Ion Energy Distribution Function Research Articles

Numerical characterization of capacitively coupled plasma driven by tailored frequency modulated radio frequency source

Abstract Capacitively coupled plasma (CCP) is widely used in plasma etching and deposition processes because of its low cost, simple structure, and easy generation of a uniform plasma in large areas. Conventional CCPs are operated under a fixed frequency power source; however, CCPs driven by a variable frequency power source are poorly understood. In this paper, numerical simulations of CCPs driven by frequency modulated (FM) radio frequency (RF) sources within the frequency range of 2 MHz to 18 MHz are carried out with a Particle-in-Cell/Monte Carlo collision model. Our research indicates that the CCP driven by an FM RF source can maintain a stable glow discharge and form a time-dependent plasma. Plasma density, electron and ion current, energy and heating rate, ion flux, and energy on the electrodes fluctuate consistently with the FM period. The electron and ion energy distribution function can also be modulated by the frequency variation of the FM source. A multi-peak structure that varies and shifts with frequency variation is observed in the ion energy distribution function. In addition, by fixing the chirp period while varying the start or end frequency of the chirp signal (start frequency from 0.4 to 6 MHz, or end frequency from 18 to 48 MHz), effective modulations can be produced on the electron density, electron energy, and the shape of the EEPF and IEDF.

Argon Admixture-driven Enhanced Ionization and Performance of a 5-kW Hall Thruster on Krypton

Abstract Utilizing alternative propellants has been recognized as a strategy to reduce the total cost of propellants in electric propulsion-based missions. The aim of this study is to quantify the Hall effect thruster (HET) performance and operating characteristics using a Kr-Ar mixture to enable mission designers to evaluate the impact on mission and spacecraft design. We present the performance and plume plasma properties of the P5 5 kW-class HET operated with a Kr-Ar mixture with Ar volumetric flow rate fractions from 0 to 100%. The thruster is characterized at discharge power levels of 2.6 kW and 4.1 kW at constant discharge current and voltage over the range of Ar fractions. Despite higher ionization energy and lower mass of Ar, the thruster exhibited a similar level of thrust within 2% when comparing the pure Kr and 26%-Ar mixture cases. The derived ion energy distribution functions and analytical modeling suggest that the characteristic length for the ionization region is extended as the Ar fraction increases. The increased residence time of Kr at the extended ionization region and background energetic electrons from the ionized Ar neutrals are considered to cause this enhanced ionization of the injected Kr neutrals, leading to a 6% higher Kr ion density at the 26%-Ar case even at the 16% reduced injected neutral density than in the pure Kr case. The enhanced Kr ionization and generated Ar ions in the 26%-Ar case consequently led to a comparable thrust with that of the pure Kr case. The study indicates that mixing Ar with approximately 26% volumetrically with Kr can provide a similar or even higher thrust performance at the same discharge power. This will be particularly advantageous for various space missions that require high impulses by reducing the total cost of the propellant.

Uniformity of low-pressure capacitively coupled plasmas: Experiments and two-dimensional particle-in-cell simulations

Radio-frequency capacitively coupled plasmas (CCPs) are one of the key technologies enabling the latest etching processes in 3D NAND and FinFET manufacturing. These processes rely crucially on the precise control of the uniformity of ion/radical fluxes and ion angular and energy distribution function (IAEDF) in CCPs. The plasma behavior and scaling properties are dependent on the plasma chemistry in these processes, e.g., electro-positive Ar plasmas vs highly electro-negative O2 plasmas. With the large number of process and design parameters influencing the plasma properties, computational modeling has become an important tool in conjunction with experimental diagnostics in understanding the intricate physical mechanisms in CCPs. In this paper, a 2D particle-in-cell plasma model is used to study the kinetic behavior of low-pressure (<5 Pa) CCPs in two different representative chemistries: Ar and O2. The low-frequency RF source is at 1.356 MHz while 27.12 MHz is used for the high frequency. Simulations show a shift of the peak in the plasma density from the center of the chamber to the edge as the pressure increases from 0.3 to 2.6 Pa. The computed magnitude and spatial profile of electron density compare reasonably with experimental measurements over a range of pressure. Comparison between electro-positive and electro-negative plasmas are discussed. Modeling results for the dual frequency CCP highlight the effect of plasma uniformity on the IAEDF, especially near the outer edge of the electrodes. Collisions in the sheath increase the population of low-energy ions as the pressure is increased to 2.6 Pa.

Effects of low-frequency voltage on nonlinear standing wave excitation, plasma uniformity, and ion dynamics in dual-frequency asymmetric capacitive discharges

It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage VL on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage VL at 2 MHz varies from 0 to 700 V while the HF voltage VH at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. VL= 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as VL increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher VL , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔE becomes wider with the increase of VL . The IEDF at the radial center of the powered electrode exhibits a broader ΔE than that at the edge. For the IADF, an increased VL results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.

Effects of power on ion behaviors in radio-frequency magnetron sputtering of indium tin oxide (ITO)

Abstract This study delves into ion behavior at the substrate position within RF magnetron discharges utilizing an indium tin oxide (ITO) target. The positive ion energies exhibit an upward trajectory with increasing RF power, attributed to heightened plasma potential and initial emergent energy. Simultaneously, the positive ion flux escalates owing to amplified sputtering rates and electron density. Conversely, negative ions exhibit broad ion energy distribution functions (IEDFs) characterized by multiple peaks. These patterns are clarified by a combination of radiofrequency oscillation of cathode voltage and plasma potential, alongside ion transport time. This elucidation finds validation in a one-dimensional model encompassing the initial ion energy. At higher RF power, negative ions surpassing 100 eV escalate in both flux and energy, posing a potential risk of sputtering damages to ITO layers.

Time-resolved ion energy measurements using a retarding potential analyzer for electric propulsion applications.

To completely characterize the evolving state of a plasma, diagnostic tools that enable measurements of the time-resolved behavior are required. In this study, a gridded ion source with superimposed oscillations was utilized to verify the functionality of a high-speed retarding potential analyzer (HSRPA), at frequencies equivalent to the low frequency oscillations occurring in Hall effect thrusters (HETs). The verification of this device provides an effective alternative to existing diagnostics for measuring time-resolved ion energies. Retarding potential analyzers (RPAs) have established themselves as a fundamental diagnostic in the field of electric propulsion (EP), enabling the measurement of ion energy distributions within the plumes of EP thrusters. The work presented here has demonstrated the capability of a standard RPA in conjunction with high-speed circuitry and data fusion techniques to produce time-resolved ion energy distribution functions (IEDFs) at higher frequencies and beam potentials than have previously been investigated. Tested frequencies ranged between 20 and 80kHz with 10V peak-to peak oscillations at a mean beam potential of 570V. In addition, measurements were conducted with several waveforms, functioning as the superimposed oscillation, including a sine wave, triangle wave, and noisy sine wave. Data from the HSRPA were successfully reconstructed into time series utilizing two data fusion techniques: the empirical transfer function method and shadow manifold interpolation. Time-resolved IEDFs were produced at all frequency set points and waveforms. This investigation has demonstrated the HSRPA effectiveness at producing time-resolved measurements under conditions similar to those occurring in HETs.

Hybrid simulation of radio frequency biased inductively coupled Ar/O<sub>2</sub>/Cl<sub>2</sub> plasmas

In the etching process, a bias source is usually applied to the substrate of the inductively coupled plasma (ICP) to realize independent modulation of the ion energy and ion flux. In this work, a hybrid model, i.e. a global model combined bi-directionally with a fluid sheath model, is employed to investigate the plasma properties and ion energy distribution function (IEDF) in biased inductively coupled Ar/O<sub>2</sub>/Cl<sub>2</sub> plasmas. The results indicate that at a bias frequency of 2.26 MHz, the Cl<sup>–</sup> ion density and ClO<sup>+</sup> ion density first increase with bias voltage rising, and then they decrease, and finally they rise again, which is different from the densities of other charged species, such as O and Cl atoms. At the bias frequency of 13.56 MHz and 27.12 MHz, except Cl<sup>–</sup> and <inline-formula><tex-math id="M3">\begin{document}$ {\text{Cl}}_2^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231369_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231369_M3.png"/></alternatives></inline-formula> ions, the evolutions of other species densities with bias voltage are similar to the results at lower bias frequency. The evolution of the species densities with bias frequency depends on the bias voltage. For instance, in the low bias voltage range (< 200 V), the densities of charges species, O and Cl atoms increase with bias frequency increasing due to a significant increase in the heating of the plasma by the bias source. However, when the bias voltage is high, say, higher than 300 V, except <inline-formula><tex-math id="M4">\begin{document}$ {\text{Cl}}_2^ + $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231369_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231369_M4.png"/></alternatives></inline-formula> and Cl<sup>–</sup> ions, the densities of other charged species, O and Cl atoms first decrease with bias frequency increasing and then they increase due to a decrease and then an increase in the heating of the plasma by the bias source. In addition, as the bias frequency increases, the peak separation of IEDF becomes narrow, the high energy peak and low energy peak approach each other and they almost merge into one peak at high bias frequency. The results obtained in this work are of significant importance in improving the etching process.

Impact of plasma operating conditions on the ion energy and angular distributions in dual-frequency capacitively coupled plasma reactors using CF4 chemistry

A two-dimensional hybrid model is used to simulate an industrial dual-frequency capacitively coupled plasma reactor working at closely spaced frequencies (13.56–40.68 MHz) in pure CF4 chemistry. The goal is to understand how plasma operating conditions (pressure, low-frequency and high-frequency RF powers, and chamber wall conditions) influence critical etching parameters such as the ion energy and angular distribution (IEAD) and the ion flux at the wafer. In base case conditions, the ionic and radical composition at the center of the plasma is analyzed, revealing CF3+ and F− as the primary ions, and F, CF, CF3, CF2, and F2 as the predominant radicals (by decreasing density). The impact of the surface recombination coefficient of F radicals into F2 at the reactor walls, γ(rec,F > F2), is then explored; it is found that increasing γ(rec,F > F2) has a strong impact on the final plasma composition, decreasing CF and F densities while increasing CF3, CF2, and F densities, which highlights the importance of properly considering wall conditions in CF-based plasmas simulation. The IEAD at the wafer is then characterized, showing that the total IEAD shape is affected by the plasma ion composition: heavy ions such as CF3+ (69 amu) form the core of the distribution while lighter species such as F+ (19 amu) form the wing of the distribution due to their lower mass. The low frequency (LF) power (100–900 W) is shown to substantially modify the ion energy distribution function (IEDF) owing to sheath voltage changes, but to also marginally increase the ion flux at the wafer. Conversely, the high-frequency (HF) power (100–1500 W) strongly impacts the ion flux at the wafer due to HF voltage fluctuations, while the IEDF remains mostly unaffected. This study also reveals some coupling between the effects of the LF (13.56 MHz) and HF (40.68 MHz) power, a phenomenon attributable to their proximity in frequency which should not be neglected. Finally, increasing the pressure from 30 to 200 mTorr is found to increase the electronegativity by a factor 4 and to strongly impact the plasma structure, primarily due to variations in ion mobility; it also widens the ion angular spread, potentially influencing etch uniformity. Notably, higher pressures exceeding 100 mTorr result in a decrease in the average ion density and the emergence of a low-energy peak in the ion energy distribution, attributed to charge exchange collisions.

Ion Trajectory Control in Processing Plasmas for Nano-Fabrication

To realize ion trajectory control in processing plasmas for nano-fabrication, we applied amplitude modulation (AM) discharges to control of ion trajectory in high aspect trenches. We investigated behavior of incident ions in AR25 (aspect ratio = 25) trench structure in AM discharges using data of Ar+ ion with ion energy and ion angular distribution functions (IEDF and IADF) on the substrate obtained by the PIC-MCC model. AM discharges have higher ion flux onto the trench sidewalls than the continuous waveform (CW) discharges, whereas AM discharges have almost the same ion energy as CW ones. SRIM simulation results suggest that AM discharges can desorb more hydrogen atoms from TEOS-PECVD SiO2 films on the trench sidewall than CW ones, which explains the previous results of improved SiO2 film quality on trench sidewall by AM discharges.

Ion behavior impact on ITO thin film fabrication via DC magnetron sputtering with external anode

“Sputtering damage” arising from high-energy negative ions plays a pivotal role in shaping the characteristics of indium tin oxide (ITO) thin films deposited through direct-current magnetron sputtering (DCMS). To mitigate this issue, we employ DCMS with an external anode. The increment in anode bias VA from 0 to +60V effectively diminishes the average kinetic energy of negative ions such as O−, O2− and InO− by reducing the cathode voltage. Additionally, the flux of positive ions (e.g., Ar+, In+, Sn+, O+) increases and their ion energy distribution functions (IEDFs) exhibit supplementary peaks at plasma potentials. Both facilitate film crystallization, as evidenced by the structural transition from subgrain to grain formations. Heightened surface roughness markedly enhances optical transmittance. Due to a reduced oxygen sticking coefficient, films grown with higher VA values exhibit increased oxygen vacancies, which serve as the primary charge carriers for ITO films. Consequently, ITO films attain their lowest resistivity (7.81×10−4Ωcm) and highest optical transmittance (78.71 %) at VA = +60V. This investigation underscores the significant influence of the external anode bias on both ion behavior and film growth, providing a viable approach to enhance the electrical and optical properties of ITO films.

Ion acceleration in expanding plasma in small radio frequency plasma thruster with a magnetic cusp

Ambipolar electric field is formed in the expanding plasma of the small radio frequency plasma thruster using a cusp-shaped magnetic field. A highly energized group of ion energy distribution function is observed in the z-direction, indicating the presence of axial ion acceleration downstream the magnetic nozzle owing to the electric field. The mean velocity profile of the beam ions along the z axis is evaluated using the energy distribution functions along the z axis. The high axial ion velocity profile stretches downstream, although the evaluated dimensionless velocity profile is lower than that calculated using quasi-one-dimensional models. It is suggested that ion momentum loss can result from ion-neutral collision, leading to beam divergence in the magnetic nozzle of the proposed small thruster.

Investigation of EDF evolution and charged particle transport in E × B plasma based negative ion sources using kinetic simulations

A spatially varying transverse magnetic filter field (TMF) is present in an E times B plasma-based negative ion source to improve negative ion yield. The TMF strength ranges from 1 to 10 mT, causing the plasma electrons to become magnetized while leaving the ions either unmagnetized or partially magnetized. As a consequence, plasma drift, particle trapping, double layer (DL), and instabilities are observed in a negative ion source. The transport of plasma through the TMF is influenced by these phenomena, subsequently affecting the energy distribution functions (EDFs) of both electrons and ions in the plasma. Measurement of EDFs in such systems is a challenging task due to the presence of a strong magnetic field. To address this, a 2D-3V Particle-in-Cell Monte Carlo Collision (PIC MCC) model is employed to study the spatio-temporal evolution of the EDFs separately for electrons and ions. The electron EDF (EEDF) remains Maxwellian, while ion EDF (IEDF) gradually transitions to non-Maxwellian as measurements are taken closer to the TMF region. The present study reveals that the IEDF is more sensitive to the operational conditions compared to the EEDF, as evidenced by the changes observed in both EDFs under different plasma operational conditions.

Numerical and experimental study of ion energy distribution function in a dual-frequency capacitively coupled oxygen discharge

The plasma dynamics of a low pressure oxygen capacitively coupled plasma driven by dual frequencies (27.12 MHz and 271.2 kHz) is studied experimentally and numerically in this work. A retarding field energy analyzer system is employed in the experiment to measure the ion energy distribution function (IEDF) at the grounded electrode for different combinations of low-frequency voltages and pressures. One-dimensional particle-in-cell simulations of the oxygen plasma are conducted at the experimental conditions. A typical bimodal IEDF is observed and good agreement is obtained between experiments and simulations. A semi-analytical model based on the Child law sheath and fitted sheath voltage is constructed to study the structure of the IEDF. It is found that for the investigated conditions the low-energy peak of the IEDF is independent of the low frequency (LF) voltage but determined by the minimum sheath voltage during the sheath collapse; the energy spread of IEDF scales linearly with the LF voltage; both an increase of LF voltage and pressure create more low-energy ions.

Kinetic Model of Vacuum Plasma Expansion in a Cylindrical Gap

Results of a theoretical description of collisionless kinetics of radial expansion of two-component (electron–ion) plasma in the one-dimensional cylindrical formulation of the problem are presented. The electric-field mechanism of supersonic expansion of the plasma flame due to the motion of the electron–ion ensemble and self-consistent electric field in the diode with the potential difference applied to it is demonstrated. The spatiotemporal evolution of the ion energy distribution function, electric potential, and rate of expansion of the emission boundary of the plasma flame is shown. The calculated rates of flame expansion at the copper cathode (~1.5 × 106 cm/s) well agree with the experimental data.

Kinetic Model of Vacuum Plasma Expansion in a Cylindrical Gap

Results of a theoretical description of collisionless kinetics of radial expansion of two-component (electron–ion) plasma in the one-dimensional cylindrical formulation of the problem are presented. The electric-field mechanism of supersonic expansion of the plasma flame due to the motion of the electron–ion ensemble and self-consistent electric field in the diode with the potential difference applied to it is demonstrated. The spatiotemporal evolution of the ion energy distribution function, electric potential, and rate of expansion of the emission boundary of the plasma flame is shown. The calculated rates of flame expansion at the copper cathode (~1.5 × 106 cm/s) well agree with the experimental data.

Study on the plasma plume structures in a cylindrical Hall thruster

The structures of two typical plume modes (divergent and convergent plume) and their respective formation mechanisms in a cylindrical Hall thruster are investigated. The non-monotonic distribution of the two-dimensional ion energy distribution function map is obtained to segment the plume into 5 levels with different energy interval. The test results of the ion current fraction indicate that the ion beams in Level III and IV were the main components of the two plume modes. For Level IV (enhanced significantly in the convergent mode), these ions with focusing structure could only originate from the upstream E × B field due to their similar high potential and identical variation tendency in the mode transition, where the electric field converges towards the axis. This is mainly responsible for the formation of convergent mode. On the other hand, for Level III (dominating the divergent mode), these ions with hollow structure and less acceleration voltage are speculated to originate from the downstream magnetic mirror field, where the electric field manifests a defocusing characteristic along the diverging magnetic field lines. This is mainly responsible for the formation of divergent mode. Through the thrust equivalent calculation method, it is revealed that the upstream acceleration associated with the E × B field is the dominant contributor to the enhancement of thrust in the convergent mode. This study on the complex plume structure would facilitate the understanding of the CHT acceleration mechanism and provide useful ideas for the optimization of electric field structure and enhancement of plume efficiency.

Experimental observation of a field-aligned ion beam produced by magnetic reconnection of two flux ropes

An ion beam field-aligned to the background guide field (B0=330 G) was observed in a reconnection experiment on the Large Plasma Device and, to the authors' knowledge, is the first experimental observation of its kind. Two kink-unstable flux ropes (L = 11 m, d = 7.6 cm) were made to collide, which allows magnetic reconnection to occur. Sub-Alfvénic ion beams with energies of up to 15 eV were then observed from measurements of the local ion energy distribution function. The beam ions do not appear to be heated. They were correlated with the collision of the ropes and appear to be energized by magnetic reconnection. The results and interpretation of the measurements are supported by three-dimensional gyrokinetic particle simulations of the merging flux ropes and electric field measurements from previous experiments [W. Gekelman et al., Astrophys. J. 853, 33 (2018)]. The mechanism behind the acceleration appears to be non-local.

Spatial flux and energy asymmetry in a low pressure capacitively coupled plasma discharge excited by sawtooth waveform: A harmonic study

Plasma asymmetry generation in capacitively coupled plasma (CCP) discharges provides control over vital parameters that are useful in many plasma processing applications. In this article, using the particle-in-cell simulation technique, we investigated the spatial plasma asymmetry creation by a temporally asymmetric (sawtooth) waveform by varying its number of harmonics (N). The simulation results predict a non-linear increase in the plasma density and ion flux with an increase in N, i.e., it first decreases, reaching to a minimum value for a critical value of N and then increases almost linearly with a further rise in N. The ionization asymmetry increases with N, and higher harmonics on the instantaneous sheath position are observed for higher values of N. These higher harmonics generate multiple ionization beams that are generated near the expanding sheath edge and are responsible for an enhanced plasma density. The ion energy distribution function (IEDF) depicts a bi-modal shape for different values of N. DC self-bias is observed on the powered electrode, its magnitude with respect to the plasma potential decreases with increasing N, and therefore, the corresponding ion energy on the powered electrode decreases. The results conclude that by changing N of a sawtooth waveform in a collisionless CCP system, the ion flux asymmetry is not altered, whereas sheath symmetry could be significantly affected causing a systematic variation in the ion energy asymmetry. Due to an increase in the higher harmonic contents in the sawtooth waveform, a transition from broad bi-modal to narrow-shaped IEDFs is found.

Energy distribution function of substrate incident negative ions in magnetron sputtering of metal-doped ZnO target measured by magnetized retarding field energy analyzer

The energy distribution function of the substrate incident negative ions during magnetron sputtering of a metal-doped zinc oxide target was measured using a home-made retarding field energy analyzer (RFEA) with a magnetic field region. The cross-field region in front of the RFEA injection aperture allows the bulk electrons in the plasma into the RFEA are dramatically suppressed, while the inflow of negative ions emitted from the oxide target is largely unaffected. Negative ions were found to be mainly emitted from the target erosion area and incident on the opposing substrate with ion energy equivalent to the target applied voltage. Compared to energy-resolved mass spectrometers, which require differential pumping and are large and not very portable, magnetized RFEA is inexpensive, compact and easy to sweep in space, although there is no mass separation.

The influence of keeper current on the performance of magnetically enhanced hollow cathode thruster

Magnetically enhanced hollow cathode thruster is a novel electric thruster that makes use of Hall effect to enhance ionization and acceleration of plasma generated by the hollow cathode. It is a self-neutralizing device without an additional neutralizer, and it can provide thrust 1.5–2 mN, specific impulse 500–600 s with a power consumption of 50 W by using Xenon as the propellant. It is extremely appealing for space propulsion, especially for Cube-sats and micro-satellites, due to its characteristics of simple design, small size, and low cost. In this work, the effect of keeper current on thruster's performance is reported. The parameters including current-voltage characteristics, thrust, and specific impulse at different keeper currents are analyzed. Additionally, plasma potential, plume profiles, and ion energy distribution function are measured by the Langmuir probe, Faraday probe and RPA, respectively. Finally, an analysis of discharge current oscillations is presented to give an overview of the effect of the keeper current on the performance of the MHCT.