One-dimensional model of a helicon discharge
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TEMPERATURE PLASMA
One-Dimensional Model of a Helicon Discharge V. A. Sazontov, V. E. Semenov, and A. I. Smirnov Institute of Applied Physics, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhni Novgorod, 603950 Russia Received February 5, 2007
Abstract—A simplified model describing the steady state of a helicon discharge in a low-pressure plasma is considered. The electron Langmuir frequency of the plasma produced by the discharge is shown to be much higher than the electron gyrofrequency. It is found that the gas medium is ionized and the electrons are heated primarily by the extraordinary mode. The calculated electron density depends nonmonotonically on the magnetic field, in agreement with the results of numerous experiments. PACS numbers: 52.50.Dg DOI: 10.1134/S1063780X07110086
1. INTRODUCTION In resent years, RF inductive discharges in constant magnetic fields have received much attention. Interest in such discharges stems primarily from the creation of low-power plasma sources [1–4] used in devices for etching semiconductors, as well as in space engineering, accelerators, and electron optics. The plasma sources in question, which are often called helicon sources, usually have a power of ~1 kW and operate with a constant magnetic field of ~1 kG at working frequencies (10–100 MHz) lying in the whistler frequency range. They can very efficiently produce plasmas with an electron density of up to 1013 cm–3 and a degree of ionization as high as 30% (see, e.g., [5–7]) at low working gas pressures (p ~ 0.1–100 mTorr). At the same time, a systematic theory of RF discharges in a strong constant magnetic field has not yet been developed and is still being widely discussed in the literature. It should be noted that, in view of the complexity of the problem, specific results on the subject have been obtained only numerically [8–11]. In the present paper, we construct a model of lowpressure helicon discharges that makes it possible to analytically calculate the main parameters of helicon plasma sources and to qualitatively explain such experimentally observed effects as a substantial increase in the plasma density (in comparison with that of an isotropic plasma) and a nonmonotonic dependence of the electron density on the magnetic field.
conductors placed outside the tube. In this discharge system, the role of the magnetic field is twofold. First, it slows transverse diffusion in the plasma, thereby substantially reducing diffusive losses to the side wall. Second, it makes the energy exchange between the RF field and the plasma more efficient, which allows one to raise the electron density far above the critical level. This effect can be qualitatively understood even in terms of the very simple model to be described below. Let a plasma be created in a layer between two parallel planes z = –L and z = L (see Fig. 1) and let a constant magnetic field B0 be directed along the z axis of the Cartesian coordinate system. The RF field in the plasma is excited by a harmonic surface current with the density
2. FORMULATION OF T
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