基于扩散限制刻蚀模型的等离子体刻蚀模拟研究
摘要
随着制造加工技术的进步,微电子工艺不断向前发展。刻蚀工艺不仅作为微电子工艺中的关键技术一直受到人们的关注,而且在新兴的微机电系统,光电集成系统等微细加工中也将得到重要应用。等离子体刻蚀是一种重要的微加工方法,在硅器件的微细加工中己经得到广泛应用。但是其机理至今还不是很明确,刻蚀工艺的研究主要还是依赖经验和反复试探。利用计算机对这一过程进行模拟可以节省许多人力物力,并可作为做实验的参考。本文首次提出用扩散限制腐蚀模型(Diffusion Limited Erosion)对等离子体蚀刻过程进行模拟。
首先讨论了刻蚀工艺的基本原理,分析了等离子体刻蚀过程中的各个参量与模型中参数对应关系。然后对扩散限制腐蚀模型进行改进,并且编程实现该模型的算法。
在单周期掩模条件对模型进行模拟计算。研究鞘区电压对刻蚀剖面的影响。调制几率对应等离子体刻蚀中鞘区电压。当鞘区电压升高时,模型中的调制几率增大。研究发现当调制几率为0.25时刻蚀为各向同性,对应刻蚀过程中的纯化学刻蚀过程。当调制几率为1时,刻蚀为完全各向异性,横向刻蚀速率为零。模型对应离子轰击过程。当调制几率逐渐增加时,刻蚀速率的各向异性性增强,钻蚀效应减弱。但是调制几率增加的同时也导致刻蚀槽表面的粗糙度增加。所以在等离子体刻蚀过程中,鞘区电压是影响刻蚀质量的重要参数。
更改掩模结构,采用周期性掩模。模拟计算结果表明当调制几率较小时,由于钻蚀,形成锥状结构。当刻蚀继续进行时,锥状结构被抹平。增大调制几率到0.6时可以得到高深宽比结构的刻蚀剖面。模拟过程中出现了深宽比依赖效应,即当刻蚀槽深度远大于宽度时,刻蚀深度降低。模拟结果与文献中的等离子刻蚀硅实验结果进行比较。说明本模型是有效的。
扩散限制刻蚀模型是一种新的等离子体刻蚀模拟方法,期望本论文的工作对等离子体刻蚀工艺改善提供帮助。
With the development of manufacture technology, microelectronic process is going forward. As an important step of microelectronic process, etching technology has gained much attention. It will play an important role in micro fabrication such as new-made microelectronics mechanism and photo electronics integration system. Plasma etching has been widely used in the etching process of Si devices. Plasma etching is an important method in micro manufacture, but the mechanism of this process is not sure today. Researchers always rely on experiment and experience to study etching technology. Computer simulations can save a lot of time and money, and can also be predictive in its applications to the technology of device manufacture. A diffusion limited erosion (DLE) model is suggested to study plasma etching.
First the mechanism of plasma etching process was introduced, common modes and simulation method was introduced too. Then the DLE model was improved and the simulation program was finished.
The influence of sheath electric filed on plasma etching process was investigated with simple mask. In our model, hopping probability ( ) represent the magnitude of sheath electric filed. Simulations were performed with various . When , the etching process is totally isotropic. When , this model changed to ballistic etching. Etching process became more anisotropic and undercut decreased as increased, but the roughness of grooves increased. So the magnitude of sheath electric filed is an important parameter of plasma etching.
Simulations were performed with periodic mask. A serials of taper like structure were appeared when the vale of is small, as the result of strong undercut effect. That structure was eliminated as etching process continues. High aspect ratio grooves were showed when PePe = 0.6. Aspect Ratio Dependent Etching was observed in simulation results. Simulation results were almost same with experimental results in other papers.
DLE model is a new method in plasma etching simulations. We hope though further development this model can be used to guide etching industry.
首先讨论了刻蚀工艺的基本原理,分析了等离子体刻蚀过程中的各个参量与模型中参数对应关系。然后对扩散限制腐蚀模型进行改进,并且编程实现该模型的算法。
在单周期掩模条件对模型进行模拟计算。研究鞘区电压对刻蚀剖面的影响。调制几率对应等离子体刻蚀中鞘区电压。当鞘区电压升高时,模型中的调制几率增大。研究发现当调制几率为0.25时刻蚀为各向同性,对应刻蚀过程中的纯化学刻蚀过程。当调制几率为1时,刻蚀为完全各向异性,横向刻蚀速率为零。模型对应离子轰击过程。当调制几率逐渐增加时,刻蚀速率的各向异性性增强,钻蚀效应减弱。但是调制几率增加的同时也导致刻蚀槽表面的粗糙度增加。所以在等离子体刻蚀过程中,鞘区电压是影响刻蚀质量的重要参数。
更改掩模结构,采用周期性掩模。模拟计算结果表明当调制几率较小时,由于钻蚀,形成锥状结构。当刻蚀继续进行时,锥状结构被抹平。增大调制几率到0.6时可以得到高深宽比结构的刻蚀剖面。模拟过程中出现了深宽比依赖效应,即当刻蚀槽深度远大于宽度时,刻蚀深度降低。模拟结果与文献中的等离子刻蚀硅实验结果进行比较。说明本模型是有效的。
扩散限制刻蚀模型是一种新的等离子体刻蚀模拟方法,期望本论文的工作对等离子体刻蚀工艺改善提供帮助。
With the development of manufacture technology, microelectronic process is going forward. As an important step of microelectronic process, etching technology has gained much attention. It will play an important role in micro fabrication such as new-made microelectronics mechanism and photo electronics integration system. Plasma etching has been widely used in the etching process of Si devices. Plasma etching is an important method in micro manufacture, but the mechanism of this process is not sure today. Researchers always rely on experiment and experience to study etching technology. Computer simulations can save a lot of time and money, and can also be predictive in its applications to the technology of device manufacture. A diffusion limited erosion (DLE) model is suggested to study plasma etching.
First the mechanism of plasma etching process was introduced, common modes and simulation method was introduced too. Then the DLE model was improved and the simulation program was finished.
The influence of sheath electric filed on plasma etching process was investigated with simple mask. In our model, hopping probability ( ) represent the magnitude of sheath electric filed. Simulations were performed with various . When , the etching process is totally isotropic. When , this model changed to ballistic etching. Etching process became more anisotropic and undercut decreased as increased, but the roughness of grooves increased. So the magnitude of sheath electric filed is an important parameter of plasma etching.
Simulations were performed with periodic mask. A serials of taper like structure were appeared when the vale of is small, as the result of strong undercut effect. That structure was eliminated as etching process continues. High aspect ratio grooves were showed when PePe = 0.6. Aspect Ratio Dependent Etching was observed in simulation results. Simulation results were almost same with experimental results in other papers.
DLE model is a new method in plasma etching simulations. We hope though further development this model can be used to guide etching industry.
引文
1杨国光、侯西云等.微系统与微光学的发展.光子学报. 1994, Vo1.23: 22
2李志坚.微电子技术的又一次革命.微电子机械系统(MEM)s发展展望.科技导报. 1997 (9):3-5
3陈立俊.微电子材料与制程.第一版.复旦大学出版社. 2005: 115-120
4 G. Dipeso, V. Vahedi, D. W. Hewett. Two-dimensional Self-consistent Fluid Simulation of Radio Frequency Inductive Sources. J. Vac Sci. Technol. A: 1994, 12(4): 1387
5 M. Meyyappan, T. R. Govindan. Radio Frequency Discharge Modeling Moment Equations Approach. J. Appl. Phys. 1993, 74(4): 2250
6 U. Kortshagen. Fast Two-dimensional Self-consistent KineticModeling of Low-pressure Inductively Coupled RF Discharges. Appl. Phys. Lett. 1994, 65(11): 1355
7 M. Ardehali, H. Matsumoto. An Efficient Monte Carlo Simulator for Low-pressure RF Plasmas. IEEE Trans. Plasma Sci. :1997, 25(5): 1081
8 V. Vahedi, M. Surendra. A Monte Carlo Collision Model for the Particle-in-cell Method Application to Argon and Oxygen Discharge. Computer Physics Communications. 1995, 87: 179～198
9 T. J. Cotler, M. S. Barnes, M. E. Elta. A. Monte Carlo Microtopography Model for Investigating Plasma/Reactive Ion Etch Profile Evolution. J. Vac. Sci. Tech. B 1988, 6(2): 542
10 M. L. Hudson, T. J. Bartel. Direct Simulation Monte Carlo Computation of Reactor-feature Scale Flows. J. Vac. Sci. Tech. A. 1997, 15(3): 559
11胡作启,李佐宜,熊锐等.磁控靶溅射刻蚀的模拟研究.华中理工大学学报. 1997, 25 (11): 42
12 S. K. Park, D. J. Economou. Parametric Study of Radio frequency Glow Discharge Using Continuum Model . J. Appl. Phys. 1990, 68 (9): 4888
13 Ventzek, L. G. Peter, M. Grapperhaus, M. J. Kushner. Investigation of Electron Source and Ion Flux Uniformity in HighPlasma Density Inductively Coupled Etching Tools UsingTwo-dimensional Modeling. J. Vac. Sci. Tech. B. 1994, 12(6): 3118
14 S. Rauf, M. J. Kushner. Model for Noncollisional Heating in Inductively Coupled Plasma Processing Sources. J. Appl. Phys. 1997, 81 (9): 5956
15 U. M. Kelkar, M. H. Gordon, Roe L A et al. Diagnostics and Modeling in a Pure Argon Plasma: Energy Balance Study. J. Vac. Sci. Tech. A. 1999, 17(1): 125
16 E. A. Edelberg, E. S. Aydil. Modeling of the Sheath and theEnergy Distribution of Ions Bombarding rf-biased Substrates in High Density Plasma Reactors and Comparison to Experimental Measurements. J. Appl. Phys. 1999, 86(9): 4801
17 S. Raul, M. J. Kushner. The Effect of Radio Frequency Plasma Processing Reactor Circuitry on Plasma Characteristics. J. Appl. Phys. 1998, 83(10): 5087
18 S. Desa, S. Ghosal, R. L. Kosut et al. Reactor-scale Models for RF Diode Sput tering of Thin Films. J. Vac. Sci. Tech. A. 1999, 17(4): 1926
19 T. E. F. M. Standaert, M. Schaepkens, N. R. Rueger. High Density Fluorocarbon Etching of Silicon in an Inductively Coupled Plasma :Mechanism of Etching Through a Thick Steady State Fluorocarbon Layer. J. Vac. Sci. Tech. A. 1998, 16(1): 239
20 P. C. Karulkar, M. A. Wirzbicki. Characterization of Etchingof Silicon Dioxide and Photoresist in a Fluorocarbon Plasma. J. Vac. Sci. Tech. B. 1988, 6(5): 1595
21 J. D. Plummer, M. D. Deal, P. B. Griffin. Silicon VLSI Technology : Fundamentals. Practice. Fist edition: 2005 485-502
22 F. H. Dill, A. R. Neureuther, J. A. Tuttle,et al. Modeling projection printing of positive photoresists. IEEE Trans. Electron Devices. 1975,Vol.ED-22: 456-464
23 R. E. Jewett, P. I. Hagouel, A. R. Neureuther, et al. Line-profile resist development simulation techniques. Polymer Eng. Sci. 1977, 17(6): 381-384
24 N. Takashi. Structural transition in pitting corrosion of binary alloys. Phys. Rev. E. 1991, 45(4): 2480
25 P. I. Hagouel. X-ray lithographic fabrication of blazed diffraction gratings Ph.D.Dissertation, Univ.of California, Berkeley, 1976
26 A. Moniwa, T. Matsuzawa, T. Ito,et al. A three-dimensional photorisist imaging process simulator for strong standing-wave effect environment. IEEE Trans. Computer-Aided Design, 1987, CAD-6: 431-437
27 J. P. Card. Dynamic Neural Control for a Plasma Etch Process. IEEE Trans. Neural Work, 1997, 8(4): 883
28 Chen Junghui, P. T. Chu, D. S. H. Wong et al. Optimal Design Using Neural Network and Information Analysis in Plasma Etching. J. Vac. Sci. Technol. B. 1999, 17(1):1 45
29 T.A.Witten,L.M Sander. Diffusion-LimitedAggregation,a Kinetic Critieal Phenomenon. Phys. Rev. Lett. 1981, 47: 1400-1402
30孙斌,任大志等.铅的电沉积枝晶生长.武汉大学学报(理学版). 2002,48: 81-83.
31 J.W.Evans. Random and cooperative sequential adsorption. Rev. Mod. Phys. 1993, 65: 1281-1283.
32 J. Nittman, G. Daccord, H. E. Stanley. Fraetal Growth of Viscous Fingers. Quantitative Characterization of a Fluid Instability Phenomenon. Nature (London). 1985, 314: 141-144.
33 T. C. Halsey, P. Meakin. I. Proeaeeia. Sealing Structure of The Surface Layer of Diffusion-Limited Aggregates. Phys. Rev. Lett. 1986, 56: 854-856.
34 L. Benguigui, M. Daoud. Is the Suburban Railway Systema Fractal. Geographical Analysis. 1991, 23: 362-368.
35 P. Meakin, J. M. Deutch. The formation of surface by diffusion limited annihilation. J. Chem. Phys. 1986, 85: 2320
36 Y. Kim, S. Y. Yoon. Effect of biased diffusion on dynamical surface structures for the A+B→0 reaction. Phys. Rev. E. 2002, 66: 031105
37 Hsin-Fei Meng and E. G. D. Cohen. Catalytic interface erosion. Phys. Rev. E. 1995, 51: 3417 - 3426
38 Y. Kim, S. Y. Yoon. Surface growth models with a random-walk-like non-locality. Phys. Rev. E.:2003, 68: 036221
39 S. Y. Yoon, Yup Kim. A theoretical suggestion for making clean surfaces. Journal of the Korean Physical Society. 2006, 48: 253
40 Yup Kim, S. Y. Yoon. Time-reversed dielectric breakdown model for the erosion phenomena. Phys. Rev. E. 2003, 67: 056111
41 A..R. Tzafriri, A. D. Levin, E. R. Edelman. Diffusion-limited binding explains binary dose response for local arterial and tumour drug delivery. Cell Proliferation. 2009, 42: 348
42 Connaughton Colm, R. Rajesh, Zaboronski Oleg. Constant flux relation for diffusion-limited cluster-cluster aggregation. Phys. Rev. E.2008, 78: 041403
43 M. Agrawal, S. B. Santra, R. Anand. et al. Effect of macromolecular crowding on the rate of diffusion-limited enzymatic reaction. Paramana-journal of Physics. 2008, 71: 359
44 M. D. Baker, C. D. Himmel, G. S. May. Time Series Modeling of Reactive Ion Etching Using Neural Work. IEEE Trans. Semicond. Manuf. 1995, 8(1): 62
2李志坚.微电子技术的又一次革命.微电子机械系统(MEM)s发展展望.科技导报. 1997 (9):3-5
3陈立俊.微电子材料与制程.第一版.复旦大学出版社. 2005: 115-120
4 G. Dipeso, V. Vahedi, D. W. Hewett. Two-dimensional Self-consistent Fluid Simulation of Radio Frequency Inductive Sources. J. Vac Sci. Technol. A: 1994, 12(4): 1387
5 M. Meyyappan, T. R. Govindan. Radio Frequency Discharge Modeling Moment Equations Approach. J. Appl. Phys. 1993, 74(4): 2250
6 U. Kortshagen. Fast Two-dimensional Self-consistent KineticModeling of Low-pressure Inductively Coupled RF Discharges. Appl. Phys. Lett. 1994, 65(11): 1355
7 M. Ardehali, H. Matsumoto. An Efficient Monte Carlo Simulator for Low-pressure RF Plasmas. IEEE Trans. Plasma Sci. :1997, 25(5): 1081
8 V. Vahedi, M. Surendra. A Monte Carlo Collision Model for the Particle-in-cell Method Application to Argon and Oxygen Discharge. Computer Physics Communications. 1995, 87: 179～198
9 T. J. Cotler, M. S. Barnes, M. E. Elta. A. Monte Carlo Microtopography Model for Investigating Plasma/Reactive Ion Etch Profile Evolution. J. Vac. Sci. Tech. B 1988, 6(2): 542
10 M. L. Hudson, T. J. Bartel. Direct Simulation Monte Carlo Computation of Reactor-feature Scale Flows. J. Vac. Sci. Tech. A. 1997, 15(3): 559
11胡作启,李佐宜,熊锐等.磁控靶溅射刻蚀的模拟研究.华中理工大学学报. 1997, 25 (11): 42
12 S. K. Park, D. J. Economou. Parametric Study of Radio frequency Glow Discharge Using Continuum Model . J. Appl. Phys. 1990, 68 (9): 4888
13 Ventzek, L. G. Peter, M. Grapperhaus, M. J. Kushner. Investigation of Electron Source and Ion Flux Uniformity in HighPlasma Density Inductively Coupled Etching Tools UsingTwo-dimensional Modeling. J. Vac. Sci. Tech. B. 1994, 12(6): 3118
14 S. Rauf, M. J. Kushner. Model for Noncollisional Heating in Inductively Coupled Plasma Processing Sources. J. Appl. Phys. 1997, 81 (9): 5956
15 U. M. Kelkar, M. H. Gordon, Roe L A et al. Diagnostics and Modeling in a Pure Argon Plasma: Energy Balance Study. J. Vac. Sci. Tech. A. 1999, 17(1): 125
16 E. A. Edelberg, E. S. Aydil. Modeling of the Sheath and theEnergy Distribution of Ions Bombarding rf-biased Substrates in High Density Plasma Reactors and Comparison to Experimental Measurements. J. Appl. Phys. 1999, 86(9): 4801
17 S. Raul, M. J. Kushner. The Effect of Radio Frequency Plasma Processing Reactor Circuitry on Plasma Characteristics. J. Appl. Phys. 1998, 83(10): 5087
18 S. Desa, S. Ghosal, R. L. Kosut et al. Reactor-scale Models for RF Diode Sput tering of Thin Films. J. Vac. Sci. Tech. A. 1999, 17(4): 1926
19 T. E. F. M. Standaert, M. Schaepkens, N. R. Rueger. High Density Fluorocarbon Etching of Silicon in an Inductively Coupled Plasma :Mechanism of Etching Through a Thick Steady State Fluorocarbon Layer. J. Vac. Sci. Tech. A. 1998, 16(1): 239
20 P. C. Karulkar, M. A. Wirzbicki. Characterization of Etchingof Silicon Dioxide and Photoresist in a Fluorocarbon Plasma. J. Vac. Sci. Tech. B. 1988, 6(5): 1595
21 J. D. Plummer, M. D. Deal, P. B. Griffin. Silicon VLSI Technology : Fundamentals. Practice. Fist edition: 2005 485-502
22 F. H. Dill, A. R. Neureuther, J. A. Tuttle,et al. Modeling projection printing of positive photoresists. IEEE Trans. Electron Devices. 1975,Vol.ED-22: 456-464
23 R. E. Jewett, P. I. Hagouel, A. R. Neureuther, et al. Line-profile resist development simulation techniques. Polymer Eng. Sci. 1977, 17(6): 381-384
24 N. Takashi. Structural transition in pitting corrosion of binary alloys. Phys. Rev. E. 1991, 45(4): 2480
25 P. I. Hagouel. X-ray lithographic fabrication of blazed diffraction gratings Ph.D.Dissertation, Univ.of California, Berkeley, 1976
26 A. Moniwa, T. Matsuzawa, T. Ito,et al. A three-dimensional photorisist imaging process simulator for strong standing-wave effect environment. IEEE Trans. Computer-Aided Design, 1987, CAD-6: 431-437
27 J. P. Card. Dynamic Neural Control for a Plasma Etch Process. IEEE Trans. Neural Work, 1997, 8(4): 883
28 Chen Junghui, P. T. Chu, D. S. H. Wong et al. Optimal Design Using Neural Network and Information Analysis in Plasma Etching. J. Vac. Sci. Technol. B. 1999, 17(1):1 45
29 T.A.Witten,L.M Sander. Diffusion-LimitedAggregation,a Kinetic Critieal Phenomenon. Phys. Rev. Lett. 1981, 47: 1400-1402
30孙斌,任大志等.铅的电沉积枝晶生长.武汉大学学报(理学版). 2002,48: 81-83.
31 J.W.Evans. Random and cooperative sequential adsorption. Rev. Mod. Phys. 1993, 65: 1281-1283.
32 J. Nittman, G. Daccord, H. E. Stanley. Fraetal Growth of Viscous Fingers. Quantitative Characterization of a Fluid Instability Phenomenon. Nature (London). 1985, 314: 141-144.
33 T. C. Halsey, P. Meakin. I. Proeaeeia. Sealing Structure of The Surface Layer of Diffusion-Limited Aggregates. Phys. Rev. Lett. 1986, 56: 854-856.
34 L. Benguigui, M. Daoud. Is the Suburban Railway Systema Fractal. Geographical Analysis. 1991, 23: 362-368.
35 P. Meakin, J. M. Deutch. The formation of surface by diffusion limited annihilation. J. Chem. Phys. 1986, 85: 2320
36 Y. Kim, S. Y. Yoon. Effect of biased diffusion on dynamical surface structures for the A+B→0 reaction. Phys. Rev. E. 2002, 66: 031105
37 Hsin-Fei Meng and E. G. D. Cohen. Catalytic interface erosion. Phys. Rev. E. 1995, 51: 3417 - 3426
38 Y. Kim, S. Y. Yoon. Surface growth models with a random-walk-like non-locality. Phys. Rev. E.:2003, 68: 036221
39 S. Y. Yoon, Yup Kim. A theoretical suggestion for making clean surfaces. Journal of the Korean Physical Society. 2006, 48: 253
40 Yup Kim, S. Y. Yoon. Time-reversed dielectric breakdown model for the erosion phenomena. Phys. Rev. E. 2003, 67: 056111
41 A..R. Tzafriri, A. D. Levin, E. R. Edelman. Diffusion-limited binding explains binary dose response for local arterial and tumour drug delivery. Cell Proliferation. 2009, 42: 348
42 Connaughton Colm, R. Rajesh, Zaboronski Oleg. Constant flux relation for diffusion-limited cluster-cluster aggregation. Phys. Rev. E.2008, 78: 041403
43 M. Agrawal, S. B. Santra, R. Anand. et al. Effect of macromolecular crowding on the rate of diffusion-limited enzymatic reaction. Paramana-journal of Physics. 2008, 71: 359
44 M. D. Baker, C. D. Himmel, G. S. May. Time Series Modeling of Reactive Ion Etching Using Neural Work. IEEE Trans. Semicond. Manuf. 1995, 8(1): 62