中文摘要：

为了给实际的纳米光刻对准工作提供理论研究基础，主要分析推导了莫尔条纹复振幅以及光强的空间分布规律。在理论分析的基础上通过仿真，定量地确定了莫尔条纹复振幅分布的近似数学模型。分析表明，当对准光路通过掩模硅片上的两个对准标记受到两次光栅的调制并发生复杂的衍射和干涉时，将形成有规律的、呈一定周期分布的莫尔条纹。并且当两光栅周期相近时，莫尔条纹将表现为一个与两光栅周期相关的空间拍信号。在近似模型中该拍信号主要由两光栅基频的乘积调制与振幅调制信号组成。两调制信号的群峰值周期相等、与拍信号的群峰值周期一致，并且该周期相对于两光栅周期被大幅度放大，因而具有很好的位移探测灵敏度，有利于纳米级对准的实际应用。

英文摘要：

Grating-based Moire technique in the alignment of lithography has the property of high definition and strong anti-jamming ability. In order to provide a basis for practical research of alignment of nanolithography, the rule of complex amplitude and intensity distribution of Moire fringes was deduced and concluded. On the basis of theoretical analysis, approximate mathematical model of amplitude distribution of Moire fringes was built via simulation. The results indicate that light is modulated by two gratings when they travel through two alignment marks on the wafer and mask in the process of nanometer lithography and then regular periodic-distributed Moire patterns are formed. Furthermore, when the periods of two gratings are slightly different the Moire fringes appear to be a spatial beat signal, which includes two parts in the approximate model： the multiplication-modulated signal and amplitude modulation signal of fundamental harmonics of two gratings. And the envelop periods of two parts are the same as the Moire period which is magnified with respect to the periods of two gratings. Therefore, the Moire fringes with magnified periods have high detection sensitivity and can be helpful in the application of nanometer alignment of lithography.