- Email: [email protected]
Fabrication tolerance analysis of grating couplers between optical fibers and silicon waveguide
Journal Pre-proof Fabrication tolerance analysis of grating couplers between optical fibers and silicon waveguide Yu Zheng, Xiaochao Kai, Piaopiao Gao, Ji’an Duan
PII:
S0030-4026(19)31388-9
DOI:
https://doi.org/10.1016/j.ijleo.2019.163490
Reference:
IJLEO 163490
To appear in:
Optik
Received Date:
26 May 2019
Revised Date:
22 September 2019
Accepted Date:
26 September 2019
Please cite this article as: Zheng Y, Kai X, Gao P, Duan J, Fabrication tolerance analysis of grating couplers between optical fibers and silicon waveguide, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163490
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Fabrication tolerance analysis of grating couplers between optical fibers and silicon waveguide Yu Zheng1,2, Xiaochao Kai1,2, Piaopiao Gao1,2,*,Ji’an Duan1,2 1
State Key Laboratory of High Performance Complex Manufacturing, Changsha 410083, China
2
College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China
∗
E-mail: [email protected]
Abstract: The grating structure and its performance for coupling between fiber and silicon-based waveguide are studied and analyzed. The coupling mechanism is illustrated through the grating Bragg diffraction condition, and the effect of physical parameters and alignment parameters of the grating coupler on the coupling efficiency is analyzed by FDTD (Finite-difference time-domain). The optimum design values of the period, duty cycle, etching depth and alignment parameters of the grating coupler are obtained, and at the same time, the deviation analysis on the optimal size is carried out. We present high-efficiency grating
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couplers fabricated both in EBL (Electron Beam Lithography) and Deep Silicon Etching through process optimization on device dimension, which can be useful for grating coupler fabrication.
Keywords: Grating coupler; Coupling efficiency; Silicon-on-Insulator; Tolerance analysis
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1. Introduction
Silicon-based optical waveguide with high refraction index [1] contrast can be fabricated by advanced micro-machining compatible with CMOS (Complementary Metal Oxide Semiconductor) technology,
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techniques and has the advantage of being
which can realize optical interconnection and optical coupling in a confined space of nanometer scale. Therefore, silicon optical waveguides have broad application in integrated optics. The coupling between silicon-based waveguide and the outside world
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(optical fiber) still remains a serious issue for optical input and output, the conventional waveguides are about 200nm thick and 500nm wide. However, the diameter of standard single mode fiber is about 9μm [2], which leads to a serious mode mismatch [3] and results in a large insert loss. To solve the fiber-chip coupling problem, many new strategies [4] are proposed, following one of these approaches: lateral coupling (in-plane coupling) and vertical coupling (out-plane coupling), and vertical coupling technology is
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widely used [5,6,7] for its simplicity and utility, which has flexible location on the substrate and allows for wafer-scale testing [8]. However, grating couplers have disadvantages in micro-fabrication, which cause a deviation between fabricated parameters and designed one, and further affects coupling efficiency. We have analyzed the effect of parameters on grating coupler’s performance and deviation produced by fabricating and aligning. Through theoretical analysis and improvement of simulation results,
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combining with process technology to improve the coupling efficiency of physical devices, which can provide reference and guidance for the fabrication and application of silicon optical devices.
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2. Theory and Model
The grating coupler is a periodic structure that implements the input and output of signals between devices. The light source is incident on the grating structure through the optical fiber, and light is coupled into the silicon optical waveguide through the diffraction of grating. Conversely, the light propagating in silicon optical waveguide can be coupled into the optical fiber. For first-order diffraction, the wave vector relationship between incident and diffracted waves can be described as Bragg condition: k in
s in m
2
(1)
Where β—constant of the guided mode, neff—effective index of optical mode in grating waveguide, kin—incident wave vector, ntop—background refractive index, λ0—the desired wavelength, θ—incidence angle, Λ—grating period, and m— Integer of diffraction order. The distance between the center of fiber and the beginning of grating in z direction [9] (represented by Lc,opt) with maximum output power can be expressed as: 1
L c ,o p t
w0
(2)
1 .3 7 c o s
Where w 0 is the half width of mode field diameter of Gaussian incident beam and is the incidence angle, meanwhile, the theoretical grating period can be obtained from (1) [9,10,11] : th e o r y
0
(3)
n e ff n to p s in
The calculation of neff is shown in Fig.1: where neff_gap is the effective index of etched region and neff_toothis the region without etching, and the two above can be obtained through the conventional effective index calculation method, then for uniform grating coupler, the global effective index can be obtained as follows:
1
ff
n e ff
_ gap
f f n e ff
(4)
_ to o th
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n e ff
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Fig. 1. Effective index calculation
Cross section schematic of Uniform Output Grating Coupler based on SOI is shown in Fig.2, ff defined as ff=W/Λ denotes duty cycle, etch—etchd depth, W—grating tooth width, Pwg—input optical power, Pup and Pdown denotes the energy that propagates
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upward and below the wafer respectively (Si core layer of 220nm thickness and SiO2 buried oxide of 1μm thickness).
Fig. 2 Schematic diagram of the grating coupler
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3.Simulation
A simplified two-dimensional grating coupling simulation mode is shown in Fig.3. Number 1 is an incident optical fiber, usually a certain small angle is needed to reduce light reflection because a completely vertical angle reflection can lead to lower coupling efficiency [12]; Number 2 is the simulation area; Number 3 is a frequency domain power monitor collecting in simulation frequency domain; Number 4 and 8 are PML (Perfectly Matching Layers) that can avoid parasitic reflection effects [13] ;
Number
5,6,7 represent top layer silicon(220nm), oxide layer(3μm) and silicon substrate respectively.
2
Fig. 3 Grating coupler simulation model
The initial simulation parameters of grating coupler are given in Table 1. The effect of grating structure parameters on device performance after establishing optical field mode is analyzed, including physical parameter (grating period, duty cycle and etching
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depth) [14] and alignment parameter. 3.1 Physical parameters
Considering the better distribution of TE(Transverse Electric) mode field in silicon optical waveguide than that of
TM(Transverse Magnetic) mode field, and the better optical field confinement, most SOI devices are designed as polarization propagation in TE mode nowadays. Therefore, the TE polarization mode is selected for simulation in this study. It can be seen from the grating theory that the changing of physical parameters of grating coupler will affect coupling performance, including
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grating period, duty cycle, and etching depth. In this paper, the physical parameters are scanned and optimized first, and corresponding parameter values are obtained in optimal coupling efficiency, then the tolerance of optimal size is analyzed.
transmission
0.4
665 667.5 670 672.5 675
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transmission
0.4
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0.6
0.6
0.2
0.2
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0.0
600
1.4
650 700 period (nm)
(a)
1.5 1.6 wavelength (μm)
1.7
(b)
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Fig. 4 (a) The coupling efficiency versus period Λ (b) Tolerance analysis on period Λ
The effect of periodΛ on coupling performance of grating coupler is shown in Fig.4. A strong relationship can be found
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between coupling efficiency and various periods from Fig.4 (a). For the incident light with 1550nm wavelength, the maximum coupling efficiency 56% has reached at period of 660nm, when period Λ changes beyond or below 660nm , the coupling efficiency decreased significantly. Fig.4(b) shows the tolerance analysis of size for optimal period Λ, when period deviated with a step of 2.5nm, the coupled center wavelength will generate a 3nm shift step by step along the wavelength direction , while the coupling efficiency will be slightly reduced with the shift direction, and the step deviation is about 1.25%.
3
0.6 transmission
transmission
0.6
0.5
0.4
305 307.5 310 212.5 315
0.4
0.2
0.0 250
300 350 ff （ nm）
400
(a)
1.4
1.5 1.6 wavelength (μm)
1.7
(b)
Fig. 5 (a)The coupling efficiency versus duty cycle ff
(b) Tolerance analysis of duty cycle ff
The effect of duty cycleff on coupling performance of grating coupler is shown in Fig.5. Taking the grating teeth width 335nm for duty cycle 0.5 with period 670nm for fabrication, and the duty cycle is equal to grating teeth width (horizontal axis shown in Fig.5(a)) divided by period. It can be seen from Fig.5 (a) that coupling efficiency varied with duty cycle. For the incident
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light with wavelength of 1550nm, the maximum coupling efficiency 54% has been achieved at duty of 310nm, when duty cycleff increases or decreases, the coupling efficiency decreased significantly. Fig.5 (b) is the tolerance analysis of optimal size for duty cycle ff, when the duty deviated with a step of 2.5nm, the shift of coupled center wavelength is not obvious, only 1nm along the wavelength direction, and there is no obvious change in coupling efficiency, the step deviation is only 0.1%. 0.6
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0.4
0.4 0.2
0.3
0.0 60
70
80 etch（ nm）
90
100
1.4
1.5 1.6 wavelength （ μm）
1.7
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0.2
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transmission
0.5
transmission
75 77.5 80 82.5 85
0.6
(a)
(b)
Fig. 6. (a)The coupling efficiency versus etch (b) Tolerance analysis of etch
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The effect of etching depth etch on coupling performance of grating coupler is shown in Fig.6. It can be seen from Fig.6 (a) that coupling efficiency changes obviously with various etching depth. For incident light with wavelength of 1550nm, the maximum coupling efficiency 58% has achieved at etching depth of 80nm, when etching depth increases or decreases, the coupling efficiency decreased significantly. Fig.6 (b) is the tolerance analysis of optimal size for etching depth, when the etching
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depth deviated with a step of 2.5nm, the coupled center wavelength generates a 3.2nm shift step by step along the short wavelength direction, while the coupling efficiency is reduced gradually along the shift direction, and the step deviation is 2.5%.
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3.2 Alignment parameters
The alignment coupler and optical fiber can affect the coupling performance in optical test of grating coupler. To improve the accuracy and reliability of measurement, the main alignment parameters such as coupling angle, horizontal position and vertical height of fiber core were analyzed, the parameters corresponding to optimal coupling efficiency are obtained by parameter scanning, then analyze the tolerance of optimal size.
4
0.6
transmission
transmission
0.6
0.4
18 19.5 21 22.5 24
0.4
0.2
0.2
0.0 15
20 θ（ ）
25
30
1.4
1.5
1.6
1.7
wavelength （ μm）
(a)
(b)
Fig. 7 (a) The coupling efficiency versus coupling angle θ (b) Tolerance analysis of coupling angle θ The effect of coupling angle θ on coupling performance of grating coupler is shown in Fig.7. It can be seen from Fig.7(a) that the coupling efficiency changes obviously with various coupling angle. For the incident light with wavelength of 1550nm, the maximum coupling efficiency 56% has achieved at coupling angle of 21°, when coupling angle θ increases or decreases, the
ro of
coupling efficiency decreased significantly. Fig7.(b) is the tolerance analysis of optimal size for coupling angle θ, when the angle deviated with a step of 1.5°, the coupled center wavelength generates a 8.5nm shift step by step along the short wavelength direction , while the coupling efficiency is slightly increased in the shift direction, and the step deviation is about 1%. 0.6
0.32 0.28 0.24 0
4
3 2 x (μm)
1
0.4
0.2
0.0
5
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transmission
transmission
0.36
2.8 2.9 3 3.1 3.2
1.4
1.5
1.6
wavelength （ μm）
1.7
(b)
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(a)
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0.40
Fig. 8 (a)The coupling efficiency versus horizontal position x (b) Tolerance analysis of horizontal position x The effect of horizontal position of fiber core x on coupling performance of grating coupler is shown in Fig.8. It can be seen
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from Fig.8 (a) that the coupling efficiency varied with horizontal position. For the incident light with wavelength of 1550nm, the maximum coupling efficiency 39% has achieved at horizontal position of x=3μm, when horizontal position x increases or decreases, the coupling efficiency decreased significantly. Fig.8(b) is the tolerance analysis of optimal size for horizontal position x, when the horizontal position deviated with a step of 100nm, the shift of coupled center wavelength does not occur substantially,
0.39 0.36 0.33
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transmission
0.42
0.30 1.0
(a)
transmission
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also there is no obvious change in coupling efficiency, the step deviation is only 0.1%.
1.5
2.0 y (μm)
2.5
0.6
0.4
0.2
0.0
3.0
1 1.1 1.2 1.3 1.4
1.4
1.5
1.6
wavelength （ μm）
1.7
(b)
Fig. 9 (a) The coupling efficiency versus vertical height y (b) Tolerance analysis of vertical height y The effect of vertical height of fiber core y on coupling performance of grating coupler is shown in Fig.9. It can be seen from Fig.9(a) that the coupling efficiency varied like a sine function with vertical height. For incident light with wavelength of 1550nm, 5
the maximum coupling efficiency 40% is achieved at vertical height of y=1.2μm; Fig.9(b) is the tolerance analysis of optimal size for vertical height y, when the vertical height deviated with a step of 100nm, the shift of coupled center wavelength is almost drift free, while the coupling efficiency changes up and down, and the step deviation is about 1.5% . Through the simulation and optimization of the structure parameters and alignment parameters of coupled grating and the analysis and evaluation of size tolerance, it can be seen that the influence of the period and etching depth of structure parameters in grating coupler on the central wavelength offset is obviously stronger than that of the duty cycle parameters.Therefore, it is necessary to ensure that the fabrication tolerance of the structure dimension is not too large in the fabrication of coupled gratings.When aligning fiber and coupled grating, the incident angle has the greatest influence on the center wavelength offset. The sub-micron alignment tolerance of horizontal distance and vertical height has little effect on the offset of central wavelength, which can be neglected.The coupling efficiency can be increased by increasing etching depth, adjusting duty cycle and incident angle slightly. And the simulation results can be used as a reference for dimension tolerance of subsequent fabrication of focused coupled gratings. 4.Fabrication EBL and Deep Silicon Etching can be used to achieve nano-scale maskless processing of grating coupler with high accuracy
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and reliability. The design of grating coupler mask layout is shown in Fig.10. A grating coupler is designed at both ends for optical input and output. The middle area is a strip waveguide. Two lithography process are required for fabrication due to different etched depth of grating and waveguide, therefore a strict mask alignment is required. Fig.11 shows the fabrication process of grating coupler: (a) gumming (b) EBL writing (c) developing (d) Deep Silicon Etching (e) glue. Silicon optical waveguide process
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also follows the same process, repeat above process to obtain the fabrication of grating coupler.
(b) EBL writing
(c)developing
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(a)gumming
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Fig. 10 The mask layout of silicon optical waveguide grating coupler
(d) Deep Silicon Etching
(e) glue
Fig .11 The grating preparation process
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5.Measurment results The SEM (Scanning Electron Microscope) measurement of fabricated grating coupler shows that there is an error between the measured value and the best value obtained before.This is because there are many uncertainties in the process, which is difficult to search or solve directly.In order to make the fabricated structure size close to the design values, the main variables and results of each process have been fitted and analyzed to improve the process and obtain the appropriate design parameters again. Fig.12 shows the fitting diagram of relationship between the dose intensity and the pattern width after development in EBL process. The equation can be obtained as follows: (5)
y 1 2 9 3 .8 0 .3 3 6 A
Where y1 is the pattern width after development and A is the dose intensity of EBL. After EBL process, using a microscope to observe development effect of patterns, when the dose intensity is too small, the pattern exposure is too shallow as shown in Fig.13 (a), and when the dose intensity is too large, the pattern is overexposed as shown in Fig.13(b). Therefore, only in a suitable
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dose range can get a better development pattern and determine the best dose intensity from the optimal pattern.
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Fig. 12 The fitting curve of dose intensity versus pattern width after development
(b) Strong dose
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(a) Weak dose
Fig. 13 Development patterns at different dose intensity Fig.14 shows the fitting diagram of relationship between the pattern width after development and the pattern width after
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etched in Deep Silicon Etching. The equation can be obtained as follows: y 2 1 4 7 .1 4 0 .5 2 y 1
(6)
Wherey2 is the pattern width after etching, and y1 is the pattern width after development. SEM observation shows that the effect of pattern after etching is related to the effect of pattern after exposure and development in the previous step. A good pattern can be obtained from a good development, which is then selected for data processing to obtain a fitting curve of the pattern width after development and the pattern width after etching.
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Fig. 14 The fitting curve of pattern width after development versus pattern width after etched
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Fig. 15 The fitting curve of pattern width of mask versus pattern width after development
Fig.15 shows the fitting diagram of relationship between the initial designed pattern width of mask and the pattern width after development. The equation can be obtained as follows:
(7)
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y 1 6 6 .8 4 1 .1 1 B
Wherey1 is the pattern width after development, and B is the pattern width of mask. At the optimal dose, the relationship between the pattern width after etching and dose intensity of EBL and pattern width of mask can be calculated as: y 2 1 8 1 .9 0 .5 7 7 B
(8)
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y 2 2 9 9 .9 2 0 .1 7 5 A
From Fig.12-15, four groups of variables are the pattern width of mask, the dose intensity, the width pattern after development, the pattern width after etched respectively. According to Fig.12, for a certain group of mask width, better data for the pattern width after development can be picked out as a reference for subsequent experimental data under a series of exposure
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doses. According to the pattern after etching, A good etch pattern is selected as experimental data in Fig.14. According to Fig.15, select best etched pattern to determine optimal dose intensity, then use the fitting relation between pattern width of mask and pattern width after development, redesign the pattern width of mask.
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The above method is repeated to optimize the fabrication process of grating coupler with optimal duty ratio ff = 0.46 (the pattern width of mask is 360nm). At first time fabricated by optimal ff, the measured pattern shown in Fig.16(a) width after etched is 384nm, deviation of 24nm, while using Formula (8) redesign the pattern width of mask for 310nm, fabricating again and using SEM measurement shown in Fig.16(b) can obtained the pattern width after etched for 353nm, and deviation is 7nm, compared with the previous process, the size accuracy of structure parameters has improved significantly, so the method can be used to continuously improve the fabrication process. The influence of other process parameters, such as exposure mode, exposure time, etching rate and etching method, on manufacturing tolerance can also be discussed, and appropriate parameters can be selected to reduce manufacturing tolerance. The manufacturing tolerance can also be reduced by replacing more accurate processing equipment.
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(a) Before
(b) After
Fig. 16 The SEM observation of grating coupler after etching According to the series of optimized designs above, finally silicon-based waveguide and grating coupler is fabricated.
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Further SEM measurements shows that the deviations of structure parameters are compared to the designed ones, indicating that the fabrication is successful. 6.Conclusion
The coupling efficiency of grating coupler is simulated. The influencing factors of coupling efficiency of grating coupler are theoretically studied and simulated in the process of fabricating. The results show that the physical parameters such as grating
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period, duty cycle and etching depth have an obvious influence on coupling efficiency and need to be optimized. The alignment parameters include vertical coupling angle, horizontal position and vertical height of fiber also affect the coupling efficiency.
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According to the tolerance analysis of various parameters, the actual parameters are continuously optimized when the grating coupler is fabricated by utilizing the relationship among variables in the process, finally obtain the fabricated device with a better performance, which is of great significance for further research and fabrication of vertical grating coupler.
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Acknowledgments
Supported by the National Natural Science Foundation of China (Grant No. 51475479), The National Key Research and Development Program of China (Grant No. 2017YFB1104800), the Key Research and Development Program of Hunan Province,
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China (Grant No. 2016GK2098), the State Key Laboratory of High Performance Complex Manufacturing, Central South University (Grant No. ZZYJKT2017-07), the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2017zzts417), and the Key Laboratory for Precision & Non-traditional Machining of Ministry of Education,
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Dalian University of Technology (Grant No. JMTZ201804).
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Reference [1] Bogaerts W., Baets R., Dumon P., Wiaux V., et al.: ‘Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology’, Journal of Lightwave Technology, 2005, 23(1), pp.401-412 [2] Zhang Z.: ‘Sensitivity of the Thin-Cladding Long Period Fiber Gratings to Refractive Index’, Chinese Journal of Sensors & Actuators, 2009, 22(8), pp.1105-1108 [3] Lin Q., Painter O J., Agrawal G P.: ‘Nonlinear optical phenomena in silicon waveguides: modeling and applications’, Optics Express, 2007, 15(25), pp.16604-16644 [4] Mekis A., Gloeckner S., Masini G., et al.: ‘A Grating-Coupler-Enabled CMOS Photonics Platform’, IEEE Journal of Selected Topics in Quantum Electronics, 2011, 17(3), pp.597-608 [5] Chen X., Li C., Tsang H K.: ‘Fabrication-Tolerant Waveguide Chirped Grating Coupler for Coupling to a Perfectly Vertical Optical Fiber’, IEEE Photonics Technology Letters,2008, 20(23), pp.1914-1916 [6] Liang Z., Zhi-Yong L.,Yu Z., Yun-Tao L., et al.: ‘ A novel highly efficient grating coupler with large filling factor used for optoelectronic integration’, Chinese Physics B,2010,19(12), pp.323-327 hybrid photodetector integration’, Optical Engineering,2014, 53(5), pp.057105
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[7] Hong-Qiang L., Yu L., Wen-qian Z., et al.: ‘Highly efficient polarization-independent grating coupler used in silica-based [8] Can Z., Jing-Hua S., Xi X., et al.: ‘High efficiency grating coupler for coupling between single-mode fiber and SOI waveguides’, Chinese Physics Letters,2013,30(1), pp.014207
[9] Vivien L., Pascal D., Lardenois S., et al.: ‘Light Injection in SOI micro waveguides Using High-Efficiency Grating Couplers’, Journal of Lightwave Technology, 2006, 24(10), pp.3810-3815
[10] Tsuchizawa T., Yamada K., Fukuda H., et al.: ‘Microphotonics devices based on silicon microfabrication technology’, IEEE
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Journal of Selected Topics in Quantum Electronics,2005, 11(1), pp.232-240
[11] Taillaert D.: ‘Grating couplers as Interface between Optical Fibres and Nanophotonic Waveguides’, Ghent University, 2004 [12] Zhou Z., ‘Silicon photonic devices based on binary blazed gratings’, Optical Engineering,2013, 52(9), pp.091708
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[13] Bienstman P., Derudder H., Baets R., et al.: ‘Analysis of cylindrical waveguide discontinuities using vectoral eigenmodes and perfectly matched layers’, IEEE Transactions on Microwave Theory & Techniques, 2001, 49(2), pp.349-354
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[14] Taillaert D., Van Laere F., Ayre M., et al.: ‘Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides’, Japanese Journal of Applied Physics, 2006, 45(45), pp.6071-6077
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[15] Conejos J V G.: ‘Addressing Fiber-to-Chip Coupling Issues in Silicon Photonics’, Universidad Politécnica de Valencia, 2010
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Table 1. The initial parameters of grating coupler for simulation Initial Value
Wavelength λ (μm)
1.55
Grating period Λ (nm)
670
Etch depth etch (nm)
70
Duty cycle ff
0.5
Number of period
26
coupling angle θ (°)
20
Waveguide width (nm)
500
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ro of
Parameters
11
PII:
S0030-4026(19)31388-9
DOI:
https://doi.org/10.1016/j.ijleo.2019.163490
Reference:
IJLEO 163490
To appear in:
Optik
Received Date:
26 May 2019
Revised Date:
22 September 2019
Accepted Date:
26 September 2019
Please cite this article as: Zheng Y, Kai X, Gao P, Duan J, Fabrication tolerance analysis of grating couplers between optical fibers and silicon waveguide, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163490
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Fabrication tolerance analysis of grating couplers between optical fibers and silicon waveguide Yu Zheng1,2, Xiaochao Kai1,2, Piaopiao Gao1,2,*,Ji’an Duan1,2 1
State Key Laboratory of High Performance Complex Manufacturing, Changsha 410083, China
2
College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China
∗
E-mail: [email protected]
Abstract: The grating structure and its performance for coupling between fiber and silicon-based waveguide are studied and analyzed. The coupling mechanism is illustrated through the grating Bragg diffraction condition, and the effect of physical parameters and alignment parameters of the grating coupler on the coupling efficiency is analyzed by FDTD (Finite-difference time-domain). The optimum design values of the period, duty cycle, etching depth and alignment parameters of the grating coupler are obtained, and at the same time, the deviation analysis on the optimal size is carried out. We present high-efficiency grating
ro of
couplers fabricated both in EBL (Electron Beam Lithography) and Deep Silicon Etching through process optimization on device dimension, which can be useful for grating coupler fabrication.
Keywords: Grating coupler; Coupling efficiency; Silicon-on-Insulator; Tolerance analysis
-p
1. Introduction
Silicon-based optical waveguide with high refraction index [1] contrast can be fabricated by advanced micro-machining compatible with CMOS (Complementary Metal Oxide Semiconductor) technology,
re
techniques and has the advantage of being
which can realize optical interconnection and optical coupling in a confined space of nanometer scale. Therefore, silicon optical waveguides have broad application in integrated optics. The coupling between silicon-based waveguide and the outside world
lP
(optical fiber) still remains a serious issue for optical input and output, the conventional waveguides are about 200nm thick and 500nm wide. However, the diameter of standard single mode fiber is about 9μm [2], which leads to a serious mode mismatch [3] and results in a large insert loss. To solve the fiber-chip coupling problem, many new strategies [4] are proposed, following one of these approaches: lateral coupling (in-plane coupling) and vertical coupling (out-plane coupling), and vertical coupling technology is
na
widely used [5,6,7] for its simplicity and utility, which has flexible location on the substrate and allows for wafer-scale testing [8]. However, grating couplers have disadvantages in micro-fabrication, which cause a deviation between fabricated parameters and designed one, and further affects coupling efficiency. We have analyzed the effect of parameters on grating coupler’s performance and deviation produced by fabricating and aligning. Through theoretical analysis and improvement of simulation results,
ur
combining with process technology to improve the coupling efficiency of physical devices, which can provide reference and guidance for the fabrication and application of silicon optical devices.
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2. Theory and Model
The grating coupler is a periodic structure that implements the input and output of signals between devices. The light source is incident on the grating structure through the optical fiber, and light is coupled into the silicon optical waveguide through the diffraction of grating. Conversely, the light propagating in silicon optical waveguide can be coupled into the optical fiber. For first-order diffraction, the wave vector relationship between incident and diffracted waves can be described as Bragg condition: k in
s in m
2
(1)
Where β—constant of the guided mode, neff—effective index of optical mode in grating waveguide, kin—incident wave vector, ntop—background refractive index, λ0—the desired wavelength, θ—incidence angle, Λ—grating period, and m— Integer of diffraction order. The distance between the center of fiber and the beginning of grating in z direction [9] (represented by Lc,opt) with maximum output power can be expressed as: 1
L c ,o p t
w0
(2)
1 .3 7 c o s
Where w 0 is the half width of mode field diameter of Gaussian incident beam and is the incidence angle, meanwhile, the theoretical grating period can be obtained from (1) [9,10,11] : th e o r y
0
(3)
n e ff n to p s in
The calculation of neff is shown in Fig.1: where neff_gap is the effective index of etched region and neff_toothis the region without etching, and the two above can be obtained through the conventional effective index calculation method, then for uniform grating coupler, the global effective index can be obtained as follows:
1
ff
n e ff
_ gap
f f n e ff
(4)
_ to o th
ro of
n e ff
-p
Fig. 1. Effective index calculation
Cross section schematic of Uniform Output Grating Coupler based on SOI is shown in Fig.2, ff defined as ff=W/Λ denotes duty cycle, etch—etchd depth, W—grating tooth width, Pwg—input optical power, Pup and Pdown denotes the energy that propagates
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upward and below the wafer respectively (Si core layer of 220nm thickness and SiO2 buried oxide of 1μm thickness).
Fig. 2 Schematic diagram of the grating coupler
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3.Simulation
A simplified two-dimensional grating coupling simulation mode is shown in Fig.3. Number 1 is an incident optical fiber, usually a certain small angle is needed to reduce light reflection because a completely vertical angle reflection can lead to lower coupling efficiency [12]; Number 2 is the simulation area; Number 3 is a frequency domain power monitor collecting in simulation frequency domain; Number 4 and 8 are PML (Perfectly Matching Layers) that can avoid parasitic reflection effects [13] ;
Number
5,6,7 represent top layer silicon(220nm), oxide layer(3μm) and silicon substrate respectively.
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Fig. 3 Grating coupler simulation model
The initial simulation parameters of grating coupler are given in Table 1. The effect of grating structure parameters on device performance after establishing optical field mode is analyzed, including physical parameter (grating period, duty cycle and etching
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depth) [14] and alignment parameter. 3.1 Physical parameters
Considering the better distribution of TE(Transverse Electric) mode field in silicon optical waveguide than that of
TM(Transverse Magnetic) mode field, and the better optical field confinement, most SOI devices are designed as polarization propagation in TE mode nowadays. Therefore, the TE polarization mode is selected for simulation in this study. It can be seen from the grating theory that the changing of physical parameters of grating coupler will affect coupling performance, including
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grating period, duty cycle, and etching depth. In this paper, the physical parameters are scanned and optimized first, and corresponding parameter values are obtained in optimal coupling efficiency, then the tolerance of optimal size is analyzed.
transmission
0.4
665 667.5 670 672.5 675
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0.6
0.6
0.2
0.2
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0.0
600
1.4
650 700 period (nm)
(a)
1.5 1.6 wavelength (μm)
1.7
(b)
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Fig. 4 (a) The coupling efficiency versus period Λ (b) Tolerance analysis on period Λ
The effect of periodΛ on coupling performance of grating coupler is shown in Fig.4. A strong relationship can be found
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between coupling efficiency and various periods from Fig.4 (a). For the incident light with 1550nm wavelength, the maximum coupling efficiency 56% has reached at period of 660nm, when period Λ changes beyond or below 660nm , the coupling efficiency decreased significantly. Fig.4(b) shows the tolerance analysis of size for optimal period Λ, when period deviated with a step of 2.5nm, the coupled center wavelength will generate a 3nm shift step by step along the wavelength direction , while the coupling efficiency will be slightly reduced with the shift direction, and the step deviation is about 1.25%.
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0.6 transmission
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0.6
0.5
0.4
305 307.5 310 212.5 315
0.4
0.2
0.0 250
300 350 ff （ nm）
400
(a)
1.4
1.5 1.6 wavelength (μm)
1.7
(b)
Fig. 5 (a)The coupling efficiency versus duty cycle ff
(b) Tolerance analysis of duty cycle ff
The effect of duty cycleff on coupling performance of grating coupler is shown in Fig.5. Taking the grating teeth width 335nm for duty cycle 0.5 with period 670nm for fabrication, and the duty cycle is equal to grating teeth width (horizontal axis shown in Fig.5(a)) divided by period. It can be seen from Fig.5 (a) that coupling efficiency varied with duty cycle. For the incident
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light with wavelength of 1550nm, the maximum coupling efficiency 54% has been achieved at duty of 310nm, when duty cycleff increases or decreases, the coupling efficiency decreased significantly. Fig.5 (b) is the tolerance analysis of optimal size for duty cycle ff, when the duty deviated with a step of 2.5nm, the shift of coupled center wavelength is not obvious, only 1nm along the wavelength direction, and there is no obvious change in coupling efficiency, the step deviation is only 0.1%. 0.6
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0.4 0.2
0.3
0.0 60
70
80 etch（ nm）
90
100
1.4
1.5 1.6 wavelength （ μm）
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75 77.5 80 82.5 85
0.6
(a)
(b)
Fig. 6. (a)The coupling efficiency versus etch (b) Tolerance analysis of etch
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The effect of etching depth etch on coupling performance of grating coupler is shown in Fig.6. It can be seen from Fig.6 (a) that coupling efficiency changes obviously with various etching depth. For incident light with wavelength of 1550nm, the maximum coupling efficiency 58% has achieved at etching depth of 80nm, when etching depth increases or decreases, the coupling efficiency decreased significantly. Fig.6 (b) is the tolerance analysis of optimal size for etching depth, when the etching
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depth deviated with a step of 2.5nm, the coupled center wavelength generates a 3.2nm shift step by step along the short wavelength direction, while the coupling efficiency is reduced gradually along the shift direction, and the step deviation is 2.5%.
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3.2 Alignment parameters
The alignment coupler and optical fiber can affect the coupling performance in optical test of grating coupler. To improve the accuracy and reliability of measurement, the main alignment parameters such as coupling angle, horizontal position and vertical height of fiber core were analyzed, the parameters corresponding to optimal coupling efficiency are obtained by parameter scanning, then analyze the tolerance of optimal size.
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0.4
18 19.5 21 22.5 24
0.4
0.2
0.2
0.0 15
20 θ（ ）
25
30
1.4
1.5
1.6
1.7
wavelength （ μm）
(a)
(b)
Fig. 7 (a) The coupling efficiency versus coupling angle θ (b) Tolerance analysis of coupling angle θ The effect of coupling angle θ on coupling performance of grating coupler is shown in Fig.7. It can be seen from Fig.7(a) that the coupling efficiency changes obviously with various coupling angle. For the incident light with wavelength of 1550nm, the maximum coupling efficiency 56% has achieved at coupling angle of 21°, when coupling angle θ increases or decreases, the
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coupling efficiency decreased significantly. Fig7.(b) is the tolerance analysis of optimal size for coupling angle θ, when the angle deviated with a step of 1.5°, the coupled center wavelength generates a 8.5nm shift step by step along the short wavelength direction , while the coupling efficiency is slightly increased in the shift direction, and the step deviation is about 1%. 0.6
0.32 0.28 0.24 0
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3 2 x (μm)
1
0.4
0.2
0.0
5
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0.36
2.8 2.9 3 3.1 3.2
1.4
1.5
1.6
wavelength （ μm）
1.7
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Fig. 8 (a)The coupling efficiency versus horizontal position x (b) Tolerance analysis of horizontal position x The effect of horizontal position of fiber core x on coupling performance of grating coupler is shown in Fig.8. It can be seen
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from Fig.8 (a) that the coupling efficiency varied with horizontal position. For the incident light with wavelength of 1550nm, the maximum coupling efficiency 39% has achieved at horizontal position of x=3μm, when horizontal position x increases or decreases, the coupling efficiency decreased significantly. Fig.8(b) is the tolerance analysis of optimal size for horizontal position x, when the horizontal position deviated with a step of 100nm, the shift of coupled center wavelength does not occur substantially,
0.39 0.36 0.33
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transmission
0.42
0.30 1.0
(a)
transmission
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also there is no obvious change in coupling efficiency, the step deviation is only 0.1%.
1.5
2.0 y (μm)
2.5
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0.2
0.0
3.0
1 1.1 1.2 1.3 1.4
1.4
1.5
1.6
wavelength （ μm）
1.7
(b)
Fig. 9 (a) The coupling efficiency versus vertical height y (b) Tolerance analysis of vertical height y The effect of vertical height of fiber core y on coupling performance of grating coupler is shown in Fig.9. It can be seen from Fig.9(a) that the coupling efficiency varied like a sine function with vertical height. For incident light with wavelength of 1550nm, 5
the maximum coupling efficiency 40% is achieved at vertical height of y=1.2μm; Fig.9(b) is the tolerance analysis of optimal size for vertical height y, when the vertical height deviated with a step of 100nm, the shift of coupled center wavelength is almost drift free, while the coupling efficiency changes up and down, and the step deviation is about 1.5% . Through the simulation and optimization of the structure parameters and alignment parameters of coupled grating and the analysis and evaluation of size tolerance, it can be seen that the influence of the period and etching depth of structure parameters in grating coupler on the central wavelength offset is obviously stronger than that of the duty cycle parameters.Therefore, it is necessary to ensure that the fabrication tolerance of the structure dimension is not too large in the fabrication of coupled gratings.When aligning fiber and coupled grating, the incident angle has the greatest influence on the center wavelength offset. The sub-micron alignment tolerance of horizontal distance and vertical height has little effect on the offset of central wavelength, which can be neglected.The coupling efficiency can be increased by increasing etching depth, adjusting duty cycle and incident angle slightly. And the simulation results can be used as a reference for dimension tolerance of subsequent fabrication of focused coupled gratings. 4.Fabrication EBL and Deep Silicon Etching can be used to achieve nano-scale maskless processing of grating coupler with high accuracy
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and reliability. The design of grating coupler mask layout is shown in Fig.10. A grating coupler is designed at both ends for optical input and output. The middle area is a strip waveguide. Two lithography process are required for fabrication due to different etched depth of grating and waveguide, therefore a strict mask alignment is required. Fig.11 shows the fabrication process of grating coupler: (a) gumming (b) EBL writing (c) developing (d) Deep Silicon Etching (e) glue. Silicon optical waveguide process
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also follows the same process, repeat above process to obtain the fabrication of grating coupler.
(b) EBL writing
(c)developing
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(a)gumming
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Fig. 10 The mask layout of silicon optical waveguide grating coupler
(d) Deep Silicon Etching
(e) glue
Fig .11 The grating preparation process
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5.Measurment results The SEM (Scanning Electron Microscope) measurement of fabricated grating coupler shows that there is an error between the measured value and the best value obtained before.This is because there are many uncertainties in the process, which is difficult to search or solve directly.In order to make the fabricated structure size close to the design values, the main variables and results of each process have been fitted and analyzed to improve the process and obtain the appropriate design parameters again. Fig.12 shows the fitting diagram of relationship between the dose intensity and the pattern width after development in EBL process. The equation can be obtained as follows: (5)
y 1 2 9 3 .8 0 .3 3 6 A
Where y1 is the pattern width after development and A is the dose intensity of EBL. After EBL process, using a microscope to observe development effect of patterns, when the dose intensity is too small, the pattern exposure is too shallow as shown in Fig.13 (a), and when the dose intensity is too large, the pattern is overexposed as shown in Fig.13(b). Therefore, only in a suitable
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dose range can get a better development pattern and determine the best dose intensity from the optimal pattern.
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Fig. 12 The fitting curve of dose intensity versus pattern width after development
(b) Strong dose
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(a) Weak dose
Fig. 13 Development patterns at different dose intensity Fig.14 shows the fitting diagram of relationship between the pattern width after development and the pattern width after
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etched in Deep Silicon Etching. The equation can be obtained as follows: y 2 1 4 7 .1 4 0 .5 2 y 1
(6)
Wherey2 is the pattern width after etching, and y1 is the pattern width after development. SEM observation shows that the effect of pattern after etching is related to the effect of pattern after exposure and development in the previous step. A good pattern can be obtained from a good development, which is then selected for data processing to obtain a fitting curve of the pattern width after development and the pattern width after etching.
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Fig. 14 The fitting curve of pattern width after development versus pattern width after etched
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Fig. 15 The fitting curve of pattern width of mask versus pattern width after development
Fig.15 shows the fitting diagram of relationship between the initial designed pattern width of mask and the pattern width after development. The equation can be obtained as follows:
(7)
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y 1 6 6 .8 4 1 .1 1 B
Wherey1 is the pattern width after development, and B is the pattern width of mask. At the optimal dose, the relationship between the pattern width after etching and dose intensity of EBL and pattern width of mask can be calculated as: y 2 1 8 1 .9 0 .5 7 7 B
(8)
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y 2 2 9 9 .9 2 0 .1 7 5 A
From Fig.12-15, four groups of variables are the pattern width of mask, the dose intensity, the width pattern after development, the pattern width after etched respectively. According to Fig.12, for a certain group of mask width, better data for the pattern width after development can be picked out as a reference for subsequent experimental data under a series of exposure
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doses. According to the pattern after etching, A good etch pattern is selected as experimental data in Fig.14. According to Fig.15, select best etched pattern to determine optimal dose intensity, then use the fitting relation between pattern width of mask and pattern width after development, redesign the pattern width of mask.
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The above method is repeated to optimize the fabrication process of grating coupler with optimal duty ratio ff = 0.46 (the pattern width of mask is 360nm). At first time fabricated by optimal ff, the measured pattern shown in Fig.16(a) width after etched is 384nm, deviation of 24nm, while using Formula (8) redesign the pattern width of mask for 310nm, fabricating again and using SEM measurement shown in Fig.16(b) can obtained the pattern width after etched for 353nm, and deviation is 7nm, compared with the previous process, the size accuracy of structure parameters has improved significantly, so the method can be used to continuously improve the fabrication process. The influence of other process parameters, such as exposure mode, exposure time, etching rate and etching method, on manufacturing tolerance can also be discussed, and appropriate parameters can be selected to reduce manufacturing tolerance. The manufacturing tolerance can also be reduced by replacing more accurate processing equipment.
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(a) Before
(b) After
Fig. 16 The SEM observation of grating coupler after etching According to the series of optimized designs above, finally silicon-based waveguide and grating coupler is fabricated.
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Further SEM measurements shows that the deviations of structure parameters are compared to the designed ones, indicating that the fabrication is successful. 6.Conclusion
The coupling efficiency of grating coupler is simulated. The influencing factors of coupling efficiency of grating coupler are theoretically studied and simulated in the process of fabricating. The results show that the physical parameters such as grating
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period, duty cycle and etching depth have an obvious influence on coupling efficiency and need to be optimized. The alignment parameters include vertical coupling angle, horizontal position and vertical height of fiber also affect the coupling efficiency.
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According to the tolerance analysis of various parameters, the actual parameters are continuously optimized when the grating coupler is fabricated by utilizing the relationship among variables in the process, finally obtain the fabricated device with a better performance, which is of great significance for further research and fabrication of vertical grating coupler.
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Acknowledgments
Supported by the National Natural Science Foundation of China (Grant No. 51475479), The National Key Research and Development Program of China (Grant No. 2017YFB1104800), the Key Research and Development Program of Hunan Province,
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China (Grant No. 2016GK2098), the State Key Laboratory of High Performance Complex Manufacturing, Central South University (Grant No. ZZYJKT2017-07), the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2017zzts417), and the Key Laboratory for Precision & Non-traditional Machining of Ministry of Education,
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Dalian University of Technology (Grant No. JMTZ201804).
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Reference [1] Bogaerts W., Baets R., Dumon P., Wiaux V., et al.: ‘Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology’, Journal of Lightwave Technology, 2005, 23(1), pp.401-412 [2] Zhang Z.: ‘Sensitivity of the Thin-Cladding Long Period Fiber Gratings to Refractive Index’, Chinese Journal of Sensors & Actuators, 2009, 22(8), pp.1105-1108 [3] Lin Q., Painter O J., Agrawal G P.: ‘Nonlinear optical phenomena in silicon waveguides: modeling and applications’, Optics Express, 2007, 15(25), pp.16604-16644 [4] Mekis A., Gloeckner S., Masini G., et al.: ‘A Grating-Coupler-Enabled CMOS Photonics Platform’, IEEE Journal of Selected Topics in Quantum Electronics, 2011, 17(3), pp.597-608 [5] Chen X., Li C., Tsang H K.: ‘Fabrication-Tolerant Waveguide Chirped Grating Coupler for Coupling to a Perfectly Vertical Optical Fiber’, IEEE Photonics Technology Letters,2008, 20(23), pp.1914-1916 [6] Liang Z., Zhi-Yong L.,Yu Z., Yun-Tao L., et al.: ‘ A novel highly efficient grating coupler with large filling factor used for optoelectronic integration’, Chinese Physics B,2010,19(12), pp.323-327 hybrid photodetector integration’, Optical Engineering,2014, 53(5), pp.057105
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[7] Hong-Qiang L., Yu L., Wen-qian Z., et al.: ‘Highly efficient polarization-independent grating coupler used in silica-based [8] Can Z., Jing-Hua S., Xi X., et al.: ‘High efficiency grating coupler for coupling between single-mode fiber and SOI waveguides’, Chinese Physics Letters,2013,30(1), pp.014207
[9] Vivien L., Pascal D., Lardenois S., et al.: ‘Light Injection in SOI micro waveguides Using High-Efficiency Grating Couplers’, Journal of Lightwave Technology, 2006, 24(10), pp.3810-3815
[10] Tsuchizawa T., Yamada K., Fukuda H., et al.: ‘Microphotonics devices based on silicon microfabrication technology’, IEEE
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Journal of Selected Topics in Quantum Electronics,2005, 11(1), pp.232-240
[11] Taillaert D.: ‘Grating couplers as Interface between Optical Fibres and Nanophotonic Waveguides’, Ghent University, 2004 [12] Zhou Z., ‘Silicon photonic devices based on binary blazed gratings’, Optical Engineering,2013, 52(9), pp.091708
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[13] Bienstman P., Derudder H., Baets R., et al.: ‘Analysis of cylindrical waveguide discontinuities using vectoral eigenmodes and perfectly matched layers’, IEEE Transactions on Microwave Theory & Techniques, 2001, 49(2), pp.349-354
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[14] Taillaert D., Van Laere F., Ayre M., et al.: ‘Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides’, Japanese Journal of Applied Physics, 2006, 45(45), pp.6071-6077
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[15] Conejos J V G.: ‘Addressing Fiber-to-Chip Coupling Issues in Silicon Photonics’, Universidad Politécnica de Valencia, 2010
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Table 1. The initial parameters of grating coupler for simulation Initial Value
Wavelength λ (μm)
1.55
Grating period Λ (nm)
670
Etch depth etch (nm)
70
Duty cycle ff
0.5
Number of period
26
coupling angle θ (°)
20
Waveguide width (nm)
500
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Parameters
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