Dual Frequency Capacitive Discharges Research Articles

Acceleration of particle-in-cell simulations using sparse grid algorithms. I. Application to dual frequency capacitive discharges

The use of sparse particle-in-cell (PIC) algorithms to accelerate the standard explicit PIC scheme has recently been successfully applied in the context of single-frequency capacitively coupled plasma discharges [Garrigues et al., J. Appl. Phys. 129, 153303 (2021)]. We have extended the sparse PIC scheme to model dual-frequency capacitive discharges. Comparisons between standard and sparse PIC algorithms show that the plasma properties as well as the electron and ion distribution functions can be retrieved with a maximum error of 2%. This work opens the interest of using the sparse PIC algorithm to perform 2D and 3D simulations under real operating conditions of capacitively coupled plasma discharges.

Analytical plasma impedance model of dual frequency capacitive discharges with ion dynamics

Based on a fluid simulation, an analytical equivalent circuit model was developed for collisional plasmas with dual frequency (DF) excitation. Primary focus is on a fully collisional sheath and a low frequency (LF) below the ion plasma frequency. In the analytical model, the high frequency (HF) component is expressed as a series RC circuit, which matches the classical result for the limit of single frequency radio frequency discharges. The LF circuit is expressed as a parallel RC circuit to consider the response of ions to the LF voltage. The model requires three main parameters: the magnitudes of the HF and LF voltages, which are known during discharge operation and the space and time averaged ion density, which is in general unknown and needs to be determined by other means. Explicit formulas for the calculation of the HF and LF impedances are provided. Good agreement is found between the new analytical model and the fluid simulation. It is worth noting that previously published analytical models fail to reproduce the impedances, predominantly because the dynamic ion behavior and the parallel nature of the resulting ion current in respect to the LF displacement current are not considered. A practical application of the model is the calculation of the ion density in the discharge from measured impedances. For this purpose both the LF and the HF impedances can be used. A comparison of the densities estimated from the different impedances and the average density in the simulation show again good agreement.

Electron Information in Single- and Dual-Frequency Capacitive Discharges at Atmospheric Pressure

Determining the electron properties of weakly ionized gases, particularly in a high electron-neutral collisional condition, is a nontrivial task; thus, the mechanisms underlying the electron characteristics and electron heating structure in radio-frequency (rf) collisional discharges remain unclear. Here, we report the electrical characteristics and electron information in single-frequency (4.52 MHz and 13.56 MHz) and dual-frequency (a combination of 4.52 MHz and 13.56 MHz) capacitive discharges within the abnormal α-mode regime at atmospheric pressure. A continuum radiation-based electron diagnostic method is employed to estimate the electron density (ne) and temperature (Te). Our experimental observations reveal that time-averaged ne (7.7–14 × 1011 cm−3) and Te (1.75–2.5 eV) can be independently controlled in dual-frequency discharge, whereas such control is nontrivial in single-frequency discharge, which shows a linear increase in ne and little to no change in Te with increases in the rf input power. Furthermore, the two-dimensional spatiotemporal evolution of neutral bremsstrahlung and associated electron heating structures is demonstrated. These results reveal that a symmetric structure in electron heating becomes asymmetric (via a local suppression of electron temperature) as two-frequency power is simultaneously introduced.

Comparison of plasma excitation, ionization, and energy influx in single and dual frequency capacitive discharges

Argon (Ar) plasma characteristics in a single and dual-frequency (DF), capacitively coupled plasma processing system are compared for drive frequencies 13.56 MHz, 320 MHz and their mixture as dual frequencies (DF). We present frequency dependent changes that occur in discharges in terms of plasma parameters such as plasma density, electron temperature, electron energy distribution function, optical emission, gas temperature, and metastable Ar density in a pressure range of 10−150 mTorr. Additionally, this work also presents the formulation and characterization of energy fluxes from plasma to a substrate/probe during the plasma generation. By variation of the operating pressure and plasma excitation frequency, the different contributions originating from the kinetic energy, the recombination of charge carriers such as electrons and ions at the surface along with the contributions from the neutral and excited species are determined. Data reveals that Ar metastable density in low-frequency radio frequency (RF) plasma is not a strong function of operating pressure even though plasma ionization increases with pressure. However, in the case of high-frequency and DF, the excitation of Ar metastable decreases and ionization increases due to enhanced collisions and efficient electron-neutral momentum/energy transfer. Also, data reveals that energy flux in the low-frequency RF plasmas is very high compared to that of high-frequency and DF operations.

Nonlinear series resonance and standing waves in dual-frequency capacitive discharges

It is well-known that the nonlinear series resonance in a high frequency capacitive discharge enhances the electron power deposition and also creates standing waves which produce radially center-high rf voltage profiles. In this work, the dynamics of series resonance and wave effects are examined in a dual-frequency driven discharge, using an asymmetric radial transmission line model incorporating a Child law sheath. We consider a cylindrical argon discharge with a conducting electrode radius of 15 cm, gap length of 3 cm, with a base case having a 60 MHz high frequency voltage of 250 V and a 10 MHz low frequency voltage of 1000 V, with a high frequency phase shift between the two frequencies. For this phase shift there is only one sheath collapse, and the time-averaged spectral peaks of the normalized current density at the center are mainly centered on harmonic numbers 30 and 50 of the low frequency, corresponding to the first standing wave resonance frequency and the series resonance frequency, respectively. The effects of the waves on the series resonance dynamics near the discharge center give rise to significant enhancements in the electron power deposition, compared to that near the discharge edge. Adjusting the phase shift from π to 0, or decreasing the low frequency from 10 to 2 MHz, results in two or more sheath collapses, respectively, making the dynamics more complex. The sudden excitation of the perturbed series resonance current after the sheath collapse results in a current oscillation amplitude that is estimated from analytical and numerical calculations. Self-consistently determining the dc bias and including the conduction current is found to be important. The subsequent slow time variation of the high frequency oscillation is analyzed using an adiabatic theory.

Modeling of Single and Dual Frequency Capacitive Discharge in Argon Hydrogen Mixture − Dynamic Effects and Ion Energy Distribution Functions

Single (SF) and dual frequency capacitively coupled plasma (DF CCP) in (0–50%) H2/Ar mixtures was studied numerically with 1D hybrid (Particle‐in‐cell with Monte Carlo Collision + fluid) model. In SF (81 MHz) discharge the effect of hydrogen dilution is studied for the fixed discharge input power. Mechanisms of the plasma density decrease and variation of ions composition with H2 percentage are discussed. The effect of low‐frequency voltage on plasma density, ions composition, ions fluxes, and ions energy was studied in DF CCP (1.76–81 MHz) discharge in 5% H2/Ar gas mixture at low (20 mTorr) and high (100 mTorr) pressures.

Investigation of wave emission phenomena in dual frequency capacitive discharges using particle-in-cell simulation

Dual frequency capacitively coupled discharges are widely used during fabrication of modern-day integrated circuits, because of low cost and robust uniformity over broad areas. At low pressure, stochastic or collisionless electron heating is important in such discharges. The stochastic heating occurs adjacent to the sheath edge due to energy transfer from the oscillating high voltage electron sheath to electrons. The present research discusses evidence of wave emission from the sheath in such discharges, with a frequency near the electron plasma frequency. These waves are damped very promptly as they propagate away from the sheath towards the bulk plasma, by Landau damping or some related mechanism. In this work, the occurrence of strong wave phenomena during the expanding and collapsing phase of the low frequency sheath has been investigated. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. The characteristics of waves in the dual-frequency case are entirely different from the single-frequency case studied in earlier works. The existence of a field reversal phenomenon, occurring several times within a lower frequency period in the proximity of the sheath is also reported. Electron trapping near to the field reversal regions also occurs many times during a lower frequency period. The emission of waves is associated with these field reversal regions. It is observed that the field reversal and electron trapping effects appear under conditions typical of many recent experiments, and are consequently of much greater practical interest than similar effects in single frequency discharges, which occur only under extreme conditions that are not usually realized in experiments.

Critical evaluation of analytical models for stochastic heating in dual-frequency capacitive discharges

Dual-frequency capacitive discharges are widespread in the semiconductor industry and are used, for example, in etching of semiconductor materials to manufacture microchips. In low-pressure dual radio-frequency capacitive discharges, stochastic heating is an important phenomenon. Recent theoretical work on this problem using several different approaches has produced results that are broadly in agreement insofar as scaling with the discharge parameters is concerned, but there remains some disagreement in detail concerning the absolute size of the effect for the case of dual-frequency capacitive discharges. In this work, we investigate the dependence of stochastic heating on various discharge parameters with the help of particle-in-cell (PIC) simulation. The dual-frequency analytical models are in fair agreement with PIC results for values of the low-frequency current density amplitude Jlf (or dimensionless control parameter Hlf ∼ 5) typical of many modern experiments. However, for higher values of Jlf (or higher Hlf), new physical phenomena (like field reversal, reflection of ions, etc) appear and the simulation results deviate from existing dual-frequency analytical models. On the other hand, for lower Jlf (or lower Hlf) again the simulation results deviate from analytical models. So this research work produces a relatively extensive set of simulation data that may be used to validate theories over a wide range of parameters.

Dual frequency capacitive plasmas in Fe and Ni sputter applications: correlation of discharge properties on thin film properties

Dual frequency capacitively coupled plasmas (CCPs) are widely used in (large area) etching and plasma enhanced chemical vapor deposition processes. However, applications in physical vapor deposition (PVD) are still sparse due to the well-established dc magnetron cathode discharges. Nevertheless, there exist critical applications such as ferromagnetic or ceramic thin film deposition which are difficult to handle even for dc magnetron systems. For these materials systems dual frequency CCPs pose a good alternative, because for insulators charging can be avoided and for ferromagnetic materials the target thickness becomes independent of the magnetron configuration at comparable deposition rates.In this work we investigate two separate subjects. First, in dual frequency capacitive discharges a complex coupling of the applied excitation frequencies can be observed, which from a plasma parameter point of view limits the separability of ion flux (usually controlled by frequencies >60 MHz) and ion bombarding energy (usually controlled by frequency <15 MHz) onto the sputter target. By performing deposition experiments it was found that by following simple tuning guidelines a very good degree of separability is achievable. Additionally, the deposition homogeneity is not affected.Second, we correlate the growth conditions with crystalline and magnetic properties as well as the degree of O content for Fe and Ni films. Therefore, we applied different signals as a substrate bias to influence thin film growth. It was found that the crystalline and magnetic properties can be influenced for both Fe and Ni films but is more pronounced for Ni.

Effect of Electron Heating Mode on Charge-Up Damage in Dual-Frequency Capacitive Discharges

In dual-frequency capacitive discharges, the effect of electron heating mode on charge-up damage is investigated through a 3-D charge-up simulator coupled with a 1-D particle-in-cell Monte Carlo collision simulation. The local charge-up damage on the trench decreases as the electron heating mode is changed from collisionless to collisional heating.

Electron heating and the electrical asymmetry effect in dual-frequency capacitive CF4 discharges

The electron heating and the electrical asymmetry effect (EAE) in electronegative dual-frequency capacitive CF4 discharges are investigated by particle-in-cell simulations and analytical modeling. One electrode is driven at 13.56 and 27.12 MHz with fixed but adjustable phase shift, θ, between the driving harmonics. First, the electron heating and ionization rates are studied, space and time resolved, for different phase shifts and pressures. The results are compared with those obtained for an electropositive gas (argon). In contrast to classical α- or γ-mode operation, we observe the electron heating and ionization rates to be high inside the bulk. This bulk heating mode is a consequence of the high electronegativity of CF4 discharges, where the conductivity in the bulk is low due to the low density of electrons. Thus, a high electric field builds up to drive the RF current through the bulk causing a high electron mean energy and ionization rate in the discharge center. Second, we investigate the consequences of the bulk heating on the EAE. We focus on the electrical generation of a dc self-bias as a function of θ and the quality of the separate control of the ion mean energy and flux at the electrodes by tuning θ. Compared with argon discharges the high voltage drop across the plasma bulk and the specific ionization dynamics affect the bias generation and the separate control of ion properties. These effects are described and explained by an analytical model.

The effect of secondary electrons on the separate control of ion energy and flux in dual-frequency capacitively coupled radio frequency discharges

Dual-frequency capacitive discharges are used to separately control the mean ion energy, ε¯ion, and flux, Γion, at the electrodes. We study the effect of secondary electrons on this separate control in argon discharges driven at 2+27 MHz at different pressures using Particle in Cell simulations. For secondary yield γ≈0, Γion decreases as a function of the low frequency voltage amplitude due to the frequency coupling, while it increases at high γ due to the effective multiplication of secondary electrons inside the sheaths. Therefore, separate control is strongly limited. ε¯ion increases with γ, which might allow an in situ determination of γ-coefficients.

The influence of the relative phase between the driving voltages on electron heating in asymmetric dual frequency capacitive discharges

The influence of the relative phase between the driving voltages on electron heating in asymmetric phase-locked dual frequency capacitively coupled radio frequency plasmas operated at 2 and 14 MHz is investigated. The basis of the analysis is a nonlinear global model with the option to implement a relative phase between the two driving voltages. In recent publications it has been reported that nonlinear electron resonance heating can drastically enhance the power dissipation to electrons at moments of sheath collapse due to the self-excitation of nonlinear plasma series resonance (PSR) oscillations of the radio frequency current. This work shows that depending on the relative phase of the driving voltages, the total number and exact moments of sheath collapse can be influenced. In the case of two consecutive sheath collapses a substantial increase in dissipated power compared with the known increase due to a single PSR excitation event per period is observed. Phase resolved optical emission spectroscopy (PROES) provides access to the excitation dynamics in front of the driven electrode. Via PROES the propagation of beam-like energetic electrons immediately after the sheath collapse is observed. In this work we demonstrate that there is a close relation between moments of sheath collapse, and thus excitation of the PSR, and beam-like electron propagation. A comparison of simulation results to experiments in a single and dual frequency discharge shows good agreement. In particular the observed influence of the relative phase on the dynamics of a dual frequency discharge is described by means of the presented model. Additionally, the analysis demonstrates that the observed gain in dissipation is not accompanied by an increase in the electrode's dc-bias voltage which directly addresses the issue of separate control of ion flux and ion energy in dual frequency capacitively coupled radio frequency plasmas.

Dual-frequency capacitive radiofrequency discharges: effect of low-frequency power on electron density and ion flux

The dependence of electron density and ion flux on radiofrequency (RF) power has been measured in a 2 + 27 MHz dual-frequency capacitive discharge with silicon electrodes at 6.7 Pa gas pressure. In Ar/O2 mixtures the electron density and the ion flux vary in a very similar way (i.e. their ratio, υ, is constant), in good agreement with the simple electropositive transport theory. Both 27 and 2 MHz RF powers have a significant effect on the plasma density and the ion flux. The effect of the 2 MHz power is likely a combination of enhanced plasma heating by dual-frequency excitation and ionization caused by secondary electron beams, which are known to be produced efficiently at oxidized silicon surfaces. In contrast, in Ar/C4F8/O2 mixtures such as those used for industrial dielectric etching, υ is always bigger than the theoretical electropositive value, and becomes very high when the ratio of 2 to 27 MHz power is high. Under these conditions the electron density is very small, whereas the ion flux remains considerable. We attribute the increased plasma transport to the presence of a significant density of F− negative ions, combined with increased penetration of the 2 MHz electric field into the plasma bulk at high 2/27 MHz power ratios.

Role of low-frequency power in dual-frequency capacitive discharges

Changes in plasma characteristics depending on low-frequency power in dual-frequency capacitive discharges were found from the measurement of electrical characteristics and electron energy probability functions. It is shown that as the low-frequency (2 MHz) power increases for the fixed high-frequency (27.12 MHz) current, the ion bombardment energy, and the ion flux onto the electrode increase simultaneously. It is also shown that the coupling between the low-frequency power and the ion flux originates from change in electron heating mechanisms when varying the low-frequency power. Depending on the discharge pressure, changes in the collisional electron heating in the bulk plasma and participation of the secondary electron emission in the ionization process are observed.

Temporal structure of electron heating in asymmetric single-frequency and dual-frequency capacitive discharges

The power dissipation in asymmetric capacitively coupled low-pressure plasmas can be drastically enhanced by the self-excitation of collective resonances. This applies to both Ohmic heating, which is related to collisions of electrons with neutrals, and stochastic heating which reflects the energy transfer from the oscillating plasma boundary sheath to the electrons. This work studies the phase-resolved structure of the power dissipation in asymmetric single-frequency and dual-frequency discharges on the basis of a self-consistent global model. A resonance-free global model (which represents the “traditional” scenario of the heating process) is consulted for comparison. It is shown that the energy dissipation in asymmetric capacitive discharges is enhanced around the moment of the sheath collapse but assumes the nonresonant value when the sheath extension is large. In the dual-frequency case, the effect is synchronized with the low-frequency cycle but strongly dependent on the value of the high-frequency power.

Electron Kinetic Property of a Magnetized Dual-Frequency Capacitively-Coupled Plasma

Spatially resolved electron-energy-distribution functions (EEPFs) in a magnetized dual-frequency (60 and 2 MHz) capacitive discharge are numerically investigated by using one-dimensional particle-in-cell/Monte Carlo collision simulations. It is shown that the electron kinetic property of the EEPFs of the total energy in different spatial positions changes from being nonlocal to local by the magnetic field. Though the nonlocal property of the electrons between the discharge center and the vicinity of the high-frequency electrode disappears for a magnetic field of 100 G, the nonlocal property of the low-energy electrons is nearly conserved between the discharge center and the vicinity of the low-frequency electrode due to the secondary electrons emitted from the LF electrode. [1] S. J. You and H. Y. Chang, Phys. Plasmas 13, 043503 (2006)

Nonlinear dynamics of dual frequency capacitive discharges: a global model matched to an experiment

The dynamics of dual frequency capacitively coupled plasmas (2f-CCPs) is investigated using an approach that integrates theoretical insight and experimental data. Basis of the analysis is a recently published model which casts the high-frequency behavior of asymmetric 2f-CCPs in terms of a nonlinear second-order differential equation, or equivalently, a lumped element equivalent circuit (Mussenbrock et al 2006 Phys. Plasmas 13 083501). The model comprises a nonlinear capacitor (the electrode boundary sheath), a lossy inductance (electron inertia and Ohmic losses in the bulk), a blocking capacitor and two ideal voltage sources in series (the 2f excitation). In contrast to Mussenbrock et al (2006 Phys. Plasmas 13 083501) which conducted a general parameter study, the current work bases the choice of its model parameters on the data obtained by an actual 2f-CCP experiment conducted by Semmler et al (2007 Plasma Sources Sci. Technol. 16 839, and 2008 private communication). A good quantitative correspondence is obtained. The analysis shows that the system is governed by a nonlinear interaction of the applied RF with the inner dynamics of the discharge, particularly with the collective oscillation mode known as the plasma series resonance (PSR). With respect to the power dissipation, two distinct paths can be identified which contribute in approximately equal parts. The first path is non-resonant and corresponds to the traditional picture of 2f-CCPs; the second path is resonant and identical with the mechanism of nonlinear electron resonance heating (NERH) proposed by Mussenbrock et al (2006 Phys. Plasmas 13 083501, 2006 Appl. Phys. Lett. 88 151503). The results change the understanding of 2f-CCPs considerably.

Particle simulation of a magnetically enhanced dual-frequency capacitively coupled plasma

One-dimensional particle-in-cell/Monte Carlo simulations have been carried out to investigate the magnetic field effects on the asymmetric dual-frequency (27 and 2 MHz) capacitive discharge. Variations of the plasma characteristics such as plasma density, electrical property and ion-energy-distribution functions (IEDFs) for the various magnetic fields are examined. The increase in the magnetic field up to a few tens of gauss is found to increase the width of the IEDF and the plasma density. However, for a larger magnetic field less than 125 G, the width of the IEDF is found to be continuously decreasing with the reduction of the high-frequency-averaged sheath potential, while the plasma density increases.

Electron heating mechanisms in dual-frequency capacitive discharges

We discuss electron heating mechanisms in the sheath regions of dual-frequency capacitive discharges, with the twin aims of identifying the dominant mechanisms and supplying closed-form expressions from which the heating power can be estimated. We show that the heating effect produced by either Ohmic or collisionless heating is much larger when the discharge is excited by a superposition of currents at two frequencies than if either current had acted alone. This coupling effect occurs because the lower frequency current, while not directly heating the electrons to any great extent, strongly affects the spatial structure of the discharge in the sheath regions.