Francis F. Chen

Plasma ionization by helicon waves

The dispersion relation for helicon waves in a uniform, bounded plasma is derived with both collisional and Landau damping. It is shown that the latter can explain the very high absorption efficiency of helicon waves in plasma sources and can lead to plasma generators with a controlled primary electron energy. The wave pattern and other features of helicon waves are pointed out.

Helicons-the past decade

First observed in gaseous plasmas in the early 1960s, helicon discharges lay like a sleeping giant until they emerged in the 1980s, when their usefulness as efficient plasma sources for processing microelectronic circuits for the burgeoning semiconductor industry became recognized. Research on helicons spread to many countries; new, challenging, unexpected problems arose, and these have spawned solutions and novel insights into the physical mechanisms in magnetized radio-frequency discharges. Among the most baffling puzzles were the reason for the high ionization efficiency of helicon discharges and the dominance of the right-hand polarized mode over the left-hand one. The most recent results indicate that a nonobvious resolution of these problems is at hand.

Helicons-the early years

Helicon waves are right-hand polarized (RHP) waves which propagate in radially confined magnetized plasmas for frequencies /spl omega//sub ci//spl Lt//spl omega//spl Lt//spl omega//sub ce/ where /spl omega//sub ci/ is the ion cyclotron frequency and /spl omega//sub ce/ is the electron cyclotron frequency. They are part of a much larger family of waves which can propagate down to zero frequency and constitute a very rich field for studying complex propagation characteristics and wave-particle interactions. This paper gives a historical perspective of the waves and their relationship to plasma source development up to the mid 1980s, presents a simple description of their propagation characteristics in free and bounded plasmas, and finishes with their first reported use in plasma processing experiments.

RF compensated probes for high-density discharges

A Langmuir probe for the study of high-density RF discharges has been developed and tested in a helicon discharge in which the RF potential ( approximately=100 V) is much larger than the electron temperature ( approximately=4 eV). Carbon probe tips are used to minimize erosion by ion sputtering. Miniature RF chokes located close to the probe tip present RF impedances of 150 k Omega at the operating frequency of 27.12 MHz and 300 k Omega at the first harmonic at 54.24 MHz. It is further necessary to drive the probe tip to follow the RF fluctuations by coupling it to a larger floating electrode. We have been able to measure Te values as low as 3.4 eV in argon plasmas of 1013 cm-3 density; these temperatures are 1.6 eV lower than ones measured by probes with chokes alone, and 2.3 eV lower than measured by uncompensated probes.

Experiments on helicon plasma sources

This work concerns a search for novel plasma generators with applications to materials processing and advanced accelerators and radiation sources. Experimental measurements, together with a summary of the theory, are presented on the production of high‐density plasmas using radio‐frequency (rf) excitation of helicon waves. Plasma densities above 3 × 1013 cm−3 have been achieved with 2 kW of rf power. The required power agrees with classical diffusion theory. The scaling of density with magnetic field agrees with the theory of helicon waves. The effect of different antenna designs is demonstrated. Unexpected observations include: (a) a density maximum occurring at very low magnetic fields, (b) an increase in peak density with nonuniform fields, and (c) the strong effects of dc wall potentials on the behavior of the discharge. Tentative explanations of these phenomena are presented.

Amplification and absorption of electromagnetic waves in overdense plasmas

The spatial variation of the amplitude of electromagnetic radiation propagating into an inhomogeneous plasma is discussed in reference to nonlinear interaction of HCN laser radiation with plasmas and to experiments on r.f. heating of the ionosphere. Previous results on the ordinary wave and on the extraordinary wave at normal incidence are reviewed with emphasis on the physical processes affecting the amplitude behaviour. New numerical results are obtained starting from an integral representation of the solution of the wave equation for waves in a cold, inhomogeneous, magnetized plasma slab. Resonance absorption is discussed for the cases of normal incidence in the presence of a magnetic field (the Budden problem) and oblique incidence in the absence of a magnetic field.

Langmuir probe analysis for high density plasmas

High-density, radio-frequency plasmas used in semiconductor processing have progressed to densities n⩾5×1011 cm−3, where the methods used to interpret Langmuir probe characteristics in low-density (109–11 cm−3) plasma reactors are no longer valid. Though theory and computations for arbitrarily dense collisionless plasmas exist, they are difficult to apply in real time. A new parametrization and iteration scheme is given which permits rapid analysis of Langmuir probe data using these theories. However, at high n, measured ion saturation curves are shown which do not agree in shape with the “correct” theory, yielding anomalously high values of n. The discrepancy with independent measures of n, which can exceed a factor of 2, is believed to be caused by charge-exchange collisions well outside the sheath. Probe designs for avoiding this discrepancy are suggested.

Numerical computations for ion probe characteristics in a collisionless plasma

Numerical results in ranges of experimental interest are presented in graphical form for the potential profile around negatively biased spherical and cylindrical probes in a collisionless plasma and for the saturation ion current-voltage characteristics. The computations were made on the basis of the theories of Allen, Boyd and Reynolds (1957) for zero ion temperature and of Bernstein and Rabinowitz (1959) for monoenergetic ions. These theories are useful primarily for small probes. For large probes the theory of Lam (1964) is applicable. For completeness we have also included whatever curves are necessary for the use of Lams theory.

Physics of helicon discharges

Because of their high density, low‐pressure discharges ionized by helicon waves are being studied for their possible use in cluster tools for the fabrication of next‐generation computer chips. How helicon waves are related to whistler waves and waves in a plasma‐filled waveguide is explained, and the mystery of the high ionization efficiency is outlined. Experimental data on the waves and the equilibrium properties of the discharge are shown, and the status of our current understanding of the physical processes therein is summarized. The importance of kinetic effects and of a short‐wavelength mode arising at low magnetic fields is evaluated. Applications of helicon discharges to such diverse fields as plasma accelerators, microwave generators, and tokamak physics are illustrated. Low‐temperature plasma physics is often considered a discipline so different from high‐temperature plasma physics that there is little overlap, but these studies show that the techniques developed in fusion and space plasma physi...

Generalized theory of helicon waves. II. Excitation and absorption

Helicon waves in a plasma confined by a cylinder are treated. The undamped normal modes of the helicon (H) and Trivelpiece–Gould (TG) waves have distinctly different wave patterns at high magnetic fields but at low fields have similar patterns and therefore interact strongly. Damping of these modes, their excitation by antennas, and the rf plasma absorption efficiency are considered. Nonuniform plasmas are treated by solving a fourth-order ordinary differential equation numerically. A significant difference between this and earlier codes which divide the plasma into uniform shells is made clear. Excitation of the weakly damped H wave, followed by conversion to the strongly damped TG wave which leads to high helicon discharge efficiency, is examined for realistic density profiles. A reason for the greater heating efficiency of the m=+1 vs the m=−1 mode for axially peaked profiles is provided.