摘要
首次研究了以(111)面为衬底硅材料,金属-绝缘体-半导体-绝缘体-金属(MISIM)结构的样品,在外加直流电场作用下,硅材料在1.3μm波长处基于克尔效应和弗朗兹-凯尔迪什效应的电致双折射,并由克尔效应计算出三阶非线性极化率张量χ~((3))的分量χ~(3)_(xyyx)。在实验上直接观察到了由Franz-Keldysh效应引起折射率的变化,并且发现它和入射光的偏振态有关。测得了由克尔效应引起的折射率之差为Δn = 5.49×10~(-16) E_0~2,而弗朗兹-凯尔迪什效应引起的折射率之差为Δn' = 2.42×10~(-16) E02.5。首次在理论上和实验上证实了场致线性电光效应的存在,选用(111)面半绝缘硅材料为衬底,设计金属-绝缘体-半导体(MIS)结构的样品,选用改进的塞纳蒙补偿器设计横向电光调制器,测得输出电光信号与外加交流调制电压的成线性关系。并用MIS结构的样品,当光沿[1(1|-)0]方向入射时,观察到了光整流信号的各向异性。这些研究结果证明表面电场破坏了硅材料的对称性,从而产生场致线性电光效应。
The basic definition of the electro-optic effect is an induced change in the refractive index, the absorption coefficient and the dispersion of a material with an applied electric field. Electro-optic effect included the change of optical property with the directly electric field and with the indirectly electric field. The Pockels effect and the Kerr effect are the directly electro-optic effect; The Franz-Keldysh effect and the plasma dispersion effect are the indirectly electro-optic effect. The electro-optic devices based on electro-optic effect are used in the photon-electronic field. The most important application is used to design electro-optic modulator. It also can be used to design the electro-optic optical switch, the electro-optic deflection and the electrooptical sampling techniques and detection.
It is well known that the manufacturing technology of silicon devices is mature and the cost of silicon material is low. The silicon is transparent for the windows wavelength of the fiber-optic( 1. 3μm and 1. 5μm).Guided-wave components for operation at 1. 3μm fiber-optic wavelength were constructed in crystalline silicon. A continuous-wave Raman silicon laser was demonstrated by the Intel company in 2005.If an effective modulator could also be realized in silicon, data processing and transmission could potentially be performed by all-silicon electronic and optical components. But the perfect bulk of crystalline silicon possessing a center of inversion symmetry which belongs to the m3m symmetry group, second-order nonlinear optical susceptibility is zero in the bulk of silicon at dipole approximation. The linear electro-optic effect do not exist, thus to solve the problem of optical modulation the plasma dispersion effect is commonly adopted, in order to change the silicon refractive index by varying electron and hole distribution within the material. However, changing the carrier concentration requires a large a.c.current of~ 0.2A(r.m.s) through the silicon structure. Moreover, the speed of the silicon modulator is limited by charge mobility or charge recombination times. So the new electro-optic modulator based on other electro-optic effects need to be developed for the significant increase of the modulation speed. However ,we have found that the symmetry can be broken by applying an direct electric field, hence creating a linear electro-optic effect in silicon. We theoretically and experiment studied electric field-induced linear electro-optic effect.
First we developed the semi-insulating Si material with into a metal-insulator-semiconductor- insulator- metal (MISIM) structure and a bottom of (111)plane; In the experiments, the electro-induced birefringence based on Kerr effect and Franz-Keldysh effect in bulk silicon crystal at 1.3μm wavelengths has been measured, and the element of the third-order nonlinear susceptibility tensorχx( y3x)y has been calculated. We find the change of refractive index induced by Franz-Keldysh effect is dependent on the polarization of the probing beam. Previously someone only found the change of the absorption coefficient induced by Franz-Keldysh effect is dependent on the polarization of the probing beam. Moreover, we deduce that the silicon crystal will become a single-axis crystal from an isotropy crystal when a silicon crystal is biased along [111] crystallographic direction, and the phenomena of birefringence will occur as long as the light propagate perpendicularly to the optical axis of silicon crystal. In the experiment, we deduced the differences of refractive indices induced by Kerr effect and Franz-Keldysh effect wereΔn =5.49×10~(-16) E_0~2 andΔn / = 2.42×10~(-16) E02.5 respectively. If the applied electro-field is E = 105V cm, the differences of refractive indices induced by Kerr effect reaches 10~(-6) and the differences of refractive indices induced by Franz-Keldysh effect reaches 10~(-4) ,So the impact of Franz-Keldysh effect is stronger than the Kerr effect at the same applied electric field.
We developed the research on electric field-induced linear electro-optic effect. First we deduced the existence of electric field-induced linear electro-optic effect in silicon with classical theory and detailed analysed the impact of refraction index when the direct electric field, low-frequency modulating field and optical field are applied on the silicon with dipole approximation, the knowledge of electromagnetics, nonlinear optics and group theory are used. The relation and distinguishing are obtained between electric field-induced linear electro-optic effect and other effects(electro-optic Kerr effect,self-focusing) that can induce the differences of refractive indices. Specifically, the forms of electric field-induced effective second–order susceptibilities agree with those of the C_(3v), C_(2v), C_(4v) symmetry groups of crystals when the electric fields applied to silicon are along the [111]、[011]、[001] direction. We deduced the electric field-induced effective electro-optic tensor. Then based on the refractive index ellipsoid method, one can further study the electric field-induced linear electro-optic effect.
We developed the semi-insulating Si material into a metal-insulator-semiconductor (MIS) structure and a bottom of (111)plane and designed transverse direction electro-optic modulator. The a.c modulating electric field is biased along [111] crystallographic direction, the phenomena of linear electro-optic effect will occur as long as the light propagate perpendicularly to [110] of silicon crystal. We first find that the output electro-optic signal and the applied a.c.signal are in accordance with the relationship of Ve o = -0.04402 + 0.10744V_(appl).We hold the symmetry of a non-strained silicon crystal was broken by the surface electric field along [111] direction,hence creating a linear electro-optic effect. In the experiment, the surface symmetry of silicon is different from the bulk symmetry, the surface inversion symmetry extinct, also inducing a linear electro-optic effect.
Because the linear electro-optic effect and the optical rectification are the second-order nonlinear optical effects, they must exist at the same time. The field of the broken symmetry exists in the sample with MIS structure, there is a effective two-order susceptibility, optical rectification will be generated. In the optical rectification experiment, the sample also is MIS structure, the laser beam is incident to [1(1|-)0]. We measured the dependence of photo-voltage on the polarization direction of the incident linear polarization light. From the experimental and theoretical analysis, it is concluded that the symmetry of a silicon crystal was broken by the surface electric field along [111] direction, there is second-order nonlinear effect exist in silicon.
The research on electro-optic effect of silicon can drive the utility in the photoelectricity field. Such as manufacturing optical guide, electro-optic modulator, the electro-optic optical switch, the optical rectification, the optical parameter amplifier, optical oscillator and the electro-optic deflection. The electrooptical sampling techniques and detection based on electro-optic effect also has been used to study the electric parameter distribute(voltage, charge, electric field) distribute in the devices and electric circuit. Thus, the discovered linear electro-optic effect may provide a decisive step towards utilization of active silicon-based photonics.
引文
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[1] Trinh,P.D.,Yegnanarayanan,S.,Coppinger,F.&Jalali,B.Silicon-on-insulator(SOL)phased-array wavelength multi/demultiplexer with extremely low-polarization sensitivity.IEEE Photon.Technol.Lett.9,1997,p940-942
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[4] Rune s.Jacobsen,Karin N.Andersen,Peter i.Borel.Strained silicon as a new electro-optic material. Nature ,2006,441:199-202
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