linearly increasing radiative lifetime with temperature.
Further, the lasing action is observed in optically pump crystalline Core-shell InGaN/GaN MQWs nanorod arrays arranged in a 12-fold symmetric quasicrystal pattern. Under optical pumping, multiple lasing peaks emerged from broad emission background. The sample was fabricated from a GaN epitaxial substrate by nano patterned etching and epitaxial regrowth. The regrowth grew core-shell MQWs and crystalline facets on nanorods. Under optical pumping, multiple lasing peaks emerged from broad emission background. The irregular multiple lasing wavelengths and the inverse dependence of threshold pump intensity on pump spot area resembles the characteristics of random lasing. The irregularity of resonant peaks is qualitatively explained by a simplified FDTD simulation.
5.6 References
[1] S. Nakamura, et al., The Blue Laser Diode: Springer, Berlin, 2000.
[2] S. Nakamura, et al., "InGaN-based multi-quantum-well-structure laser diodes,"
Jpn. J. Appl. Phys., vol. 35, pp. L74–L76, 1996.
[3] T. Mukai, et al., "Amber InGaN-based light-emitting diodes operable at high ambient temperatures," Jpn. J. Appl. Phys., vol. 37, pp. L479–L481, 1998.
[4] S. Chichibu, et al., "Exciton localization in InGaN quantum well devices," J. Vac.
Sci. Technol. B, vol. 16, pp. 2204–2214, 1998.
[5] G. Sun, et al., "Investigation of fast and slow decays in InGaN/GaN quantum wells," Appl. Phys. Lett., vol. 99, p. 081104, 2011.
[6] Y. Yamane,, et al., "Largely variable electroluminescence efficiency with current and temperature in a blue InGaN multiple-quantum-well diode," Appl. Phys. Lett.
vol. 91, p. 073501, 2007.
[7] T. Kanata-Kito, et al., "Photoreflectance characterization of built-in potential in MBE-produced As-grown GaAs surface," Proc SPIE, vol. 56, p. 1286, 1990.
[8] S. M. Sze and K. K. Ng, Physics of semiconductor devices, 3rd Edition:
Wiley-Blackwell, p. 722 ,2007.
[9] A. Chtanov, et al., "Excitation-intensity-dependent photoluminescence in semiconductor quantum wells due to internal electric fields," Physical Review B, vol. 53, p. 4704, 1996.
[10] X. Yin, et al., "Photoreflectance study of the surface Fermi level at (001) n and p type GaAs surfaces," Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, vol. 10, pp. 131-136, 1992.
[11] G. Bastard, et al., "Variational calculations on a quantum well in an electric field," Physical Review B, vol. 28, p. 3241, 1983.
[12] E. F. Schubert, Light-emitting diodes: Cambridge Univ Pr, 2006.
[13] N. Ohta, et al., Colorimetry: fundamentals and applications: Wiley, 2005.
[14] J. Hernandez-Andres, et al., "Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities," Applied optics, vol. 38, pp. 5703-5709, 1999.
[15] S. Watanabe, et al., ”Internal quantum efficiency of highly-efficient InxGa1-xN-based near-ultraviolet light-emitting diodes,” Appl. Phys. Lett., vol.
83, p. 4906, 2003.
[16] C. C. Yu, et al., ”Electrical and optical properties of beryllium-implanted Mg-doped GaN,” J. Appl. Phys., vol. 92, p. 1881, 2002.
[17] Y. H. Cho, et al., “S-shaped” temperature-dependent emission shift and carrier dynamics in InGaN/GaN multiple quantum wells,” App. phys. lett., vol. 73, pp.
1370–1372, 1998.
[18] C. A. Tran, et al., “Phase separation in InGaN/GaN multiple quantum wells and its relation to brightness of blue and green LEDs,” Journal of crystal growth, vol.
195, p. 397, 1998.
[19] H. P. D. Schenk, et al., “Luminescence and absorption in InGaN epitaxial layers and the van Roosbroeck–Shockley relation,” J. Appl. Phys., vol. 88, p. 1525, 2000.
[20] A. Bell, S. Srinivasan, et al., “Exciton freeze-out and thermally activated relaxation at local potential fluctuations in thick AlxGa1-xN layers,” J. Appl.
Phys., vol. 95, p. 4670, 2004.
[21] Y. Narukawa, et al., “Radiative and nonradiative recombination processes in ultraviolet light-emitting diode composed of an In0.02Ga0.98N active layer,”
Appl. Phys. Lett., vol. 74, p. 558, 1999.
[22] T. Li, et al., “Carrier localization and nonradiative recombination in yellow emitting InGaN quantum wells,” Appl. Phys. Lett., vol. 96, p. 013906, 2010.
[23] P. G. Eliseev, et al., “Blue temperature-induced shift and band-tail emission in InGaN-based light sources,” Appl. Phys. Lett., vol. 71, p. 569, 1997.
[24] T. Kim, et al., "Highly efficient yellow photoluminescence from {11–22} InGaN multiquantum-well grown on nanoscale pyramid structure," Appl. Phys. Lett., vol.
97, p. 241111, 2010.
[25] H. Yu, et al., "Photoluminescence study of semipolar {10-11} InGaN/GaN multiple quantum wells grown by selective area epitaxy," Applied Physics Letters, vol. 90, p. 141906, 2007.
[26] S. F. Chichibu, et al., “Recombination dynamics of localized excitons in cubic InxGa1-xN/GaN multiple quantum wells grown by radio frequency molecular beam epitaxy on 3C–SiC substrate,” J. Vac. Sci. Technol. B, vol. 21, pp.
1856-1862, 2003.
[27] R. Metzler and J. Klafter, “From stretched exponential to inverse power-law:
fractional dynamics, Cole–Cole relaxation processes, and beyond,” Journal of Non-Crystalline Solids, vol. 305, pp. 81-87, 2002.
[28] T. Wunderer, et al., “Time-and locally resolved photoluminescence of semipolar GaInN/GaN facet light emitting diodes,” Appl. Phys. Lett., vol. 90, p. 171123, grown on γ-LiAlO2(100) by plasma-assisted molecular-beam epitaxy,” Phys. Rev.
B, vol. 67, p. 041306R, 2003.
[31] T. Onuma, et al., “Localized exciton dynamics in nonpolar (11math0) InxGa −xN multiple quantum wells grown on GaN templates prepared by lateral epitaxial overgrowth,” Appl. Phys. Lett., vol. 86, p. 151918, 2005.
[32] Y. Narukawa, et al., “Dimensionality of excitons in laser-diode structures composed of InxGa1-xN multiple quantum wells,” Phys. Rev. B, vol. 59, p.
10283, 1999.
[33] S.-P. Chang, et al., “Electrically driven nanopyramid green light emitting diode,”
Appl. Phys. Lett., vol. 100, p. 061106, 2012.
[34] N. K. van der Laak, et al., “Role of gross well-width fluctuations in bright, green-emitting single InGaN/GaN quantum well structures,” Appl. Phys. Lett., vol. 90, p. 121911, 2007.
[35] A. Hangleiter, et al., “Suppression of nonradiative recombination by V-shaped pits in GaInN/GaN quantum wells produces a large increase in the light emission efficiency,” Phys. Rev. Lett., vol. 95, p. 127402, 2005.
[36] F. Qian, et al., “Core/Multishell nanowire heterostructures as multicolor, high-efficiency light-emitting diodes,” Nano Lett., vol. 5, pp. 2287–2291, 2005.
[37] R. Chen, et al., “Optically pumped ultraviolet lasing from nitride nanopillars at room temperature,” Appl. Phys. Lett., vol. 96, p. 241101, 2010.
[38] H. Sekiguchi, et al., "Emission color control from blue to red with nanocolumn diameter of InGaN/GaN nanocolumn arrays grown on same substrate," Applied Physics Letters, vol. 96, p. 231104, 2010.
[39] H. Sekiguchi, et al., “Structural and optical properties of GaN nanocolumns grown on (0001) sapphire substrates by rf-plasma-assisted molecular-beam epitaxy,” J. Cryst. Growth, vol. 300, pp. 259–262, 2007.
[40] Y. Sun, et al., “High efficiency and brightness of blue light emission from dislocation-free InGaN/GaN quantum well nanorod arrays,” Appl. Phys. Lett., vol. 87, p. 093115, 2005.
[41] Y. Kawakami, et al., “Origin of high oscillator strength in green-emitting InGaN/GaN nanocolumns,” Appl. Phys. Lett., vol. 89, p. 163124, 2006.
[42] S. Gradečak, et al., “GaN nanowire lasers with low lasing thresholds,” Appl.
Phys. Lett., vol. 87, p. 173111, 2005.
[43] T. Kouno, et al., “Two-dimensional light confinement in periodic InGaN/GaN nanocolumn arrays and optically pumped blue stimulated emission,” Opt.
Express, vol. 17, pp. 20440–20447, 2009.
[44] M. Sakai, et al., “Random laser action in GaN nanocolumns,” Appl. Phys. Lett., vol. 97, p. 151109, 2010.
[45] H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A, vol. 38, pp. 10497–10535, 2005.
[46] Y. Lai, et al., “Anomalous properties of the band-edge states in large twodimensional photonic quasicrystals,” Phys. Rev. B, vol. 76, p. 165132, 2007.
[47] M. E. Zoorob, et al., “Complete photonic bandgaps in -fold symmetric quasicrystals,” Nature, vol. 404, pp. 740–743, 2000.
[48] L. Mahler, et al., “Quasi-periodic distributed feedback laser,” Nat. Photonics, vol.
4, pp. 165–169, 2010.
[49] K. Nozaki and T. Baba, “Lasing Characteristics of -Fold Symmetric Quasi-periodic Photonic Crystal Slab Nanolasers,” Jpn. J. Appl. Phys., vol. 45, pp. 6087–6090, 2006.
[50] A. L. Burin, et al., “Understanding and control of random lasing,” Physica B, vol.
338, pp. 212–214, 2003.
[51] Y. Ling, et al., “Investigation of random lasers with resonant feedback,” Phys.
Rev. A, vol. 64, pp. 063808–063815, 2001.
Table 5-1. The integration of sample HT with the indium content, the thickness of wells and barriers, the IEF (F0), and the multiple peaks fitting wavelength from the PL spectrum.
In (%)
Well/Barrier (nm)
F0
(MV/cm)
PL (nm)
CL (nm)
APSYS (nm)
A 19.8 5.5/14.4 0.4 511 N/A 507
B 16.4 3.4/14.1 N/A 468 460 460
C 25 3.5/16.5 0.02 527 520 520
D 14.6 2.7/6.0 0.05 418 420 460
E 11.6 2.7/6.0 0.05 418 420 415
F 30 5.3/15.0 N/A N/A N/A N/A
Table 5-2. CIE 1931 Colorimetric Epicenters xe, ye and Constants for Equation 5.20.
Constants Valid CCT Range (K)
3000–50,000 50,000–8 x 105
xe 0.3366 0.3356
ye 0.1735 0.1691
A0 2949.86315 36284.48953
A1 6253.80338 0.00228
t1 0.92159 0.07861
A2 28.70599 5.4535 x 1036
t2 0.20039 0.01543
A3 0.00004 N/A
t3 0.07125 N/A
Table 5-3. The x, y, z, n and CCT of sample HT and sample LT were obtained from Equation 5.17-5.21.
x y z n CCT (K)
Sample HT 0.149213 0.206843 0.643944 -8.686 625050.97
Sample LT 0.297198 0.412882 0.28992 -0.1533 6650.45367
Table 5-4. IQE, activation energy and binding energy for HT- sample.
Table 5-5. IQE, activation energy and binding energy for LT-sample.
Figure 5-1. The PL spectra as a function of the excitation power for (a) sample HT and (d) sample LT. Multiple peaks fitting of MQWs emission ranging from blue to green with the ensemble PL spectrum of (b) sample HT and (e) sample LT. The emission wavelength as the function of the pumping power of (c) sample HT and (f) sample LT.
Figure 5-2. (a) Computed wavelength of sample HT by APSYS. (b) The corresponding
position and wavelength of the spatially resolved CL image. (c) Multiple peaks fitting
position and wavelength of the spatially resolved CL image. (c) Multiple peaks fitting