Embed Size (px)
Citation preview
Optics Communications 287 (2013) 250–253
Contents lists available at SciVerse ScienceDirect
Optics Communications
0030-40
http://d
n Corr
and Nan
200433
E-m
journal homepage: www.elsevier.com/locate/optcom
Enhanced light emission in semiconductor nanowire arrays
Chun Xu a,b,c,n, Rana Biswas a,b, Kai-Ming Ho a
a Ames Laboratory; Department of Physics and Astronomy; Iowa State University, Ames, IA 50011, USAb Microelectronics Research Center, Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, USAc Department of Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
a r t i c l e i n f o
Article history:
Received 26 October 2011
Accepted 25 September 2012Available online 11 October 2012
Keywords:
Nanowire arrays
Transfer-matrix method
Photonic crystals
Local density of photonic states
18/$ - see front matter & 2012 Elsevier B.V. A
x.doi.org/10.1016/j.optcom.2012.09.049
esponding author at: Department of Physics
o Photonic Structures (Ministry of Education
, China. Tel.: þ86 21 55665498.
ail address: [email protected] (C. Xu).
a b s t r a c t
We use rigorous transfer-matrix method to investigate light emission from dipole sources embedded in
nanowire arrays. The dependence of the emission spectra on the structural parameters of the nanowire
arrays is described and the parameters to realize high emission are obtained. Numerical simulations
show that output power is significantly enhanced with a frequency greater than guided resonance
frequency of nanowire arrays. The enhanced power could be 5–30 larger than that from planar
structures. We also find that the enhanced emission mostly comes from the region close to the surface
of nanowires. It is possible to realize higher output power by manipulating dipoles in the nanowire. All
these qualities make nanowire arrays a novel candidate for designing high performance light-emitting
devices.
& 2012 Elsevier B.V. All rights reserved.
1. Introduction
Semiconductor nanowires [1] have attracted an explosion ofinterest in the last decade due to their unique optoelectronicproperty. High quality semiconductor nanowires have been fab-ricated and studied for applications of light emission, includinglasers [2–5], light-emitting diodes (LEDs) [6–12], and single-photon sources[13,14]. Despite the presence of extensive experi-mental work on light emission and several theoretical studies onsingle nanowire emission characters [15–19], quantitative theo-retical study on nanowire arrays remain untouched. In fact, moststructures for light emission are nanowire arrays. Unlike singlenanowire, nanowire arrays possess two dimensional propertywhich affects the propagation of light. The emission power iseither enhanced or inhibited in the structure. Therefore, it isnecessary to further investigate the emission properties of nano-wire arrays to realize greater light emissions.
In this paper, we develop a rigorous transfer-matrix method[20] to investigate detailed emission characters of dipolesembedded in nanowire arrays. The dependence of the emissionspectra on the structural parameters of the nanowire arrays isdescribed. Results show that when frequency is greater than theguided resonance frequency of nanowire arrays, emission poweris significantly enhanced. The enhanced power could be 5–30larger than that from planar structures. It is also found that most
ll rights reserved.
and Key Laboratory of Micro
), Fudan University, Shanghai
of the enhanced emission comes from the region close to thesurface of nanowires. These results are expected to have valuableimplications for the design of nanowire-based emission devices.
2. Simulation method
The nanowire array model in the study is a square lattice (X–Y
plane) of dielectric rods in air (Fig. 1). We take the dielectricconstant of nanowire to be 6.0, which is close to that for ZnO andGaN at the optical and ultraviolet frequencies. The dipoles arelocalized at the central cross section of the nanowires. In order tobest simulate the common experimental situation, we assume thedipoles are distributed uniformly in the circular cross section ofthe nanowires and we average emission of dipoles at differentpositions.
Different methods have been used to study emissions of dipolein a structure [21–24]. Our theoretical approach is based on aplane-wave based Transfer-Matrix method (TMM) [25,26] tocalculate the emission of dipole in a periodic structure. Thesource inside the structure is treated through the well-developed formalisms of Whittaker and Culshaw [26] and Rigen-ault et al. [27] as an oscillating dipole at position (r0, z0), with acurrent density J. Just like the electromagnetic fields expand intothe 2D Fourier space, the localized dipole J can be expanded usingthe usual spectral decomposition of the d function,
J r,zð Þ ¼ J0d r�r0ð Þd z�z0ð Þ ¼X
k,G
JkðGÞexp½i kþGð ÞUr�d z�z0ð Þ, ð1Þ
where JkðGÞ ¼ J0exp½�i kþGð ÞUr0�. The localized source is convertedinto a superposition of pseudoperiodic sources with the same
Fig. 1. Nanowire arrays model. Light emits from the central cross sectional disc of
nanowires in X–Y plane.
C. Xu et al. / Optics Communications 287 (2013) 250–253 251
amplitude but differing phase. Since we only consider the weakcoupling limit, the amplitude of dipole J0 is independent of thelocal fields. Due to the source current, there is a discontinuity ofthe parallel components of the electromagnetic fields at the layercontaining the dipole. The discontinuity can be incorporated withthe TMM treatment to obtain the emission out of the structure.The dipoles need to be oriented randomly in the 3D space. To getthe emission for isotropic dipole, we need to average the emissionof three primary orientations Jx, Jy, and Jz [21–24]. We note that inour 2D nanowire array model, emissions of Jx and Jy are identical.In order to investigate structure influence on emission, we adopt a‘‘white’’ source model, namely, the amplitude of dipole J0 isindependent of frequency. In reality, the emission spectrum ofthe emitter needs to be taken into account.
It is noteworthy to mention that our study focus on theemission power out of a structure, which differs from previousstudies on local density of photonic states (LDOS) [21,23,28]. Aswe know, LDOS derived from Green function corresponds to thetotal radiated power from emitter, including the power emittedout of the structure and power confined in the structure. Hereonly the power out of a structure is studied. The output powercorresponds to the LDOS modulated by extraction efficiency. Weuse this approach to study emission characters of dipoles innanowire arrays.
3. Simulation results and discussions
The nanowire array model we studied is actually a 2D photoniccrystal slab. Unlike a planar structure, Bragg scattering in the 2Dperiodic structure eliminates the total internal reflection so that noconfined mode can exist in nanowire arrays. However, the 2Dperiodicity of nanowire arrays may not exhibit completely if thelight wavelength is much greater than the pitch. The wholestructure will behave like a bulk slab. There will be index guidingto confine light in the third dimension, which is well discussed inpapers of Fan et al. [29–31]. Most power from emitter will coupleinto the slab guided modes, resulting in low extraction efficiencyand so low emission power.
The photonic band diagram of a nanowire array is shown inFig. 2(a). The region above the light cone corresponds to thecontinuum of states (radiation modes) which extend infinitelyoutside the structure. The slab guided modes exist in the regionsoutside the light cone (odd modes and even modes). Hence, theextraction efficiency of the 2D nanowire is expected to be low in
the region below the light cone. Fig. 2(a) also shows some guidedmode bands touch the light cone. These modes are guidedresonances, which couple into radiation modes and lead to verylarge emissions at the corresponding frequencies. These reso-nances also induce a high LDOS for these frequencies.
Fig. 2(b) shows the simulation results of emission out of thenanowire arrays. The emission intensities are normalized to thecase of the dipole in air. In the low-frequency region (oo0.5 o0,o0a/2pc¼1.0), the emission intensity is low. Most power radiatedby the dipoles is confined in the nanowire array due to the slabguided modes. At about 0.5o0, the guided resonances emerge,and the emission intensity increases dramatically. When thefrequency is greater than that of the top of light cone (about0.7o0), no guided mode exists in nanowire arrays. All powerradiated by dipoles will couple into radiation modes. Especially,the emission spectra of Z oriented dipoles Jz (solid blue line)shows a resonance behavior in the high frequency region: emis-sion peaks emerge periodically as frequency increases. Thisbehavior is similar to the case for single nanowire [18]. The LDOSis large at these resonance frequencies and causes abundantpower output.
For comparison, we also show emission from the same numberof dipoles in a dielectric slab with the same dielectric constantand height as nanowire (dashed lines). Due to total internalreflection in Z direction, the emission intensity is low and onlythose dipoles oriented in X–Y plane primarily contribute to theoutput power. By contrast, the power radiated by all orientationsof dipoles can couple out of the structure in the nanowire arrays.Numerically, the emission intensity from nanowire arrays is 5–30times of that from dielectric slab (Fig. 2b). A similar experimentalresult was reported about the enhanced photoluminescence fromZnO nanowire arrays [32]. This indicates that light-emittingdevices based on nanowire arrays could be much more efficientthan conventional planar structured devices.
The emission characters of nanowire arrays are stronglyinfluenced by the geometrical structure of the arrays.Fig. 3(a) shows the emission spectra of four different structureswith nanowire radii varying from 0.1a to 0.4a. For the smallradius (r¼0.1a), in the low frequency region the emission char-acters of Jx (Jy) and Jz are close to the result of a single nanowire[18]. The emission intensity of Jz is greater than that of Jx. For thelarge radius case, emission spectra of nanowire arrays are verydifferent from the case of single nanowire. Effects of the slabguided modes and guided resonances become distinct. In the lowfrequency region the emission intensity is small due to the guidedmodes. At the guided resonance frequencies, emission intensityincreases dramatically. As the radius increases, the effectiverefractive index of nanowire arrays increases accordingly. Hence,the photonic bands compress to the lower frequency region. Theguided resonance frequencies will shift to lower frequency region,causing emission peaks in spectra moving to lower frequencyregions as well. In the high frequency region, emission spectra ofJz shows the resonance behavior when nanowire radius is 0.3a.However, this behavior vanishes when the radius increasesto 0.4a.
Fig. 3(b) shows the emission spectra of four different nanowirearrays with heights varying from 0.2a to 100.0a. When the heightof nanowire increases from 0.2a to 1.0a, emission spectra com-press to the lower frequency region. This phenomenon can also beexplained by an increase of effective refractive index of nanowirearrays [33]. For the case of h¼100.0a, the emission intensitybecomes relatively stable when o40.45 o0 (0.45o0 correspondsto guided resonance frequency). The stability is similar to dipolesplaced in a homogeneous material with dielectric constant equalsto that of nanowire. Emission intensities of Jx (Jy) and Jz are veryclose in this case.
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.01
0.1
1
10
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Nor
mal
ized
em
issi
on in
tens
ity
ωa/2 πc
ωa/2
πc
odd even
ΜΧ ΓΓ
Fig. 2. (a) Band structure for odd and even guided modes of nanowire arrays. The height of the nanowire is h¼0.5a and the radius is r¼0.3a (a is the lattice constant).
(b) Normalized emission intensity of dipoles embedded in nanowire arrays (solid lines) and in a slab with the same dielectric constant (e¼6) and height (h¼0.5a) as
nanowire (dashed lines). The red lines correspond to X or Y oriented dipoles (Jx or Jy). The blue lines correspond to Z oriented dipoles (Jz). The black lines correspond to
isotropic oriented dipoles. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.1
r = 0.2 a
r = 0.3 a
10
1
0.110
1
0.110
1
0.110
1
ω a /2π c
r = 0.1 a
r = 0.4 a
Nor
mal
ized
em
issi
on in
tens
ity h = 0.2 a
h = 0.5 a
ω a /2π c
Nor
mal
ized
em
issi
on in
tens
ity
h = 1.0 a
10
1
0.110
1
0.110
1
0.110
1
h = 100.0 a0.1
Fig. 3. (a) Emission spectra for nanowire arrays with radius of 0.1a, 0.2a, 0.3a, and 0.4a when height is fixed to h¼0.5a. (b) Emission spectra for nanowire arrays with
height of 0.2a, 0.5a, 1.0a and 100.0a when radius is fixed to r¼0.3a (a is the lattice constant). The red lines correspond to X or Y oriented dipoles (Jx or Jy). The blue lines
correspond to Z oriented dipoles (Jz). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
C. Xu et al. / Optics Communications 287 (2013) 250–253252
Results presented in Fig. 3 allow us to obtain output power fornanowire-based light-emitting devices with different lattice con-stant, radius, and height. To obtain high output power at visiblewavelengths, we need to set up nanowire arrays with a latticeconstant greater than 200 nm and a height greater than 100 nm.By adjusting structure parameters, we can also tune the emissionpeaks in the spectra so that they overlap with the emissionwavelength of the emitter material. In this way, we are able toattain a very large output power.
Unlike the case of planar structure, LDOS varies at differentpositions in the cross section of nanowire, as it is illustrated inRef. [28]. In our work, we studied distribution of LDOS modulatedby the extraction efficiency. It helps us better understand theorigin of high emission in nanowire arrays. Fig. 4 shows thedistribution of normalized emission intensity in the cross sectionof nanowire. We present two cases: o¼0.735 o0 ando¼0.861o0. They correspond to the valley and peak of emissionintensity in Fig. 2(b), respectively. For X–Y oriented dipoles, highemission always occurs from the center of nanowire, and inten-sity doubles from the valley to the peak. However, for Z orienteddipoles, high emission comes from the surface of nanowire at the
emission peak frequency, which means a large LDOS in thisregion. More interestingly, the emission intensity increases toabout 14 times of that at the emission valley. This feature makesit possible to increase the intensity of emission peak even higherif we could localize the dipoles at the surface of nanowire andconfine the orientation of dipoles in Z direction [34].
4. Conclusion
In summary, we study emission characters of dipoles innanowire arrays and find that nanowire arrays perform substan-tially larger emissions than the planar structure. To realize higheremissions, the frequency should be greater than the guideresonance frequency of nanowire arrays. To obtain visible spectraemission, we need to design nanowire arrays with a latticeconstant greater than 200 nm and a height greater than 100 nm.Moreover, the 2D periodic property of nanowire arrays providesus additional structural variables to tune the emission spectra.We believe that nanowire arrays provide a promising approachfor designing high performance light-emitting devices.
0.0 0.1 0.2 0.3 0.4 0.50.0
0.1
0.2
0.3
0.4
0.5
00.61.21.82.43.03.64.24.85.46.0
0.0 0.1 0.2 0.3 0.4 0.50.0
0.1
0.2
0.3
0.4
0.5
01.42.84.25.67.08.49.811.212.614.0
0.0 0.1 0.2 0.3 0.4 0.50.0
0.1
0.2
0.3
0.4
0.5
00.40.81.21.62.02.42.83.23.64.0
0.0 0.1 0.2 0.3 0.4 0.50.0
0.1
0.2
0.3
0.4
0.5
00.20.40.60.81.01.21.41.61.82.0
0.0 0.1 0.2 0.3 0.4 0.50.0
0.1
0.2
0.3
0.4
0.5
00.20.40.60.81.01.21.41.61.82.0
0.0 0.1 0.2 0.3 0.4 0.50.0
0.1
0.2
0.3
0.4
0.5
00.20.40.60.81.01.21.41.61.82.0
Fig. 4. Dependence of the normalized emission intensity emitted by X–Y oriented dipoles (Jxy), Z oriented dipoles (Jz), and isotropic oriented dipoles (Jiso) on the dipole’s
position. We present the dipoles distributed in a quarter size of unit cell. The radius of nanowire is 0.3a and the height is 0.5a (same as Fig. 2). The case of o¼0.735o0
corresponds to an emission valley in Fig. 2(b), and the case of o¼0.861o0 corresponds to an emission peak.
C. Xu et al. / Optics Communications 287 (2013) 250–253 253
Acknowledgment
This work is supported by the Ames Laboratory that isoperated for the Department of Energy by Iowa State Universityunder contract No. DE-AC0207CH11385 and the 973 Program(Grant Nos. 2007CB613200 and 2006CB921700). We acknowl-edge use of computational resources at the National EnergyResearch Scientific Computing Center (NERSC). C. Xu alsoacknowledges support from Postdoc Research Funding of Shang-hai (Grant No. KLH1615106).
References
[1] P.J. Pauzauskie, P.D. Yang, Materials Today 9 (2006) 36.[2] M.H. Huang, S. Mao, H. Feick, H.Q. Yan, Y.Y. Wu, H. Kind, E. Weber, R. Russo,
P.D. Yang, Science 292 (2001) 1897.[3] J.C. Johnson, H.J. Choi, K.P. Knutsen, R.D. Schaller, P.D. Yang, R.J. Saykally,
Nature Mater. 1 (2002) 106.[4] X. Duan, Y. Huang, R. Agarval, C.M. Lieber, Nature (London) 421 (2003) 241.[5] J.C. Johnson, H.Q. Yan, P.D. Yang, R.J. Saykally, Journal of Physical Chemistry B
107 (2003) 8816.[6] F. Qian, Y. Li, S. Gradecak, D. Wang, C.J. Barrelet, C.M. Lieber, Nano Letters 4
(2004) 1975.[7] R. Konenkamp, R.C. Word, C. Schlegel, Applied Physics Letters 85 (2004) 6004.[8] C.Y. Chang, F.C. Tsao, C.J. Pan, G.C. Chi, H.T. Wang, J.J. Chen, F. Ren, D.P. Norton,
S.J. Pearton, K.H. Chen, L.C. Chen, Applied Physics Letters 88 (2006) 173503.[9] M.C. Jeong, B.Y. Oh, M.H. Ham, S.W. Lee, J.M. Myoung, Small 3 (2007) 568.
[10] A. Nadarajah, R.C. Word, J. Meiss, R. Konenkamp, Nano Letters 8 (2008) 534.[11] E. Lai, W. Kim, P. Yang, Nano Research 1 (2008) 123.[12] R. Guo, J. Nishimura, M. Matsumoto, M. Higashihata, D. Nakamura, T. Okada,
Applied Physics B 94 (2009) 33.[13] M.T. Borgstrom, V. Zwiller, E. Muller, A. Imamoglu, Nano Letters 5 (2005)
1439.
[14] C. Grillet, C. Monat, C.L.C. Smith, B.J. Eggleton, D.J. Moss, S. Frederick,D. Dalacu, P.J. Poole, J. Lapointe, G. Aers, R.L. Williams, Optics Express 15
(2007) 1267.
[15] A.V. Maslov, C.Z. Ning, Applied Physics Letters 83 (2003) 1237.[16] A.V. Maslov, C.Z. Ning, Optics Letters 29 (2004) 572.[17] A.V. Maslov, C.Z. Ning, Physical Review B 72 (2005) 161310, R.[18] A.V. Maslov, M.I. Bakunov, C.Z. Ning, Journal Applied Physics 99 (2006)
024314.[19] I. Friedler, C. Sauvan, J.P. Hugonin, P. Lalanne, J. Claudon, J.M. Gerard, Optics
Express 17 (2009) 2095.[20] R. Biswas, C. Xu, W. Zhao, R. Liu, R. Shinar, J. Shinar, Journal of Photomics for
Energy 1 (2011) 011016.[21] D.P. Fussell, R.C. McPhedran, C. Martijn de Sterke, Physical Review E 70
(2004) 066608.[22] A. Chutinan, K. Ishihara, T. Asano, M. Fujita, S. Noda, Organic Electronics 6
(2005) 3.[23] F. Romer, B. Witzigmann, O. Chinellato, P. Arbenz, Optical Quantum Electro-
nics 39 (2007) 341.[24] S. Nowy, B.C. Krummacher, J. Frischeisen, N.A. Reinke, W. Brutting, Journal of
Applied Physics 104 (2008) 123109.[25] Z.Y. Li, L.L. Lin, Physica Review E 67 (2003) 046607.[26] D.M. Whittaker, I.S. Culshaw, Physical Review B 60 (1999) 2610.[27] H. Rigneault, F. Lemarchand, A. Sentenac, Journal of Optical Society of
America A 17 (2000) 1048.[28] J. Kupec, R.L. Stoop, B. Witzigmann, Optics Express 18 (2009) 27589.[29] S. Fan, P.R. Villeneuve, J.D. Joannopoulos, Physical Review Letters 78 (1997)
3294.[30] S.G. Johnson, S. Fan, P.R. Villeneuve, J.D. Joannopoulos, Physical Review B 60
(1999) 5751.[31] S. Fan, J.D. Joannopoulos, Physical Review B 65 (2002) 235112.[32] K. Wang, J. Chen, W. Zhou, Y. Zhang, Y. Yan, J. Pern, A. Mascarenhas, Advanced
Material 20 (2008) 3248.[33] T. Prasad, V.L. Colvin, D.M. Mittleman, Journal of Optical Society of America B
25 (2008) 633.[34] J. Frischeisen, D. Yokoyama, C. Adachi, W. Brutting, Applied Physical Letters
96 (2010) 073302.
