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1、光学精密工程Optics and Precision Engineering卿16卷第2期2008年2月Vol. 16 No. 2Feb. 2008文章第号 1004724X2008)0202294)6凹球面基底离心式涂胶的数学模型及实验验证巴音贺希格I,张浩泰李文昊2(1.中国科学院长春光学旃密机械与饬理研究所，吉林长春130033t2.中国科学氏研究生院，北京100049)立了凹球面基底克心式涂胶的数学模SL基于流体力学理论对旋转凹球面上的光划胶做了受力分析根据凹球 面的面形给出了浪体方程的边界条件并引入和建立了光刻胶嫖发速率对涂胶基底面形的响应关系式最块得到了一个 描述光刻胶厚度随转逮墓
2、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除胶的数学模 .涂胶实验结果衷明在凹球面上和平面上的光刻胶孕度理论计算值与测虽值吻合箱度达到了纳米级所建立的模 型有较好的預见性和实用性 关 ft 词心氏滄4U凹球面；光则胶 中图分类号:TN335.7文就标识凹：AMathematic model and experiment verification ofspin-coating on concave spherical substrateBayanheshig1 ZHANG HaotaZ.LI Wen-hao1,2(1. Changchun Institute of Opti
3、cs * Fine Mechanics and Physics 9 Chinese Academy of SciencesChangchun 130033 fChinai2. Graduate School of the Chinese Academy of Sciences 9 Beijing 100049Chna)Abstract: In order to guide the spin-coating technology on concave spherical substrate* a mathematic model was established. On the basis of
4、the hydrodynamics the acting force of spin-coated photo-resist on concave spherical substrate was analyzed Then, the boundary condition of the hydrodynamic equa- tion was present according to substrate topography. Furthermore lhe evaporation rate was considered when spin-coating on different substra
5、tes. 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
6、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 Key words： mathematic model； spin-coating； concave spherical surface $ photo-resist收稿日期:2007-09-20订日 W：2007-11-22.墓金项目：国家自於科学基金資助 0 (No. 60478034)；中国科学院“优霁博士学位论文、院长奖获得書科研启动令 頊资金”资助現目广十一五国家科技支挥计划重大项目(No 2006BAK03AJ2h吉林省科技发農计划资 助項目(No. 20070523)
凹球面基底离心式涂胶的数学模型及实验验证
