Low pressure semiconductor processing transport property modeling using direct simulation Monte Carlo

Zheng Li, Hao Deng, D. Levin
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引用次数: 1

Abstract

Summary form only given. In order to extend the capability of the Hybrid Plasma Equipment Model (HPEM)1 simulation code to increasingly lower operating pressure conditions, the direct simulation Monte Carlo (DSMC)2 method is used to improve the modeling of the heavy particle species in a hollow cathode magnetron (HCM) plasma reactor, a device used to implement the Ionized Metal Physical Vapor Deposition (IMPVD) technology.The DSMC, at the current stage, is inserted between the fluid kinetics-Poisson module (FKPM) and plasma chemistry Monte Carlo module (PCMCM) module of HPEM as an correction to the FKPM at the low-pressure condition. The DSMC module initializes a large number of simulated particles (each represents 109 real atoms) at different computation cells in the plasma reactor with positions and instantaneous velocities according to the number density, temperature, flux from the FPKM. The continuous process of particle movement and interaction is uncoupled, i. e., at each time step every particle is moved according to its velocity subjecting to the electric and magnetic fields, then, the interaction between the particles is modeled by appropriate by collision and reaction models where the heavy-heavy particle reactions are implemented by total collision energy model while the electron impact reactions are introduced by the electron impact rate coefficients and source functions. In each HPEM iteration, the time-accurate DSMC calculation will be performed for a physical time of 1 μ, same as the FKPM module, with 10,000 DSMC steps. Sampling will be performed after 9,000 steps and the number density, temperature, and flux will be obtained by averaging the sampled particles at difference cells for different species. These properties along with the electric field will be output to the PCMCM module. Detailed models and simulation results will be presented in the conference paper.
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利用蒙特卡罗直接模拟低压半导体加工输运特性建模
只提供摘要形式。为了使混合等离子体设备模型(HPEM)1仿真代码能够适应越来越低的工作压力条件,采用直接模拟蒙特卡罗(DSMC)2方法改进了用于实现电离金属物理气相沉积(IMPVD)技术的空心阴极磁控管(HCM)等离子体反应器中重粒子的建模。现阶段,DSMC被插入到HPEM的流体动力学泊松模块(FKPM)和等离子体化学蒙特卡罗模块(PCMCM)之间,作为低压条件下FKPM的校正。DSMC模块在等离子体反应器的不同计算单元中初始化大量模拟粒子(每个代表109个真实原子),根据FPKM的数量密度、温度、通量,具有位置和瞬时速度。粒子运动和相互作用的连续过程是不耦合的,即在每个时间步,每个粒子在电场和磁场作用下按其速度运动,则:粒子间的相互作用采用适当的碰撞和反应模型,其中重粒子反应采用总碰撞能量模型,电子碰撞反应采用电子碰撞率系数和源函数。在每次HPEM迭代中,与FKPM模块相同,在1 μ的物理时间内进行时间精确的DSMC计算,并进行10,000个DSMC步长。采样将在9000步后进行,通过对不同种类的不同细胞的采样颗粒进行平均,获得数量密度、温度和通量。这些特性以及电场将输出到PCMCM模块。详细的模型和仿真结果将在会议论文中提出。
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