Particle-in-Cell/Monte Carlo simulation of CF4 discharge in capacitively coupled plasma reactor
We present the structures of the CF4 radio-frequency discharge between parallel electrodes using the Particle-in-Cell/ Monte Carlo method. The simulation takes into account four types of charged species, CF3 , CF − 3 , F − ions, and electrons. The cross-sections of electron-CF4 collision processes are based on the paper of Kurihara et al. [1]. Positive–negative ion recombination which plays an important role in the charged particle balance is also considered in the model using method proposed by Nanbu and Denpoh [2]. The structure of the CF4 discharge is typically electronegative discharge and is characterized by the presence of negative ions (F− and CF3 ), which are the dominant negative charged species (see Fig. 1(a)). The electron density profile and electric field at phase in a rf period are shown in Fig. 1. The local maxima of the electron density is significant feature of electronegative discharges, which cannot be observed in electropositive discharges. Moreover, we can observe the double-layer structure (i.e. the local maxima or minima of the electric field) and the field reversal near the bulk-sheath interface. Historically, the double layer phenomena were first described experimentally and theoretically in rf glow SiH4 discharge by T. Makabe et al. [3]. In conclusion, the abundance of negative ions is one of the main features in the discharges and this profoundly influences the sheath dynamics such as electric field reversal, double layer structure and local maxima of electron density.
Transport coefficients and scattering cross-sections for plasma modelling in CF4-Ar mixtures: a swarm analysis
Electron transport coefficients and the excitation, attachment and ionization rates in pure CF4 and in CF4-Ar mixtures have been calculated for a set of cross-sections which was based on the work of Nakamura (1991 Gaseous Electronics and Their Applications ed R W Crompton et al (Tokyo: KTK Scientific) pp 178-200) but which was modified to include more complex dissociation and ionization kinetics required to develop an adequate plasma chemical model. The procedure for the calculation was the direct numerical procedure (DNP) solution to the Boltzmann equation which makes no approximations in the number of terms used to represent the anisotropy of the distribution function in the velocity space. However, its accuracy may be limited by the density of the grid used. In this paper, we apply the DNP technique to establish its adequacy for plasma modelling in pure CF4 and in 5% CF4-Ar mixture, as well as establishing the adequacy of the cross-section set that was used.
Dimensional Errors of Fixtures, Locating and Measurement Datum Features in the Stream of Variation Modeling in Machining
Machining processes are usually multi-station processes involving a large number of operations and several locating datum changes. Machining errors are thus introduced, transformed and accumulated as the workpiece is being machined. This paper introduces procedures for expressing the influence of errors in fixtures, locating datum features and measurement datum features on dimensional errors in machining. These procedures are essential in the derivation of the Stream of Variation model of dimensional machining errors using the CAD/CAPP parameters of the machining process. The linear state space form of the Stream of Variation model allows for advanced control theory achievements to be employed in formal solutions to problems in multi-station machining. Modeling procedures presented in this paper were experimentally verified in machining of an automotive cylinder head.