3D Mask Diffraction With Finite Time Domain Difference

Over the years,with the rapid development of semiconductor lithography technology and the rapid development of integrated circuits to miniaturization,the research of lithography researchers has higher requirements,that is,lithography people use more precise process flow and innovation.Break through the limits of lithography technology.Therefore,a variety of analog simulation devices have also been developed.A more traditional method is an approximation method based on a thin mask,sometimes called the Kirchhoff Approach.However,this This method is not suitable for calculating the spatial image of a threedimensional mask.After consulting a considerable amount of lithography-related literature,online courses,and browsing some network resource platforms,we introduced another model in this simulation experiment,namely the strict electromagnetic field solution model(EMF),and adopted finite difference time domain The algorithm solves it,and the model makes the calculation of the spatial image value of the three-dimensional mask more accurate.The model uses a grid to accurately calculate Maxwell's equations on the time axis in a discretized form,discretizes Maxwell's divergence equation in a central difference method,and analyzes the electric field strength(E)and magnetic field strength(H)The interaction between them is updated at a certain time step,and then the electromagnetic field intensity under the near field of the photolithography mask is calculated.The key research contents of this simulation experiment are as follows:First,the finite difference time domain algorithm is introduced into the Maxwell divergence equation,and the equation is discretized and deduced with the idea of central difference.A three-dimensional grid is established in Cartesian Cartesian coordinate system and the equation is applied to the grid.,And analyze the interaction of electric field and magnetic field strength,find the relationship,update the value of electric field and magnetic field in half time step,avoid using the method of integration,simplify the update process of electric field and magnetic field,and then calculate Obtain the near-field electric field strength under the multilayer mask.Then,after further understanding of the FDTD algorithm,a three-dimensional lithography model is constructed,and its process is accurately simulated by writing python code,and the electric field simulation diagram of the mask near field is drawn.On this basis,using the method of projection imaging,fourier transform is used to convert the case in the time domain into the case in the frequency domain,and the frequency domain spectrum analysis is performed,and low-pass filtering is used at the pupil,and then At the exit pupil,the light is converged through a lens to obtain an aerial image.This article uses a FDTD-based lithography three-dimensional model,calculates with a strict electromagnetic field solution model,and uses a projection imaging method to image the obtained near-field data.