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Electron Heating in Technological Plasmas
The etching of sub micrometer high-aspect-ratio (HAR) features into dielectric materials in low pressure radio frequency technological plasmas is limited by the accumulation of positive surface charges inside etch trenches. These are, at least partially, caused by highly energetic positive ions that are accelerated by the sheath electric field to high velocities perpendicular to the wafer. In contrast to these anisotropic ions, thermal electrons typically reach the electrode only during the sheath collapse and cannot penetrate deeply into HAR features to compensate the positive surface charges. This problem causes significant reductions of the etch rate and leads to deformations of the features due to ion deflection, i.e. the aspect ratio is limited. Here, we demonstrate that voltage waveform tailoring can be used to generate electric field reversals adjacent to the wafer during sheath collapse to accelerate electrons towards the electrode to allow them to penetrate deeply into HAR etch features to compensate positive surface charges and to overcome this process limitation. Based on 1D3V particle-in-cell/Monte Carlo collision simulations of a capacitively coupled plasma operated in argon at 1 Pa, we study the effects of changing the shape, peak-to-peak voltage, and harmonics’ frequencies of the driving voltage waveform on this electric field reversal as well as on the electron velocity and angular distribution function at the wafer. We find that the angle of incidence of electrons relative to the surface normal at the wafer can be strongly reduced and the electron velocity perpendicular to the wafer can be significantly increased by choosing the driving voltage waveform in a way that ensures a fast and short sheath collapse. This is caused by the requirement of flux compensation of electrons and ions at the electrode on time average in the presence of a short and steep sheath collapse.
A thorough understanding of the energy transfer mechanism from the electric field to electrons is of utmost importance for optimization and control of different plasma sources and processes. This mechanism, called electron power absorption, involves complex electron dynamics in electronegative capacitively coupled plasmas (CCPs) at low pressures, that are still not fully understood. Therefore, we present a spatio-temporally resolved analysis of electron power absorption in low pressure oxygen CCPs based on the momentum balance equation derived from the Boltzmann equation. Data are obtained from 1d3v Particle-In-Cell / Monte Carlo Collision simulations. In contrast to conventional theoretical models, which predict 'stochastic/collisionless heating' to be important at low pressure, we observe the dominance of Ohmic power absorption. In addition, there is an attenuation of ambipolar power absorption at low pressures due to the strong electronegativity, and the presence of electropositive edge regions in the discharge, which cause a high degree of temporal symmetry of the electron temperature within the RF period.
In low temperature plasmas, the interaction of the electrons with the electric field is an important current research topic that is relevant for many applications. Particularly, in the low pressure regime (≤10 Pa), electrons can traverse a distance that may be comparable to the reactor dimensions without any collisions. This causes “nonlocal,” dynamics which results in a complicated space- and time-dependence and a strong anisotropy of the distribution function. Capacitively coupled radio frequency (CCRF) discharges, which operate in this regime, exhibit extremely complex electron dynamics. This is because the electrons interact with the space- and time-dependent electric field, which arises in the plasma boundary sheaths and oscillates at the applied radio frequency. In this tutorial paper, the fundamental physics of electron dynamics in a low pressure electropositive argon discharge is investigated by means of particle-in-cell/Monte Carlo collisions simulations. The interplay between the fundamental plasma parameters (densities, fields, currents, and temperatures) is explained by analysis (aided by animations) with respect to the spatial and temporal dynamics. Finally, the rendered picture provides an overview of how electrons gain and lose their energy in CCRF discharges.
The electron power absorption dynamics in radio frequency driven micro atmospheric pressure capacitive plasma jets are studied based on experimental phase resolved optical emission spectroscopy and the computational particle in cell simulations with Monte Carlo treatment of collisions. The jet is operated at 13.56 MHz in He with different admixture concentrations of N2 and at several driving voltage amplitudes. We find the spatio-temporal dynamics of the light emission of the plasma at various wavelengths to be markedly different. This is understood by revealing the population dynamics of the upper levels of selected emission lines/bands based on comparisons between experimental and simulation results. The populations of these excited states are sensitive to different parts of the electron energy distribution function and to contributions from other excited states. Mode transitions of the electron power absorption dynamics from the Ω- to the Penning-mode are found to be induced by changing the N2 admixture concentration and the driving voltage amplitude. Our numerical simulations reveal details of this mode transition and provide novel insights into the operation details of the Penning-mode. The characteristic excitation/emission maximum at the time of maximum sheath voltage at each electrode is found to be based on two mechanisms: (i) a direct channel, i.e. excitation/emission caused by electrons generated by Penning ionization inside the sheaths and (ii) an indirect channel, i.e. secondary electrons emitted from the electrode due to the impact of positive ions generated by Penning ionization at the electrodes.
Single frequency, geometrically symmetric Radio-Frequency (RF) driven atmospheric pressure plasmas exhibit temporally and spatially symmetric patterns of electron heating, and consequently, charged particle densities and fluxes. Using a combination of phase-resolved optical emission spectroscopy and kinetic plasma simulations, we demonstrate that tailored voltage waveforms consisting of multiple RF harmonics induce targeted disruption of these symmetries. This confines the electron heating to small regions of time and space and enables the electron energy distribution function to be tailored.
Geometrically symmetric capacitively coupled oxygen plasmas are studied experimentally by optical emission spectroscopy and probe measurements as well as via numerical simulations using the kinetic Particle-in-Cell/Monte Carlo collision (PIC/MCC) approach. The experiments reveal that at a fixed pressure of 20 mTorr and a driving frequency of 13.56 MHz, the central electron density increases with an increased electrode gap, while the time averaged optical emission of atomic oxygen lines decreases. These results are reproduced and understood by the PIC/MCC simulations performed under identical conditions. The simulations show that the electron density increases due to a mode transition from the Drift-Ambipolar-mode to the α-mode induced by increasing the electrode gap. This mode transition is due to a drastic change of the electronegativity and the mean electron energy, which leads to the observed reduction of the emission intensity of an atomic oxygen line. The observed mode transition is also found to cause a complex non-monotonic dependence of the O 2 + ion flux to the electrodes as a function of the electrode gap. These fundamental results are correlated with measurements of the etch rate of amorphous carbon layers at different gap distances.
- Moritz Oberberg
- Jens Kallähn
- Peter Awakowicz
- Julian Schulze
The electrical asymmetry effect allows control of the discharge symmetry, the DC self-bias, and charged particle energy distribution functions electrically by driving a capacitive radio frequency discharge with multiple consecutive harmonics with fixed, but adjustable relative phases. Recently, Trieschmann et al (2013 J. Phys. D: Appl. Phys. 46 084016) and Yang et al (2017 Plasma Process. Polym. 14 1700087; 2018 Plasma Sources Sci. Technol. 27 035008) computationally predicted that the discharge symmetry can also be controlled magnetically via the magnetic asymmetry effect (MAE). By particle-in-cell simulations they demonstrated that a magnetic field, that is parallel to the electrodes and inhomogeneous in the direction perpendicular to the electrodes, induces a discharge asymmetry due to different ion densities adjacent to both electrodes. This, in turn, is predicted to lead to the generation of a DC self-bias as a function of the difference of the magnetic field at both electrodes. In this way the MAE should allow control of the mean ion energy at both electrodes as a function of the magnetic field configuration. Here, we present the first experimental investigation of the MAE. In a low pressure discharge operated in argon at 13.56 MHz, we use a magnetron-like magnetic field configuration at the powered electrode, which leads to an inhomogeneous profile of the magnetic field perpendicular to the electrodes. By measuring the DC self-bias and the ion flux-energy distribution function at the grounded electrode as a function of the magnetic field strength at the powered electrode, the driving voltage amplitude and the neutral gas pressure we experimentally verify the concept of the MAE and demonstrate this technology to be a powerful method to control the discharge symmetry and process relevant energy distribution functions.
We investigate the energy and angular distributions of the ions reaching the electrodes in low-pressure, capacitively coupled oxygen radio-frequency discharges. These distributions, as well as the possibilities of the independent control of the ion flux and the ion energy are analysed for different types of excitation: single- and classical dual-frequency, as well as valleys- and sawtooth-type waveforms. The studies are based on kinetic, particle-based simulations that reveal the physics of these discharges in great details. The conditions cover weakly collisional to highly collisional domains of ion transport via the electrode sheaths. Analytical models are also applied to understand the features of the energy and angular distribution functions.
- Sebastian Wilczek
- Jan Trieschmann
- Julian Schulze
- Thomas Mussenbrock
In simulation as well as analytical modeling studies of low-pressure capacitively coupled radio frequency (CCRF) discharges, the assumption of both a driving voltage source and a driving current source is commonly used. It is unclear, however, how and to what extent the choice of the mode of driving, that prescribes either a sinusoidal discharge voltage or a sinusoidal discharge current, itself defines the discharge dynamics that results from these studies. To address this issue, 1d3v cylindrical Particle-In-Cell/Monte Carlo collisions (PIC/MCC) simulations of asymmetric capacitively coupled radio frequency discharges are performed in the low pressure regime (p < 2 Pa). We study the nonlocal and nonlinear dynamics of these discharges on a nanosecond timescale. We find that the excitation of the plasma series resonance (PSR) in the voltage driven case strongly enhances the nonlinear electron power dissipation. However, this resonance is suppressed when a current source is used, because the excitation of harmonics in the RF current is not allowed. Consequently, significant differences between both driving sources are observed in the plasma density as well as in the electron and the power coupling dynamics. We conclude that caution is advised in comparisons between simulations and experiments, as in the former the discharge dynamics is partly defined by the method of driving of the plasma source, while in the latter the addressed resonance phenomena are inherently present at low pressures.
The behavior of a dual frequency capacitively coupled plasma (2f CCP) driven by 2.26 and 13.56 MHz radio frequency (rf) source is investigated using an approach that integrates a theoretical model and experimental data. The basis of the theoretical analysis is a time dependent dual frequency analytical sheath model that casts the relation between the instantaneous sheath potential and plasma parameters. The parameters used in the model are obtained by operating the 2f CCP experiment (2.26 MHz + 13.56 MHz) in argon at a working pressure of 50 mTorr. Experimentally measured plasma parameters such as the electron density, electron temperature, as well as the rf current density ratios are the inputs of the theoretical model. Subsequently, a convenient analytical solution for the output sheath potential and sheath thickness was derived. A comparison of the present numerical results is done with the results obtained in another 2f CCP experiment conducted by Semmler et al (2007 Plasma Sources Sci. Technol. 16 839). A good quantitative correspondence is obtained. The numerical solution shows the variation of sheath potential with the low and high frequency (HF) rf powers. In the low pressure plasma, the sheath potential is a qualitative measure of DC self-bias which in turn determines the ion energy. Thus, using this analytical model, the measured values of the DC self-bias as a function of low and HF rf powers are explained in detail.
- Frederik Schmidt
- Julian Schulze
- Erik V. Johnson
- Thomas Mussenbrock
Customized voltage waveforms composed of a number of frequencies and used as the excitation of radio-frequency plasmas can control various plasma parameters such as energy distribution functions, homogeneity of the ion flux, or ionization dynamics. So far this technology, while being extensively studied in academia, has yet to be established in applications. One reason for this is the lack of a suitable multi frequency matching network that allows for maximum power absorption for each excitation frequency that is generated and transmitted via a single broadband amplifier. In this work, a method is introduced for designing such a network based on network theory and synthesis. Using this method, a circuit simulation is established that connects an exemplary matching network to an equivalent circuit plasma model of a capacitive radio-frequency discharge. It is found that for a range of gas pressures and number of excitation frequencies the matching conditions can be satisfied, which proves the functionality and feasibility of the proposed concept. Based on the proposed multi frequency impedance matching, tailored voltage waveforms can be used at an industrial level.
We investigate the electrical asymmetry effect (EAE) and the current dynamics in a geometrically asymmetric capacitively coupled radio frequency plasma driven by multiple consecutive harmonics based on a nonlinear global model. The discharge symmetry is controlled via the EAE, i.e., by varying the total number of harmonics and tuning the phase shifts ðh k Þ between them. Here, we systematically study the EAE in a low pressure (4 Pa) argon discharge with different geometrical asymmetries driven by a multifrequency rf source consisting of 13.56 MHz and its harmonics. We find that the geometrical asymmetry strongly affects the absolute value of the DC self-bias voltage, but its functional dependence on h k is similar at different values of the geometrical asymmetry. Also, the values of the DC self-bias are enhanced by adding more consecutive harmonics. The voltage drop across the sheath at the powered and grounded electrode is found to increase/decrease, respectively, with the increase in the number of harmonics of the fundamental frequency. For the purpose of validating the model, its outputs are compared with the results obtained in a geometrically and electrically asymmetric 2f capacitively coupled plasmas experiment conducted by Schuengel et al. [J. Appl. Phys. 112, 053302 (2012)]. Finally, we study the self-excitation of nonlinear plasma series resonance oscillations and its dependence on the geometrical asymmetry as well as the phase angles between the driving frequencies. Published by AIP Publishing. https://doi.
Power absorption by electrons from the space- and time-dependent electric field represents the basic sustaining mechanism of all radio-frequency driven plasmas. This complex phenomenon has attracted significant attention. However, most theories and models are, so far, only able to account for part of the relevant mechanisms. The aim of this work is to present an in-depth analysis of the power absorption by electrons, via the use of a moment analysis of the Boltzmann equation without any ad-hoc assumptions. This analysis, for which the input quantities are taken from kinetic, particle based simulations, allows the identification of all physical mechanisms involved and an accurate quantification of their contributions. The perfect agreement between the sum of these contributions and the simulation results verifies the completeness of the model. We study the relative importance of these mechanisms as a function of pressure, with high spatial and temporal resolution, in an electropositive argon discharge. In contrast to some widely accepted previous models we find that high space- and time-dependent ambipolar electric fields outside the sheaths play a key role for electron power absorption. This ambipolar field is time-dependent within the RF period and temporally asymmetric, i.e., the sheath expansion is not a 'mirror image' of the sheath collapse. We demonstrate that this time-dependence is mainly caused by a time modulation of the electron temperature resulting from the energy transfer to electrons by the ambipolar field itself during sheath expansion. We provide a theoretical proof that this ambipolar electron power absorption would vanish completely, if the electron temperature was constant in time. This mechanism of electron power absorption is based on a time modulated electron temperature, markedly different from the Hard Wall Model, of key importance for energy transfer to electrons on time average and, thus, essential for the generation of capacitively coupled plasmas.
Radio frequency (rf) discharges are widely used for technological applications. Despite this, power dissipation mechanisms in these discharges are not yet fully understood. The limited understanding is mainly caused by the complexity of underlying phenomena and very restricted experimental access. Recent advances in phase resolved optical emission spectroscopy (PROES) in combination with adequate modeling of the population dynamics of excited states allow deeper insight into underlying fundamental processes. This paper discusses the application of PROES in a variety of rf‐discharges, such as: capacitively coupled plasmas (CCP), dual‐frequency CCP (2f‐CCP), inductively coupled plasmas (ICP), and magnetic neutral loop discharges (NLD).
Low pressure inductively coupled plasmas (ICP) operated at 27.12 MHz with capacitive substrate biasing (CCP) at 13.56 MHz are investigated by Phase Resolved Optical Emission Spectroscopy, voltage, and current measurements . Three coupling mechanisms are found potentially limiting the separate control of ion energy and flux: (i) Sheath heating due to the substrate biasing affects the electron dynamics even at high ratios of ICP to CCP power. At fixed CCP power, (ii) the sub-strate sheath voltage and (iii) the amplitude as well as frequency of Plasma Series Resonance (PSR) oscillations of the RF current are affected by the ICP power.
Unlike α- and γ-mode operation, electrons accelerated by strong drift and ambipolar electric fields in the plasma bulk and at the sheath edges are found to dominate the ionization in strongly electronegative discharges. These fields are caused by a low bulk conductivity and local maxima of the electron density at the sheath edges, respectively. This drift-ambipolar mode is investigated by kinetic particle simulations, experimental phase-resolved optical emission spectroscopy, and an analytical model in CF(4). Mode transitions induced by voltage and pressure variations are studied.