球面旋涂光刻胶膜厚分布的数学模型

Evolvement model of photoresist spin coating thickness on spherical surface

提出了球面旋涂微米级厚度光刻胶膜层薄化率公式及径向位置演变公式,并得到了膜厚分布的演变公式。与平面涂胶相比,球面涂胶离心力及重力分量是在不断的变化。根据平面旋涂运动方程及球面面形特征,给出了球面旋涂运动方程;结合流体层流的表面条件及不可压缩流体的质量连续方程,推导出了膜厚h及径向位置r对时间t的演变公式,并得到了在径向位置r处初始厚度为h0的膜厚演变的数学模型。通过对模型参数的分析可知,球面旋涂光刻胶应采用主从轴偏心旋涂,旋涂时工件的开口应朝向侧面(旋转轴水平)。

The mathematics model that showed photoresist spin coating thickness evolvement on spherical surface was put forward. For the vector of centrifugal force change continually in spherical surface spin coating compared to plane, and the characteristic of spherical surface, the spherical surface movement equation was given out based on the plane. The equation linked up laminar flow surface condition and incompressed liquid mass continued equation, the formula for coating thickness h to time t, radial position r to time t, and evolvement of coating thickness which initial value ;s h0 under condition of radial position r were evolved. The results show that photoresist coating on spherical surface should be spread with two disaecord horizontal axis.