Designing gallium nitride slot waveguide operating ... - Springer Link

Opt Quant Electron (2015) 47:3705–3713 DOI 10.1007/s11082-015-0239-6

Designing gallium nitride slot waveguide operating within visible band Xian Xiao1 • Xiangdong Li1 • Xue Feng1 • Kaiyu Cui1 • Fang Liu1 • Yidong Huang1

Received: 13 April 2015 / Accepted: 23 July 2015 / Published online: 2 August 2015 Springer Science+Business Media New York 2015

Abstract The transmission loss of gallium nitride slot waveguide is investigated by numerical simulation. After properly optimizing the structural parameters, the gallium nitride slot waveguide could operate within visible band (400–800 nm) with loss coefficient of 0.4–1.0 dB/cm due to material absorption. Moreover, after considering sidewall roughness and taking the scattering loss into account, the total transmission loss is also calculated and discussed. Keywords loss

GaN slot waveguide High absorption Low transmission loss Scattering

1 Introduction Visible band has attracted widespread interest due to its chemical and physical applications such as spectroscopy (Go´mez et al. 2006; Rossel et al. 2006) and photocatalysis (Asahi et al. 2001; Kim et al. 2005). Moreover, with visible light served as excitation, a variety of quantum dots (Medintz et al. 2005; Wu et al. 2002) and fluorescent molecules (Higashi et al. 2007; Biskup et al. 2006) could be applied in bio-imaging, labelling, sensing, and medical localization and expression. In recent years, performing these laboratory operations on lab-on-a-chip (LOC) devices draws much effort since it could reduce the time to synthetic and analyze products, greater control the molecular concentrations and interactions, and reduce the reagent costs as well as chemical waste (Daw and Finkelstein 2006; Stone et al. 2004). In order to make the LOC system more portable, it is a trend to integrate light source, waveguide, and functional components on the same chip (Balslev et al. 2005; & Xue Feng [email protected] Xian Xiao [email protected] 1

Department of Electronic Engineering, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China

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Vannahme et al. 2011). For visible light source, Gallium nitride (GaN) based light emitting diodes and lasers are good candidates because they could cover most of the visible band with outstanding performance (Ponce and Bour 1997; Ko et al. 2014) and could be fabricated on silicon substrate (Reiher et al. 2009). In some unique cases, GaN nanowires (Gradecˇak et al. 2005), nanotubes (Goldberger et al. 2003) and nanorods (Kim et al. 2002) could also serve as light source with compact footprint. If the light source and waveguides are defined in the same material and process, the waveguide could be aligned more accurately and the fabrication costs would be much lower. Actually, GaN waveguide based photonic circuits have been demonstrated to realize photonic crystal cavity (VicoTrivino et al. 2013) and second order optical nonlinearity (Xiong et al. 2011). However, the operating wavelength in VicoTrivino et al. (2013) and Xiong et al. (2011) is still 1:5 lm so that the advantage of adopting III–V material is not fully taken especially with III–V emitter. In order to applying the GaN material on LOC operating in visible band, the absorption loss of transmitting lightwave has to be addressed. For example, the material absorption coefficient at 450 nm is 600 dB/cm. As demonstrated on silicon (Li et al. 2013) and other III–V materials such as GaAs (Tu et al. 2010) and InP (Li et al. 2014b), slot waveguide is a candidate to overcome such obstacle. For slot waveguide, the optical field is confined in low-refractive-index slot region embedded between two high-refractive-index strips (Almeida et al. 2004) so that relatively low transmission loss could be achieved if the slot region is fulfilled with low absorption material. Moreover, slot waveguide could also serve as fluidic channel and provide more functions in chemical and biological analysis including optofluidic transport (Lee et al. 2009), nanoparticles and biomolecules manipulation (Yang et al. 2009a, b), as well as label-free biosensing (Barrios et al. 2008). In our previous work (Li et al. 2013), the silicon slot waveguide could operate within the high material absorption band (800–1100 nm). However, for LOC system based on silicon slot waveguide, it is hard to operate at shorter wavelength band not only due to high material absorption but also lack of practical silicon light source and detector that could cover the visible band. Thus, the material is considered as the GaN due to the aforementioned outstanding properties of GaN based light sources. In this work, as the first step towards LOC system operating within visible band, we have investigated the transmission loss of GaN slot waveguide within the wavelength range of 400–800 nm by the finite element method (FEM). Here, three structural parameters of the total width wt , the height h, and the duty cycle factor g are concerned and optimized to obtain the minimum transmission loss caused by material absorption (denoted as aa ). According to the simulation results, the transmission loss of GaN slot waveguide could be as low as 0.4–1.0 dB/cm within the wavelength range of 400– 800 nm, which is in par with that of silicon strip waveguide at 1550 nm. Obviously, GaN slot waveguide is a promising candidate as a transmission line in GaN chip. Furthermore, we have also calculated the scattering loss caused by sidewall roughness (denoted as as ) of the slot waveguide. It is found that the transmission loss would be increased several dB/cm dependent on the roughness and the structure parameters of slot waveguide.

2 Model and method As shown in Fig. 1a, the GaN slot waveguide is considered as two symmetrical and identical GaN strips. There have been two approaches to implement GaN waveguide on silicon substrate with low cost. The first one (Approach I) is reported by VicoTrivino et al. (2013), where GaN waveguides and photonic crystal cavities are achieved with

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Fig. 1 a Schematic of GaN slot waveguide. b The complex refractive index of GaN material within the wavelength band of 400–800 nm

freestanding structure supported by tethers on silicon (111) substrates. The other one (Approach II) is demonstrated by Xiong et al. (2011), where second order optical nonlinearity is demonstrated with integration of single-crystalline GaN on silica with a bonding process. In our simulation, both approaches are considered as the GaN strips are filled with and surrounded by air (refractive index of 1) or silica (refractive index of 1.54). The total width of the slot waveguide is denoted as wt ¼ ws þ 2w, where ws and w represent the width of slot region and GaN strip, respectively. Here, the duty cycle factor g is defined as ws ¼ g wt . Then the structure of a slot waveguide can be determined with three parameters of the total width wt , duty cycle factor g, and height h. The complex refractive index of GaN within the wavelength band of 400–800 nm is expressed as nGaN ¼ n þ ik. In Fig. 1b, the scatters are the original data of n and k from Dollinger et al. (1998) and the corresponding curves are obtained by B-Spline fitting. The imaginary part of the refractive index (k) represents the absorption of GaN material. It could be seen that the absorption coefficient of GaN varies from 30 to 240 cm1 . For example, at 450 nm, which is the operating wavelength of GaN-based blue light emitting devices, the value is 138 cm1 . Apparently, the material absorption is too high to transmit light wave. For a set of parameters of wt , h, and g, the complex effective index of slot waveguide neff ¼ nreff þ inieff could be calculated by FEM where nreff represents the effective index. In our calculation, only the eigenmode of TE mode is considered since the transmission loss of TM mode is much higher. Thus, the transmission loss could be obtained from the imaginary part of the complex effective index nieff by: aa ¼

40pnieff lg e k

ð1Þ

where e is base of natural logarithm and k is the transmission wavelength. The heights of both the buried oxide layer and the cladding layer are set to be 2 lm. It should be mentioned that such calculation can only reveal the transmission loss due to material absorption since the scattering loss due to sidewall roughness has not yet been taken into account. Here, we will first discuss the absorption loss and then address the scattering loss in a latter section so that the influence of different loss mechanism could be distinguished.

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3 Simulation results In our first simulation, the operating wavelength is set constant with value of k ¼ 450 nm. Figure 2 shows the calculated absorption loss aa with different duty cycle factor g. The total width is set as wt ¼ 300 nm and the height h is 200 nm (stars), 300 nm (circles), and 400 nm (triangles). The mode profiles of jEj for two approaches (g ¼ 50 %; h ¼ 300 nm) are also shown in the inset of Fig. 2. It could be seen that the aa is significantly reduced from several hundred dB/cm to several ten dB/cm, while g increases from 10 to 90 % for each value of height. However, there is a maximum value of g that is defined as optimized duty cycle factor. As discussed in our previous work (Li et al. 2013), if g is larger than the maximum value, the effective index of slot waveguide will be lower than that of surrounding material, so that the transmission mode will convert into radiation mode. Thus the optimized (maximum) g corresponds to the minimum aa of a certain structure. From Fig. 2, it could be found that the slot structure exhibits low height sensitivity than total width. The reason is that for TE mode, the value of aa is determined by field distribution which is mainly related to the dimension in x direction in Fig. 1a. For more clarity, the optimized g and corresponding minimum aa are re-plotted in contour map (Fig. 3). Figure 3a, b are for Approach I while Fig. 3c, d are for Approach II. It could be found that as h and wt increases, the optimized g increases from 76.1 to 91.6 % and the corresponding aa decreases from 0.63 to 0.41 dB/cm, for the freestanding slot waveguide. The similar relationship is also obtained with the slot waveguide on silica, but both the optimized g and aa are higher, which are in the range of 88.6–94.9 % and 0.73–0.96 dB/cm respectively. To achieve such GaN slot waveguide practically, the fabrication error should be considered. As an example, we design the parameters as wt ¼ 300 nm, h = 300 nm, g ¼ 87 and 91.9 % which correspond to the optimized g for two approaches. When the slot region is over etched, which means the actual g is larger than the optimized one, the eigenmode will be radiative and the transmission loss would increase dramatically. On the other hand, when the slot region is under etched, the absorption loss aa would also be affected. Figure 4 shows the aa with different fabrication errors which represent the additional width of each strip due to under etching. As we can see, in order to guarantee the aa \2 dB/cm, the fabrication error should be controlled under 7 and 3 nm for two approaches, respectively. Next, the considered wavelength range is expanded into 400–800 nm. Because the aa remains in a small range with varied h and wt , we utilize the parameters of h ¼ 300 nm and wt ¼ 300 nm for convenience. The calculated results show that the aa of GaN slot Fig. 2 The aa with different duty cycle factor g. The stars, circles and triangles present the calculation results for total width wt ¼ 300 nm, and height h = 200, 300, and 400 nm, respectively. All the results above are for the fundamental TE eigenmode of the GaN slot waveguide at the wavelength of 450 nm

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Fig. 3 The contour plot of: a optimized g for Approach I; b The corresponding absorption loss; c optimized g for Approach II; d the corresponding absorption loss. Both the height and total width are in the range of 200–400 nm

Fig. 4 The aa with different fabrication errors. The h and wt of the slot and strip waveguide are both 300 nm

waveguide is in the range of 0.4–1.0 dB/cm (Fig. 5a). Obviously, the slot structure could dramatically reduce the material absorption. As shown in Fig. 5b, the optimized g monotonically decreases while the wavelength increases. According to previous discussion, smaller g results in lager aa . Thus the aa of slot waveguide increases a little while k increases after 600 nm (Fig. 6a), in spite of the reduction of GaN material absorption. Till now, we have calculated the transmission loss introduced by material absorption. Besides, the scattering loss due to surface roughness plays another critical role in practical device which could be calculated by Vlasov and McNab (2004):

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Fig. 5 a The absorption loss of slot waveguide within the wavelength range of 400–800 nm. The h and wt of the slot and strip waveguide are both 300 nm. The star and circle represent Approach I and II respectively. b The corresponding optimized g

Fig. 6 a Scattering loss of slot waveguide with different g at 450 nm. b Scattering loss of slot waveguide with different wavelength. The standard deviation of roughness r is 1 nm. The height h and total width wt are 300 nm

as ¼

k02 ðnGaN ncladding Þ2 neff

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2GaN n2eff 2ðE2 E2 Þ Rs1 2 s2 r2 E dx

ð2Þ

where k0 is the free space wave number, nGaN is the refractive index of GaN material, ncladding is the refractive index of cladding material (air or silica), and neff is the effective index of slot waveguide. Es1 and Es2 are the electric field intensity at Rthe outside and inside 2 2 interfaces of the symmetrical GaN strips, respectively. 2ðEs1 þ Es2 Þ= E2 dx represents the normalized electric field intensity of all the four interfaces of slot waveguide. r is the standard deviation of interface roughness. Here, only sidewall roughness is considered since the GaN layer is grown by metalorganic chemical vapor deposition (MOCVD) so that the top and bottom interfaces would be quite smooth. Using the same method introduced by Li et al. (2014a), the value of as could be calculated with the mode distribution obtained by FEM. Figure 6a shows the calculated as versus duty cycle factor g at wavelength of 450 nm. The r is set as r ¼ 1 nm, and the height h and total width wt are both 300 nm. With higher

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Fig. 7 Total transmission loss of optimized slot waveguide: a Approach I; b Approach II. The height and total width are 300 nm

g, both the effective index and the normalized electric field intensity decrease, so that the curves exhibit a peak in the middle. The rightmost points correspond to the optimized g as well as minimum as . Next, the calculation is mainly focused on the case of optimized g since both aa and as attain the lowest value. For convenience, the r is set as 1 nm. We can see in Fig. 6b that, the as of Approach II is generally lower than that of Approach I due to higher effective index and lower normalized electric field intensity brought by higher g. At last, the total transmission loss at of optimized GaN slot waveguide within the wavelength range of 400–800 nm is calculated and shown in Fig. 7. The r is set as 0, 0.5, 1, 1.5, and 2 nm, respectively. As we can see, at of Approach I is generally higher than that of Approach II with the same r since the scattering loss (as ) is dominant. For instance, the r that guarantees at lower than 2 dB/cm within 450–800 nm is 1 nm for Approach II while that is 0.5 nm for Approach I. There is another comparison, we assume the total loss of transmission line should be \10 dB. Then, with r ¼ 2 nm the at of Approach II is 4.8 dB/ cm at wavelength of 450 nm which could transmit light for 2 cm, while the corresponding transmission distance of Approach I is only 0.54 cm. These results indicate that the GaN slot waveguide on silica (Approach II) is more suitable.

4 Conclusion In this paper, we proposed the GaN slot waveguide and investigated its transmission loss operating in the wavelength range of 400–800 nm. Two implementing approaches are considered. In Approach I, GaN slot waveguide is freestanding structure and surrounded by air, while GaN is surrounded by silica in Approach II. With properly optimized structural parameters, the GaN slot waveguide could operate within the range of 0.4–1.0 dB/cm due to material absorption. Furthermore, after considering sidewall roughness and taking the scattering loss into account, the total transmission loss at is also calculated. If the standard deviation of interface roughness r is 1 nm, the at of Approach II is 1–2.5 dB/cm. Thus we believe that GaN slot waveguide is a promising candidate as a transmission line and functional unit in lab-on-a-chip system which utilize GaN-based light source and could operate within visible band (400–800 nm). It should be mentioned that, the fabrication requirement of GaN slot waveguide is still challenging since the operation wavelength is

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much shorter and the mode profile is more confined compared with a conventional strip waveguide operating in 1:5 lm band. Acknowledgments This work was supported by the National Basic Research Program of China (Nos. 2011CBA00608, 2011CBA00303), the National Natural Science Foundation of China (Grant Nos. 61307068 and 61321004). The authors would like to thank Mr. Yihang Li for his valuable discussions and helpful comments.

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