Verification of frequency scaling laws for capacitive radio-frequency discharges using two-dimensional simulations*

Abstract

Weakly ionized processing plasmas are studied in two dimensions using a bounded particle-in-cell (PIC) simulation code with a Monte Carlo collision (MCC) package. The MCC package models the collisions between charged and neutral particles, which are needed to obtain a self-sustained plasma and the proper electron and ion energy loss mechanisms. A two-dimensional capacitive radio-frequency (rf) discharge is investigated in detail. Simple frequency scaling laws for predicting the behavior of some plasma parameters are derived and then compared with simulation results, finding good agreements. It is found that as the drive frequency increases, the sheath width decreases, and the bulk plasma becomes more uniform, leading to a reduction of the ion angular spread at the target and an improvement of ion dose uniformity at the driven electrode.

Loading and Injection of Maxwellian Distributions in Particle Simulations

“…5. For clarity, examples will be given in one dimension (XPDP1 [11]); however, the general second-order method is implemented in XOOPIC [32] and XPDP2 [33,34] in 2D. A uniform time-independent external magnetic field, B, is imposed parallel to the cathode surface along z.…”

Accelerating a Particle-in-Cell Simulation Using a Hybrid Counting Sort

“…The push and accumulate routines are implementations of numerical algorithms similar to those used in the University of California-Berkeley Plasma Theory and Simulation Group code PDP2 described in Vahedi et al [7] and Vahedi and DiPeso [8]. However, both the unsorted and sorted routines have been heavily optimized for minimal flop count and memory traffic.…”

“…The particle advance and accumulate are the same algorithms used by the code PDP2, (see Vahedi et al [7] and Vahedi and DiPeso [8] for a description of the code; see Birdsall and Langdon [1] for an analysis of this type of particle advance). Unlike PDP2, all operations are done in double precision as is appropriate for larger simulations.…”

“…In fact, many FORTRAN compilers on commodity workstations convert source code to C and compile the result with a C compiler. While FORTRAN is a staple in the supercomputing community and recent incarnations support object oriented programming, the object-oriented language C++ (ANSI-C is a subset of C++) has been a particularly popular language for PIC simulation as object-oriented coding techniques map well onto simulations which have to handle numerous types of boundary conditions; C and C++ based PIC codes include PDP1 (Verboncoeur et al [9], PDP2 (Vahedi et al [7] and Vahedi and DiPeso [8]), OOPIC (Verboncoeur et al [10]), POOMA (Cummings and Humphrey [11]) and ICEPIC (Blahovec et al [12]). …”

Hydrodynamic and Kinetic Modelling of Dust Free and Dusty Radio‐Frequency Discharges

“…The criterion when to use these models is of course that in the situation of interest the mean free path exceeds characteristic lengths of the discharge, or fast transients occur. For RF discharges either full kinetic models, using the Particle-In-Cell plus Monte Carlo approach [14][15][16][17][18], or hybrid models, using a hydrodynamic description coupled to a Monte Carlo model to obtain the relevant kinetic properties [19,20], are in use.…”