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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5391–5400
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Method for characterization of Si waveguide propagation loss

Michele Moresco, Marco Romagnoli, Stefano Boscolo, Michele Midrio, Matteo Cherchi, Ehsan Shah Hosseini, Douglas Coolbaugh, Michael R. Watts, and Birendra Dutt  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 5391-5400 (2013)
http://dx.doi.org/10.1364/OE.21.005391


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Abstract

A new method for measuring waveguide propagation loss in silicon nanowires is presented. This method, based on the interplay between traveling ring modes and standing wave modes due to back-scattering from edge roughess, is accurate and can be used for on wafer measurement of test structures. Examples of loss measurements and fitting are reported.

© 2013 OSA

1. Introduction

The silicon waveguide is the basic building block of a silicon photonic circuit and the quality of the waveguide is also an indication of the quality of all the passive components of the circuit. In this paper we analyze a reliable method for the characterization of the waveguide loss that can implemented in specific test structures placed in any mask design for photonic wafers fabrication.

To the authors knowledge there is not a standard for waveguide loss measurement. Commonly used methods are cut back [3

3. D. B. Keck and R. Tynes, “Spectral response of low-loss optical waveguides,” Appl. Opt. 11(7), 1502–1506 (1972). [CrossRef] [PubMed]

], Fabry-Perot loss modulation [4

4. S. Taebi, M. Khorasaninejad, and S. S. Saini, “Modified Fabry-Perot interferometric method for waveguide loss measurement,” Appl. Opt. 47(35), 6625–6630 (2008). [CrossRef] [PubMed]

,5

5. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic wires and ring resonators fabricated With deep UV lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004). [CrossRef]

], variable length clips [6

6. J. Hu, V. Tarasov, A. Agarwal, L. Kimerling, N. Carlie, L. Petit, and K. Richardson, “Fabrication and testing of planar chalcogenide waveguide integrated microfluidic sensor,” Opt. Express 15(5), 2307–2314 (2007). [CrossRef] [PubMed]

], and critical coupling configuration with all-pass single microring structures [7

7. T. R. Bourk, M. M. Z. Kharadly, and J. E. Lewis, “Measurement of waveguide attenuation by resonance methods,” Electron. Lett. 4(13), 267–268 (1968). [CrossRef]

]. In this paper we propose a method based on a simple microring structure in and under coupled condition. This method has the advantage of being independent of input coupling losses or reflections and of being tolerant to the choice of the bus to ring gap size.

Commonly used Si nanowire waveguides have a cross-section of 220x480nmand most of the propagation loss can be attributed to the side wall roughness [8

8. K. K. Lee, D. R. Lim, L. Hsin-Chiao, A. J. Agarwal,, L. C. Foresi, and Kimerling.,” Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77, 1617–1619 (2000). [CrossRef]

]. Roughness is a typical result of the lithography and etch processes [9

9. M. Williamson and A. Neureuther, “Enhanced, quantitative analysis of resist image contrast upon line edge roughness (LER),” Proc. SPIE 5039, 423–432 (2003). [CrossRef]

]. Typical values for the roughness are of the order of 2nm with a correlation length of ~40nm. These values lead to a propagation loss of the order of 2dB/cm. [10

10. T. Barwicz and H. A. Haus, “Three-dimensional analysis os scattering losses due to sidewall roughness in microphotonic waveguides,” J. Lightwave Technol. 23(9), 2719–2732 (2005). [CrossRef]

]. Improved waveguide fabrication process will decrease the loss and as a consequence measurement becomes more challenging [11

11. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 26(23), 1888–1890 (2001). [CrossRef]

].

2. Theory

In this paper we propose a bus waveguide coupled to a microring structure, as shown in Fig. 1
Fig. 1 Scheme of the bus waveguide coupled to a microring. The four input and output field describe propagation in all directions.
. The bus waveguide is 220x400nm whereas the waveguide in the ring is 220x480nm. The width of the bus is shrunk to 400nm in order to expand the mode further into the gap thus making its coupling to the microring more efficient. In the experiment the behavior for different bus to ring gaps ranging from 100nm to 590nm with incremental steps of 10nm will be presented.

The system in Fig. 1 shows a microring coupled to a straight waveguide. Propagation is in both directions both in the bus and is in the ring. The sidewall roughness of the microring waveguide scatters the light travelling in the waveguide. The scattered light can either be transmitted along the waveguide in the same direction or back scattered in the opposite direction. To account for both propagation directions the system is described by a 4x4 scattering matrix:
[b1b2b3b4]=[00tik00ikttik00ikt00][a1a2a3a4]
(1)
Where ai (i=1,4) are the four inputs and bj(j=1,4)the four outputs. The real coefficients t and k account respectively for the field transmission and coupling of the bus to ring directional coupler with the additional condition t2+k2=1.

The scattering matrix in Eq. (1) combines with the feedback of the ring as follows:
a2=ab4eiφ+ρcb2 (2.a)
a4=ab2eiφ+ρcb4 (2.b)
where ρc=ρeiψis the reflection coefficient in the two directions arising from scattering due to roughness, a and φ are the field loss and phase accumulated over one round respectively. Reflectivity ρis a stochastic average and can be computed through the antenna theory as described in [12

12. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22(1), 4–6 (1997). [CrossRef] [PubMed]

]. We approximate the phase of the reflection coefficient using the relation ψ+φ=π2 that applies for lossless circuits [13

13. R. E. Collin, Foundation for Microwave Engineering, 2nd ed. (McGraw-Hill, N.Y., 2000).

]. Equations (4) and (5) in Ref [12

12. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22(1), 4–6 (1997). [CrossRef] [PubMed]

]. present an integral and an analytic expression for ρ respectively. Reflectivity ρ can be viewed as a measure of the correlation length and the rms value of the surface roughness. a can be expressed in terms of loss per unit length as a=eαπR, where R is the ring radius and αis expressed in dB/cm.

The output at port Eq. (3) of the bus waveguide is obtained by solving Eq. (1) and Eq. (2) for a3=0, and reads
T=b3a1|a3=0=taeiφDtρc2D21ρc2(tD)2
(3)
whereas the reflection at port Eq. (1) reads
R=b1a1|a3=0=ρcDttaeiφD11ρc2(tD)2
(4)
where D=1ateiφ.

This model is a generalization of the approach described in Ref [14

14. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000). [CrossRef]

], which does not include backward propagation due to reflections.

3. Experiment and results

To test the theory we have fabricated a number of microrings with variable bus to ring gaps from 100nm to 590nm in steps of 10nm. The bus waveguide, in the coupling region, is 220nm high and 400nm wide. The waveguide in the ring is 220nm high and 480nm wide. In order to make bending loss negligible compared to scattering loss the radii of the microrings were set to 10μm. The test structure was designed as follows: each bus waveguide is coupled to five microrings placed in series far enough from each other not to interact. In each one of the five rings the radius is progressively increased by 25nm, which corresponds to a difference in free spectral range of 1nm approximately. This is enough to make the five resonances perfectly distinguishable. Also, the amount of coupling of the bus to each of the microrings is varied by varying the gaps. By varying the gap by 100nm one can make sure to cover the whole spectrum from strongly over coupled to strongly under coupled. Additionally, the design presented above has been repeated 10 times and each time all the five gaps are increased by 10nm. In this way we can map the microring response with gaps ranging from 100nm to 590nm with a 10nm variation. The spectral scans are obtained by employing an Agilent lightwave measurements system 8164B with integrated tunable laser source and photoreceiver. All scans have been taken with a spectral resolution of 60MHz. Light is subsequently processed by a fiber polarization controller to ensure TE polarization and a lensed fiber to efficiently couple into the device under test.

Critical coupling occurs somewhere between 310nm and 410nm gaps. Interestingly, even by varying the gaps by 10nm from waveguide to waveguide, the critically coupled condition was never encountered. Due to this fact, methods that measure the waveguide loss by assuming the critical coupling condition is met are not very accurate since such condition is extremely intolerant and difficult to spot. In the over coupled condition the coupling prevails on other effects such as waveguide loss.

Vice versa in the under coupling condition, in which the microring quality factor is very large, the effect of the waveguide loss prevails on the bus to ring coupling. This is the ideal situation to accurately measure waveguide loss. However due to the resonance splitting one has to fit the experimental results with a model that includes such phenomenon, such as the one described above.

The response in the under coupled regime is highly sensitive to α, which reflects on the depth of the split resonances. On the other hand in the over coupled regime losses do not affect the resonance as much. Furthermore the more one moves deep into the under (over) coupled regime the larger (lower) the sensitivity of the response as respect to α.

Figure 4
Fig. 4 Effect of absorption (α) caused by waveguide donor doping (n) on the transmission spectrum. Blue curve: undoped aveguide, red curve; n = 2 × 1017 cm−3 (α = 2 cm−1), green curve: n = 3 × 1017 cm−3 (α = 3 cm−1), black curve: n = 7 × 1017 cm−3 (α = 5 cm−1).
shows the impact of a variation in the absorption, α, caused by waveguide doping on the filter response. By varying the concentration of donor from 2x1017cm−3 to 3x1017cm−3 and 7x1017cm−3 one induces a loss of α = 2, 3 and 5 cm−1 respectively. It is clear that an increase in the loss due to absorption induces a change in the coupling condition by shifting it toward under coupling. Notice the position of the peaks is not altered meaning the amount of reflection stays constant. Therefore this method could be easily used to measure loss induced by doping, which is the case in active devices such as modulator and tunable filters.

Figure 5
Fig. 5 Experimental (red line) and fit (blue line) are shown for three measurements. a) α=2.3dB/cm, ρ=0.008, t=0.9965 b) α=1.7dB/cm, ρ=0.015, t=0.9991 c) α=2.1dB/cm, ρ=0.0303, t=0.9979
presents a comparison of some of the experimental spectral scans with the theoretical fit obtained from the model described above. The fitting is achieved by letting vary α, ρ and t. The ultimate goal of the fit is to estimate the propagation loss α. The three spectra depicted in insets (a), (b) and (c) respectively are such that back reflections ρ changes from 0.008 to 0.015 to 0.0303. In fact as the amount of light being back reflected increases the separation between the two peaks increases too, as already predicted in Ref [12

12. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22(1), 4–6 (1997). [CrossRef] [PubMed]

].

The influence of the reflectivity coefficient on the amount of splitting may be understood from Eq. (2) in which each reflection introduces a phase shift of π/2. Assuming for instance an individual scattering center located in any position along the ring, the propagating light is in part transmitted and in part back scattered with a certain efficiency. The back-scattered light is phase shifted by π/2.

After a full round trip the same light is back reflected by the same scattering center in the forward direction thus adding anotherπ/2 phase shift. After the back- and then the forward- scattering from each scattering center the phase is πshifted and a standing wave within the ring is formed. Being the standing wave and a travelling wave out of phase, their interaction leads to destructive interference. In fact when light is scattered inside a high Q cavity the resulting field may be high enough to cancel the field of the light propagating in the ring. For this reason the usual transmission dip that one would expect at resonance disappears, as shown in Fig. 4, and a black fringe appears growing larger when increasing the reflectivity ρ.

On the contrary for ρ=0 there would be only one transmission dip centered at the resonance. In other words the intracavity light scattering determines a standing wave similarly to what happens in a Fabry Perot cavity whereas the light propagating in the ring is a case of traveling wave cavity. The transmission dip cancellation is the result of the competition between the two types of cavity and the phenomenon and is more easily understood as a dark fringe in the middle of the transmission spectrum.

The amplitude of the reflection coefficient ρ depends on the correlation length of the correlation function describing the random edge roughness fluctuation [12

12. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22(1), 4–6 (1997). [CrossRef] [PubMed]

]. Assuming a constant value of average edge roughness, the reflectivity ρ increases with correlation length. In addition to back reflection due to surface roughness the radiation can even be reflected by the the directional coupler which perturbs the propagation of the mode. However we verified with a 3D-FDTD simulation the magnitude of the coupler-induced reflection is orders of magnitude lower than value of ρ needed to fit the spectra. We conclude therefore the roughness only induces reflection. In fact, as confirmed by experiments,there is no correlation between the amount of coupling and reflectivityρ.

Finally Fig. 7
Fig. 7 Statistics of 64 samples gathered on waveguide loss. Average loss is 1.7dB/cm, standard deviation 0.25dB/cm.
shows the statistics over 64 samples in terms of propagation loss thus obtained. The measured average loss is 1.7dB/cm and the standard deviation is0.25dB/cm. Notice the loss resulting from the erroneous fitting of the single resonances in Fig. 4 would have led to a value of 1.1dB/cm.

The method described in the paper applies to ring waveguides fabricated with a good ring discretization in the mask. In the present case the discretization was 1 nm. Viceversa, for rough discretizations the measured value of waveguide loss would be affected by this extra effect.

4. Conclusions

In conclusion we presented a method for measuring the loss in submicron Si waveguides by means of fitting the transmission of a single under coupled microring structure. This method could also be useful as a test structure for inline characterization of the waveguide loss, assuming in this case vertically light coupling and extraction. In the discussion we have gone through the physical understanding of the double peaked observed transmission and we have concluded that it arises exclusively from intra cavity light scattering. We have shown also an example of measurement over a population of 64 rings giving an average loss of 1.7dB/cm.

Acknowledgments

References and links

1.

D. A. B. Miller, “Optical interconnects to electronic chips,” Appl. Opt. 49(25), F59–F70 (2010). [CrossRef] [PubMed]

2.

S. J. B. Yoo, “Future prospects of silicon photonics in next generation communication and computing systems,” Electron. Lett. 45(12), 584–588 (2009). [CrossRef]

3.

D. B. Keck and R. Tynes, “Spectral response of low-loss optical waveguides,” Appl. Opt. 11(7), 1502–1506 (1972). [CrossRef] [PubMed]

4.

S. Taebi, M. Khorasaninejad, and S. S. Saini, “Modified Fabry-Perot interferometric method for waveguide loss measurement,” Appl. Opt. 47(35), 6625–6630 (2008). [CrossRef] [PubMed]

5.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic wires and ring resonators fabricated With deep UV lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004). [CrossRef]

6.

J. Hu, V. Tarasov, A. Agarwal, L. Kimerling, N. Carlie, L. Petit, and K. Richardson, “Fabrication and testing of planar chalcogenide waveguide integrated microfluidic sensor,” Opt. Express 15(5), 2307–2314 (2007). [CrossRef] [PubMed]

7.

T. R. Bourk, M. M. Z. Kharadly, and J. E. Lewis, “Measurement of waveguide attenuation by resonance methods,” Electron. Lett. 4(13), 267–268 (1968). [CrossRef]

8.

K. K. Lee, D. R. Lim, L. Hsin-Chiao, A. J. Agarwal,, L. C. Foresi, and Kimerling.,” Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett. 77, 1617–1619 (2000). [CrossRef]

9.

M. Williamson and A. Neureuther, “Enhanced, quantitative analysis of resist image contrast upon line edge roughness (LER),” Proc. SPIE 5039, 423–432 (2003). [CrossRef]

10.

T. Barwicz and H. A. Haus, “Three-dimensional analysis os scattering losses due to sidewall roughness in microphotonic waveguides,” J. Lightwave Technol. 23(9), 2719–2732 (2005). [CrossRef]

11.

K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett. 26(23), 1888–1890 (2001). [CrossRef]

12.

B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22(1), 4–6 (1997). [CrossRef] [PubMed]

13.

R. E. Collin, Foundation for Microwave Engineering, 2nd ed. (McGraw-Hill, N.Y., 2000).

14.

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36(4), 321–322 (2000). [CrossRef]

15.

Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express 16(7), 4621–4630 (2008). [CrossRef] [PubMed]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.3120) Optical devices : Integrated optics devices
(230.5750) Optical devices : Resonators
(230.7370) Optical devices : Waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: December 19, 2012
Revised Manuscript: February 4, 2013
Manuscript Accepted: February 5, 2013
Published: February 26, 2013

Citation
Michele Moresco, Marco Romagnoli, Stefano Boscolo, Michele Midrio, Matteo Cherchi, Ehsan Shah Hosseini, Douglas Coolbaugh, Michael R. Watts, and Birendra Dutt, "Method for characterization of Si waveguide propagation loss," Opt. Express 21, 5391-5400 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5391


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References

  1. D. A. B. Miller, “Optical interconnects to electronic chips,” Appl. Opt.49(25), F59–F70 (2010). [CrossRef] [PubMed]
  2. S. J. B. Yoo, “Future prospects of silicon photonics in next generation communication and computing systems,” Electron. Lett.45(12), 584–588 (2009). [CrossRef]
  3. D. B. Keck and R. Tynes, “Spectral response of low-loss optical waveguides,” Appl. Opt.11(7), 1502–1506 (1972). [CrossRef] [PubMed]
  4. S. Taebi, M. Khorasaninejad, and S. S. Saini, “Modified Fabry-Perot interferometric method for waveguide loss measurement,” Appl. Opt.47(35), 6625–6630 (2008). [CrossRef] [PubMed]
  5. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic wires and ring resonators fabricated With deep UV lithography,” IEEE Photon. Technol. Lett.16(5), 1328–1330 (2004). [CrossRef]
  6. J. Hu, V. Tarasov, A. Agarwal, L. Kimerling, N. Carlie, L. Petit, and K. Richardson, “Fabrication and testing of planar chalcogenide waveguide integrated microfluidic sensor,” Opt. Express15(5), 2307–2314 (2007). [CrossRef] [PubMed]
  7. T. R. Bourk, M. M. Z. Kharadly, and J. E. Lewis, “Measurement of waveguide attenuation by resonance methods,” Electron. Lett.4(13), 267–268 (1968). [CrossRef]
  8. K. K. Lee, D. R. Lim, L. Hsin-Chiao, A. J. Agarwal,, L. C. Foresi, and Kimerling.,” Effect of size and roughness on light transmission in a Si/SiO2 waveguide: Experiments and model,” Appl. Phys. Lett.77, 1617–1619 (2000). [CrossRef]
  9. M. Williamson and A. Neureuther, “Enhanced, quantitative analysis of resist image contrast upon line edge roughness (LER),” Proc. SPIE5039, 423–432 (2003). [CrossRef]
  10. T. Barwicz and H. A. Haus, “Three-dimensional analysis os scattering losses due to sidewall roughness in microphotonic waveguides,” J. Lightwave Technol.23(9), 2719–2732 (2005). [CrossRef]
  11. K. K. Lee, D. R. Lim, L. C. Kimerling, J. Shin, and F. Cerrina, “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction,” Opt. Lett.26(23), 1888–1890 (2001). [CrossRef]
  12. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett.22(1), 4–6 (1997). [CrossRef] [PubMed]
  13. R. E. Collin, Foundation for Microwave Engineering, 2nd ed. (McGraw-Hill, N.Y., 2000).
  14. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett.36(4), 321–322 (2000). [CrossRef]
  15. Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express16(7), 4621–4630 (2008). [CrossRef] [PubMed]

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