Miles M. Turner

Standing wave and skin effects in large-area, high-frequency capacitive discharges

Large-area capacitive discharges driven at frequencies higher than the usual industrial frequency of 13.56 MHz have attracted recent interest for materials etching and thin film deposition on large-area substrates. Standing wave and skin effects can be important limitations for plasma processing uniformity, which cannot be described by conventional electrostatic theory. An electromagnetic theory is developed for a discharge having two plates of radius R and separation 2l, which accounts for the propagation of surface and evanescent waves from the discharge edge into the centre and the role of capacitive and inductive fields in driving the power absorption. Examples of discharge fields are given having substantial standing wave and/or skin effects. The conditions for a uniform discharge without significant standing wave and skin effects are found to be, respectively, λ0>>2.6(l/s)1/2R and δ>>0.45(dR)1/2, where λ0 is the free space wavelength, s is the sheath width, δ = c/ωp is the collisionless skin depth, with c the speed of light and ωp the plasma frequency, and d = l-s is the plasma half-width. Taking the equality for these conditions for a discharge radius of 50 cm, plate separation of 4 cm, and sheath width of 2 mm, there is a substantial skin effect for plasma densities 1010 cm-3, and there is a substantial standing wave effect for frequencies f70 MHz.

Hysteresis and the E-to-H transition in radiofrequency inductive discharges

Typical inductive discharges, such as are used for plasma processing, exhibit two modes of operation: the true inductive discharge known as the H mode, and a weak capacitive discharge known as the E mode. Experimentally, the transition between these modes as the coil current is increased is clear and is marked by a large increase in discharge power, plasma density and optical emission occurring as the H mode appears. According to simple theory, this transition and the reverse transition occur at a single well defined current. In practice, this is usually not the case. The E-to-H transition occurs at a larger coil current than the H-to-E transition, and a range of currents between these values supports either E or H mode. This effect is called hysteresis. In this paper we show that hysteresis can be understood to arise from nonlinear effects, most notably in the electron power balance equation. We survey various mechanisms that can produce hysteresis and attempt to provide quantitative estimates of their significance.

Frequency coupling in dual frequency capacitively coupled radio-frequency plasmas

An industrial, confined, dual frequency, capacitively coupled, radio-frequency plasma etch reactor (Exelan®, Lam Research) has been modified for spatially resolved optical measurements. Space and phase resolved optical emission spectroscopy yields insight into the dynamics of the discharge. A strong coupling of the two frequencies is observed in the emission profiles. Consequently, the ionization dynamics, probed through excitation, is determined by both frequencies. The control of plasma density by the high frequency is, therefore, also influenced by the low frequency. Hence, separate control of plasma density and ion energy is rather complex.

Characterization of the E to H transition in a pulsed inductively coupled plasma discharge with internal coil geometry: bi-stability and hysteresis

Electrodeless radiofrequency discharges exhibit two modes of operation: a low-density mode in which the power is capacitively coupled to the plasma and which is known as the E-mode, and a higher density mode which is an inductive discharge known as the H-mode. The transition between these modes exhibits hysteresis, i.e. the E to H transition occurs at a different coil current than the reverse H to E transition. Recent theoretical results show that the hysteresis can be qualitatively understood in terms of electron power balance assuming that either the power dissipated or the power absorbed by the plasma electrons has a nonlinear dependence on the electron density. Experiments have been carried out to examine this hypothesis, both by characterizing steady-state E- and H-mode plasmas with a Langmuir probe, and by using a new approach consisting of measuring the internal plasma parameters in a pulsed discharge. In the latter case, the power is time modulated with increasing and decreasing power ramps. This approach allows us to investigate the hysteresis in detail and to study the dynamics of the transition. A number of time-resolved diagnostics including Langmuir probes, current and voltage sensors, optical emission and B-dot probes have been used.

Simulation benchmarks for low-pressure plasmas: Capacitive discharges

Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently developed particle-in-cell codes. We show that the results of these simulations are statistically indistinguishable, within bounds of uncertainty that we define. We, therefore, claim that the results of these simulations represent strong benchmarks, which can be used as a basis for evaluating the accuracy of other codes. These other codes could include other approaches than particle-in-cell simulations, where benchmarking could examine not just implementation accuracy and efficiency, but also the fidelity of different physical models, such as moment or hybrid models. We discuss an example of this kind in the Appendix. Of course, the methodology that we have developed can also be readily extended to a suite of benchmarks with coverage of a wider range of physical and chemical phenomena.

Collisionless heating in radio-frequency discharges: a review

A negative-charging electrophotographic photosensitive member comprising an aluminum-based substrate and a silicate film and a light-receiving layer in this order. The silicate film has a layer thickness of 0.5 nm to 15 nm and comprises at least aluminum atoms, silicon atoms and oxygen atoms. The light-receiving layer has at least a lower-part charge injection blocking layer formed of a non-single crystal silicon film comprising at least silicon atoms, nitrogen atoms and oxygen atoms, not doped with any impurities, a photoconductive layer formed of a non-single crystal silicon film comprising at least silicon atoms, an upper-part charge injection blocking layer formed of a non-single crystal silicon film comprising at least silicon atoms, carbon atoms and atoms belonging to the Group 13 of the periodic table, and a surface protective layer formed of a non-single crystal silicon film comprising at least silicon atoms and containing carbon atoms.

One-dimensional particle-in-cell simulation of a current-free double layer in an expanding plasma

A one-dimensional particle-in-cell code using Monte Carlo collision techniques (MCC/PIC) for both ions and electrons is used to simulate our earlier experimental results which showed that a current-free electric double layer (DL) can form in a plasma expanding along a diverging magnetic field. These results differ from previous experimental or simulation systems where the double layers are driven by a current or by imposed potential differences. Both experiment and simulation show accelerated ions with energies up to about 60 eV on the low potential side of the plasma. A new numerical method is added to the conventional PIC scheme to simulate inductive electron heating, as distinct from the more common capacitively driven simulations. A loss process is introduced along the axis of the simulation to mimic the density decrease along the axis of an expanding plasma in a diverging magnetic field. The results from the MCC/PIC presented here suggest that the expansion rate compared to the ionization frequency i...

Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions

The particle-in-cell method with Monte Carlo collisions is frequently used when a detailed kinetic simulation of a weakly collisional plasma is required. In such cases, one usually desires, inter alia, an accurate calculation of the particle distribution functions in velocity space. However, velocity space diffusion affects most, perhaps all, kinetic simulations to some degree, leading to numerical thermalization (i.e., relaxation of the velocity distribution toward a Maxwellian), and consequently distortion of the true velocity distribution functions, among other undesirable effects. The rate of such thermalization can be considered a figure of merit for kinetic simulations. This article shows that, contrary to previous assumption, the addition of Monte Carlo collisions to a one-dimensional particle-in-cell simulation seriously degrades certain properties of the simulation. In particular, the thermalization time can be reduced by as much as three orders of magnitude. This effect makes obtaining strictly converged simulation results difficult in many cases of practical interest.

Comparison of measurements and particle-in-cell simulations of ion energy distribution functions in a capacitively coupled radio-frequency discharge

The ion dynamics in the high-voltage sheath of a capacitively coupled radio-frequency plasma has been investigated using mass-resolved ion energy analysis in combination with a two-dimensional particle-in-cell (PIC) code. A symmetric confined discharge is designed allowing highly accurate comparisons of measured ion energy distribution functions in high-voltage sheaths with simulation results. Under the conditions investigated, the sheaths are not only collisional, but also chemically complex. This situation is common in applications but rare in laboratory experiments. Excellent agreement has been found for a hydrogen discharge benchmarking the code. Hydrogen is of particular interest since its light mass gives detailed insight into sheath dynamics, and an extensive database of collisional cross sections is available. The H3+ ion was found to be the dominant ion in the sheaths and the plasma bulk under most conditions investigated. H3+ exhibits the typical saddle-shaped ion energy distribution function in...

Measured and simulated electron energy distribution functions in a low-pressure radio frequency discharge in argon

We report a combined experimental and computational study of a low‐pressure radio frequency discharge in argon. We have determined the electron energy distribution function experimentally using a Langmuir probe system and by simulation using the particle in cell method. A close comparison of these data shows good agreement over pressures from 20 to 200 mTorr. This pressure range encompasses the putative transition from a stochastic to an ohmic electron heating mode [V. A. Godyak and R. B. Piejak, Phys. Rev. Lett. 65, 996 (1990)]. The simulation does show such a transition, and we agree with earlier estimates of the transition pressure.