Two-dimensional light confinement in periodic InGaN/GaN nanocolumn arrays and optically pumped blue stimulated emission

Two-dimensional light confinement in periodic InGaN/GaN nanocolumn arrays and optically

pumped blue stimulated emission

Tetsuya Kouno1, 3

, Katsumi Kishino1, 2, 3,*

, Kouji Yamano

1, 3, and Akihiko Kikuchi

1, 2, 3

1Department of Engineering and Applied Sciences 2 Sophia Nanotechnology Research Center,

Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan 3CREST, Japan Science and Technology Agency

*[email protected]

Abstract: Two-dimensional (2D) light diffraction in a uniform array of GaN nanocolumns arranged in a rectangular lattice dramatically enhanced the light intensity at a specific wavelength, indicating the function of 2D distributed feedback (DFB). Here a GaN rectangular-lattice nanocolumn array, which integrated InGaN/GaN multiple quantum wells (MQWs) in the top region of the nanocolumns, was grown by rf-plasma-assisted molecular beam epitaxy (rf-MBE). At a specific wavelength of 471.1 nm, the first observation of stimulated emission from 2D-DFB in an InGaN-based nanocolumn array was obtained. The specific wavelength is calculated by the 2D finite-difference time domain (2D-FDTD) method on the assumption of a refractive index dispersion of GaN; a simple expression for specific wavelength, which is a function of the array period L and the hexagon side length S of each nanocolumn, is proposed, which is convenient for producing a simple design of a GaN nanocolumn array structure in a square lattice.

©2009 Optical Society of America

OCIS codes: (160.4236) Materials; Nanomaterials; (160.6000) Materials; Semiconductor materials;

References and links

1. M. Yoshizawa, A. Kikuchi, N. Fujita, K. Kushi, H. Sasamoto, and K. Kishino, “Self-organization of GaN nano-structures on c-Al2O3 by RF-radical gas source molecular beam epitaxy,” Jpn. J. Appl. Phys. 36, L459 (1997).

2. N. Thillosen, K. Sebald, H. Hardtdegen, R. Meijers, R. Calarco, S. Montanari, N. Kaluza, J. Gutowski, and H. Lüth, “The state of strain in single GaN nanocolumns as derived from micro-photoluminescence measurements,” Nano Lett. 6(4), 704–708 (2006).

3. M. A. S. Garcia, E. Calleja, E. Monroy, F. J. Sanchez, F. Calle, E. Munoz, and R. Beresford, “The effect of the III/V ratio and substrate temperature on the morphology and properties of GaN- and AlN-layers grown by molecular beam epitaxy on Si(111),” J. Cryst. Growth 183(1-2), 23–30 (1998).

4. E. Calleja, M. A. S. Garcia, F. J. Sanchez, F. Calle, F. B. Naranjo, E. Munoz, U. Jahn, and K. Ploog, “Luminescence properties and defects in GaN nanocolumns grown by molecular beam epitaxy,” Phys. Rev. B 62(24), 16826 (2000).

5. K. Kishino, T. Hoshino, S. Ishizawa, and A. Kikuchi, “Selective-area growth of GaN nanocolumns on titanium-mask-patterned silicon (111) substrates by RF-plasma-assisted molecular-beam epitaxy,” Electron. Lett. 44(13), 819 (2008).

6. H. Sekiguchi, K. Kishino, and A. Kikuchi, “Ti-mask Selective-Area Growth of GaN by RF-Plasma-Assisted Molecular-Beam Epitaxy for Fabricating Regularly Arranged InGaN/GaN Nanocolumns,” Appl. Phys. Express 1, 124002 (2008).

7. K. Kishino, H. Sekiguchi, and A. Kikuchi, “Improved Ti-mask selective-area growth (SAG) by rf-plasma-assisted molecular beam epitaxy demonstrating extremely uniform GaN nanocolumn arrays,” J. Cryst. Growth 311(7), 2063–2068 (2009).

8. S. D. Hersee, X. Sun, and X. Wang, “The controlled growth of GaN nanowires,” Nano Lett. 6(8), 1808–1811 (2006).

9. X. Wang, X. Sun, M. Fairchild, and S. D. Hersee, “Fabrication of GaN nanowire arrays by confined epitaxy,” Appl. Phys. Lett. 89(23), 233115 (2006).

10. A. Kikuchi, T. Hoshino, S. Ishizawa, H. Sekiguchi, and K. Kishino, “GaN nanowalls grown by RF-plasma assisted molecular beam epitaxy” 2007 MRS Fall Meeting, Q4.6, Boston, MA, USA, November 26–30, 2007.

#116145 - $15.00 USD Received 27 Aug 2009; revised 10 Oct 2009; accepted 11 Oct 2009; published 23 Oct 2009

(C) 2009 OSA 26 October 2009 / Vol. 17, No. 22 / OPTICS EXPRESS 20440

11. T. Kouno, K. Kishino, H. Sekiguchi, and A. Kikuchi, “Ti-mask selective-area growth of GaN nanorings by RF-plasma-assisted molecular-beam epitaxy,” Phys. Stat. Sol. C 6(S2), 52 (2009).

12. H. Kogelnik, and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971).

13. D. R. Scifres, R. D. Burnham, and W. Streifer, “Highly collimated laser beams from electrically pumped SH GaAs/GaAlAs distributed-feedback lasers,” Appl. Phys. Lett. 26(2), 48–50 (1975).

14. K. Kishino, and S. Arai, Handbook of Semiconductor Lasers and Photonic Integrated Circuits, edited by Y. Suematsu and A. R. Adams, Chap.11, Chapman & Hall, 1994.

15. S. Nojima, “Polarization anisotropy of optical gain in two-dimensional photonic crystals with active lattice points,” Jpn. J. Appl. Phys. 37, L565–L567 (1998).

16. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999).

17. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett. 75(3), 316–318 (1999).

18. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008).

19. R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Nature of the photonic band-gap- some insights from a field analysis,” J. Opt. Soc. Am. B 10(2), 328–332 (1993).

20. N. Antoine-Vincent, F. Natali, M. Mihailovic, A. Vasson, J. Leymarie, P. Disseix, D. Byrne, F. Semond, and J. Massies, “Determination of the refractive indices of AlN, GaN, and AlxGa1-xN grown on (111)Si substrates,” J. Appl. Phys. 93(9), 5222–5226 (2003).

1. Introduction

GaN-based one-dimensional (1D) nanocrystals, known as GaN nanocolumns [1–4], have attracted much attention for their potential application in novel functional nanodevices. GaN nanocolumns possess dislocation-free [1] and strain-relaxed properties [2]. Self-assembly has long been used to prepare GaN nanocolumns [1,3,4], but the recently developed selective-area growth (SAG) technique has enabled the fabrication of periodically arranged GaN nanocolumns in square and triangular lattices, using rf-plasma-assisted molecular beam epitaxy (rf-MBE) [5–7] and metal organic chemical vapor deposition (MOCVD) [8,9]. In previous studies, uniform arrays of nanowalls [10] and nanorings [11] were also successfully fabricated. The periodic arrangement in these dielectric nanocrystals causes light diffraction at a specific wavelength, inducing strong spatial light confinement; the specific wavelength corresponds to the Bragg wavelength in diffraction or the optical band edge wavelength in photonic crystals. In their original works, Kogelnik and Shank demonstrated laser action in a 1D periodic-gain medium, now referred to as a distributed feedback (DFB) laser [12], and Scifres et al. fabricated GaAs/GaAlAs DFB lasers with a fourth-order diffraction grating, obtaining a highly collimated laser beam, which is coupled normal to the junction plane [13]. In the following years, GaInAsP/InP DFB laser diodes were extensively investigated as optical communication light sources [14].

Since then, photonic band gap (PBG) technology has rapidly developed. It has theoretically been discussed that strong light confinement occurs at the optical band edge, inducing optical gain enhancement [15]. Laser actions based on a 2D-DFB scheme in photonic crystals were obtained one after another in 1999 [16,17]. Here, the most notable achievement is the fabrication of 2D-DFB GaInAsP/InP laser diodes [17], in which the laser beam radiated perpendicularly to the surface, similarly to that in the case of the above 1D-DFB lasers. Very recently, the same concept has been applied to the study of blue-violet GaN 2D-DFB laser action [18]. In such lasers, the periodic air-hole structures induce the 2D light confinement. An air-hole (air-rod) array in a square lattice is used in PBG technology, because it has a large gap for TE modes. In the case of an array of dielectric cylinders (rods or nanocolumns), a large gap is opened for TM modes but not for TE modes [19], and no 2D-DFB lasers with such an array have been demonstrated. In InGaN/GaN systems, however, a high-density nanocolumn array having a dielectric cylinder structure is logically preferable for high-performance laser action, because high crystal quality is easily obtained using the bottom-up nanostructure.

In this study, GaN nanocolumn arrays arranged in a rectangular lattice, which included InGaN/GaN multiple quantum wells (MQWs), were fabricated by rf-MBE, and light-intensity



enhancement was observed at a specific wavelength, corresponding to the optical band edge wavelength. The first success in optically pumped stimulated emission of InGaN-based nanocolumns was obtained at a specific wavelength of 471.1 nm. In addition, a numerical approach by the 2D-FDTD method was carried out, revealing the structural dependence of the specific wavelength for GaN nanocolumn arrays.

2. Fabrication of GaN-based nanocolumn arrays

GaN rectangular-lattice nanocolumn arrays with different nanocolumn sizes and lattice constants (samples 1, 2 and 3), in which 8-period InGaN/GaN MQWs were prepared at the top regions of the nanocolumns, were grown on an MOCVD-grown (0001) GaN template of 3.5 µm thickness by rf-MBE. During the growth, atomic nitrogen was supplied through an rf-plasma source with 99.9999% pure nitrogen gas, and In and Ga were supplied from conventional elemental source effusion cells. The back surfaces of the substrate were coated with Ti (300 nm) to enhance heat absorption. Prior to the growth, Ti (5 nm) films were deposited on the surface of the GaN template, followed by the preparation of nanohole patterns in a Ti mask by electron-beam lithography (EBL) and dry etching. The patterned Ti-mask surfaces were nitrided at 400 °C under active-nitrogen-beam irradiation for 10 min in the rf-MBE chamber; subsequently, GaN nanocolumns were grown at approximately 900 °C for 3 h at a nitrogen flow rate of 0.75 sccm. The SAG on the nanohole Ti-mask patterns produced uniform arrays of GaN nanocolumns; then, in the top region of the nanocolumns, 8-period InGaN/GaN MQWs and GaN cap layers were grown at approximately 650 °C. The growth mechanism of SAG was discussed in detail in ref [7]. Figure 1 shows typical scanning electron microscopy (SEM) images of a nanocolumn array sample fabricated in this study (sample 1). Note that each GaN nanocolumn possessed a hexagonal cross section; the side length of a hexagon was 92 nm and the height of a nanocolumn along the c-axis was approximately 850 nm. The GaN nanocolumns were arranged in a rectangular lattice, with a horizontal lattice constant (Lh) of 230 nm and a vertical lattice constant (Lv) of 245 nm (see Fig. 1 (b)); here the horizontal direction was the <11-20> crystal direction. We grew another two rectangular-lattice nanocolumn arrays (samples 2 and 3), whose structural parameters are described in Table 1.

1.0μ m1.0μ m 1.0μ m1.0μ m1.0μ m1.0μ m

(a) (b)

1.0μ m1.0μ m1.0μ m1.0μ m 1.0μ m1.0μ m1.0μ m1.0μ m

(a) (b)

Fig. 1. Scanning electron microscopy (SEM) images; (a) bird’s-eye and (b) top views of typical regularly arranged GaN nanocolumns with 8-period InGaN/GaN MQWs.



Table 1. Specific wavelength and size of fabricated InGaN/GaN nanocolumn arrays

Sample No.

Hexagon Side

Length S (nm)

Horizontal Lattice const. Lh(nm)

Vertical Lattice const. Lv(nm)

Specific Wavelength

λs(nm)

1111 92 230 245 471.1

2222 88 249 216 454.8

3333 95 249 238 474.4

3. Two-dimensional light confinement

Sample 1 was excited with a 325 nm He-Cd laser of 1.0 mW light output to evaluate its low-excitation RT-PL spectrum, as shown in Fig. 2 (a). The emission from the InGaN MQWs, with a peak at 526.8 nm, was widely spread with a full width at half maximum (FWHM) of approximately 250 meV. At a shorter wavelength than that of the main peak, however, a specific emission peak appeared at 471.3 nm that rose substantially to three times the height of the bottom of the broad InGaN emission spectrum. This peak was narrower with an FWHM of 108 meV. The 2D periodic arrangement of nanocolumns induced 2D light confinement at a specific wavelength, as described in refs [13]. and [15], where it was reported that optical gain is enhanced in the vicinity of the optical band edge of 2D gain photonic crystals, at which the group velocity markedly decreased causing an optical gain enhancement. Thus, light intensity is dramatically enhanced at a specific wavelength determined by the periodic arrangement.

In this study, a numerical approach by the 2D-FDTD method is applied to analyze the GaN nanocolumn arrangement of the sample shown in Fig. 1, then the TE-mode light response spectrum, i.e., the electric field polarized on the c-face, is calculated assuming the refractive index dispersion of GaN reported in ref [20], as shown in Fig. 2 (b). In the 2D-FDTD approach, an impulse light signal (white light) is generated inside the nanocolumn

400 450 500 550 600

Calculation

by 2D-FDTD method

TE-mode response

465.2 nm

Op

tica

l re

sp

on

se

(a

.u.)

Wavelength (nm) 400 450 500 550 600

R.T.

He-Cd laser

325 nm, 1.0 mW

471.3 nm

526.8 nm

RT

-PL

in

ten

sity (

a.u

.)

Wavelength (nm)

（a）（b）

Fig. 2. (a) Low-excitation RT-PL spectra of 8-period InGaN/GaN MQWs, which were prepared on top of a GaN rectangular-lattice nanocolumn array (sample 1), and (b) light response spectrum for sample 1 calculated by the 2D-FDTD method.



150 200 250 300 350 400 450 500

350

400

450

500

550

600

650

700

s

dotted lines :

by approx expression

λ = 3.56S + 0.565L

: Experimental

S=120 nm

70 nm

80 nm

90 nm

100 nm

110 nm

60 nm

S: hexagon side length

Sp

ecific

wa

vele

ngth

λ (n

m)

Array period of nanocolumn L (nm)

Fig. 3. Specific wavelength (λs) of GaN square-lattice nanocolumn arrays as a function of array period (L) calculated for TE mode by 2D-FDTD method. The parameter is the hexagonal side

length of a nanocolumn (S). Stars indicate the experimental data (Table 1) and asterisks

indicate the optical band edge wavelength calculated by 2D plane-wave expansion method.

array, and then the light signal remaining in the structure after a long time is analytically detected as a function of wavelength. As is well known, the very wide wavelength spectrum of white light is filtered by the wavelength response of the structure, so that the light is preferentially confined at a specific wavelength. Thus, the response spectrum of 2D structural resonance can be calculated. From Fig. 2, note that the peak wavelength of the calculated response spectrum is 465.2 nm, which approximately coincides with the experimental specific peak wavelength of 471.3 nm. Thus, the specific peak in the experiment originates from the 2D light enhancement effect.

Arrayed nanocolumns in a square lattice, which consists of GaN nanocolumns with a hexagonal geometry, are systematically analyzed by clarifying the dependences of the specific wavelength on L and S, as shown in Fig. 3; the 2D-FDTD method is performed for the TE mode assuming the wavelength dispersion of the refractive index given in ref [20]. An interesting point in Fig. 3 is that the specific wavelength λs tends to change linearly with L and S; therefore, we fit straight lines to the dependences of λs on L and S, shown by the dotted lines in Fig. 3, to obtain the expression

3.56 0.565sp

S Lλ = × + × (1).

Using this approximate expression, we can easily deduce the approximate structure of the 2D nanocolumn array corresponding to a specific wavelength; thus, the expression is useful in experiments where rapid design and application are crucial.

In this calculation, we do not take the existence of the InGaN/GaN MQWs into account. However, the designed thickness of the InGaN quantum well was 4 nm compared with a nanocolumn height of 850 nm, thus, the volume ratio of InGaN to GaN is approximately 4%, indicating the very small contribution of InGaN to the change in refractive index. Thus, the specific wavelength is mainly determined by the structural arrangement of GaN nanocolumns, while the InGaN MQWs provide optical gain.

The optical band structure of the GaN square-lattice nanocolumn array is calculated by the 2D plane-wave expansion method assuming a GaN refractive index of 2.42 at a wavelength of 500 nm. The array period at which the optical band edge (Γ11 point) wavelength is 500 nm is calculated for hexagon side lengths of 100 nm, 90 nm, 80 nm and 70 nm, as shown by asterisks in Fig. 3. Note that the results of the 2D-FDTD calculation agree well with those of the optical band calculation by the 2D plane-wave expansion method.



4. Stimulated emission observation and specific wavelength control

Sample 1 was optically pumped with a 355 nm Nd:YAG laser with a pulse width of 5 ns at 20 Hz. Excitation power density was changed from 100 kW/cm

2 to 730 kW/cm

2 while observing

RT emission spectra, as shown in Fig. 4 (a). With increasing excitation intensity, a sharp and strong emission peak appeared at a wavelength of approximately 471 nm and the intensity increased nonlinearly as a function of excitation power density, as shown in Fig. 4 (b). The result of this experiment evinced the occurrence of stimulated emission, where the threshold power density was approximately 320 kW/cm

2 and the emission wavelength was 471.1 nm at

730 kW/cm2. The emission wavelength coincided with the specific wavelength determined

from the 2D arrangement of the nanocolumn array (see Fig. 1). The 2D light confinement enhanced the optical gain at a specific wavelength [14], inducing the stimulated emission at this wavelength. The oscillation wavelength of a nanocolumn array can be controlled by adjusting the lattice constant L and the hexagonal side length S of the nanocolumns.

(b) (a)

400 450 500 550 600

471.1 nm

(FWHM:

22meV)

R. T.

Nd:YAG 355 nm

5ns 20Hz

Excitation Intensity

730KW/cm2

380KW/cm2

230KW/cm2

100KW/cm2

Lig

ht in

ten

sity (

a u

)

Wavelength (nm) 0 200 400 600 800

Lig

ht in

ten

sity (

a u

)

Excitation intensity (kW/cm2)

RT

pulsed

Fig. 4. (a) High-excitation RT-PL spectra, and (b) dependence of RT-PL emission peak intensity of an InGaN-based nanocolumn array (sample 1). The emission light was polarized in TE mode.

The PL spectra of samples 2 and 3 were evaluated at RT under an excitation density of 720 kW/cm

2, while observing TE-polarized emissions at wavelengths of 454.8 nm and 474.4

nm, respectively, as shown in Fig. 5. For TE-polarized light, the 2D-FDTD calculation of the light response spectrum is also performed using the structural parameters of samples 2 and 3 (Table 1), obtaining light response spectra with peaks at 450 nm and 477.5 nm, respectively; good agreement for the results of a rectangular-lattice nanocolumn array with the peak wavelengths in the experiment is obtained. These samples (sample 1, 2 and 3) were fabricated simultaneously on the same GaN template but with a different lattice constant and hexagon side length (see Table 1). For all samples, broad emission peaks from the InGaN MQWs were observed accompanying sharp specific peaks at shorter wavelength than that of the main peak, similarly to in Fig. 2 (a). Then the specific peaks became dominant under the high-excitation condition as shown in Fig. 5, although sample 2 and 3 did not undergo stimulated emission. However, a specific wavelength shift corresponding to the structural parameter change was observed, which was also proved theoretically by 2D-FDTD (see Fig. 5).



400 450 500 550 600

450 nm

454.8 nmR. T.

Nd:YAG 355 nm

5ns 20Hz


730 KW/cm2

R. T.

Experiment

Wavelength (nm)

2D-FDTD

Lig

ht

Inte

nsit

y (

a u

)

400 450 500 550 600

477.5 nm

474.4 nmR. T.

Nd:YAG 355 nm

5ns 20Hz


730 KW/cm2

R. T.

Experiment

Wavelength (nm)

Lig

ht

Inte

nsit

y (

a u

)

2D-FDTD

(a) (b)

400 450 500 550 600

450 nm

454.8 nmR. T.

Nd:YAG 355 nm

5ns 20Hz


730 KW/cm2

R. T.

Experiment

Wavelength (nm)

2D-FDTD

Lig

ht

Inte

nsit

y (

a u

)

400 450 500 550 600

477.5 nm

474.4 nmR. T.

Nd:YAG 355 nm

5ns 20Hz


730 KW/cm2

R. T.

Experiment

Wavelength (nm)

Lig

ht

Inte

nsit

y (

a u

)

2D-FDTD

(a) (b)

Fig. 5. (a) High-excitation RT-PL spectra of sample 2, and light response spectrum for sample 2 calculated by the 2D-FDTD method. (b) Those for sample 3.

Thus, we successfully controlled the specific wavelength by appropriately designing the structure of GaN nanocolumn arrays.

The experiment was performed for rectangular lattices, that is, lattices having different lattice constants in the horizontal and vertical directions; here, we calculate the average lattice constants in the horizontal and vertical directions, and plot the specific wavelengths of samples 1, 2 and 3 using stars in Fig. 3, which are calculated on the assumption of a square lattice. The data points are scattered around the area between the lines representing S = 80 nm and 90 nm; the experimental values of S were in the range from 88 nm to 95 nm (see Table 1). Thus, Fig. 3 shows that the approximate expression can be conveniently utilized for designing the specific wavelength of a square-lattice nanocolumn array.

5. Fine spectral structure of stimulated emission

Figure 4 (a) shows the averaged spectrum of sample 1 for excitation by a large number of optical pulses;

440 460 480 500

Excitation

Intensity

450 KW/cm2

R. T.

Nd:YAG 355nm

5ns 20Hz

470.8 nm

(FWHM:

2meV)

Lig

ht

Inte

nsit

y (

a u

)

Wavelength (nm)

Fig. 6. RT-PL spectrum of sample 1 for one pulse excitation.

thus, the pulse jittering of 5 ns duration and 20 Hz repetition rate possibly cause the wavelength to vary resulting in a broad spectrum. The lasing spectrum for a single pulse used in this experiment was observed as shown in Fig. 6. The excitation density was 450 kW/cm

2

and a region of the nanocolumn array with 36 µm diameter was excited, this area included



approximately 1.8x104 nanocolumns. Multiple-peak emission, which consisted of sharp peaks

with a typical FWHM of 2 meV at the peak wavelength of 470.8 nm, was observed. This fine structure of the spectrum a little changed per each pulse, resulting in the broad emission spectrum (in Fig. 4 (a)). We speculate that the fine spectral structure is caused by the refractive index change of GaN through the carrier plasma effect, during the short duration of pulse excitation at a wavelength of 355 nm. We also observed that the nanocolumn size and shape fluctuated slightly in the nanocolumn array, and this fluctuation logically resulted in optical localization. A fine specific wavelength possibly shifts from one localization area to the other. A detailed investigation of the fine structure is a future task. In this experiment, the specific wavelength was determined using the averaged array structure. Under continuous-wave operation for a uniform nanocolumn array, however, lasing with a single sharp peak should be obtained.

6. Summary

Two-dimensional light diffraction in periodic GaN nanocolumn arrays, i.e., arrays of dielectric cylinders, enabled 2D light confinement, and light intensity was dramatically enhanced at a specific wavelength. The stimulated emission of an InGaN-based rectangular-lattice nanocolumn array was observed at a specific wavelength of 471.1 nm. This is the first demonstration of stimulated emission from 2D-DFB in an InGaN-based dielectric cylinder photonic crystal, not in an air-hole structure; the emission was polarized in the TE mode. The specific wavelength of a square-lattice array was calculated by the 2D-FDTD method on the assumption of a refractive index dispersion of GaN; a simple expression for the specific wavelength, which is a function of the array period L and the hexagon side length S of each nanocolumn, is proposed, which is convenient for the design of GaN square-lattice nanocolumn array structures. This simple expression for the relationship between λs and L or D gives insight into the light enhancement phenomena observed in the experiment.

Acknowledgements

The authors thank Mr. Y. Inose for his contribution to the optical band calculation and Dr. M. Sakai for his assistance with the optical measurement. This study was partly supported by Grants-in-Aid for Scientific Research on Priority Areas #18069010 and (B) #21310087 from the Ministry of Education, Culture, Sports, Science and Technology of Japan.



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Two-dimensional light confinement in periodic InGaN/GaN nanocolumn arrays and optically pumped blue stimulated emission