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首页> 外文会议>Charged Particle Optics IV >Simulation of discrete Coulomb interactions in high-current projection and multibeam columns
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Simulation of discrete Coulomb interactions in high-current projection and multibeam columns

机译：大电流投影和多光束柱中离散库仑相互作用的模拟

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Abstract: A new method is presented for simulating discrete Coulomb interaction effects in electron and ion beam columns. The method is applicable to the latest high-throughput electron and ion beam projection systems currently under development as possible candidates for next generation lithography. Monte Carlo simulation is used to trace bunches of several thousand particles simultaneously down the column. Compared with previous simulations, two key improvements have been made: (1) Instead of using thin lens approximations, the real fields of the magnetic and electrostatic lenses are used, which enables the lens properties and aberrations to be accurately included in the computation; (2) The N-body inter-particle Coulomb forces are computed with a hierarchical tree-code algorithm, which is orders of magnitude faster that the direct pair-wise force evaluation method used previously. The real lens fields are accurately computed with second-order finite element method ('SOFEM'), and the lens fields are then fitted with Fourier-Bessel series that accurately represent the real lens fields while simultaneously being exact solutions of Laplace's equation. The discrete inter-particle Coulomb fields, evaluated with the new tree-code algorithm, are then added to the external fields of the lenses. Trajectories through these combined fields are then computed by direct ray-tracing, using a fifth-order Runge-Kutta formula, to an internal self- consistency of better than 1 picometer. This method enables, for the first time, the combined effects of the discrete Coulomb interactions and the lens aberrations to be predicted accurately in a completely unified and self-consistent way. The method is illustrated for the case of a magnet doublet projection system. The method can equally well be applied to multi-beam columns, electrostatic lenses, cathode lenses and electron mirrors. !11
机译：摘要：提出了一种模拟电子和离子束柱中离散库仑相互作用效应的新方法。该方法适用于当前正在开发的最新的高通量电子和离子束投影系统，作为下一代光刻的可能候选者。蒙特卡罗模拟用于同时追踪色谱柱中数千个粒子的束。与以前的模拟相比，进行了两个关键的改进：（1）代替使用薄透镜近似，使用了电磁和静电透镜的真实场，这使得透镜特性和像差可以精确地包括在计算中； （2）使用分层树码算法计算N体粒子间库仑力，该算法比以前使用的直接成对力评估方法快几个数量级。使用二阶有限元方法（'SOFEM'）可以精确计算出实际的镜片视场，然后将镜片视场装配傅立叶-贝塞尔级数，该序列可以精确地表示实际的镜片视场，同时又是拉普拉斯方程的精确解。然后，使用新的树码算法评估的离散粒子间库仑场将添加到镜片的外部场中。然后，使用五阶Runge-Kutta公式，通过直接射线追踪，计算出通过这些组合场的轨迹，从而获得优于1皮克的内部自一致性。该方法首次实现了以完全统一和自洽的方式准确预测离散的库仑相互作用和透镜像差的组合效果。该方法是针对磁铁双峰投影系统的情况进行说明的。该方法同样可以很好地应用于多光束柱，静电透镜，阴极透镜和电子镜。 ！11

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