利用粒子群優化演算法設計符合IMEC製程限制的三階段高效率光柵耦合器

Design of Three-Stage High-Efficiency Grating Coupler Compatible with IMEC Fabrication Rules Using Particle Swarm Optimization Algorithm

詹尊揚(Tsun-yang Chan)

指導教授 ： 黃定洧

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202200025

摘要

本篇論文的目的是設計出符合IMEC矽光子製程代工廠之技術規範與其最小線寬限制，並用於將C-Band 波段由SMF-28單模光纖入射之TE極化光場耦合進入矽光子波導之高效率光柵耦合器。在此高效率光柵耦合器的結構設計方面，本論文將各個光柵週期分為四個等分的小區塊，運用次波長光柵結構 (Sub-wavelength Grating) 之等效介質折射率概念，在小區塊中填入適當的寬度方向次波長光柵結構，依序使其各小區塊之等效介質折射率對應於L型光柵的設計特性，其中次波長光柵結構採用單階段及三階段蝕刻之截面結構以提供不同的設計自由度，在元件特性模擬方面，本論文使用商用光學模擬軟體Lumerical來模擬光場在元件中的傳播情形，並透過粒子群演算法對光柵耦合器的光柵周期、小區塊折射率、單階段或三階段蝕刻深度之不同組合、上下包覆層採用二氧化矽或是空氣之組合、寬度方向次波長光柵結構之填空比等參數進行優化。
為了簡化模擬流程、減少計算時間，首先假設光柵耦合器寬度方向為無限延伸之二維等價結構，因此可將光柵耦合器的設計使用二維時域有限差分法 (2-D FDTD) 模擬，藉此設計出四組不同設計參數的元件，並針對此簡化後之設計命題進行初步的設計參數優化。模擬結果顯示其中有兩組不同的設計皆可得到高耦合效率，分別是元件三和元件四。元件三 (二維等價)：考量未來IMEC可提供蝕刻去除下包覆層且最小線寬可縮減至130 nm、上包覆層為二氧化矽且其中包含一層氮化矽、下包覆層為空氣的製程條件下，針對1554 nm之TE極化入射之光纖模態場的耦合效率為86.2%，1-dB頻寬約為37 nm，3-dB頻寬約為71 nm。元件四 (二維等價)：考量最小線寬為150 nm為製程限制、上包覆層若為二氧化矽且其中包含一層氮化矽、下包覆層為二氧化矽的製程條件下，針對1550 nm之TE極化入射之光纖模態場的耦合效率為85%，1-dB頻寬約為39 nm，3-dB頻寬約為71 nm。
以二維等價命題得到的兩組不同製程條件之優化設計之後，本論文進一步透過有限差分特徵模態求解器 (Finite Difference Eigenmode) 的輔助，將二維等價命題轉換回三維結構之命題，其各小區塊之寬度方向採用不同填空比之次波長光柵結構取代，並使其等效介質折射率等同於二維等價命題之優化後的介質折射率，最後採用三維時域有限差分法 (3-D FDTD) 模擬此完整的三維光柵耦合器結構之耦合效率。結果顯示兩組採用次波長光柵之三維光柵耦合器依然可以得到高耦合效率。元件三(三維次波長光柵)：下包覆層空氣，針對1554 nm之TE極化入射之光纖模態場的耦合效率為83.2%，1-dB頻寬約 40 nm且3-dB頻寬為76 nm。元件四(三維次波長光柵)：下包覆層為二氧化矽，針對1550 nm之TE極化入射之光纖模態場的耦合效率為其峰值耦合效率約為83%，1-dB頻寬為 43 nm且3-dB頻寬為74 nm。
本論文亦針對光纖對準誤差及製程誤差容忍度進行分析，對兩種元件設計而言，當光纖入射角度朝x方向變化時，若Δθx = +5°，其頻譜藍移約30 nm，若Δθx = －5°，其頻譜紅移約40 nm，原峰值波長維持44%以上的耦合效率。在兩種元件設計中，當光纖入射角度朝z方向變化，不論是正方向或負方向頻譜皆為藍移現象，元件三之頻譜藍移約30 nm，元件四頻譜藍移約50 nm，若Δθz = ±5°，效率降至約34%。在兩種元件設計中，當光纖入射位置在x方向平移ΔPx = ±2 μm，原峰值波長可維持在65%以上的耦合效率；入射位置在z方向平移 ΔPz = ±2 μm，原峰值波長仍可維持80%以上的耦合效率。對元件三而言，製程誤差若造成光柵週期在x方向有些微的縮放時，若ΔΛx = +5 nm，其頻譜紅移約38 nm，原本的峰值效率會下降至42%，若ΔΛx = －5 nm時，其頻譜紅移約30 nm，原本的峰值效率會下降至54%；對元件四而言，若ΔΛx = +5 nm，其頻譜紅移約35 nm，原本的峰值效率會下降至40%，若ΔΛx = －5 nm，其頻譜藍移約33 nm，原本的峰值效率會下降至42%。在兩種元件中，若光柵在z方向上之次波長光柵的週期有些微的縮放時，會有下列影響，若ΔΛz = ±5 nm，效率仍能維持81%以上的效率，而頻譜偏移5 nm，此誤差變化對效率影響甚小。製程誤差若是造成總體光柵結構在厚度方向d的些微縮放，對元件三而言，其影響如下，若Δd = +20 nm，其頻譜紅移約29 nm，原本的峰值效率會下降至43%，若Δd = －20 nm，其頻譜藍移約32 nm，原本的峰值效率會下降至48%；對元件四而言，若Δd = +20 nm，其頻譜紅移約34 nm，若Δd = －20 nm，其頻譜藍移約32 nm，原本的峰值效率皆會下降至45%。
與文獻中相似的高效率光柵耦合器相比，若文獻中的光柵耦合器最小線寬為100 nm以上且沒有額外在絕緣層上添加布拉格反射夾層，本論文所提出的兩組優化設計元件的耦合效率皆比文獻高5~10%，且本論文所提出的元件四完全符合IMEC矽光子製程代工廠目前的製程技術，具有極佳的可製造性。

關鍵字

高效率光柵耦合器 ； 最小線寬 ； 次波長光柵耦合器 ； 三階段蝕刻 ； L 型光柵 ； IMEC ； 絕緣上矽 ； SMF-28 ； 矽光子學

並列摘要

The goal of this thesis is to design a high-efficiency grating coupler which couples the C-Band TE polarized light from SMF-28 optical fiber into silicon photonic waveguide under the constraints of minimum feature size defined by the process specifications of the silicon photonics foundry IMEC. As for the design of such a high-efficiency grating coupler, each period of the grating coupler is divided into four segments with each segment composed of subwavelength gratings (SWG) in the width direction based on the effective medium theory. The effective medium index of each segment is arranged in a way to fit the optical properties of an L-Shaped grating coupler. With the optional cross-sections formed by the combinations of single-step etching and three-step etching, higher degrees of freedom for designing the grating coupler can be achieved. As for the simulations of device performances, the commercial software Lumerical was chosen to simulate the propagation of optical fields in the device. With the help of the particle swarm optimization algorithm, the design parameters, such as the grating period, refractive index of each segment, combination of the single-step etching and three-step etching, use of SiO2 or air as the upper/lower cladding materials, and duty-cycle of each sub-wavelength grating in the width direction, are determined to achieve the highest possible coupling efficiency.
To simplify the simulation process and reduce the time consumption, the grating coupler is equivalent to a two-dimensional (2-D) grating structure based on the assumption that the grating structure is invariant in the width direction. Hence, the equivalent 2-D grating structure can be simulated using the two-dimensional finite-difference time-domain (2-D FDTD) technique, and four devices (Devices 1¬¬–4) with different design parameters are simulated. In addition, the design parameters for the equivalent 2-D grating structure are optimized. The simulation results show that two device designs (Device 3 and Device 4) with high coupling efficiency can be obtained. Device 3 (2-D Equivalent): We expect IMEC will continue to improve its etching technology to allow the removal of the lower cladding layer someday and a smaller feature size of 130 nm, so this device has the waveguide structure with the upper cladding of SiO2 as well as an inter-layer of Si3N4, and the lower cladding of air. The coupling efficiency for the TE polarized incident light at 1554 nm is 86.2% with 1-dB bandwidth of 37 nm and 3-dB bandwidth of 71 nm. Device 4 (2-D Equivalent): When the minimum feature size of 150 nm and the cross-sectional structure with the upper cladding of SiO2 as well as an inter-layer of Si3N4, and the lower cladding of Air are considered, the coupling efficiency for the TE polarized incident light at 1550 nm is 85% with 1-dB bandwidth of 39 nm and 3-dB bandwidth of 71 nm.
After the two designed of 2-D equivalent devices are obtained according to their respective fabrication conditions, they are further converted back into their three-dimensional (3-D) counterparts with the help of the finite-difference eigenmode (FDE) technique, with the effective medium index of each segment equal to the medium index of an associated segment in the 2-D equivalent structure by adjusting the duty cycle of the subwavelength grating for each segment. Finally, the entire structure is analyzed numerically by using the three-dimensional finite-difference time-domain (3D-FDTD) technique to obtain the overall coupling efficiency of the complete 3-D grating coupler. The results show that the two designs of the 3-D grating couplers with subwavelength grating structures can still maintain high coupling efficiency. Device 3 (3-D SWG): With the lower cladding of air, the coupling efficiency for the TE polarized incident light at 1554 nm is 83.2% with 1-dB bandwidth of 40 nm and 3-dB bandwidth of 76 nm. Device 4 (3-D SWG): With the lower cladding of SiO2, the coupling efficiency for the TE polarized incident light at 1550 nm is 83% with 1-dB bandwidth of 43 nm and 3-dB bandwidth of 74 nm.
In this thesis, the tolerances of the two designs to the fiber misalignment and fabrication error are also analyzed. For both designs, the performance may vary when the angular misalignment of the incident light in the x-direction occurs: for Δθx = 5°, the spectrum has a blueshift about 30 nm with the coupling efficiency maintaining at 44%; for Δθx = –5°, the spectrum has a redshift about 40 nm with the coupling efficiency maintaining at 44%. For both designs, the performance may vary when the angular misalignment of the incident light in the z-direction occurs: the spectrum has a blueshift of 30 nm and 50 nm for Device 3 and Device 4, respectively; for Δθz = ±5°, the spectrum has a blueshift with the coupling efficiency maintaining at 34%. For both designs, the performance may vary when the position misalignment of the incident light in the x-direction occurs: for ΔPx = ±2 μm, the coupling efficiency maintaining at 65%; the performance may vary when the position misalignment of the incident light in the z-direction occurs: for ΔPz = ±2 μm, the coupling efficiency still maintains at 80%, however, only the coupling efficiency decreases with the position misalignment in the z-direction, the spectrum shift is not observed. For Device 3, the performance may vary when the grating periods are slightly expanded or shrunk in the x-direction: for ΔΛx = +5 nm, the spectrum has a redshift of 38 nm with a decreased coupling efficiency of 42%; for ΔΛx = －5 nm the spectrum has a blueshift of 30 nm with a decreased coupling efficiency of 54%; For Device 4, the performance varies: for ΔΛx = +5 nm, the spectrum has a redshift of 35 nm with a decreased coupling efficiency of 40%; for ΔΛx = －5 nm the spectrum has a blueshift of 33 nm with a decreased coupling efficiency of 42%. For both devices, if the period of the subwavelength grating is expanded or shrunk, the following effects may occur: if ΔΛz = ±5 nm, the coupling efficiency can still maintain 81% or higher, while the spectrum has a shift of ±5 nm and this fabrication error has nearly no effect on the coupling efficiency. For Device 3, the performance may vary when the depths are slightly etching misalignment: for Δd = +20 nm, the spectrum has a redshift of 29 nm with a decreased coupling efficiency of 43%; for Δd = －20 nm, the spectrum has a blueshift of 32 nm with a decreased coupling efficiency of 48%；For Device 4, the performance varies: for Δd = +20 nm, the spectrum has a redshift of 44 nm with a decreased coupling efficiency of 45%; for Δd = －20 nm, the spectrum has a blueshift of 32 nm with a decreased coupling efficiency of 45%.
Compared to the high-efficiency grating couplers shown in previous literatures in which the minimum feature size of 100 nm is considered and there is no Bragg reflector in below the buried oxide, the coupling efficiencies of the two device designs are 5–10% higher than those shown in the literature. Especially, Device 4 proposed in this thesis is compatible with the state-of-art foundry services (IMEC) which implies a high degree of manufacturability.

並列關鍵字

High efficiency grating coupler ； Minimum feature sizes ； Subwavelength grating coupler ； Three-step etching ； L-Shaped grating ； IMEC ； SOI ； SMF-28 ； Silicon photonics

參考文獻

[1] G. T. Reed and A. P. Knights, Silicon photonics: an introduction. John Wiley Sons, 2004.

[2] D. Thomson et al., "Roadmap on silicon photonics," Journal of Optics, vol. 18, no. 7, p. 073003, 2016.

[3] A. Rahim, T. Spuesens, R. Baets, and W. Bogaerts, "Open-access silicon photonics: Current status and emerging initiatives," Proceedings of the IEEE, vol. 106, no. 12, pp. 2313-2330, 2018.

[4] L. Chrostowski and M. Hochberg, Silicon photonics design: from devices to systems. Cambridge University Press, 2015.

[5] D. Liang and J. E. Bowers, "Recent progress in lasers on silicon," Nature photonics, vol. 4, no. 8, pp. 511-517, 2010.