Nonlocal electron kinetics in a low-pressure inductively coupled radio-frequency discharge

Abstract

The Boltimann equation for electrons is analyzed for a low-pressure inductively coupled rf discharge in argon driven by a planar-coil. Spatially resolved probe measurements of the electron distribution function (EDF) indicate that the total energy of electrons is an argument of the EDF. Pressure dependence of the light emission distribution is explained on the basis of nonlocal electron kinetics. -Inductively coupled rf discharges are currently being investigated as plasma sources for material processing.' For the pressure range of interest, l-100 mTorr, the electron energy relaxation length exceeds the characteristic discharge dimensions (of the order of 10 cm) and the electron distribution function' (EDF) is not in equilibrium with the local electric field (see for example Ref. 3 and references therein). In such a nonlocal regime, a kinetic treatment of electrons is necessary to calculate the ionization rate, plasma density, electron current density, etc. In this letter we analyze the main consequences of nonlocal electron kinetics by examining the Boltzmann equation for a given spatial distribution of electric fields (both electrostatic and rf fields) to explain experimental data for a planar inductively coupled discharge in argon. The discharge's most distinguishing feature appears in the spatial separation of electron heating and ionization. Though the electron heating occurs in the region of a high rf field, a substantial portion of ionization is produced near the maximum of the electrostatic potential where the rf field is absent.The discharge is driven by the electric field from a spiral coil placed on the dielectric roof of a squat cylinder with metallic walls and bottom (Fig. 1). The azimuthal r-f field EB is localized in the vicinity of the antenna and peaks in an annular region at roughly half of the chamber radius. The electron heating mechanism depends on the relative magnitude of the three characteristic dimensions: field penetration depth S, electron mean-free path h, and the length V/W which electron passes during the field period." When X is the smallest of them, the ohmic heating take place, when the smallest is 6, the collisionless heating is expected to occur.5Since the electron energy relaxation length exceeds the spatial scale, the total energy E=W -e +(z,r) is the argument of the EDE6-* The observed profile of the electrostatic potential &,r) is shown schematically in Fig. 2. Curves 1 and 2 correspond to axial distribution of &z,r) at r =0 and at the point r-a, where the maximal amplitude of the rf field is reached. The potential of the metallic wall rl with respect to the plasma exceeds the excitation potential E*. The dashed area indicates the region in (~,z,r) space where inelastic collisions occur. The electrons with E>E* have a kinetic energy M, sufficient for excitation only in a region slightly above curve 3, where their potential energy is approximately zero.We will consider here the case of small anisotropy of the EDF when the conventional two-term approximation is applicable f=f...

Electron energy flux control using dual power in side-type inductively coupled plasma

“…In low pressure discharges, electrons heated by the local field can penetrate into other regions without energy loss due to low inelastic collision frequency. [4][5][6] In the absence of energyloss collisions and a heating electric field, the total electron energy is constant as the electrons bounce back and forth within the confining potential of the ambipolar field. Hence the electron energy probability function (EEPF) is a function only of the total energy.…”

Kinetic two-dimensional modeling of inductively coupled plasmas based on a hybrid kinetic approach

“…The NLA was originally developed byBernstein and Holstein 17] and Tsendin 18]. Within the past few years it has been successfully applied to the modeling of low pressure glow discharges 14, [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The basic idea of the NLA is to describe the EDF in terms of the total energy of electrons (kinetic plus potential energy in the ambipolar space charge eld).…”

Self-consistent kinetic modeling of low-pressure inductively coupled radio-frequency discharges

“…This idea proved to be effective in application to various gas discharge problems [10][11][12][13] and has recently been applied to ICP modeling. 7,14 The experimental data 13,14 demonstrate that for the majority of electrons the EDF is a function of total electron energy only and does not depend explicitly on the coordinates. However, a relatively small fraction of electrons in an ICP cannot be treated using the spatially averaged kinetic equation as indicated by Kolobov and Hitchon.…”