Ralf Peter Brinkmann

Nonlinear electron resonance heating in capacitive radio frequency discharges

Technological processing plasmas are frequently operated at relatively low gas pressure (<10Pa). A characteristic feature of this regime is that collisions of the electrons with the atoms or molecules of the neutral background are relatively rare, and the so-called collisional or Ohmic heating ceases to be an effective mechanism of energy deposition into the plasma. Experiments indicate that at low pressure an alternative mechanism of electron heating exists which can sustain the plasma. Despite 30years of intense research, the exact nature of this “anomalous” heating mechanism is still under discussion. The two standard models are known as “stochastic heating” and “pressure heating,” respectively. This work proposes a third explanation of anomalous electron heating and suggests that, in the last analysis, all three mechanisms may contribute to the observed effect.

Stochastic heating in asymmetric capacitively coupled RF discharges

Electron dynamics in a strongly asymmetric capacitively coupled radio-frequency (RF) discharge at low pressures is investigated by a combination of various diagnostics, analytical models and simulations. Electric fields in the sheath are measured phase and space resolved using fluorescence dip spectroscopy in krypton. The results are compared with a fluid sheath model. Experimentally obtained input parameters are used for the model. The excitation caused by beam-like highly energetic electrons is measured by phase resolved optical emission spectroscopy (PROES) and compared with the results of a hybrid Monte Carlo model based on the electric field resulting from the sheath model. The plasma itself is characterized by Langmuir probe measurements in terms of electron density, electron mean energy and electron energy distribution function (EEDF). The RF voltage and the current to the chamber wall are measured in parallel. At low pressures the plasma series resonance (PSR) effect is observed. It leads to high frequency oscillations of the current (non-sinusoidal RF current waveforms) and, consequently, to a faster sheath expansion. The measured current is compared with an analytical PSR model. Another analytical model using experimentally obtained input parameters determines the influence of beams of highly energetic electrons on the time averaged isotropic EEDF as measured by Langmuir probes. The main result is the observation of beams of highly energetic electrons during the sheath expansion phase, that are enhanced by the PSR effect. The paper shows that the nature of stochastic heating is closely related to electron beams and the PSR effect.

Electron beams in asymmetric capacitively coupled radio frequency discharges at low pressures

The generation of directed energetic electrons by the expanding sheath is observed in asymmetric capacitively coupled radio frequency discharges at low pressures (≤ 1 Pa) in different gases. The phenomenon of such electron beams is investigated by a combination of experimental diagnostics, an analytical model and simulations. At sufficiently low pressures multiple reflections of electron beams at the plasma boundaries are observed. An analytical model shows how these beams lead to an enhanced high energy tail of the electron energy distribution function. Thus, stochastic heating is closely related to electron beams.

The multipole resonance probe: A concept for simultaneous determination of plasma density, electron temperature, and collision rate in low-pressure plasmas

A diagnostic concept is presented which enables the simultaneous determination of plasma density, electron temperature, and collision rate in low-pressure gas discharges. The proposed method utilizes a radio-frequency driven probe of particular spherical design which is immersed in the plasma to excite a family of spatially bounded surface resonances. An analysis of the measured absorption spectrum S(ω) of the probe provides information on the distribution of the plasma in its vicinity, from which the values of the plasma parameters can be inferred. In its simplest realization, the probe consists of two dielectrically shielded, conducting hemispheres, which are symmetrically driven by an radio-frequency source, and the excited resonances can be classified as multipole fields, which allows an analytical evaluation of the measured signal. The proposed method is robust, calibration free, economical, and can be used for ideal and reactive plasmas alike.

The effects of nonlinear series resonance on Ohmic and stochastic heating in capacitive discharges

The flow of electron and ion conduction currents across a nonlinear capacitive sheath to the electrode surface self-consistently sets the dc bias voltage across the sheath. We incorporate these currents into a model of a homogeneous capacitive sheath in order to determine the enhancement of the Ohmic and stochastic heating due to self-excitation of the nonlinear series resonance in an asymmetric capacitive discharge. At lower pressures, the series resonance can enhance both the Ohmic and stochastic heating by factors of 2–4, with the Ohmic heating tending to zero as the pressure decreases. The model was checked, for a particular set of parameters, by a particle-in-cell (PIC) simulation using the homogeneous sheath approximation, giving good agreement. With a self-consistent Child-law sheath, the PIC simulation showed increased heating, as expected, whether the series resonance is important or not.

The lock-on effect in electron-beam-controlled gallium arsenide switches

The authors analyze the lock-on effect, which is the inability of photoconductive or electron-beam-controlled semiconductor switches to recover to their initial hold-off voltages following the application of the laser or electron-beam pulse, if the applied voltage exceeds a certain value. For GaAs this threshold voltage corresponds to average electric fields in the range from 4 to 12 kV/cm. Experimental results on semi-insulating GaAs switches indicate that the corresponding lock-on current after e-beam irradiation is identical with the steady-state dark current. The highly resistive state of the switch before e-beam irradiation is shown to be a transient phase towards the much lower steady-state dark resistance, with a duration which depends on the impurity content of the switch material and the applied voltage. The irradiation of the GaAs samples with electrons or photons causes an acceleration of this temporal evolution; at sufficiently high laser or e-beam intensities, lock-on of the dark current after termination of the driving ionization source is observed. Based on the experimental results, a model is developed which describes the lock-on effect in terms of double injection and carrier trapping in deep intraband levels. The model explains the major characteristics of the lock-up effects and is supported by the qualitative agreement of the calculated current-voltage curves with the experimental data. >

The multipole resonance probe: characterization of a prototype

The multipole resonance probe (MRP) was recently proposed as an economical and industry compatible plasma diagnostic device (Lapke et al 2008 Appl. Phys. Lett. 93 051502). This communication reports the experimental characterization of a first MRP prototype in an inductively coupled argon/nitrogen plasma at 10?Pa. The behavior of the device follows the predictions of both an analytical model and a numerical simulation. The obtained electron densities are in excellent agreement with the results of Langmuir probe measurements.

Electric field reversals in the sheath region of capacitively coupled radio frequency discharges at different pressures

Electric field reversals in single and dual-frequency capacitively coupled radio frequency discharges are investigated in the collisionless (1Pa) and the collisonal (65Pa) regimes. Phase resolved optical emission spectroscopy is used to measure the excitation of the neutral background gas caused by the field reversal during sheath collapse. The collisionless regime is investigated experimentally in asymmetric neon and hydrogen single frequency discharges operated at 13.56MHz in a GEC reference cell. The collisional regime is investigated experimentally in a symmetric industrial dual-frequency discharge operated at 1.937 and 27.118MHz. The resulting spatio-temporal excitation profiles are compared with the results of a fluid sheath model in the single frequency case and a particle-in-cell/Monte Carlo simulation in the dual-frequency case. The results show that field reversals occur in both regimes. An analytical model gives an insight into the mechanisms causing the reversal of the electric field. In the dual-frequency case a qualitative comparison between the electric fields resulting from the PIC simulation and from the analytical model is performed. The field reversal seems to be caused by different mechanisms in the respective regimes. In the collisionless case it is caused by electron inertia, whereas in the collisional regime it is caused by a combination of the low mobility of electrons due to collisions and electron inertia. Finally, the field reversal during the sheath collapse seems to be a general source for energy gain of electrons in both single and dual-frequency discharges. (Some figures in this article are in colour only in the electronic version)

Beyond the step model: Approximate expressions for the field in the plasma boundary sheath

The transition from quasineutrality to charge depletion is one of the characteristic features of the plasma boundary sheath. For modeling purposes, this transition is often described in terms of the so-called step model which assumes a sharp transition point s (electron step) where the electron density ne drops from a value equal to the ion density ni (in the bulk, x>s) to a value of zero (in the sheath, x<s). Inserted into Poisson’s equation, the step model yields an expression for the field which is realistic deep in the sheath (for x≪s) but fails to merge correctly into the ambipolar field of the bulk. This work considers the transition from quasineutrality to charge depletion more rigorously. Within the framework of asymptotic scale analysis, a family of field approximations is derived which, in the limit of weak spatial ion density variation ∂ni∕∂x≪ni∕λD, exhibit convergence to the exact solution of the Boltzmann–Poisson equation. The first of the approximations recovers only the step model. Higher o...

Modeling and simulation of the plasma absorption probe

The plasma absorption probe (PAP) was invented as an economical and robust diagnostic device to determine the electron density distribution in technical plasmas. It consists of a small antenna enclosed by a dielectric tube which is immersed in the plasma. A network analyzer feeds a rf signal to the antenna and displays the frequency dependence of the power absorption. From the absorption spectrum the value of the electron density is calculated. The original evaluation formula was based on the dispersion relation of plasma surface waves propagating along an infinite dielectric cylinder. In this letter the authors present the analysis of a less idealized configuration. The calculated spectra are in good qualitative agreement with their experimental counterparts, but differ considerably from those predicted by the surface wave ansatz. An evaluation scheme which takes our findings into account will improve the performance of the PAP technique further.