基于变量分离分解法的极紫外光刻三维掩模快速仿真方法
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摘要
提出了一种基于分离变量法的极紫外光刻三维掩模衍射谱快速仿真方法,在保证一定仿真精度的前提下提高了仿真速度。该方法将三维掩模分解为2个相互垂直的二维掩模,对2个二维掩模采用严格电磁场方法进行衍射谱仿真并将结果相乘以重构成三维衍射谱。以6°主入射角、45°线偏振光照明及22nm三维方形接触孔掩模为例,在入射光方位角0°~90°变化范围内,相同仿真参数下,该方法的仿真结果与商用光刻仿真软件Dr.LiTHO的严格仿真结果相比,图形特征尺寸误差小于0.21nm,仿真速度提高约65倍。在上述参数下,该方法与Dr.LiTHO的域分解方法及基于掩模结构分解法等快速方法相比,仿真精度和速度均提高1倍以上。该模型无需参数标定,适用于矩形图形的三维掩模快速仿真。
A fast simulation method based on variable separation is proposed for 3D mask diffraction in extremeultraviolet lithography(EUVL).The method achieves higher simulation speed while maintaining agood simulation accuracy.In this method,the 3D mask is decomposed into two orthogonal 2D masks.The diffraction spectrum simulation on two 2D masks are carried out through rigorous electromagnetic method.The results are then multiplied to reconstruct the three-dimensional diffraction spectrum.We set a premise of 6°main incident angle,45°linearly polarized light illumination and 22 nm 3Dsquare contact hole mask.Azimuth angle is ranging from 0°to90°.Under the same simulation parameters,the simulation results of this method are compared with the rigorous simulation results of commercial lithography simulation software Dr.LiTHO.The errors of the simulated criticaldimension of the proposed method are within 0.21 nm,and the simulation speed is about 65 times faster.Under the above parameters,the proposed method is compared with the domain decomposition method of Dr.LiTHO and a fast method based on mask-structure decomposition.The results show that the simulation accuracy and speed are improved more than double.The method needs no calibrations for model parameters and suits fast simulations of 3D masks that contain rectangular patterns.
A fast simulation method based on variable separation is proposed for 3D mask diffraction in extremeultraviolet lithography(EUVL).The method achieves higher simulation speed while maintaining agood simulation accuracy.In this method,the 3D mask is decomposed into two orthogonal 2D masks.The diffraction spectrum simulation on two 2D masks are carried out through rigorous electromagnetic method.The results are then multiplied to reconstruct the three-dimensional diffraction spectrum.We set a premise of 6°main incident angle,45°linearly polarized light illumination and 22 nm 3Dsquare contact hole mask.Azimuth angle is ranging from 0°to90°.Under the same simulation parameters,the simulation results of this method are compared with the rigorous simulation results of commercial lithography simulation software Dr.LiTHO.The errors of the simulated criticaldimension of the proposed method are within 0.21 nm,and the simulation speed is about 65 times faster.Under the above parameters,the proposed method is compared with the domain decomposition method of Dr.LiTHO and a fast method based on mask-structure decomposition.The results show that the simulation accuracy and speed are improved more than double.The method needs no calibrations for model parameters and suits fast simulations of 3D masks that contain rectangular patterns.
引文
[1]Wu B,Kumar A.Extreme ultraviolet lithography:a review[J].Journal of Vacuum Science&Technology B,2007,25(6):1743-1761.
[2]Pirati A,Peeters R,Smith D,et al.Performance overview and outlook of EUV lithography systems[C].SPIE,2015,9422:94221P.
[3]Turkot B,Carson S L,Lio A,et al.EUV progress toward HVM readiness[C].SPIE,2016,9776:977602.
[4]Erdmann A,Fühner T,Evanschitzky P,et al.Optical and EUV projection lithography:a computational view[J].Microelectronic Engineering,2015,132:21-34.
[5]Mack C,Jones R,Byers J.Computer-implemented method and carrier medium configured to generate a set of process parameters for a lithography process:US,6968253[P].2005-11-22.
[6]Cao Y,Wang X,Tu Y,et al.Impact of mask absorber thickness on the focus shift effect in extreme ultraviolet lithography[J].Journal of Vacuum Science&Technology B,2012,30(3):031602.
[7]Erdmann A,Evanschitzky P,Shao F,et al.Predictive modeling of EUV-lithography:the role of mask,optics,and photoresist effects[C].SPIE,2011,8171:81710M.
[8]Viala A,Erdmanna A,Schmoellerb T,et al.Modification of boundaries conditions in the FDTD algorithm for EUVmasks modeling[C].SPIE,2002,4754:890-899.
[9]Schiavone P,Granet G,Robic J Y.Rigorous electromagnetic simulation of EUV masks:influence of the absorber properties[J].Microelectronic Engineering,2001,57(3):497-503.
[10]Zhu Z,Lucas K,Cobb J L,et al.Rigorous EUV mask simulator using 2Dand 3D waveguide methods[C].SPIE,2003,5037:494-503.
[11]Evanschitzky P,Erdmann A.Three dimensional EUV simulations-a new mask near field and imaging simulation system[C].SPIE,2005,5992:59925B.
[12]Cao Yuting,Wang Xiangzhao,Bu Yang.Fast simulation model for contact hole mask in extreme-ultraviolet lithography[J].Acta Optica Sinica,2012,32(7):0705001.曹宇婷,王向朝,步扬.极紫外光刻接触孔掩模的快速仿真计算[J].光学学报,2012,32(7):0705001.
[13]Lam M C,Neureuther A R.Simplified model for absorber feature transmissions on EUV masks[C].SPIE,2006,6349:63492H.
[14]Tirapu-Azpiroz J,Burchard P,Yablonovitch E.Boundary layer model to account for thick mask effects in photolithography[C].SPIE,2003,5040:1611-1619.
[15]Gullikson E M,Cerjan C,Stearns D G,et al.Practical approach for modeling extreme ultraviolet lithography mask defects[J].Journal of Vacuum Science&Technology B,2002,20(1):81-86.
[16]Clifford C H,Neureuthe A R.Smoothing based model for images of isolated buried EUV multilayer defects[C].SPIE,2008,6921:692119.
[17]Clifford C H,Neureuther A R.Fast simulation methods and modeling for extreme ultraviolet masks with buried defects[J].Journal of Micro/Nanolithography Mems&Moems,2009,8(3):031402.
[18]Lam M C,Neureuther A R.Fast simulation methods for defective EUV mask blank inspection[C].SPIE,2004,5567:741-750.
[19]Evanschitzky P,Erdmann A,Besacier M,et al.Simulation of extreme ultraviolet masks with defective multilayers[C].SPIE,2003,5130:1035-1045.
[20]Liu Xiaolei,Li Sikun,Wang Xiangzhao.Simulation model based on equivalent layer method for defective mask multilayer in extreme ultra violet lithography[J].Acta Optica Sinica,2015,35(6):0622005.刘晓雷,李思坤,王向朝.基于等效膜层法的极紫外光刻含缺陷掩模多层膜仿真模型[J].光学学报,2015,35(6):0622005.
[21]Adam K.Domain decomposition methods for the electromagnetic simulation of scattering from three-dimensional structures with applications in lithography[D].Berkeley:University of California,2001.
[22]Erdmann A,Kalus C K,Schmoeller T,et al.Efficient simulation of light diffraction from 3-dimensional EUV-masks using field decomposition techniques[C].SPIE,2003,5037:482-493.
[23]Mailfert J,Zuniga C,Philipsen V,et al.3D mask modeling for EUV lithography[C].SPIE,2012,8322:832224.
[24]Evanschitzky P,Erdmann A.Fast near field simulation of optical and EUV masks using the waveguide method[C].SPIE,2007,6533:65330Y.
[25]Wang Shifan.Theory and application of information optics[M].Beijing:BUPT Press,2003:31-32.王仕璠.信息光学理论与应用[M].北京:北京邮电大学出版社,2003:31-32.
[26]Lucas K,Tanabe H,Strojwas J.Efficient and rigorous three-dimensional model for optical lithography simulation[J].Journal of the Optical Society of America A,1996,13(11):2187-2199.
[27]Zhou Xinjiang.Theory and method for fast simulation of optical image in lithography based on the method of separation of variables[D].Wuhan:Huazhong University of Science and Technology,2015:40-43.周新江.基于变量分离理论的光刻成像快速计算方法研究[D].武汉:华中科技大学,2015:40-43.
[28]Fühner T,Schnattinger T,Ardelean G.Dr.LiTHO-a development and research lithography simulator[C].SPIE,2007,6520:65203F.
[2]Pirati A,Peeters R,Smith D,et al.Performance overview and outlook of EUV lithography systems[C].SPIE,2015,9422:94221P.
[3]Turkot B,Carson S L,Lio A,et al.EUV progress toward HVM readiness[C].SPIE,2016,9776:977602.
[4]Erdmann A,Fühner T,Evanschitzky P,et al.Optical and EUV projection lithography:a computational view[J].Microelectronic Engineering,2015,132:21-34.
[5]Mack C,Jones R,Byers J.Computer-implemented method and carrier medium configured to generate a set of process parameters for a lithography process:US,6968253[P].2005-11-22.
[6]Cao Y,Wang X,Tu Y,et al.Impact of mask absorber thickness on the focus shift effect in extreme ultraviolet lithography[J].Journal of Vacuum Science&Technology B,2012,30(3):031602.
[7]Erdmann A,Evanschitzky P,Shao F,et al.Predictive modeling of EUV-lithography:the role of mask,optics,and photoresist effects[C].SPIE,2011,8171:81710M.
[8]Viala A,Erdmanna A,Schmoellerb T,et al.Modification of boundaries conditions in the FDTD algorithm for EUVmasks modeling[C].SPIE,2002,4754:890-899.
[9]Schiavone P,Granet G,Robic J Y.Rigorous electromagnetic simulation of EUV masks:influence of the absorber properties[J].Microelectronic Engineering,2001,57(3):497-503.
[10]Zhu Z,Lucas K,Cobb J L,et al.Rigorous EUV mask simulator using 2Dand 3D waveguide methods[C].SPIE,2003,5037:494-503.
[11]Evanschitzky P,Erdmann A.Three dimensional EUV simulations-a new mask near field and imaging simulation system[C].SPIE,2005,5992:59925B.
[12]Cao Yuting,Wang Xiangzhao,Bu Yang.Fast simulation model for contact hole mask in extreme-ultraviolet lithography[J].Acta Optica Sinica,2012,32(7):0705001.曹宇婷,王向朝,步扬.极紫外光刻接触孔掩模的快速仿真计算[J].光学学报,2012,32(7):0705001.
[13]Lam M C,Neureuther A R.Simplified model for absorber feature transmissions on EUV masks[C].SPIE,2006,6349:63492H.
[14]Tirapu-Azpiroz J,Burchard P,Yablonovitch E.Boundary layer model to account for thick mask effects in photolithography[C].SPIE,2003,5040:1611-1619.
[15]Gullikson E M,Cerjan C,Stearns D G,et al.Practical approach for modeling extreme ultraviolet lithography mask defects[J].Journal of Vacuum Science&Technology B,2002,20(1):81-86.
[16]Clifford C H,Neureuthe A R.Smoothing based model for images of isolated buried EUV multilayer defects[C].SPIE,2008,6921:692119.
[17]Clifford C H,Neureuther A R.Fast simulation methods and modeling for extreme ultraviolet masks with buried defects[J].Journal of Micro/Nanolithography Mems&Moems,2009,8(3):031402.
[18]Lam M C,Neureuther A R.Fast simulation methods for defective EUV mask blank inspection[C].SPIE,2004,5567:741-750.
[19]Evanschitzky P,Erdmann A,Besacier M,et al.Simulation of extreme ultraviolet masks with defective multilayers[C].SPIE,2003,5130:1035-1045.
[20]Liu Xiaolei,Li Sikun,Wang Xiangzhao.Simulation model based on equivalent layer method for defective mask multilayer in extreme ultra violet lithography[J].Acta Optica Sinica,2015,35(6):0622005.刘晓雷,李思坤,王向朝.基于等效膜层法的极紫外光刻含缺陷掩模多层膜仿真模型[J].光学学报,2015,35(6):0622005.
[21]Adam K.Domain decomposition methods for the electromagnetic simulation of scattering from three-dimensional structures with applications in lithography[D].Berkeley:University of California,2001.
[22]Erdmann A,Kalus C K,Schmoeller T,et al.Efficient simulation of light diffraction from 3-dimensional EUV-masks using field decomposition techniques[C].SPIE,2003,5037:482-493.
[23]Mailfert J,Zuniga C,Philipsen V,et al.3D mask modeling for EUV lithography[C].SPIE,2012,8322:832224.
[24]Evanschitzky P,Erdmann A.Fast near field simulation of optical and EUV masks using the waveguide method[C].SPIE,2007,6533:65330Y.
[25]Wang Shifan.Theory and application of information optics[M].Beijing:BUPT Press,2003:31-32.王仕璠.信息光学理论与应用[M].北京:北京邮电大学出版社,2003:31-32.
[26]Lucas K,Tanabe H,Strojwas J.Efficient and rigorous three-dimensional model for optical lithography simulation[J].Journal of the Optical Society of America A,1996,13(11):2187-2199.
[27]Zhou Xinjiang.Theory and method for fast simulation of optical image in lithography based on the method of separation of variables[D].Wuhan:Huazhong University of Science and Technology,2015:40-43.周新江.基于变量分离理论的光刻成像快速计算方法研究[D].武汉:华中科技大学,2015:40-43.
[28]Fühner T,Schnattinger T,Ardelean G.Dr.LiTHO-a development and research lithography simulator[C].SPIE,2007,6520:65203F.
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