Researches On Second-order Nonlinear Optical Effects In Si(100) And Si(110) Surface Layers

This paper researched the second-order nonlinear optical effects induced by the built-in electric field in the (100) and (110) surface layers of silicon crystals, especially focusing on the built-in induced linear electro-optic effect and optical rectification.The major advantages of silicon include cost-effective, maturity of possess and CMOS-compatible, which lead to widely used of silicon in optoelectronic integration. Silicon crystal belongs to the cubic crystal system and the point group of it is Oh. Silicon is isotropic and centrosymmetric, the second-order nonlinear susceptibility tensor X(2) of which is zero under the dipole approximation. Theoretically, silicon doesn’t possess second-order nonlinear optical effects such as frequency doubling, difference frequency, linear electro-optic effect, optical rectification and second harmonic generation. It is has been a limitation of the application of silicon to the field of nonlinear optical applications for a long time. Especially, silicon modulators haven’t been used actually so far. However, the electric field can break the central symmetry, leading to nonzero second-order nonlinear susceptibility tensor. For the designing of silicon based device, it is of important significance to research the linear electro-optic effect and optical rectification induced by built-in electric field in silicon crystal.In this paper, the classical polarization theory was used to interpret the basic concept and physical mechanism of the linear electro-optic effect and optical rectification effect. The linear electro-optic effect was analyzed using refractive index ellipsoid and Maxwell’s equations, respectively. This is the theoretical basis of this paper.This article theoretically researched the change of crystal symmetry of silicon when the electric field was along the Si-[100] and Si-[110] orientation, respectively. It proved that when the electric field was along [100] orientation, the point group of silicon crystal changed from Oh into C4v; when the electric field was along [110] orientation, the point group of silicon crystal changed into C2v-According to the calculation results of Jones matrix, we designed a transverse electro-optic modulation system, and explored the linear electro-optic effect in Si (100) and (110) surface layers. The electro-optic signal changed linearly with applied voltage which proved that the built-in electric field broke the central symmetry, leading to nonzero effective second-order susceptibility, and induced the linear electro-optic effect in surface layers of silicon. We also carried out the experiment of built-in electric field induced optical rectification. It was observed that the optical rectification signal showed a cosine dependence on the azimuth of the linearly polarized light, which agreed well with our theoretical expectations. This proved the existence of optical rectification, and was also an indirectly proof of the built-in electric field induced linear electro-optic effect. In addition, we also studied the optical rectification in various depths of surface layer, which verified the feasibility that the built-in electric field optical rectification could be applied to the detection of distribution of the electric field in the space charge region of the surface layer of silicon crystal.