Paper PS-WeA2
Global Model based Framework for Prediction of Ion Energy Distributions Under Pulsed RF-bias Conditions in Plasma Etching Processes

Wednesday, November 1, 2017, 2:40 pm, Room 23

Prediction of ion energy distributions (IEDs) under real process condition is one of the critical issues in plasma etching processes of micro-fabrication of semiconductor devices. In this study, we developed global (volume-averaged) model based framework to predict the IEDs under the real conditions with pulsed RF bias, dual/triple frequencies, and the high power sources. By employing global model as the core module, our framework achieves not only strong robustness compared with existing higher dimensional equipment simulators for the severe conditions, but also acceptable simulation time as daily simulator for extensive low pulse frequency such as 100Hz. Furthermore, our framework was applied to wide variety of plasma reactors: inductively coupled plasma, capacitively coupled plasma (CCP), and microwave-excited surface wave plasma, by cooperation with electron heating model corresponding to the reactor type and the radio-frequency (RF) sheath model. On the other hand, the framework requires larger computational cost to obtain the results than original global model of steady state problems. Thus, our effort was much paid to reduce the time by utilizing numerical algorithms such as adaptive time stepper, hybrid time-integrator, etc. Especially, employed RF sheath model was expressed by one-dimensional fluid equation for ionic species which can be solved numerically by Runge-Kutta integration scheme; the integration also demands large computational cost due to the self-consistent coupling to equivalent circuit of RF biased substrates. Therefore, some sort of evaluation way of the model was needed for the reduction. Actually, the sheath model is used to calculate sheath width only on our model for evaluation of the sheath capacity. Fitting function to the numerical solution was employed to evaluate the value quickly. The obtained function has same asymptotic behavior as Child-Langmuir law for high potential drop limit. Furthermore, the curve of the function well reproduces the numerical solution for entire ranges of the potential drop where past analytical formula failed to reproduce. By using the function, we found that the simulation gains the speed by 39.1 times for pulsed dual RF CCP plasma with Argon gas compared to the unused case. The expression of the function was also extended to the numerical solutions of the electronegative plasma such as Cl₂ gas to gain the application range.