凹球面基底离心式涂胶的数学模型及实验验证

建立了凹球面基底离心式涂胶的数学模型.基于流体力学理论对旋转凹球面上的光刻胶做了受力分析,根据凹球面的面形给出了流体方程的边界条件,并引入和建立了光刻胶蒸发速率对涂胶基底面形的响应关系式,最终得到了一个描述光刻胶厚度随转速、基底面形及光刻胶参数变化的多项式方程,从此方程又简化得到平面上离心式涂胶的数学模型.涂胶实验结果表明,在凹球面上和平面上的光刻胶厚度理论计算值与测量值吻合,精度达到了纳米级.所建立的模型有较好的预见性和实用性.

Mathematic model and experiment verification of spin-coating on concave spherical substrate

In order to guide the spin-coating technology on concave spherical substrate, a mathematic model was established. On the basis of the hydrodynamics, the acting force of spin-coated photo-resist on concave spherical substrate was analyzed. Then, the boundary condition of the hydrodynamic equation was present according to substrate topography. Furthermore, the evaporation rate was considered when spin-coating on different substrates. A polynomial equation of the film thickness related to spinning speed, substrate topography and the parameters of the photo-resist was brought forward to give the film thickness in different conditions. The mathematical model expression of spin-coating on plane was obtained after simplifying the equation. The spin-coating experiment indicates that the calculation value of the photo-resist thickness coincides with the measured value in the nanometer precision both on the concave spherical and planar substrate, which shows the model has a well predictability and a practicality.