Study of linear electro-optical effects in silicon materials under the action of continuous stress field

Abstract

To investigate the mechanism of the linear electro-optic effect in strained silicon and advance the practical application of silicon-based optical modulators, this paper addresses the limitations of existing theoretical models due to their lack of continuous strain tuning capability. By employing a self-designed uniaxial stress setup, continuous and tunable strain was applied to silicon, enabling systematic measurement of the relationship between the output electro-optic signal and strain. Through controlled variable analysis, the synergistic influence of strain and modulation electric fields was qualitatively examined. Signal separation was performed by exploiting the polarization dependence differences between the plasma dispersion effect and the Pockels effect. The results indicate that the electro-optic signal primarily originates from the plasma dispersion effect, and both this effect and the contribution from the Pockels effect enhance with increasing strain. When strain reaches the order of 10−4, the electro-optic tensor of silicon attains a magnitude of approximately 0.01 pm/V. An experimental formula describing the variation of the second-order nonlinear susceptibility tensor with strain is also provided. This study offers direct experimental evidence for elucidating the mechanism of the linear electro-optic effect in strained silicon and holds significant implications for accelerating the integration of silicon-based electro-optic modulators.