S. Dujko

Kinetic phenomena in charged particle transport in gases, swarm parameters and cross section data*

In this review we discuss the current status of the physics of charged particle swarms, mainly electrons. The whole field is analysed mainly through its relationship to plasma modelling and illustrated by some recent examples developed mainly by our group. The measurements of the swarm coefficients and the availability of the data are briefly discussed. More time is devoted to the development of complete electron?molecule cross section sets along with recent examples such as NO, CF4 and HBr. We extend the discussion to the availability of ion and fast neutral data and how swarm experiments may serve to provide new data. As a point where new insight into the kinetics of charge particle transport is provided, the role of kinetic phenomena is discussed and recent examples are listed. We focus here on giving two examples on how non-conservative processes make dramatic effects in transport, the negative absolute mobility and the negative differential conductivity for positrons in argon. Finally we discuss the applicability of swarm data in plasma modelling and the relationship to other fields where swarm experiments and analysis make significant contributions.

Monte Carlo studies of electron transport in crossed electric and magnetic fields in CF4

Electron transport in crossed electric and magnetic dc fields in CF4 is considered by employing an exact Monte Carlo simulation technique. Emphasis is placed on explicit and implicit effects of the combination of both the shape of cross-sections and magnetic field on relaxation processes and steady-state transport data. It has been shown that the application of a magnetic field changes the relaxation processes by increasing the relaxation times as well as, by introducing the oscillatory behaviour of some transport quantities during the relaxation process itself. The electron transport parameters studied here are collision frequency, mean energy, drift velocity, diffusion tensor and collisional rates for 1 E/N 1000 Td and 0 B/N 1000 Hx (1 Td = 10 −21 Vm 2 ,1 Hx= 10 −27 Tm 3 ). Special attention is paid to the study of sensitivity of transport data in E × B fields on the energy dependence and nature of the cross-sections. The validity of the effective reduced electric field concept through Tonks’ theorem is also investigated for CF4 in the evaluated range of mean energies.

Positron transport: the plasma-gas interface

Motivated by an increasing number of applications, new techniques in the analysis of electron transport have been developed over the past 30 years or so, but similar methods had yet to be applied to positrons. Recently, an in-depth look at positron transport in pure argon gas has been performed using a recently established comprehensive set of cross sections and well-established Monte Carlo simulations. The key novelty as compared to electron transport is the effect of positronium formation which changes the number of particles and has a strong energy dependence. This coupled with spatial separation by energy of the positron swarm leads to counterintuitive behavior of some of the transport coefficients. Finally new results in how the presence of an applied magnetic field affects the transport coefficients are presented.

Negative mobilities of electrons in radio frequency fields

In this paper, we perform calculations of mobilities (represented by drift velocities) of electrons in mixtures of F/sub 2/ and Ar in radio frequency (RF) fields. The conditions were chosen which correspond to those that led to observation of negative absolute mobility in dc fields in decaying plasmas. In RF fields, a similar effect is observed as the mobility corresponding to the flux drift velocity is negative. At the same time, it was found that the mobility corresponding to the bulk drift velocity is mainly positive in respect to the expected value, but that it has a large phase delay. The effect is caused by nonconservative nature of the attachment and in the absence of nonconservative collisions both mobilities are positive and in phase with the field.

Spatial profiles of electron swarm properties and explanation of negative mobility of electrons

In this paper, we explain the difference in sign of the flux and bulk drift velocities of a swarm of electrons in constant direct current (dc) and in radio frequency (RF) electric fields under conditions which lead to negative absolute mobility. We have studied (0.5%) F/sub 2//Ar decaying plasma. It was shown that there is a spatial separation of groups of electrons with high and low energy and as a result there is a localization of electron attachment in the region of low energy. Finally, we show that the positive value of the bulk mobility and its delay in RF fields may be explained by a wave of localized attachment that changes the center of mass of the electron swarm.

Fluid modeling of resistive plate chambers: impact of transport data on development of streamers and induced signals

We discuss the implementation of transport data in modeling of resistive plate chambers (RPCs), which are used for timing and triggering purposes in many high energy physics experiments. Particularly, we stress the importance of making a distinction between flux and bulk transport data when non-conservative collisions, such as attachment and/or ionization, are present. A 1.5-dimensional fluid model with photoionization is employed to demonstrate how the duality of transport data affects the calculated signals of the ATLAS triggering RPC and ALICE timing RPC used at CERN, and also a timing RPC with high content. It is shown that in the case of timing RPCs, the difference between the induced charges calculated using flux and bulk transport data can reach several hundred percent at lower operating electric fields. The effects of photoionization and space charge are also discussed.

Data for modeling of positron collisions and transport in gases

This work is supported by MNPRS Projects ON171037 and III41011 and the Australian Research Council’s Centre of Excellence Program.

Resistive Plate Chambers: electron transport and modeling

We study the electron transport in gas mixtures used by Resistive Plate Chambers (RPCs) in high energy physics experiments at CERN. Calculations are performed using a multi term theory for solving the Boltzmann equation. We identify the effects induced by non-conservative nature of electron attachment, including attachment heating of electrons and negative differential conductivity (NDC). NDC was observed only in the bulk component of drift velocity. Using our Monte Carlo technique, we calculate the spatially resolved transport properties in order to investigate the origin of these effects. We also present our microscopic approach to modeling of RPCs which is based on Monte Carlo method. Calculated results for a timing RPC show good agreement with an analytical model and experimental data. Different cross section sets for electron scattering in C2H2F4 are used for comparison and analysis.

Data Bases for Modeling Plasma Devices for Processing of Integrated Circuits

In this paper we compile the data on electron methane scattering cross-sections and transport coefficients that provide a data base for plasma models of etching, deposition and other technologies involving CH4. Cross section sets were compiled and tested against the swarm data and transport coefficients were calculated and measured for DC and RF fields. We also indicate the conditions where kinetic effects in the RF field require an extension of the present day models of plasma etching deposition and cleaning.

Transport Coefficients for Electrons in CF4 in E(t)×B(t) Fields

Low pressure discharges sustained by radio-frequency (rt) electric fields, are widely used in microelectronic fabrication and manufacture of new materials). In these applications it is desirable to generate high density, large volume nonequilibrium plasma in collision dominated regime. Most plasmas are driven by sources with frequencies ranging from several tens to several hundreds of MHz. In case of Inductively Coupled Plasmas (ICP) and magnetically enhanced plasmas, the magnetic field is present leading to spatial trapping of electrons. Investigation of electron transport and of the kinetic phenomena that may occur, in crossed dc and rf fields is highly desirable as the basis for plasma models under circumstances that are typical for plasma processing. On the other hand, modeling of gaseous dielectrics may benefit greatly from the studies of gases for plasma etching as often the same gases are used in both applications. Modeling of rf plasmas usually relies on application of dc swarm data. At very high frequencies, effective field approximation gives reasonable results while at low frequencies instantaneous field approximation gives good results. However, for a wide range of frequencies and pressures, that are typical for applications of rf plasmas these approximations may fail. Therefore, the first critical step in modeling of rf plasmas is calculating the electron transport coefficient under the influence of time resolved fields. The effect of magnetic field on electron transport is the second critical step. Namely, most models do not take into account the effect of time resolved magnetic field on electron transport. However, for example, in ICP the normalized magnetic field (BIN) may be very strong (of the order of 2000-5000 Hx in peak values) .