VOLUME 81, NUMBER 2 PHYSICAL REVIEW LETTERS 13 JULY 1998 Effect of Collisionless Heating on Electron Energy Distribution in an Inductively Coupled Plasma Valery A. Godyak OSRAM SYLVANIA Development Inc., 71 Cherry Hill Drive, Beverly, Massachusetts 01915 Vladimir I. Kolobov CFD Research Corporation, 215 Wynn Drive, Huntsville, Alabama 35805 (Received 23 March 1998) Significant frequency dependence of the electron energy distribution has been found in a low- pressure inductive discharge experiment. The observed frequency dependence reveals the presence of collisionless electron heating and appears as a result of finite electron-transit time through the skin layer. The energy distributions calculated from a kinetic equation accounting for nonlocality of electron kinetics and electrodynamics are in good agreement with the experiment. [S0031-9007(98)06549-1] PACS numbers: 52.80.– s, 52.65.– y The recent advent of high density plasma sources sus- tained by radio-frequency (rf) electromagnetic fields at low gas pressure has raised significant interest in electron heating and plasma maintenance in the near-collisionless regime where the electron mean free path l is comparable to or larger than plasma dimensions. In contrast to a col- lisionally dominated plasma with Joule heating, electron heating in the near-collisionless plasma is a combined ef- fect of electron interactions with electromagnetic fields, reflections from plasma boundaries, and collisions with gas particles [1–3]. The penetration of electromagnetic energy into such a plasma exhibits peculiarities typical to the anomalous skin effect [4–6]. Nonmonotonic distri- butions of the rf fields and current density [7], collision- less electron heating [8], and negative power absorption [9] have recently been observed in experiments with low pressure inductive plasmas and reviewed in Ref. [10]. In this Letter we report on a significant frequency depen- dence of the electron energy distribution function (EEDF) found in experiments with inductively coupled plasma (ICP) at low gas pressure. According to the developed theory, the frequency dependence of the EEDF is associ- ated with finite electron transit time through the skin layer. The experiments were carried out in a cylindrical ICP maintained by a planar inductor coil in a stainless steel chamber with a quartz bottom. Details of the experi- mental setup are published elsewhere [7,9,10]. Briefly, the chamber ID was 19.8 cm, its length L was 10.5 cm, and the quartz thickness was 1.27 cm. A five turn pla- nar induction coil was mounted 1.9 cm below the bottom surface of the discharge chamber. An electrostatic shield between the quartz and the coil has practically eliminated capacitive coupling between the induction coil and plasma to the extent that the rf plasma potential referenced to the grounded chamber was much less than 1 V. That made it possible to resolve the low energy part of the measured EEDF previously not detected in all published experiments carried out in ICP’s. A noise supression cir- cuit with an additional reference probe [11] has extended the dynamic range of the EEDF measurement up to 3– 4 orders of magnitude and enabled us to resolve elec- trons with energy far beyond the excitation and ionization thresholds of argon atoms. Measurements were made at driving frequencies v2p  3.39, 6.78, and 13.56 MHz in an argon discharge at gas pressures of 1 and 10 mTorr and discharge power P pl in a range of 12–200 W. The power dissipated in the plasma, P pl , was determined by measuring the power transmitted to the inductor coil (for- ward minus reflected power) and subtracting matcher and coil losses determined a priori as a function of coil cur- rent and temperature. Results of Langmuir probe measurement performed in the discharge center (r  0 and z  5 cm) are shown in Fig. 1 for different v and P pl . Here the electron energy distribution is given in terms of the electron energy probability function (EEPF) measured by Langmuir probe. The plasma parameters found as corresponding integrals of the measured EEPF: the electron density n e , the effective electron temperature T eff , and the electron-atom transport collision frequency n m in rf field are given in Table I together with the rms electric field E 0 near the quartz window (at r  4, z  0 cm) measured in Ref. [7]. The observed EEPF’s are non-Maxwellian and in general have a three temperature structure. There is a group of low energy electrons with temperature T e ´  d ln f 0 d´ 21 less than the effective temperature T eff of the EEPF, similar to that found in capacitive rf discharges [12]. There is also a EEPF depletion (compared to Maxwellian) at energies higher than 12 eV due to excitation and ionization of argon atoms by electron impact. Substantial changes of the EEPF slope with frequency observed at energies close to average ones (see Fig. 1) correspond to changing of the effective electron temperature shown in Table I. The frequency dependence is well pronounced at lower plasma densities (power) and gradually vanishes at higher densities where Coulomb interactions among electrons 0031-9007 98 81(2) 369(4)$15.00 © 1998 The American Physical Society 369