硅材料中电场和应力诱导的二阶非线性光学效应的研究
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摘要
本论文首先从理论上推导出直流电场和应力对硅材料对称性的改变,根据等效二阶非线性极化率张量的形式,当电场和应力沿[111]方向时,硅材料的对称性将由点群降为点群,证明了场致线性电光效应的存在,然后根据电光张量应变张量的具体形式,我们给出了电场和应力沿[111]方向时的实验方案。
此外我们采用横向电光调制系统,制作出MISIM的样品结构,沿硅的[111]方向加调制电场,从实验上证实了硅材料中场致线性电光效应的存在。然后在硅材料上同时施加外加直流电场和调制电场,从实验上也观测到电场诱导的线性电光效应,同时观测到直流电场对硅材料反演对称性破坏作用的增强作用。此外,我们还利用等离子色散效应与偏振无关的特性,设计实验,将等离子体色散效应与电场诱导的场致线性电光效应进行了有效区分。
最后应用相同的样品,我们还进行了场致光整流效应的实验。当电场沿[111]方向时,硅材料确实具有点群的对称性。同时我们也证明了硅材料中的场致光整流信号随外加直流电压的的增加而线性增大。
As a main material in micro-electronics silicon has its advantageous in production cost and processing technic.
However an ideal silicon crystal does not possess linear electro-optical effect because it has inversion symmetry centre. We cannot use silicon to make into high-speed silicon electro-optic modulators and optical switches. In recent years, we have obtained the successful development of silicon-based electro-optic modulations which are based on plasma dispersion effect.
In this thesis, the dc electric field and stress is used for breaking the inversion symmetry of silicon, as a result, the electric-field-induced linear electro-optical effect and optical rectification occur in silicon, and these effects are researched theoretically and experimentally. We have also distinguished influence on electro-optical signal between linear electro-optical effect and plasma dispersion effect .Based on this effect of electro-optic modulator can not change just because the disadvantages, for example, carrier lifetime, drift and diffusion and other factors, can not achieve high modulation speed. While on the electro-optic modulator has been optimized to greatly enhance the modulation speed, but based on this mechanism of electro-optic modulator, or significantly less than the speed of the linear electro-optic effect in silicon-based electro-optic modulator, and based on plasma dispersion effect of optical modulator structure and electrical sector is complex.
In this thesis, using electric field and strain field damage silicon inversion symmetry, it has the electric field and stress-induced linear electro-optic effect and optical rectification effect. Thesis of silicon materials for the linear electro-optic effect of field effect and optical rectification carried out theoretical and experimental study, and analyzes the distinction between the linear electro-optic effect and the plasma dispersion effect on the electro-optic signal of.
Ⅰ.Studies of electric-field-induced linear electro-optical effect
We have focused on the external electric field on silicon linear electro-optic effect.
⑴We derive when the external electric field and stress are along the [111] direction acting on the silicon material, the point group symmetry of silicon will be reduced from to , thus silicon will have the electric field and stress-induced nonlinear optical effects. The equivalent second-order nonlinear susceptibility tensor is equal to third-order nonlinear susceptibility tensor and the dot product of electric field and stress,that is
⑵We analyzed the frequency exist in the same silicon electric field, electric field, electric field polarization waves the expression, further change the refractive index formula is derived. We then according to the refractive index ellipsoid and the electro-optic tensor strain tensor related knowledge, experimental design verification of our theoretical analysis.
⑶We use the silicon material is along the (111) cut.The electric field and electric field modulation at the same time added to the sample, field observations to significantly enhance the linear electro-optic effect.
Ⅱ. Field effect of optical rectification
⑴A pplication of nonlinear optics knowledge,we analysis when the electric field along the [111] direction, the field size of optical rectification signal the relationship between the incident polarization azimuth.
⑵We use the sample is nearly intrinsic silicon, cutting direction along [111], Metal - insulator - semiconductor - insulator - metal sample structure. We observed that the built-in electric field induced optical rectification signal Field. The experiment showed that externally applied electrical field can enhance the field induced optical rectification signal. This is equivalent to our previous studies, second-order nonlinear susceptibility tensor is proportional to conform with the electric field.
ⅢDistinguish between the linear electro-optic effect with the plasma dispersion effect.
We first use of transverse electro-optic modulation system, measuring the output of the electro-optic signal. According to the research on the Jones matrix derived the specific form of the output light intensity. As the linear electro-optic effect of the applied electric field causes the phase delay associated, the plasma dispersion effect is only associated with the carrier concentration, therefore, the change of the output light intensity can distinguish between the two.
The above study has an important role, in silicon integrated optics, and many other areas that will play a great prospect. Methods and results of these studies to other materials with inversion symmetry the nonlinear study has important reference value.
此外我们采用横向电光调制系统,制作出MISIM的样品结构,沿硅的[111]方向加调制电场,从实验上证实了硅材料中场致线性电光效应的存在。然后在硅材料上同时施加外加直流电场和调制电场,从实验上也观测到电场诱导的线性电光效应,同时观测到直流电场对硅材料反演对称性破坏作用的增强作用。此外,我们还利用等离子色散效应与偏振无关的特性,设计实验,将等离子体色散效应与电场诱导的场致线性电光效应进行了有效区分。
最后应用相同的样品,我们还进行了场致光整流效应的实验。当电场沿[111]方向时,硅材料确实具有点群的对称性。同时我们也证明了硅材料中的场致光整流信号随外加直流电压的的增加而线性增大。
As a main material in micro-electronics silicon has its advantageous in production cost and processing technic.
However an ideal silicon crystal does not possess linear electro-optical effect because it has inversion symmetry centre. We cannot use silicon to make into high-speed silicon electro-optic modulators and optical switches. In recent years, we have obtained the successful development of silicon-based electro-optic modulations which are based on plasma dispersion effect.
In this thesis, the dc electric field and stress is used for breaking the inversion symmetry of silicon, as a result, the electric-field-induced linear electro-optical effect and optical rectification occur in silicon, and these effects are researched theoretically and experimentally. We have also distinguished influence on electro-optical signal between linear electro-optical effect and plasma dispersion effect .Based on this effect of electro-optic modulator can not change just because the disadvantages, for example, carrier lifetime, drift and diffusion and other factors, can not achieve high modulation speed. While on the electro-optic modulator has been optimized to greatly enhance the modulation speed, but based on this mechanism of electro-optic modulator, or significantly less than the speed of the linear electro-optic effect in silicon-based electro-optic modulator, and based on plasma dispersion effect of optical modulator structure and electrical sector is complex.
In this thesis, using electric field and strain field damage silicon inversion symmetry, it has the electric field and stress-induced linear electro-optic effect and optical rectification effect. Thesis of silicon materials for the linear electro-optic effect of field effect and optical rectification carried out theoretical and experimental study, and analyzes the distinction between the linear electro-optic effect and the plasma dispersion effect on the electro-optic signal of.
Ⅰ.Studies of electric-field-induced linear electro-optical effect
We have focused on the external electric field on silicon linear electro-optic effect.
⑴We derive when the external electric field and stress are along the [111] direction acting on the silicon material, the point group symmetry of silicon will be reduced from to , thus silicon will have the electric field and stress-induced nonlinear optical effects. The equivalent second-order nonlinear susceptibility tensor is equal to third-order nonlinear susceptibility tensor and the dot product of electric field and stress,that is
⑵We analyzed the frequency exist in the same silicon electric field, electric field, electric field polarization waves the expression, further change the refractive index formula is derived. We then according to the refractive index ellipsoid and the electro-optic tensor strain tensor related knowledge, experimental design verification of our theoretical analysis.
⑶We use the silicon material is along the (111) cut.The electric field and electric field modulation at the same time added to the sample, field observations to significantly enhance the linear electro-optic effect.
Ⅱ. Field effect of optical rectification
⑴A pplication of nonlinear optics knowledge,we analysis when the electric field along the [111] direction, the field size of optical rectification signal the relationship between the incident polarization azimuth.
⑵We use the sample is nearly intrinsic silicon, cutting direction along [111], Metal - insulator - semiconductor - insulator - metal sample structure. We observed that the built-in electric field induced optical rectification signal Field. The experiment showed that externally applied electrical field can enhance the field induced optical rectification signal. This is equivalent to our previous studies, second-order nonlinear susceptibility tensor is proportional to conform with the electric field.
ⅢDistinguish between the linear electro-optic effect with the plasma dispersion effect.
We first use of transverse electro-optic modulation system, measuring the output of the electro-optic signal. According to the research on the Jones matrix derived the specific form of the output light intensity. As the linear electro-optic effect of the applied electric field causes the phase delay associated, the plasma dispersion effect is only associated with the carrier concentration, therefore, the change of the output light intensity can distinguish between the two.
The above study has an important role, in silicon integrated optics, and many other areas that will play a great prospect. Methods and results of these studies to other materials with inversion symmetry the nonlinear study has important reference value.
引文
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[3] R. A. Roref, and B. R. Bennett, SPIE Integr. Opt. Circuit Eng. 704, 32-37 (1986).
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[7] G. V. Treyz, P. G. May, and J. M. Halbout, IEEE Electron. Device Lett. 12, 276–278 (1991).
[8] G. V. Treyz, P. G. May, and J. M. Halbout, Appl. Phys. Lett. 59, 771–773 (1991).
[9] X. Xiao, J. C. Sturm et al. IEEE Photon. Technol. Lett. 3, 230–231 (1991).
[10] Y. L. Liu, E. K. Liu et al. Electron. Lett. 30, 130–131 (1994).
[11] Y. Liu, E. Liu et al. Appl. Phys. Lett. 64, 2079–2080 (1994).
[12] C. K. Tang and G. T. Reed, Electron. Lett. 31, 451–452 (1995).
[13] C. Z. Zhao, G. Z. Li, et al. Appl. Phys. Lett. 67, 2448–2449 (1995).
[14] A. Cutolo, M. Iodice et al. Appl. Phys. Lett. 71, 199–201 (1997).
[15] C. A. Barrios, V. R. de Almeida et al. J. Lightwave Technol. 21, 1089–1098 (2003).
[16] C. E. Png, S. P. Chan et al. J. Lightwave Technol. 22, 1573–1582 (2004).
[17] F. Gan, and F. X. Kartner, IEEE Photon. Technol. Lett. 17, 1007–1009 (2005).
[18] D. Marris, E. Cassan, and L. Vivien, J. Appl. Phys. 96, 6109-6112 (2004).
[19] Y. H. Kuo, Y. K. Lee et al. Nature 437, 1334-1336 (2005).
[20] R. Lewen, S. Irmscher et al. J. Lightwave Technol. 22, 172-179 (2004).
[21] Q. Xu, B. Shmidt et al. Nature, 435, 325-327 (2005).
[22] Q. Xu, S. Manipatruni et al. Opt. Express, 15, 430-436 (2007).
[23] A. Liu, R. Jones et al. Nature, 427, 615-618 (2004).
[24] L. Liao, D. Samara-Rubio et al. Opt. Express, 13, 3129-3135 (2005).
[25] F. Y. Gardes, G. T. Reed et al. Opt. Express, 13, 8845-8854 (2005).
[26] F. Y. Gardes, K. L. Tsakmakidis et al. Opt. Express, 15, 5879-5884 (2007).
[27] A. Liu, L. Liao et al. Opt. Express, 15, 660-668 (2007).
[28] C.H.Lee,R.K.Chang, and N.Bloembergen, Nonlinear electroreflectance in silicon and silver,Phys.Rev.Lett.,1967,18(5),167-170
[29] C.K.Chen,A.R.B.De Castro, and Y.R.Shen,Surface-enhanced second-harmonic generation, Phys.Rev.Lett.,1981,46(2),145-148
[30] Renate Dworczak. and Dietmar Kieslinger,Electric Deld induced second harmonic generation (EFISH)experiments in the swivel cell : New aspects of an established method, Phys. Chem. Chem. Phys., 2000, 2, 5057-5064
[31] C.Jordan,G.Marowsky,U.Emmerichs,C.Meyer,Wavelength dependent study of laser induced metallic properties of Si(111) by surface second harmonic generation,Optics Communications,1994,113,125-132
[32] D. Bodlaki and E. Borguet, Dynamics and second-order nonlinear optical susceptibility of photoexcited carriers at Si(111)interfaces, Appl. Phys.Lett.,2003,83(12),2357-2359
[33] Yong Qiang An and Steven T. Cundiff, Phase inversion in rotational anisotropy of second harmonic generation at Si(001) interfaces, Phys. Rev. B,2003,67,193302
[34] H. Sano,and G. Mizutani, W. Wolf, R. Podloucky, Ab initio study of linear and nonlinear optical responses of Si(111)surfaces, Phys. Rev. B,2002,66,195338
[35] Dong Xiao,Euan Ramsay,Derryck T.Reid,et al.,Optical probing of a silicon integrated circuit using electric-field-induced second-harmonic generation,Appl.Phys.Lett.,2006,88,114107-1-114107-3
[36] J.I.Dadap,J.Shan,A.S.Weling,et al.,Measurement of the vector character of electric field by optical second-harmonic generation,Optics Letters,1999,24,1059-1061
[37]孟宪章,康昌鹤,《半导体物理学》,吉林大学出版社,1993,第一章
[38]石顺祥,陈国夫,赵卫,刘继芳,非线性光学,西安:西安电子科技大学出版社,2003年,第三章
[39]孙鉴波,硅材料场致普克尔斯效应和光整流效应的研究,长春:吉林大学电子学院,2009。
[40]张玉红,硅材料电光效应的研究,长春:吉林大学电子学院,2008。
[41]陈纲,廖理几,晶体物理学基础,北京:科学出版社,1992年,第三章。
[42]赵纪红,应力诱导的硅表面二次谐波的产生,长春:吉林大学电子学院,2008
[43]李家泽,晶体光学,北京:北京理工大学出版社,1989年.
[44] J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan,Interactions between Light Waves in s Nonlinear Dielectric , Phys.Rev., 1962,127(6):1918-1939
[45] M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich,Optical Rectification,Phys. Rev.Lett., 1962, 9(11):446-448
[2] Z. G. Chen, J. X. Zhao et al. Appl. Phys. Lett. 92, 251111 (2008).
[3] R. A. Roref, and B. R. Bennett, SPIE Integr. Opt. Circuit Eng. 704, 32-37 (1986).
[4] J. P. Lorenzo, and R. A. Roref, Appl. Phys. Lett. 51, 6–8 (1987).
[5] C. K. Tang, G. T. Reed et al. J. Lightwave Technol. 12, 1394–1400 (1994).
[6] B. R. Hemenway, O. Solgaard, and D. M. Bloom, Appl. Phys. Lett. 55, 349–350 (1989).
[7] G. V. Treyz, P. G. May, and J. M. Halbout, IEEE Electron. Device Lett. 12, 276–278 (1991).
[8] G. V. Treyz, P. G. May, and J. M. Halbout, Appl. Phys. Lett. 59, 771–773 (1991).
[9] X. Xiao, J. C. Sturm et al. IEEE Photon. Technol. Lett. 3, 230–231 (1991).
[10] Y. L. Liu, E. K. Liu et al. Electron. Lett. 30, 130–131 (1994).
[11] Y. Liu, E. Liu et al. Appl. Phys. Lett. 64, 2079–2080 (1994).
[12] C. K. Tang and G. T. Reed, Electron. Lett. 31, 451–452 (1995).
[13] C. Z. Zhao, G. Z. Li, et al. Appl. Phys. Lett. 67, 2448–2449 (1995).
[14] A. Cutolo, M. Iodice et al. Appl. Phys. Lett. 71, 199–201 (1997).
[15] C. A. Barrios, V. R. de Almeida et al. J. Lightwave Technol. 21, 1089–1098 (2003).
[16] C. E. Png, S. P. Chan et al. J. Lightwave Technol. 22, 1573–1582 (2004).
[17] F. Gan, and F. X. Kartner, IEEE Photon. Technol. Lett. 17, 1007–1009 (2005).
[18] D. Marris, E. Cassan, and L. Vivien, J. Appl. Phys. 96, 6109-6112 (2004).
[19] Y. H. Kuo, Y. K. Lee et al. Nature 437, 1334-1336 (2005).
[20] R. Lewen, S. Irmscher et al. J. Lightwave Technol. 22, 172-179 (2004).
[21] Q. Xu, B. Shmidt et al. Nature, 435, 325-327 (2005).
[22] Q. Xu, S. Manipatruni et al. Opt. Express, 15, 430-436 (2007).
[23] A. Liu, R. Jones et al. Nature, 427, 615-618 (2004).
[24] L. Liao, D. Samara-Rubio et al. Opt. Express, 13, 3129-3135 (2005).
[25] F. Y. Gardes, G. T. Reed et al. Opt. Express, 13, 8845-8854 (2005).
[26] F. Y. Gardes, K. L. Tsakmakidis et al. Opt. Express, 15, 5879-5884 (2007).
[27] A. Liu, L. Liao et al. Opt. Express, 15, 660-668 (2007).
[28] C.H.Lee,R.K.Chang, and N.Bloembergen, Nonlinear electroreflectance in silicon and silver,Phys.Rev.Lett.,1967,18(5),167-170
[29] C.K.Chen,A.R.B.De Castro, and Y.R.Shen,Surface-enhanced second-harmonic generation, Phys.Rev.Lett.,1981,46(2),145-148
[30] Renate Dworczak. and Dietmar Kieslinger,Electric Deld induced second harmonic generation (EFISH)experiments in the swivel cell : New aspects of an established method, Phys. Chem. Chem. Phys., 2000, 2, 5057-5064
[31] C.Jordan,G.Marowsky,U.Emmerichs,C.Meyer,Wavelength dependent study of laser induced metallic properties of Si(111) by surface second harmonic generation,Optics Communications,1994,113,125-132
[32] D. Bodlaki and E. Borguet, Dynamics and second-order nonlinear optical susceptibility of photoexcited carriers at Si(111)interfaces, Appl. Phys.Lett.,2003,83(12),2357-2359
[33] Yong Qiang An and Steven T. Cundiff, Phase inversion in rotational anisotropy of second harmonic generation at Si(001) interfaces, Phys. Rev. B,2003,67,193302
[34] H. Sano,and G. Mizutani, W. Wolf, R. Podloucky, Ab initio study of linear and nonlinear optical responses of Si(111)surfaces, Phys. Rev. B,2002,66,195338
[35] Dong Xiao,Euan Ramsay,Derryck T.Reid,et al.,Optical probing of a silicon integrated circuit using electric-field-induced second-harmonic generation,Appl.Phys.Lett.,2006,88,114107-1-114107-3
[36] J.I.Dadap,J.Shan,A.S.Weling,et al.,Measurement of the vector character of electric field by optical second-harmonic generation,Optics Letters,1999,24,1059-1061
[37]孟宪章,康昌鹤,《半导体物理学》,吉林大学出版社,1993,第一章
[38]石顺祥,陈国夫,赵卫,刘继芳,非线性光学,西安:西安电子科技大学出版社,2003年,第三章
[39]孙鉴波,硅材料场致普克尔斯效应和光整流效应的研究,长春:吉林大学电子学院,2009。
[40]张玉红,硅材料电光效应的研究,长春:吉林大学电子学院,2008。
[41]陈纲,廖理几,晶体物理学基础,北京:科学出版社,1992年,第三章。
[42]赵纪红,应力诱导的硅表面二次谐波的产生,长春:吉林大学电子学院,2008
[43]李家泽,晶体光学,北京:北京理工大学出版社,1989年.
[44] J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan,Interactions between Light Waves in s Nonlinear Dielectric , Phys.Rev., 1962,127(6):1918-1939
[45] M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich,Optical Rectification,Phys. Rev.Lett., 1962, 9(11):446-448
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