硅基BaTiO₃薄膜应力调控对其晶畴内部能量分布及电光调制特性的影响

The Influence of Stress Regulation on Domain Internal Energy Distribution and Electro-Optic Modulation Characteristics in Silicon-Based BaTiO₃ Thin Films

摘要: 硅基异质外延BaTiO₃薄膜的面内双轴压应力是调控其电光调制性能的核心因素。本文基于朗道–德文希尔铁电理论与弹性力学，建立含畴壁能修正的面内双轴应力耦合模型，明确应力–微观结构–电光性能的多参量关联关系；首次在硅基BaTiO₃应力耦合模型中定量引入畴壁能修正项优化有效电光系数公式，提出应力–畴结构–电光调制效率协同调控机制；推导了应力与晶格应变、自发极化、畴壁能、电光系数及半波电压的定量公式，结合权威文献实验数据完成模型验证与参数修正，修正后模型平均预测误差降至2.9%；通过MATLAB数值仿真量化了不同应力下薄膜关键物理参数的演化规律，明确300~500 MPa为兼顾电光性能与结构稳定性的最优应力区间。研究结果完善了硅基BaTiO₃薄膜应力调控理论，为低功耗、高集成度硅基BaTiO₃电光调制器设计提供了坚实的理论支撑。

Abstract: The in-plane biaxial compressive stress of silicon-based heteroepitaxial BaTiO₃ thin films is a core factor regulating their electro-optic modulation performance. Based on the Landau-Devonshire ferroelectric theory and elastic mechanics, a stress coupling model with domain wall energy correction was established to characterize the multi-parameter correlation among stress, microstructure and electro-optic performance. For the first time, the domain wall energy correction term was quantitatively introduced into the in-plane biaxial stress model of silicon-based BaTiO₃ thin films, and the cooperative regulation mechanism of stress-domain structure-electro-optic modulation efficiency was proposed. The quantitative formulas of stress with lattice strain, spontaneous polarization, domain wall energy, effective electro-optic coefficient and half-wave voltage were derived. Verified by experimental data from authoritative literatures, the average prediction error of the modified model is reduced to 2.9%, which is more than 15% higher than that of the traditional model without domain wall energy correction. The evolution law of key physical parameters of the film under different stresses was quantified by MATLAB numerical simulation, and 300~500 MPa was determined as the optimal stress interval balancing electro-optic performance and structural stability. The results improve the stress regulation theory of silicon-based BaTiO₃ thin films and provide a solid theoretical basis for the design of low-power and highly integrated silicon-based BaTiO₃ electro-optic modulators.