Enhanced light emission in semiconductor nanowire arrays

Enhanced light emission in semiconductor nanowire arrays

Optics Communications 287 (2013) 250–253 Contents lists available at SciVerse ScienceDirect Optics Communications journal homepage: www.elsevier.com...

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Optics Communications 287 (2013) 250–253

Contents lists available at SciVerse ScienceDirect

Optics Communications 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 b c

Ames Laboratory; Department of Physics and Astronomy; Iowa State University, Ames, IA 50011, USA Microelectronics Research Center, Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, USA 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

a b s t r a c t

Article history: Received 26 October 2011 Accepted 25 September 2012 Available online 11 October 2012

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.

Keywords: Nanowire arrays Transfer-matrix method Photonic crystals Local density of photonic states

1. Introduction Semiconductor nanowires [1] have attracted an explosion of interest in the last decade due to their unique optoelectronic property. High quality semiconductor nanowires have been fabricated and studied for applications of light emission, including lasers [2–5], light-emitting diodes (LEDs) [6–12], and singlephoton sources[13,14]. Despite the presence of extensive experimental work on light emission and several theoretical studies on single nanowire emission characters [15–19], quantitative theoretical study on nanowire arrays remain untouched. In fact, most structures for light emission are nanowire arrays. Unlike single nanowire, nanowire arrays possess two dimensional property which affects the propagation of light. The emission power is either enhanced or inhibited in the structure. Therefore, it is necessary to further investigate the emission properties of nanowire arrays to realize greater light emissions. In this paper, we develop a rigorous transfer-matrix method [20] to investigate detailed emission characters of dipoles embedded in nanowire arrays. The dependence of the emission spectra on the structural parameters of the nanowire arrays is described. Results show that when frequency is greater than the guided resonance frequency of nanowire arrays, emission power is significantly enhanced. The enhanced power could be 5–30 larger than that from planar structures. It is also found that most

n Corresponding author at: Department of Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China. Tel.: þ 86 21 55665498. E-mail address: [email protected] (C. Xu).

0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.09.049

of the enhanced emission comes from the region close to the surface of nanowires. These results are expected to have valuable implications 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 dielectric constant of nanowire to be 6.0, which is close to that for ZnO and GaN at the optical and ultraviolet frequencies. The dipoles are localized at the central cross section of the nanowires. In order to best simulate the common experimental situation, we assume the dipoles are distributed uniformly in the circular cross section of the nanowires and we average emission of dipoles at different positions. Different methods have been used to study emissions of dipole in a structure [21–24]. Our theoretical approach is based on a plane-wave based Transfer-Matrix method (TMM) [25,26] to calculate the emission of dipole in a periodic structure. The source inside the structure is treated through the welldeveloped formalisms of Whittaker and Culshaw [26] and Rigenault et al. [27] as an oscillating dipole at position (r0, z0), with a current density J. Just like the electromagnetic fields expand into the 2D Fourier space, the localized dipole J can be expanded using the usual spectral decomposition of the d function, X Jk ðGÞexp½iðkþ GÞUrdðzz0 Þ, ð1Þ Jðr,zÞ ¼ J0 dðrr 0 Þdðzz0 Þ ¼ k,G

where Jk ðGÞ ¼ J0 exp½iðk þ GÞUr 0 . The localized source is converted into a superposition of pseudoperiodic sources with the same

C. Xu et al. / Optics Communications 287 (2013) 250–253

Fig. 1. Nanowire arrays model. Light emits from the central cross sectional disc of nanowires in X–Y plane.

amplitude but differing phase. Since we only consider the weak coupling limit, the amplitude of dipole J0 is independent of the local fields. Due to the source current, there is a discontinuity of the parallel components of the electromagnetic fields at the layer containing the dipole. The discontinuity can be incorporated with the TMM treatment to obtain the emission out of the structure. The dipoles need to be oriented randomly in the 3D space. To get the emission for isotropic dipole, we need to average the emission of three primary orientations Jx, Jy, and Jz [21–24]. We note that in our 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 is independent of frequency. In reality, the emission spectrum of the emitter needs to be taken into account. It is noteworthy to mention that our study focus on the emission power out of a structure, which differs from previous studies on local density of photonic states (LDOS) [21,23,28]. As we know, LDOS derived from Green function corresponds to the total radiated power from emitter, including the power emitted out of the structure and power confined in the structure. Here only the power out of a structure is studied. The output power corresponds to the LDOS modulated by extraction efficiency. We use this approach to study emission characters of dipoles in nanowire arrays.

3. Simulation results and discussions The nanowire array model we studied is actually a 2D photonic crystal slab. Unlike a planar structure, Bragg scattering in the 2D periodic structure eliminates the total internal reflection so that no confined mode can exist in nanowire arrays. However, the 2D periodicity of nanowire arrays may not exhibit completely if the light wavelength is much greater than the pitch. The whole structure will behave like a bulk slab. There will be index guiding to confine light in the third dimension, which is well discussed in papers of Fan et al. [29–31]. Most power from emitter will couple into the slab guided modes, resulting in low extraction efficiency and so low emission power. The photonic band diagram of a nanowire array is shown in Fig. 2(a). The region above the light cone corresponds to the continuum of states (radiation modes) which extend infinitely outside the structure. The slab guided modes exist in the regions outside the light cone (odd modes and even modes). Hence, the extraction efficiency of the 2D nanowire is expected to be low in

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the region below the light cone. Fig. 2(a) also shows some guided mode bands touch the light cone. These modes are guided resonances, which couple into radiation modes and lead to very large emissions at the corresponding frequencies. These resonances also induce a high LDOS for these frequencies. Fig. 2(b) shows the simulation results of emission out of the nanowire arrays. The emission intensities are normalized to the case of the dipole in air. In the low-frequency region (o o0.5 o0, o0a/2pc ¼1.0), the emission intensity is low. Most power radiated by the dipoles is confined in the nanowire array due to the slab guided modes. At about 0.5o0, the guided resonances emerge, and the emission intensity increases dramatically. When the frequency is greater than that of the top of light cone (about 0.7o0), no guided mode exists in nanowire arrays. All power radiated 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: emission peaks emerge periodically as frequency increases. This behavior is similar to the case for single nanowire [18]. The LDOS is large at these resonance frequencies and causes abundant power output. For comparison, we also show emission from the same number of dipoles in a dielectric slab with the same dielectric constant and height as nanowire (dashed lines). Due to total internal reflection in Z direction, the emission intensity is low and only those dipoles oriented in X–Y plane primarily contribute to the output power. By contrast, the power radiated by all orientations of dipoles can couple out of the structure in the nanowire arrays. Numerically, the emission intensity from nanowire arrays is 5–30 times of that from dielectric slab (Fig. 2b). A similar experimental result was reported about the enhanced photoluminescence from ZnO nanowire arrays [32]. This indicates that light-emitting devices based on nanowire arrays could be much more efficient than conventional planar structured devices. The emission characters of nanowire arrays are strongly influenced by the geometrical structure of the arrays. Fig. 3(a) shows the emission spectra of four different structures with nanowire radii varying from 0.1a to 0.4a. For the small radius (r ¼0.1a), in the low frequency region the emission characters 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 the large radius case, emission spectra of nanowire arrays are very different from the case of single nanowire. Effects of the slab guided modes and guided resonances become distinct. In the low frequency region the emission intensity is small due to the guided modes. At the guided resonance frequencies, emission intensity increases dramatically. As the radius increases, the effective refractive index of nanowire arrays increases accordingly. Hence, the photonic bands compress to the lower frequency region. The guided resonance frequencies will shift to lower frequency region, causing emission peaks in spectra moving to lower frequency regions as well. In the high frequency region, emission spectra of Jz shows the resonance behavior when nanowire radius is 0.3a. However, this behavior vanishes when the radius increases to 0.4a. Fig. 3(b) shows the emission spectra of four different nanowire arrays with heights varying from 0.2a to 100.0a. When the height of nanowire increases from 0.2a to 1.0a, emission spectra compress to the lower frequency region. This phenomenon can also be explained by an increase of effective refractive index of nanowire arrays [33]. For the case of h ¼100.0a, the emission intensity becomes relatively stable when o 40.45 o0 (0.45o0 corresponds to guided resonance frequency). The stability is similar to dipoles placed in a homogeneous material with dielectric constant equals to that of nanowire. Emission intensities of Jx (Jy) and Jz are very close in this case.

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ωa/2 πc Fig. 2. (a) Band structure for odd and even guided modes of nanowire arrays. The height of the nanowire is h ¼ 0.5a and the radius is r¼ 0.3a (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 (e ¼ 6) and height (h ¼ 0.5a) 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.)

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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 h ¼ 0.5a. (b) Emission spectra for nanowire arrays with height of 0.2a, 0.5a, 1.0a and 100.0a when radius is fixed to r¼ 0.3a (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.)

Results presented in Fig. 3 allow us to obtain output power for nanowire-based light-emitting devices with different lattice constant, radius, and height. To obtain high output power at visible wavelengths, we need to set up nanowire arrays with a lattice constant greater than 200 nm and a height greater than 100 nm. By adjusting structure parameters, we can also tune the emission peaks in the spectra so that they overlap with the emission wavelength of the emitter material. In this way, we are able to attain a very large output power. Unlike the case of planar structure, LDOS varies at different positions in the cross section of nanowire, as it is illustrated in Ref. [28]. In our work, we studied distribution of LDOS modulated by the extraction efficiency. It helps us better understand the origin of high emission in nanowire arrays. Fig. 4 shows the distribution of normalized emission intensity in the cross section of nanowire. We present two cases: o ¼0.735 o0 and o ¼0.861o0. They correspond to the valley and peak of emission intensity in Fig. 2(b), respectively. For X–Y oriented dipoles, high emission always occurs from the center of nanowire, and intensity doubles from the valley to the peak. However, for Z oriented dipoles, high emission comes from the surface of nanowire at the

emission peak frequency, which means a large LDOS in this region. More interestingly, the emission intensity increases to about 14 times of that at the emission valley. This feature makes it possible to increase the intensity of emission peak even higher if we could localize the dipoles at the surface of nanowire and confine the orientation of dipoles in Z direction [34].

4. Conclusion In summary, we study emission characters of dipoles in nanowire arrays and find that nanowire arrays perform substantially larger emissions than the planar structure. To realize higher emissions, the frequency should be greater than the guide resonance frequency of nanowire arrays. To obtain visible spectra emission, we need to design nanowire arrays with a lattice constant greater than 200 nm and a height greater than 100 nm. Moreover, the 2D periodic property of nanowire arrays provides us additional structural variables to tune the emission spectra. We believe that nanowire arrays provide a promising approach for designing high performance light-emitting devices.

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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 o ¼ 0.735o0 corresponds to an emission valley in Fig. 2(b), and the case of o ¼0.861o0 corresponds to an emission peak.

Acknowledgment This work is supported by the Ames Laboratory that is operated for the Department of Energy by Iowa State University under contract No. DE-AC0207CH11385 and the 973 Program (Grant Nos. 2007CB613200 and 2006CB921700). We acknowledge use of computational resources at the National Energy Research Scientific Computing Center (NERSC). C. Xu also acknowledges support from Postdoc Research Funding of Shanghai (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.

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