摘要
建立了一个适用于描述低能电子散射的物理模型 ,利用 Monte Carlo方法对低能电子在多元多层介质中的散射过程进行模拟 .低能电子弹性散射采用较严格的 Mott截面描述 ,为了节约机时 ,利用查表与线性插值方法获得 Mott截面值 ;低能电子非弹性散射能量损失采用 Joy修正的 Bethe公式计算 ,并对其加以改进 ,引入多元介质平均电离电位、平均原子序数、平均原子量概念 ,利用线性插值方法给出光刻胶 PMMA对应的 k值 .对电子穿越多层介质提出一种新的边界处理方法 .在此基础上运用 Monte Carlo方法模拟高斯分布低能电子束在 PMMA-衬底中的复杂散射过程 .模拟结果表明低能电子束曝光具有曝光效率高、邻近效应低、对衬底损伤轻等优点 ,与 L ee、Peterson等人通过实验得出的结论相符 .
A Monte Carlo simulation of low energy electron scattering in multilayer and polybasic medium is performed on the basis of a physical model describing the low energy electron scattering.The more rigorous Mott cross section is adopted for the elastic scattering of low energy electrons.And the method of searching table and linear interpolation is used to save computer time.The Bethe formula modified by Joy is employed to calculate the energy loss of low energy electrons during inelastic scattering processes and improved in this work.The mean ionization potential,the mean atomic number and the mean atomic weight of polybasic medium are introduced,and the value of k of PMMA is given by means of linear interpolation.A new boundary treatment method used for low energy electron passing across the boundary between two different medium layers is proposed.On this basis,the Monte Carlo method is utilized to simulate the complex scattering of Gauss distribution low energy electron beam in PMMA substrate.The modeling results show that low energy electron beam lithography has the advantage of high throughput,low proximity effects and small damage to the underlying substrate.It is in agreement with the conclusion got from Lee et al 's and Peterson et al 's experiments.This work would provide some theoretical basis for the quantitative investigation of electron beam lithography.
关键词
电子束曝光
电子散射
蒙特卡洛法
半导体工艺
electron beam lithography
Monte Carlo method
low energy electron scattering
