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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8379–8393
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Metal-insulator-silicon-insulator-metal waveguides compatible with standard CMOS technology

Min-Suk Kwon  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8379-8393 (2011)
http://dx.doi.org/10.1364/OE.19.008379


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Abstract

Metal-insulator-silicon-insulator-metal (MISIM) waveguides are proposed and investigated theoretically. They are hybrid plasmonic waveguides, and light is highly confined to the insulator between the metal and silicon. As compared to previous ones, they are advantageous since they may be realized in a simple way by using current standard CMOS technology and their insulator is easily replaceable without affecting the metal and silicon. First, their structure and fabrication process are explained, both of which are compatible with standard CMOS technology. Then, the characteristics of the single MISIM waveguide whose insulator has its original or an adjusted refractive index are analyzed. The analysis demonstrates that its characteristics are comparable to those of previous hybrid plasmonic waveguides and that they are very effectively tuned by changing the refractive index of the insulator. Finally, the characteristics of the two coupled MISIM waveguides are analyzed. Through the analysis, it is obtained how close or far apart they are for efficient power transfer or low crosstalk. MISIM-waveguide-based devices may play an important role in connecting Si-based photonic and electronic circuits.

© 2011 OSA

1. Introduction

Plasmonics has been developing rapidly for a recent decade since it is expected to become a bridge between size-limited photonics and speed-limited electronics [1

1. M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010). [CrossRef] [PubMed]

]. As a key element of plasmonics, diverse plasmonic waveguides have been reported [2

2. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

8

8. R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide,” Opt. Lett. 35(5), 649–651 (2010). [CrossRef] [PubMed]

]. They include channel plasmon polariton waveguides [2

2. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

], dielectric-loaded surface plasmon polariton waveguides [3

3. Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34(3), 310–312 (2009). [CrossRef] [PubMed]

5

5. J. Grandidier, G. C. des Francs, L. Markey, A. Bouhelier, S. Massenot, J.-C. Weeber, and A. Dereux, “Dielectric-loaded surface plasmon polariton waveguides on a finite-width metal strip,” Appl. Phys. Lett. 96(6), 063105 (2010). [CrossRef]

], and metal slot or metal-insulator-metal waveguides [6

6. J. Tian, S. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95(1), 013504 (2009). [CrossRef]

8

8. R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide,” Opt. Lett. 35(5), 649–651 (2010). [CrossRef] [PubMed]

]. The first two types of waveguides have a propagation length of tens of micrometers, but have a mode area of the order of 1 μm2. In contrast, the metal slot waveguides have a propagation length of a few micrometers, but have a mode area smaller than 0.01 μm2. Because of the Ohmic loss of metal, all the plasmonic waveguides have a limitation on providing both a long propagation length and a small mode area. In order to alleviate such a limitation, active research on hybrid plasmonic waveguides has been carried out recently [9

9. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

16

16. D. Dai and S. He, “Low-loss hybrid plasmonic waveguide with double low-index nano-slots,” Opt. Express 18(17), 17958–17966 (2010). [CrossRef] [PubMed]

]. Hybrid plasmonic waveguides are based on the principle that electric fields are highly enhanced in thin insulator with a low refractive index (RI) between metal and dielectric with a high RI. It has been shown that their propagation length and mode area can be made quite long and small simultaneously.

This paper reports a metal-insulator-silicon-insulator-metal (MISIM) waveguide that is a different hybrid plasmonic waveguide. (Actually, the acronym of MISIM was introduced in [17

17. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17(13), 11107–11112 (2009) (Although the acronym of MISIM was introduced for the structure of the plasmonic waveguides in this paper, they were called metal-insulator-metal (MIM) waveguides rather than MISIM waveguides. The plasmonic waveguides were intended to confine enough portion of modal energy for lasing to active semiconductor cores.). [CrossRef] [PubMed]

], where S stood for semiconductor like InGaAs.) The structure of the MISIM waveguide is devised (1) to be realized in a simple way by using current standard CMOS fabrication technology and (2) to have a post-fabrication method of replacing its insulator with a functional material without influencing the structure of its metal and silicon. The dimensions of the MISIM waveguides are determined considering the limitations of standard CMOS technology. The designed MISIM waveguides are theoretically investigated. In Section 2, the structure and fabrication process of the MISIM waveguides are proposed and explained. The fabrication process is carried out with standard CMOS fabrication tools, and so it enables mass production of MISIM waveguide devices. For the metal of the MISIM waveguides, not only gold and silver but also copper and aluminum are considered since the latter are used in standard CMOS fabrication. In Section 3, the characteristics of the single MISIM waveguide are theoretically investigated. Also, changes of the effective index of its mode are handled, which are induced by respective changes of the real and imaginary parts of the RI of its insulator. Section 4 presents theoretical investigation of the coupled MISIM waveguides. Changes in the coupling of the two identical MISIM waveguides are analyzed with the distance between them varied. Finally, concluding remarks are given in Section 5.

2. Structure and fabrication process

The MISIM waveguide is based on a conventional silicon-on-insulator (SOI) wafer that is used for silicon photonics. The silicon, with a thickness hS, of an SOI wafer is patterned into a rectangular line with a width wS. The Si line and the SiO2 substrate are conformally covered by thin insulator with a thickness tI. On both sides of the Si line covered by the insulator, two rectangular metal lines with a width wM and a height hS are placed. The schematic diagram of its cross-section is shown in Fig. 1(a)
Fig. 1 (a) Cross-sectional structure of the MISIM waveguide. This structure is mainly analyzed in Section 3. (b) Cross-sectional structure of the MISIM waveguide whose insulator is partially removed by using wet-etching. The fabrication process of the MISIM waveguide consists of (c) formation of silicon patterns, (d) deposition of oxide, (e) formation of Si3N4 patterns, (f) deposition of metal, and (g) chemical-mechanical polishing. The cross-section along the line AB is shown in (h).
. (Actually, this structure is somewhat similar to those in [15

15. N.-N. Feng and L. Dal Negro, “Plasmon mode transformation in modulated-index metal-dielectric slot waveguides,” Opt. Lett. 32(21), 3086–3088 (2007). [CrossRef] [PubMed]

,16

16. D. Dai and S. He, “Low-loss hybrid plasmonic waveguide with double low-index nano-slots,” Opt. Express 18(17), 17958–17966 (2010). [CrossRef] [PubMed]

].) Using wet etching, we may remove easily its inverted U shaped insulator covering the Si line, and we obtain slots as shown in Fig. 1(b). These slots may be filled with a functional material. An example of such a functional material is electro-optic (EO) polymer with a very large EO coefficient [18

18. R. Ding, T. Baehr-Jones, Y. Liu, R. Bojko, J. Witzens, S. Huang, J. Luo, S. Benight, P. Sullivan, J.-M. Fedeli, M. Fournier, L. Dalton, A. Jen, and M. Hochberg, “Demonstration of a low V π L modulator with GHz bandwidth based on electro-optic polymer-clad silicon slot waveguides,” Opt. Express 18(15), 15618–15623 (2010). [CrossRef] [PubMed]

,19

19. C.-Y. Lin, X. Wang, S. Chakravarty, B. S. Lee, W. Lai, J. Luo, A. K.-Y. Jen, and R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010). [CrossRef]

]. If EO polymer fills the slots, the effective index of a MISIM waveguide mode may be effectively changed. Even a much larger change may be achieved if the slots are filled with liquid crystal. In these cases, the two metal lines not only play an important role in guiding a MISIM waveguide mode but also apply the electric field that controls the EO effect or the orientation of liquid crystal. In addition, if the slots are filled with a gain medium like polymer doped with quantum dots [20

20. J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9(8), 2935–2939 (2009). [CrossRef] [PubMed]

], the propagation length of a MISIM waveguide mode may be increased.

Its fabrication process is schematically shown in Figs. 1(c) to 1(g). First, the silicon is patterned by using 193-nm optical lithography and dry etching [21

21. E. Jordana, J.-M. Fedeli, L. E. Melhaoui, P. Lyan, J. P. Colonna, N. Daldosso, L. Pavesi, P. Pellegrino, B. Garrido, A. Vila, and Y. Lebour, “Deep-UV lithography fabrication of slot waveguides and sandwiched waveguides for nonlinear applications,” in Proceedings of 2007 4th IEEE International Conference on Group IV Photonics, (Institute of Electrical and Electronics Engineers, Tokyo, 2007), pp. 1–3.

,22

22. S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009). [CrossRef]

]. At this step, Si patterns for Si photonic waveguides and the MISIM waveguides are made. As shown in Fig. 1(c), for connection between the Si photonic waveguide and the MISIM waveguide, an about 450-nm-wide Si line for the former is tapered to have a width wS for the latter. Then, silicon dioxide for the insulator of the MISIM waveguide is conformally deposited on the Si patterns by using a low pressure chemical vapor deposition (LPCVD) process with tetraethyl orthosilicate (TEOS) [23

23. P. McCann, K. Somasundram, S. Byrne, and A. Nevin, “Conformal deposition of LPCVD TEOS,” Proc. SPIE 4557, 329–340 (2001). [CrossRef]

]. For the SiO2 deposition, LPCVD is superior to thermal oxidation since the former is carried out at a lower temperature than the latter. Before deposition of metal on the silicon dioxide, silicon nitride (Si3N4) patterns are formed, as shown in Fig. 1(e), by using film deposition, optical lithography, and dry etching. At this step, the Si3N4 patterns need to be aligned with the Si patterns. As inferred from Fig. 1(e), an alignment error along the x-axis does not cause a realized MISIM waveguide to deviate from its ideal structure since the width of the opened area of the Si3N4 patterns is much larger than wS. An alignment error along the z-axis may affect the transformation of a Si photonic waveguide mode into a MISIM waveguide mode, but this may not be significant. This is because the alignment error expected from the 193-nm optical lithography is quite smaller than the length of the tapered region. The purposes of the Si3N4 patterns are twofold. One purpose is to prevent the Si photonic waveguides from being covered by metal. If metal covers them, their propagation loss increases, which is undesirable. The other purpose is that the Si3N4 patterns function as a mold for metal patterns. In other words, they are necessary for Damascene technology. After the formation of the Si3N4 patterns, as shown in Fig. 1(f), metal is deposited to fill the empty space bounded by them. Finally, with chemical-mechanical polishing (CMP) employed, the surplus metal is removed until the top surfaces of the Si3N4 patterns and the silicon dioxide deposited on the Si patterns are exposed as shown in Fig. 1(g). If the metal is copper, Cu CMP can be carried out without difficulty since it is an essential step for Cu interconnect formation in present industrial CMOS fabrication. Although CMP is not as commonly applied to gold, silver, and aluminum as it is applied to copper, CMP of them is also possible [24

24. H. Ishii, S. Yagi, T. Minotani, Y. Royter, K. Kudou, M. Yano, T. Nagatsuma, K. Machida, and H. Kyuragi, “Gold damascene interconnect technology for millimeter-wave photonics on silicon,” Proc. SPIE 4557, 210–219 (2001). [CrossRef]

26

26. M. Ronay, “Development of aluminum chemical mechanical planarization,” J. Electrochem. Soc. 148(9), G494–G499 (2001). [CrossRef]

]. Figure 1(h) shows the cross-section of the finished MISIM waveguide in Fig. 1(g).

For the following theoretical investigation, it is assumed that the thickness of the deposited SiO2 film is equal to tI on the SiO2 substrate and on the top of the Si patterns. This assumption is reasonable since the LPCVD with TEOS gives very high conformality. In addition, the RI of the deposited SiO2 film is assumed to be equal to that of the SiO2 substrate. With regard to the dimensions of the Si line, hS is set to 250 nm since the Si thickness of a usual SOI wafer is around 250 nm. In the case of wS, the narrower the Si line is, the smaller the mode area of the MISIM waveguide is. Since the minimum line width that can be achieved from the 193-nm optical lithography is about 100 nm [21

21. E. Jordana, J.-M. Fedeli, L. E. Melhaoui, P. Lyan, J. P. Colonna, N. Daldosso, L. Pavesi, P. Pellegrino, B. Garrido, A. Vila, and Y. Lebour, “Deep-UV lithography fabrication of slot waveguides and sandwiched waveguides for nonlinear applications,” in Proceedings of 2007 4th IEEE International Conference on Group IV Photonics, (Institute of Electrical and Electronics Engineers, Tokyo, 2007), pp. 1–3.

,22

22. S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009). [CrossRef]

], wS is set to 100 nm. With regard to wM, it is assumed that the metal lines are so wide that the Si3N4 patterns bounding them do not affect the characteristics of the MISIM waveguide. In other words, the structure in Fig. 1(a) is mainly analyzed rather than the one in Fig. 1(h). Table 1

Table 1. Dielectric Constants of Gold, Silver, Copper, and Aluminum at a Wavelength of 1.55 μm

table-icon
View This Table
summarizes the dielectric constants ε Au, ε Ag1, ε Cu, and ε Al of gold, silver, copper, and aluminum. They are obtained from Palik’s handbook [27

27. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1998)

]. However, Johnson and Christy’s paper [28

28. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

] gives a quite different value for the dielectric constant of silver, which is denoted by ε Ag2 in Table 1. While the value of ε Ag1 was used in [13

13. Y. Song, J. Wang, Q. Li, M. Yan, and M. Qiu, “Broadband coupler between silicon waveguide and hybrid plasmonic waveguide,” Opt. Express 18(12), 13173–13179 (2010). [CrossRef] [PubMed]

], that of ε Ag2 was used in [9

9. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]

11

11. H.-S. Chu, E.-P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. 96(22), 221103 (2010). [CrossRef]

,15

15. N.-N. Feng and L. Dal Negro, “Plasmon mode transformation in modulated-index metal-dielectric slot waveguides,” Opt. Lett. 32(21), 3086–3088 (2007). [CrossRef] [PubMed]

,16

16. D. Dai and S. He, “Low-loss hybrid plasmonic waveguide with double low-index nano-slots,” Opt. Express 18(17), 17958–17966 (2010). [CrossRef] [PubMed]

]. Although the latter was used more frequently, it was reported that the former made simulation closer to experiment [29

29. P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98(4), 043109 (2005). [CrossRef]

]. Therefore, both ε Ag1 and ε Ag2 are used in the following theoretical investigation of the MISIM waveguides. Finally, the wavelength λ is set to 1.55 μm, and only the quasi-TE polarization is considered. This is because a hybrid plasmonic mode exists when its major electric field component is normal to the interface between its metal and insulator and the interface between its insulator and dielectric like silicon.

3. Characteristics of the single MISIM waveguide

3.1 Insulator with the RI of SiO2

The intensity profile, effective index, effective mode area, and normalized power of a MISIM waveguide mode were calculated when the RI of the insulator, nI is equal to the RI of SiO2, which is 1.444. For every value of tI between 10 and 100 nm, the MISIM waveguide supports only one quasi-TE mode regardless of types of metal. Figure 2
Fig. 2 Intensity profiles of the MISIM waveguide mode for εM = ε Au. For tI = 20, 40, 60, and 80 nm, they are shown in (a) to (d), respectively. (e) Intensity distributions along a horizontal line y = 125 nm for the different values of tI. An enlarged part is shown in the inset. (f) Intensity distributions along another horizontal line y = tI / 2 for the different values of tI. In (e) and (f), the black, red, green, and cyan lines correspond to the cases of tI = 20, 40, 60, and 80 nm, respectively. The correspondence between the line colors and the values of tI is used in the following figures.
shows the intensity (i.e. the magnitude of the Poynting vector Pz (r)) profiles of the MISIM waveguide mode for four different values of tI. In this calculation, the dielectric constant of the metal of the MISIM waveguide, εM was set to ε Au. As shown in Figs. 2(a) to 2(d), a large portion of the power carried by the MISIM waveguide mode is confined to the thin insulator layers between the metal lines and the Si line. The intensity in the insulator layers and the Si line decreases as tI increases, and it is almost inversely proportional to tI. This can be confirmed from Fig. 2(e), which shows the intensity distributions along a horizontal line y = 125 nm. Figure 2(f) shows the intensity distribution along another horizontal line y = tI / 2. The larger the value of tI is, the further the intensity profile spreads over the insulator below the metal lines.

Figure 3
Fig. 3 Relations of the effective index n eff to tI for different values of εM. The real and imaginary parts of n eff, Re[neff] and Im[neff] are shown in (a) and (b), respectively. (b) also shows the relations of the propagation length Lp to tI, which are represented by the dashed lines. In the inset of (a), an enlarged part is shown. The square, circle, triangle, inverted triangle, and diamond symbols correspond to the cases of εM = ε Au, ε Ag1, ε Ag2, ε Al, and ε Cu, respectively. This correspondence between the symbol shapes and the values of εM is used in the following figures.
shows the relations of the effective index n eff of the MISIM waveguide mode to tI for different values of εM. As tI increases, the real part of n eff, Re[neff] decreases, and the imaginary part of n eff, Im[neff] increases. This is because the intensity in the metal lines decreases as tI increases, as shown in the inset of Fig. 2(e). Figure 3(b) also shows the propagation length Lp of the MISIM waveguide mode, which is defined as the distance at which its field amplitude decays to 1/e (i.e. Lp=λ/(2πIm[neff])). When εM = ε Ag2, Lp increases from 41 μm ( = 26.5λ) to 136 μm ( = 87.7λ) as tI increases from 10 nm to 100 nm. Lp for εM = ε Ag1, ε Au, ε Al, and ε Cu is on average, respectively, 19.7, 18.7, 18.3, and 13.8% of Lp for εM = ε Ag2. The dependence of n eff on the values of εM is quite similar to that of the effective index n SPP of a surface plasmon polariton propagating along the interface between semi-infinite metal with a dielectric constant equal to εM and insulator with an RI equal to nI. It is well known that n SPP is calculated by using the expression nSPP=[εMnI2/(εM+nI2)]1/2. If εM is equal to ε Cu, ε Ag1, ε Au, ε Ag2, and ε Al, n SPP is 1.463 – j0.00265, 1.462 – j0.00180, 1.460 – j0.00186, 1.456 – j0.000303, and 1.450 – j0.00123, respectively. The magnitude orders of Re[nSPP] and Im[nSPP] depending on the values of εM are almost the same as those of Re[neff] and Im[neff].

The effective mode area A eff of the MISIM waveguide mode was calculated by using the expression [30

30. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008). [CrossRef]

], where W(r) is the energy density given by Eq. (3) in [30

30. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008). [CrossRef]

]. The calculated relations of A eff to tI are shown in Fig. 4(a)
Fig. 4 (a) Relations of the effective mode area A eff to tI for the different values of εM. An enlarged part is shown in the inset. The dotted curve represents the real area AR of the thin insulator region R. In addition, the thin horizontal line represents the diffraction-limited area of silicon. (b) Relations of the normalized power in R to tI for the different values of εM. An enlarged part is shown in the upper middle inset. The lower right inset shows the definition of the thin insulator region R.
. The real area AR of the thin insulator region denoted by R in the inset of Fig. 4(b) is also shown as a function of tI, which is given by 2tI(tI+hS). The ratio of AR to A eff is between 0.6 and 0.7 for all the values of tI and εM. This indicates that the region where the energy density of the MISIM waveguide mode becomes significant quite coincides with R. As shown in Fig. 4(a), A eff is smaller than the diffraction-limited area of silicon, (λ/2/nSi)2, where n Si is the RI of silicon, if tI < 55 nm. With regard to the power carried by the MISIM waveguide mode, Fig. 2 has shown that a large portion of the power is confined to R. This confinement is quantitatively confirmed from the normalized power in R, which is defined as RPz(r)dAPz(r)dA. Figure 4(b) shows the relations of the normalized power to tI. The normalized power reaches 0.6 around tI = 60 nm. As tI increases up to this value, it increases since the portion of the power, which is carried through the Si line, decreases. However, after this value, it decreases since the portion of the power, which is carried through the insulator below the metal lines, increases. The magnitude orders of the normalized power and A eff depending on the values of εM are the same as that of Re[neff] and the inverse of this order, respectively. The larger the intensity or energy density is in R, the larger it is in the metal lines. Consequently, becomes larger as explained regarding Fig. 3.

The characteristics of the MISIM waveguide need to be compared with those of the CMOS-compatible MIS waveguides [10

10. D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]

,12

12. M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express 18(11), 11728–11736 (2010). [CrossRef] [PubMed]

14

14. M. Z. Alam, J. Meier, J. S. Aitchison, and M. Mojahedi, “Propagation characteristics of hybrid modes supported by metal-low-high index waveguides and bends,” Opt. Express 18(12), 12971–12979 (2010). [CrossRef] [PubMed]

]. For comparison, the MIS waveguide was analyzed, which is a stack of the silver line (with εM = ε Ag2), the insulator line with a thickness tI, and the 250-nm-high Si line on an SiO2 substrate. The three lines have the same width as hS. When tI = 20 nm, Lp of the MISIM waveguide mode is 56% of that of the MIS waveguide mode. This is because the MISIM waveguide mode is influenced by the two metal lines. In contrast, the normalized power in R of the MISIM waveguide mode is 1.9 times larger than that in the insulator line of the MIS waveguide mode. This is because the geometrical area of the insulator line is slightly smaller than AR / 2. Interestingly, A eff of the MISIM waveguide mode is almost the same as that of the MIS waveguide. When the adjustment of the RI of the insulator induces an effective index change, the amount of such a change is almost proportional to the normalized power in the insulator as explained below. Consequently, the MISIM waveguide has about two times more effective tuning of its characteristics than the MIS waveguide at the cost of the decrease of Lp by half without changing A eff.

The results in Figs. 3 and 4 show that the characteristics of the Cu-based or Al-based MISIM waveguide are comparable to those of the Au-based one although Lp of the Cu-based one or the normalized power in R of the Al-based one is a little smaller. Therefore, instead of gold, copper or aluminum may be used for the MISIM waveguides. In the case of the Ag-based MISIM waveguide, since Lp changes significantly depending on whether εM = ε Ag1 or ε Ag2, the actual dielectric constant of an Ag film for a realized MISIM waveguide should be checked experimentally.

3.2 Insulator with the adjusted RI

The MISIM waveguide was simulated with the slots in Fig. 1(b) filled with EO polymer or a gain medium. Under the assumption that the inverted U shaped region denoted by U in the inset of Fig. 5(a)
Fig. 5 (a) Relations of the change of Re[neff], ΔRe[neff] to tI for the different values of εM. The dotted line represents the case of ΔRe[neff] = 0.001. The inset shows the inverted U shaped sub-region of the insulator, U, whose RI is nI + ΔnI. In this figure, ΔnI = 0.001. (b) Relations of ΔrRe[neff] to tI for the different values of εM. ΔrRe[neff] is the relative change of ΔRe[neff], which is given by (ΔRe[neff]/Re[neff])/(ΔnI/nI).
has an RI of nI + ΔnI, n eff was calculated as a function of tI for a fixed value of ΔnI. Figure 5(a) shows the relations of the change of Re[neff], ΔRe[neff] to tI when ΔnI = 0.001. In this case, ΔnI means an electro-optically induced index change. If the EO coefficient of EO polymer is 100 pm/V, that amount of ΔnI is induced by applying ~1 V between the two metal lines. The value of the applied voltage is estimated from a simple capacitor model, which consists of parallel plates sandwiching the insulator-metal-insulator. (Actually, it is not easy to infiltrate EO polymer into a narrow and deep slot and pole it for the EO effect. However, this was successfully done in the case of the 75-nm-wide and 230-nm-deep slot in [19

19. C.-Y. Lin, X. Wang, S. Chakravarty, B. S. Lee, W. Lai, J. Luo, A. K.-Y. Jen, and R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010). [CrossRef]

].) Since the power of the MISIM waveguide mode is well confined to R as shown in Figs. 2 and 4, ΔnI effectively affects ΔRe[neff]. In other words, ΔRe[neff]/ΔnI is close to 1, and it is even larger than 1 for some values of tI. When the relative change of Re[neff], denoted by ΔrRe[neff], is defined as (ΔRe[neff]/Re[neff])/(ΔnI/nI), the relations of to tI are shown in Fig. 5(b). Interestingly, these relations are quite similar to those of the normalized power in R shown in Fig. 4(b). This similarity is approximately explained from the perturbation theory [31

31. J. Homola, “Electromagnetic theory of surface plasmons,” in Surface Plasmon Resonance Based Sensors, J. Homola, ed. (Springer, Berlin, 2006).

] for a planar MISIM waveguide that is uniform along the y-axis. From the perturbation theory, it is obtained that

ΔneffneffnIΔnIRExHydxExHydxRPz(x)dxPz(x)dx.
(1)

In this equation, Ex (Hy) denotes the x (y) component of the electric (magnetic) field of a planar MISIM waveguide mode, and R is the region that results from extending R infinitely along the ± y directions. The second approximate equality in Eq. (1) holds since |Re[Hy]| >> |Im[Hy]| for the planar MISIM waveguide mode so that HyHy* and ExHy2Pz. The third term of Eq. (1) is the normalized power in R . As shown in Fig. 3, Re[neff] >> |Im[neff]|, and ΔRe[neff] is much larger than the change of Im[neff], ΔIm[neff] if ΔnI is real. Consequently, the first term of Eq. (1) becomes ΔrRe[neff], and it is proportional to the normalized power in R for the planar MISIM waveguide mode. Since the MISIM waveguide mode approaches the planar MISIM waveguide mode as hS increases, Eq. (1) explains the aforementioned similarity to some extent.

When U is filled with a gain medium with a gain coefficient g, it is simply assumed that ΔnI is given by jg/(4π/λ). ΔnI = j0.00617 if g is 500 cm–1, which is somewhat larger than the gain coefficient of the polymer strip-loaded plasmonic waveguide doped with quantum dots in [20

20. J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9(8), 2935–2939 (2009). [CrossRef] [PubMed]

]. Figure 6(a)
Fig. 6 (a) Relations of the change of Im[neff], ΔIm[neff] to tI for the different values of εM when ΔnI = j0.00617, which means that the gain coefficient of U is 500 cm–1. The dotted line represents the case of ΔIm[neff] = 0.00617. Also, the relations of ΔrIm[neff] to tI are shown together. ΔrIm[neff] is the relative change of ΔIm[neff], which is given by (ΔIm[neff]/Re[neff])/ (|ΔnI|/nI). (b) Relations of the increase of Lp, ΔLp to tI. Also, the gain coefficient of the MISIM waveguide mode for εM = ε Ag2 is shown as a function of tI.
shows the relations of ΔIm[neff] to tI in this case. ΔIm[neff] changes with tI in almost the same way as ΔRe[neff]. When the relative change of Im[neff], denoted by ΔrIm[neff], is defined as (ΔIm[neff]/Re[neff])/(|ΔnI|/nI), the relations of ΔrIm[neff] to tI are shown in Fig. 6(a), and they also match almost perfectly those of ΔrRe[neff] in Fig. 5(b). In Eq. (1), if ΔnI is imaginary, the first term becomes ΔrIm[neff] since ΔIm[neff] >> ΔRe[neff]. Hence, ΔrIm[neff] has almost the same dependence on tI as ΔrRe[neff]. Since ΔIm[neff] is positive, Lp increases, and Fig. 6(b) shows the relations of the increase of Lp, ΔLp to tI. The larger Im[neff] is, the larger ΔLp is. Except the case of εM = ε Cu, the gain coefficient of 500 cm–1 makes Lp increase by more than 100% for large values of tI. In the case of εM = ε Ag2, the gain of the gain medium compensates for the loss of the MISIM waveguide mode, and the mode has a gain coefficient reaching 280 cm–1.

3.3 Two considerations related to realized MISIM waveguides

When copper is used for the metal of the MISIM waveguide, a diffusion barrier needs to be formed on the deposited SiO2 layer before the metal deposition in Fig. 1(f) since copper ions diffuse well into SiO2 and silicon. As a diffusion barrier, usually, a stack of tantalum nitride and tantalum (TaN/Ta) films is used. Since the TaN/Ta stack is in contact with the insulator to which the power of the MISIM waveguide mode is well confined, it may seriously affect the characteristics of the mode. Assuming that 5-nm-thick TaN and Ta films whose respective RIs are 4.388 – j2.822 and 4.865 – j5.471 [32

32. T. Waechtler, B. Gruska, S. Zimmermann, S. E. Schulz, and T. Gessner, “Characterization of sputtered Ta and TaN films by spectroscopic ellipsometry,” in Proceedings of 8th International Conference on Solid-State and Integrated Circuit Technology, (Institute of Electrical and Electronics Engineers, Shanghai, China, 2006), pp. 2184–2186.

] are conformally deposited on the insulator, the MISIM waveguide was analyzed. Because of the TaN/Ta stack, for tI = 50 nm, its effective index changes from 1.920 – j0.01988 to 1.914 – j0.2374, and its propagation loss increases from 0.70 dB/μm to 8.4 dB/μm. Since its intensity profile changes slightly, e.g. the normalized power in R decreases just by 0.01, the huge increase in the propagation loss is mainly attributed to the large absorption of the TaN/Ta stack. Therefore, instead of the TaN/Ta stack, a diffusion barrier with low absorption is required. Silicon carbide (SiC) is also used as a diffusion barrier [33

33. S. G. Lee, Y. J. Kim, S. P. Lee, H.-S. Oh, S. J. Lee, M. Kim, I.-G. Kim, J.-H. Kim, H.-J. Shin, J.-G. Hong, H.-D. Lee, and H.-K. Kang, “Low dielectric constant 3MS α-SiC:H as Cu diffusion barrier layer in Cu dual damascene process,” Jpn. J. Appl. Phys. 40(Part 1, No. 4B), 2663–2668 (2001). [CrossRef]

], and it may be transparent at a wavelength of 1.55 μm [34

34. Y. Shoji, K. Nakanishi, Y. Sakakibara, K. Kintaka, H. Kawashima, M. Mori, and T. Kamei, “Hydrogenated amorphous silicon carbide optical waveguide for telecommunication wavelength applications,” Appl. Phys. Express 3(12), 122201 (2010). [CrossRef]

]. If a 10-nm-thick SiC film with an RI of 3.096 [34

34. Y. Shoji, K. Nakanishi, Y. Sakakibara, K. Kintaka, H. Kawashima, M. Mori, and T. Kamei, “Hydrogenated amorphous silicon carbide optical waveguide for telecommunication wavelength applications,” Appl. Phys. Express 3(12), 122201 (2010). [CrossRef]

] is used as a diffusion barrier, the MISIM waveguide mode has n eff = 2.022 – j0.02324, and its propagation loss is 0.82 dB/μm. Consequently, we had better use a SiC film rather than a TaN/Ta stack to realize the MISIM waveguides.

In realizing the MISIM waveguides, it is also necessary to consider the minimum value of wM, which is required to maintain the explained characteristics of the MISIM waveguide mode. For this purpose, the structure in Fig. 1(h) was analyzed. The RI of silicon nitride was set to 1.97, and εM was set to ε Cu. As explained above, a small portion of the power of the MISIM waveguide mode is carried through the insulator below the metal lines, and the portion increases with tI. If wM is small, light in the insulator below the metal lines is coupled to the surface plasmon polaritons that exist along the boundaries between the metal lines and the Si3N4 patterns. This coupling increases the mode area and propagation loss of the MISIM waveguide mode, and so wM should be large enough to make this coupling negligible. When neffd denotes the effective index of the deteriorated MISIM waveguide mode of the structure in Fig. 1(h), neffd was calculated with respect to wM for the four values of tI. Figure 7
Fig. 7 (a) Relations of Re[neffdneff]/Re[neff] to wM for the different values of tI. neffd denotes the effective index of the deteriorated MISIM waveguide mode of the structure in Fig. 1(h). (b) Relations of Im[neffdneff]/Im[neff] to wM for the different values of tI.
shows the relations of Re[neffdneff]/Re[neff] to wM and those of Im[neffdneff]/Im[neff]. The smaller tI is, the faster both Re[neffdneff]/Re[neff] and Im[neffdneff]/Im[neff] approach zero, i.e. the faster neffd converges to neff. If the minimum value of wM is defined as the value for which both their values become smaller than 0.001, the minimum values for tI = 20, 40, 60, and 80 nm are 290, 400, 510, and 670 nm, respectively.

4. Characteristics of the coupled MISIM waveguides

The analysis of the coupled MISIM waveguides is necessary, on the one hand, since it is necessary to know how closely the two MISIM waveguides should be placed to transfer efficiently the power of the one waveguide to the other. On the other hand, it is necessary to know how far apart they should be for negligible crosstalk between them. The coupled MISIM waveguides were analyzed by using a simple model of beating between the antisymmetric and symmetric modes of two coupled identical waveguides with loss [35

35. G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]

]. For using the model, first, calculated were the effective indexes Na and Ns of the antisymmetric and symmetric modes of the structure in Fig. 8(a)
Fig. 8 (a) Cross-sectional structure of the coupled MISIM waveguides. (b) Relations of Re[Na] (black) and Re[Ns] (red) to sM. Na and Ns are the effective indexes of the antisymmetric and symmetric modes of the structure in (a). The upper (lower) insets show the distributions of the real part of the x component of the electric field of the antisymmetric (symmetric) mode, Re[Ex(a)] (Re[Ex(s)]) along the line y = 125 nm for sM = 60 and 300 nm, respectively. (c) Relations of Im[Na] (black) and Im[Ns] (red) to sM. In the calculation for this figure, εM = ε Au, and tI = 40 nm.
. In the structure, the two MISIM waveguides share a metal line with a width sM between them. For εM = ε Au and tI = 40 nm, the real and imaginary parts of Na and Ns are shown as functions of sM in Figs. 8(b) and 8(c), respectively. As sM increases, Na and Ns approach n eff. The upper (lower) insets of Fig. 8(b) show the distributions of the real part of the x component of the electric field E(a) (E(s)) of the antisymmetric (symmetric) mode along the line y = 125 nm for sM = 60 and 300 nm, respectively. In contrast to a coupling between two dielectric waveguides, Re[Na] > Re[Ns].The reason for this is deduced from a coupling between two surface plasmon polaritons along the two sides of a metal film. It is well known that the coupling makes the metal film support antisymmetric and symmetric modes. Their effective indexes have the same relations as Na and Ns.

By using Na and Ns, a coupling length Lc was calculated. It is the distance at which the power of the left MISIM waveguide is maximally transferred to the right MISIM waveguide. P max is defined as the maximally transferred power at Lc, which is normalized with respect to the power that the left MISIM waveguide carries at the start of the structure in Fig. 8(a). Lc and P max are expressed by
Lc=2Lbπtan1(πL¯p2Lb),
(2)
Pmax=exp(2ϕcotϕ)sin2ϕ,ϕ=πLc2Lb,
(3)
where Lb is a beating length given by λ/2/Re[NaNs] and L¯p is a sort of average propagation length given by λ/π/Im[NaNs] [35

35. G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]

].

While Lb increases almost exponentially with sM, L¯pincreases but approach Lp, which is easily expected from its definition and Fig. 8(c). Since and |Im[Na]| are much smaller than Re[Na] and Re[Ns], Lb is smaller than L¯p for small sM. However, Lb becomes much larger than L¯p for large sM. This relation between Lb and L¯p makes Lc bounded by Lb for small sM and bounded by L¯p for large sM, as deduced from Eq. (2). For sufficiently large sM, LcL¯pLp << Lb, which means that the beating between the antisymmetric and symmetric modes is suppressed by the propagation loss of the MISIM waveguide mode.

Figures 10(a)
Fig. 10 (a) – (e) Relations of the coupling length Lc and the normalized, maximally-transferred power P max at Lc to sM for tI = 20, 40, 60, and 80 nm. In the calculation, εM was set to ε Au for (a), ε Ag1 for (b), ε Al for (c), ε Cu for (d), and ε Ag2 for (e). The correspondence between the line colors and the values of tI is the same as in the above figures. (f) Relations of P max in the case of sM = 60 nm to tI for the different values of εM. (g) Relations of the minimum values of sM to tI for the different values of εM. The correspondence between the symbol shapes and the values of εM is the same as in the above figures.
to 10(e) show the relations of Lc and P max to sM for the four values of tI, respectively, for εM = ε Au, ε Ag1, ε Al, ε Cu, and ε Ag2. Lc and P max for εM = ε Au, ε Ag1, ε Al, and ε Cu change quite similarly with sM or tI, and there are no large differences between the values of Lc and P max for the different values of εM. However, the relations of Lc and P max to sM for εM = ε Ag2 are quite different from those in Figs. 10(a) to 10(d) since the MISIM waveguide mode for εM = ε Ag2 has much smaller propagation loss than those for the other values of εM. The explained change of Lc with respect to sM is confirmed from Figs. 10(a) to 10(e). In Figs. 10(a) to 10(d), for small sM, although Lc is bounded by Lb, Lc does not change exactly in the same way as Lb shown in Fig. 9(a) (i.e. Lc increases simply with tI regardless of sM) since L¯p is not much larger than Lb. However, if εM = ε Ag2, for small sM, Lc changes almost in the same way as Lb shown in Fig. 9(a) since L¯p is much larger than Lb in this case. With regard to P max, it decreases as sM increases, and it decreases almost exponentially for large sM. The exponential decrease of P max for large sM is explained from Eq. (3). If sM is sufficiently large, ϕπLp/2/Lb << 1, and so P max is approximately given by exp(2)(πLp/2/Lb)2, which decreases almost exponentially. However, P max increases with tI since the propagation loss of the MISIM waveguide mode decreases so that L¯p increases with tI.

For the efficient power transfer between the two MISIM waveguides, sM should be as small as possible. In Figs. 10(a) to 10(e), the smallest value of sM is 60 nm, and Fig. 10(f) shows P max in the case of sM = 60 nm as functions of tI for the different values of εM. The best power transfer is obtained when εM = ε Ag2. As tI increases from 20 nm to 80 nm, P max increases from 0.86 to 0.89, and Lc increases from 3.8 μm to 5.3 μm. The worst power transfer is obtained when εM = ε Al. As tI increases from 20 nm to 80 nm, P max increases from 0.37 to 0.48, and Lc increases from 4.2 μm to 6.3 μm. If sM is reduced below 60 nm, P max increases a little, and Lc decreases. However, the reduction of sM is limited by the following two factors. The one is that the distance between the two silicon lines in Fig. 8(a), which is sM + 2tI, should be larger than the minimum line width of the 193-nm optical lithography. (If tI = 20 nm and the minimum line width is 100 nm, sM = 60 nm.) The other is whether the narrow channel for the shared metal line is well filled with metal.

For the low crosstalk between the two MISIM waveguides, sM should be sufficiently large. The minimum value of sM, which is large enough for the low crosstalk, is determined as follows. First, the crosstalk is quantitatively defined as the ratio of P max to the normalized power carried by the left MISIM waveguide at a distance of Lc, which is given by exp(2ϕcotϕ)cos2ϕ. Then, the crosstalk is given by exp(2)Pmax for sufficiently large sM. If the desired value of the crosstalk is 0.01, P max becomes 0.00135 for the minimum value of sM. This value is indicated as the dashed lines in Figs. 10(a) to 10(e), and the curves of P max cross these dashed lines at the minimum values of sM. Figure 10(g) shows the minimum values of sM as functions of tI for the different values of εM. On the one hand, the minimum value of sM is smallest for εM = ε Cu. It increases from 420 nm to 880 nm as tI increases from 20 nm to 80 nm. Actually, it is comparable to the distance between two coupled metal-insulator-metal (MIM) waveguides, for which the crosstalk between them is also 0.01. For example, in the case of the coupled Cu-based MIM waveguides (i.e. a 250-nm-thick Cu film with two 40-nm-wide slots, which is surround by SiO2), the crosstalk of 0.01 is obtained when the width of the metal line between the two slots is 430 nm. On the other hand, the minimum value of sM is largest for εM = ε Ag2. It increases from 660 nm to 1410 nm as tI increases from 20 nm to 80 nm. Interestingly, it is much smaller than the distance for the crosstalk of 0.01 between two coupled nanowire-based MIS waveguides, each of which has a very small mode area [36

36. Y. Song, M. Yan, Q. Yang, L.-M. Tong, and M. Qiu, “Reducing crosstalk between nanowire-based hybrid plasmonic waveguides,” Opt. Commun. 284(1), 480–484 (2011). [CrossRef]

]. Reference [36

36. Y. Song, M. Yan, Q. Yang, L.-M. Tong, and M. Qiu, “Reducing crosstalk between nanowire-based hybrid plasmonic waveguides,” Opt. Commun. 284(1), 480–484 (2011). [CrossRef]

] handled the case where two Si nanowires with the same diameter of 300 nm, each of which is surrounded by a 12-nm-thick SiO2 shell, are placed on an Ag substrate whose dielectric constant is equal to ε Ag2. Although the edge-to-edge distance between the SiO2–surrounded Si nanowires was 636 nm, the crosstalk was 0.74.

Lastly, there is one thing that is required to discuss with regard to the simple beating model. If E(l) and E(r)denote the electric fields of the left and right MISIM waveguide modes, Eqs. (2) and (3) are derived under the assumption that E(l) = E(s)/2 + E(a)/2 and E(r) = E(s)/2E(a)/2. However, as checked from the insets of Fig. 8(b), the assumption is not satisfied completely for small sM. Therefore, the results based on Eqs. (2) and (3) may have some error for small sM, and it may be necessary to polish them by using a numerical method.

5. Conclusions

This paper has proposed and investigated theoretically the MISIM waveguides that are hybrid plasmonic waveguides with the two advantages: the simple realizability based on standard CMOS technology and the possession of the post-fabrication method of replacing the insulator with a functional material. First, their structure and fabrication process, both of which are compatible with standard CMOS technology, have been explained. Then, the following characteristics of the single MISIM waveguide have been analyzed: the effective index, propagation length, effective mode area, and normalized power of the MISIM waveguide mode. In the analysis, gold, silver, aluminum, and copper have been considered for its metal. It has been explained how its characteristics change depending on which metal is employed. In addition to this analysis, it has been demonstrated that the respective changes of the real and imaginary parts of the RI of its insulator tune the effective index very effectively. Moreover, with regard to a realized MISIM waveguide, it has been discussed that a diffusion barrier with low absorption should be used and that its metal lines should have a width larger than the determined value. Finally, the two coupled MISIM waveguides have been analyzed. On the one hand, when εM = ε Ag2, tI = 20 nm, and sM = 60 nm, 86% of the power carried by the one waveguide is transferred to the other at a distance of 3.8 μm. On the other hand, when εM = ε Cu, tI = 20 nm, the crosstalk between them becomes very low for sM > 420 nm. The MISIM waveguides are expected to play an important role in connecting Si-based photonic and electronic circuits.

Acknowledgments

This research was supported by the Basic Science Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0022473).

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28.

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29.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long-range surface-plasmon-polariton waveguides,” J. Appl. Phys. 98(4), 043109 (2005). [CrossRef]

30.

R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008). [CrossRef]

31.

J. Homola, “Electromagnetic theory of surface plasmons,” in Surface Plasmon Resonance Based Sensors, J. Homola, ed. (Springer, Berlin, 2006).

32.

T. Waechtler, B. Gruska, S. Zimmermann, S. E. Schulz, and T. Gessner, “Characterization of sputtered Ta and TaN films by spectroscopic ellipsometry,” in Proceedings of 8th International Conference on Solid-State and Integrated Circuit Technology, (Institute of Electrical and Electronics Engineers, Shanghai, China, 2006), pp. 2184–2186.

33.

S. G. Lee, Y. J. Kim, S. P. Lee, H.-S. Oh, S. J. Lee, M. Kim, I.-G. Kim, J.-H. Kim, H.-J. Shin, J.-G. Hong, H.-D. Lee, and H.-K. Kang, “Low dielectric constant 3MS α-SiC:H as Cu diffusion barrier layer in Cu dual damascene process,” Jpn. J. Appl. Phys. 40(Part 1, No. 4B), 2663–2668 (2001). [CrossRef]

34.

Y. Shoji, K. Nakanishi, Y. Sakakibara, K. Kintaka, H. Kawashima, M. Mori, and T. Kamei, “Hydrogenated amorphous silicon carbide optical waveguide for telecommunication wavelength applications,” Appl. Phys. Express 3(12), 122201 (2010). [CrossRef]

35.

G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]

36.

Y. Song, M. Yan, Q. Yang, L.-M. Tong, and M. Qiu, “Reducing crosstalk between nanowire-based hybrid plasmonic waveguides,” Opt. Commun. 284(1), 480–484 (2011). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(220.4241) Optical design and fabrication : Nanostructure fabrication
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Integrated Optics

History
Original Manuscript: February 18, 2011
Revised Manuscript: April 12, 2011
Manuscript Accepted: April 14, 2011
Published: April 15, 2011

Citation
Min-Suk Kwon, "Metal-insulator-silicon-insulator-metal waveguides compatible with standard CMOS technology," Opt. Express 19, 8379-8393 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8379


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  30. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. 10(10), 105018 (2008). [CrossRef]
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  33. S. G. Lee, Y. J. Kim, S. P. Lee, H.-S. Oh, S. J. Lee, M. Kim, I.-G. Kim, J.-H. Kim, H.-J. Shin, J.-G. Hong, H.-D. Lee, and H.-K. Kang, “Low dielectric constant 3MS α-SiC:H as Cu diffusion barrier layer in Cu dual damascene process,” Jpn. J. Appl. Phys. 40(Part 1, No. 4B), 2663–2668 (2001). [CrossRef]
  34. Y. Shoji, K. Nakanishi, Y. Sakakibara, K. Kintaka, H. Kawashima, M. Mori, and T. Kamei, “Hydrogenated amorphous silicon carbide optical waveguide for telecommunication wavelength applications,” Appl. Phys. Express 3(12), 122201 (2010). [CrossRef]
  35. G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]
  36. Y. Song, M. Yan, Q. Yang, L.-M. Tong, and M. Qiu, “Reducing crosstalk between nanowire-based hybrid plasmonic waveguides,” Opt. Commun. 284(1), 480–484 (2011). [CrossRef]

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