High-precision modeling of dynamic etching in high-power magnetron sputtering

The plasma density radial profiles in capacitive discharges driven over a wide frequency range (60–220 MHz) are measured by a floating double probe, and the results measured at 60 MHz are compared with those obtained from the electrostatic models, i.e. particle in cell/Monte Carlo collision (PIC/MCC) and the fluid models. It was found that at low pressure the plasma density peaks at the center of the reactor, while it peaks at the electrode edge at high pressure, indicating that the power deposition transitions from ‘non-local’ to ‘local’ with increasing pressure. The plasma radial profiles obtained from the PIC/MCC simulation and fluid model show a qualitative agreement with the experiment at low pressure and high pressure, respectively. This is primarily due to the fact that at low pressure the fluid model substantially under-predicts sheath heating, which, however, is the main electron heating mechanism at low pressure. So the total power into electrons and therefore the plasma density is also under-predicted. In contrast, the PIC/MCC model takes into account these electron collisionless heating effects at low pressure, and thus the plasma density is enhanced in the central region of electrodes. At high pressure, due to local power deposition, both the experiment and fluid simulation show that as rf power increases, a density peak at the electrode edge appears, indicating an enhancement in edge field. Compared with the electrostatic case, at a higher frequency, the plasma density profile is determined by electromagnetic (EM) effects, especially the standing wave effect. To be specific, we found that the standing wave effect exhibits multi-node structure within the electrode at 130 MHz or above, and the wavelength becomes smaller as the excitation frequency increases. At high excitation frequency and high pressure, the rf power is mainly deposited at the electrode periphery due to the fact that the EM waves are strongly damped when they propagate from the discharge edge to the center. In addition, our experimental results show that the standing wave wavelength increases with rf power.

Particle-in-cell/Monte Carlo collision (PIC/MCC) simulations are an important tool for understanding low-temperature plasma dynamics, and benchmark work is needed to build a solid base for the correctness of PIC/MCC codes. In our recent publication (Wen <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2021), benchmarking of the object-oriented PIC/MCC oopd1 code was performed against the well-established <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xpdp1</monospace> code for a simplified argon reaction set. Furthermore, oopd1 was upgraded to incorporate the excited state atoms as space- and time-varying fluids. Here, we show more details and perform further analysis of the benchmark work. The plasma density profile transition is further explored; the “passively” flat plasma density profile in the absence of metastables is found to be parabolic at low pressure and flat at 1.6 and 5 Torr. In the presence of metastable atoms, the “parabolic” profile at 5 Torr becomes “flat” at 15 Torr due to the reduced excited state atom density in the discharge center, which decreases the step-wise ionization rates. In addition, the effects of electron elastic scattering, i.e., Coulomb-screening-based non-isotropic scattering, total elastic (and momentum transfer) cross-section-dependent non-isotropic scattering, and momentum transfer isotropic scattering on capacitive discharges, are examined, showing that at a low pressure of 50 mTorr Coulomb-screening-based scattering underestimates the plasma density and electron power absorption by around 15%. However, isotropic scattering and cross-section-dependent non-isotropic scattering give almost the same plasma density and electron power absorption. At a higher pressure of 1.6 Torr, the plasma properties are independent of electron scattering in the presence of metastable atoms. In the absence of metastable atoms, different electron scattering treatments bring a few percent difference for plasma density and electron power absorption.

A combined Monte Carlo (MC)/analytical surface model is developed to study the plasma processes occurring during the reactive sputter deposition of TiOx thin films. This model describes the important plasma species with a MC approach (i.e. electrons, Ar+ ions, ions, fast Ar atoms and sputtered Ti atoms). The deposition of the TiOx film is treated by an analytical surface model.The implementation of our so-called multi-species MC model is presented, and some typical calculation results are shown, such as densities, fluxes, energies and collision rates. The advantages and disadvantages of the multi-species MC model are illustrated by a comparison with a particle-in-cell/Monte Carlo collisions (PIC/MCC) model. Disadvantages include the fact that certain input values and assumptions are needed. However, when these are accounted for, the results are in good agreement with the PIC/MCC simulations, and the calculation time has drastically decreased, which enables us to simulate large and complicated reactor geometries.To illustrate this, the effect of larger target–substrate distances on the film properties is investigated. It is shown that a stoichiometric film is deposited at all investigated target–substrate distances (24, 40, 60 and 80 mm). Moreover, a larger target–substrate distance promotes film uniformity, but the deposition rate is much lower.

In the past three decades, first principles-based fully kinetic particle-in-cell Monte Carlo collision (PIC/MCC) simulations have been proven to be an important tool for the understanding of the physics of low pressure capacitive discharges. However, there is a long-standing issue that the plasma density determined by PIC/MCC simulations shows quantitative deviations from experimental measurements, even in argon discharges, indicating that certain physics may be missing in previous modeling of the low pressure radio frequency (rf) driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission (SEE) and excited state atoms play an important role in low pressure rf capacitive argon plasma discharges. The ion-induced secondary electrons are accelerated by the high sheath field to strike the opposite electrode and produce a considerable number of secondary electrons that lead to additional ionizing impacts and further increase of the plasma density. Importantly, the presence of excited state species even further enhances the plasma density via excited state neutral and resonant state photon-induced SEE on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1–10 Pa) that is commonly used for etching in the semiconductor industry. At the highest pressure (20 Pa) and driving voltage amplitudes 250 and 350 V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced SEE are quantitatively higher than observed in the experiments, requiring further investigation on high pressure discharges.

Understanding the spatio-temporal dynamics of charged particles in low pressure radio frequency capacitively coupled plasmas (CCP) is the basis for knowledge based process development in these plasma sources. Due to the importance of kinetic non-local effects the particle in cell/Monte Carlo collision (PIC/MCC) simulation became the primary modeling approach. However, due to computational limitations most previous PIC/MCC simulations were restricted to spatial resolution in one dimension. Additionally, most previous studies were based on oversimplified treatments of plasma-surface interactions. Overcoming these problems could clearly lead to a more realistic description of the physics of these plasma sources. In this work, the effects of the reactor geometry in combination with realistic heavy particle and electron induced secondary electron emission coefficients (SEEC) on the charged particle dynamics are revealed by GPU based 2D3V PIC/MCC simulations of argon discharges operated at 0.5 Pa and at a high voltage amplitude of 1000 V. The geometrical reactor asymmetry as well as the SEECs are found to affect the power absorption dynamics and distribution functions of electrons and ions strongly by determining the sheath voltages and widths adjacent to powered and grounded surface elements as well as via the self-excitation of the plasma series resonance. It is noticed that secondary electrons play important roles even at low pressures. Electron induced secondary electrons (δ-electrons) are found to cause up to half of the total ionization, while heavy particle induced secondary electrons (γ-electrons) do not cause much ionization directly, but induce most of the δ-electron emission from boundary surfaces. The fundamental insights obtained into the 2D-space resolved charged particle dynamics are used to understand the formation of energy distribution functions of electrons and ions for different reactor geometries and surface conditions.

The work deals with the Particle in Cell/Monte Carlo Collision (PIC/MCC) analysis of the problem of detection and identification of impurities in the nonlocal plasma of gas discharge using the Plasma Electron Spectroscopy (PLES) method. For this purpose, 1d3v PIC/MCC code for numerical simulation of glow discharge with nonlocal electron energy distribution function is developed. The elastic, excitation, and ionization collisions between electron-neutral pairs and isotropic scattering and charge exchange collisions between ion-neutral pairs and Penning ionizations are taken into account. Applicability of the numerical code is verified under the Radio-Frequency capacitively coupled discharge conditions. The efficiency of the code is increased by its parallelization using Open Message Passing Interface. As a demonstration of the PLES method, parallel PIC/MCC code is applied to the direct current glow discharge in helium doped with a small amount of argon. Numerical results are consistent with the theoretical analysis of formation of nonlocal EEDF and existing experimental data.

A parallel 1d3v Particle in Cell/Monte Carlo Collision (PIC/MCC) code was derived and applied for the investigation of the formation of photoplasma in sodium vapor. The effects of particle weighting and the Courant number on the computed plasma properties were examined, and the convergence of the numerical method with respect to these parameters was demonstrated. Simulations were carried out for the stepwise spatial profile of the resonant sodium atoms density. The basic plasma parameters (such as eedf, iedf, atomic and molecular ion and electron densities, and electric field and potential) were computed. The results of the PIC/MCC simulations were compared to those obtained from the fluid model. Simulations revealed a strong spatial non-uniformity in the electron density and the electric potential over the computational domain that provides evidence in favour of photovoltaic conversion of light energy into electrical energy.

Previously, a microplasma was discovered in the rear gap of a sliding contact. This plasma is called a ‘triboplasma’, the behaviour of which obeys the Paschen law in a gas discharge. The generation of the triboplasma has been explained to be generated by discharging of ambient air due to the intense electric field caused by tribocharging, based on the experimental findings.In this report, the mechanism of triboplasma generation is theoretically analysed using the particle-in-cell/Monte Carlo collision (PIC/MCC) simulation method for the triboplasma generated in the tribosystem, where a diamond pin slides against a sapphire disc in ambient air. Two-dimensional sideward density distributions of the electrons, ions and ions in the rear gap of the sliding contact are obtained theoretically by the PIC/MCC method. These calculated particle distributions coincided well with the triboplasma distributions experimentally observed. The previously proposed triboplasma generation due to gas discharging is verified theoretically using the PIC/MCC simulation method.

Sputtering devices are widely used in the semiconductor and display panel manufacturing process. Currently, a number of surface treatment applications using magnetron sputtering techniques are being used to improve the efficiency of the sputtering process, through the installation of magnets outside the vacuum chamber. Within the internal space of the low pressure chamber, plasma generated from the combination of a rarefied gas and an electric field is influenced interactively. Since the quality of the sputtering and deposition rate on the substrate is strongly dependent on the multi-physical phenomena of the plasma regime, numerical simulations using PIC-MCC (Particle In Cell, Monte Carlo Collision) should be employed to develop an efficient sputtering device. In this paper, the development of a magnetron sputtering simulator based on the PIC-MCC method and the associated numerical techniques are discussed. To solve the electric field equations in the 2-D Cartesian domain, a Poisson equation solver based on the FDM (Finite Differencing Method) is developed and coupled with the Monte Carlo Collision method to simulate the motion of gas particles influenced by an electric field. The magnetic field created from the permanent magnet installed outside the vacuum chamber is also numerically calculated using Biot-Savart’s Law. All numerical methods employed in the present PIC code are validated by comparison with analytical and well-known commercial engineering software results, with all of the results showing good agreement. Finally, the developed PIC-MCC code is parallelized to be suitable for general purpose computing on graphics processing unit (GPGPU) acceleration, so as to reduce the large computation time which is generally required for particle simulations. The efficiency and accuracy of the GPGPU parallelized magnetron sputtering simulator are examined by comparison with the calculated results and computation times from the original serial code. It is found that initially both simulations are in good agreement; however, differences develop over time due to statistical noise in the PIC-MCC GPGPU model.

To obtain both high ionization and high deposition rate, a modified global model for a continuous high-power DC magnetron sputtering (C-HPMS) is established by considering the continuous generation of the hot electrons and the high temperature caused by continuous high-power discharge. The results show that the plasma density is on the order of 1019 m−3 for power densities of only 183 W cm−2 (Al) and 117 W cm−2 (Cu). The ionization rate exceeds 90% of high-power impulse magnetron sputtering (HiPIMS) (peak power density of 564 W cm−2) for a DC power density of 180 W cm−2, and the total diffusion fluxes of the two targets are 26 (Al) and 30 (Cu) times that of conventional HiPIMS, leading to very high deposition rates. The work provides a theoretical basis for the realization of C-HPMS and gives an enlightenment to the development of deposition equipment for continuous high-power discharges.

‘Bohm diffusion’ causes the electrons to diffuse perpendicularly to the magnetic field lines. However, its origin is not yet completely understood: low and high frequency electric field fluctuations are both named to cause Bohm diffusion. The importance of including this process in a Monte Carlo (MC) model is demonstrated by comparing calculated ionization rates with particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations. A good agreement is found with a Bohm diffusion parameter of 0.05, which corresponds well to experiments. Since the PIC/MCC method accounts for fast electric field fluctuations, we conclude that Bohm diffusion is caused by fast electric field phenomena.

A Cartesian-coordinate two-dimensional electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) plasma simulation code is presented, including a new treatment of charge balance at dielectric boundaries. It is used to simulate an Ar plasma in a symmetric radiofrequency capacitively-coupled parallel-plate reactor with a thick (3.5 cm) dielectric side-wall. The reactor size (12 cm electrode width, 2.5 cm electrode spacing) and frequency (15 MHz) are such that electromagnetic effects can be ignored. The dielectric side-wall effectively shields the plasma from the enhanced electric field at the powered-grounded electrode junction, which has previously been shown to produce locally enhanced plasma density (Dalvie et al 1993 Appl. Phys. Lett. 62 3207–9; Overzet and Hopkins 1993 Appl. Phys. Lett. 63 2484–6; Boeuf and Pitchford 1995 Phys. Rev. E 51 1376–90). Nevertheless, enhanced electron heating is observed in a region adjacent to the dielectric boundary, leading to maxima in ionization rate, plasma density and ion flux to the electrodes in this region, and not at the reactor centre as would otherwise be expected. The axially-integrated electron power deposition peaks closer to the dielectric edge than the electron density. The electron heating components are derived from the PIC/MCC simulations and show that this enhanced electron heating results from increased Ohmic heating in the axial direction as the electron density decreases towards the side-wall. We investigated the validity of different analytical formulas to estimate the Ohmic heating by comparing them to the PIC results. The widespread assumption that a time-averaged momentum transfer frequency, vm, can be used to estimate the momentum change can cause large errors, since it neglects both phase and amplitude information. Furthermore, the classical relationship between the total electron current and the electric field must be used with caution, particularly close to the dielectric edge where the (neglected) pressure gradient term becomes significant.

High-power impulse magnetron sputtering (HiPIMS) is a new magnetron sputtering technique which can produce high-density plasmas with a high ionization rate and prepare coatings with a good performance such as large density and high adhesion. To obtain stable discharge and universal materials’ ionization rates, a cylindrical cathode is proposed based on the hollow cathode effect. However, the unusual plasma transport results in a large loss of ions and a low deposition rate. To solve these problems, an expanding electromagnetic field is proposed to control the plasma transport in this work. The particle in cell/Monte Carlo collision (PIC/MCC) method and the plasma diffusion model are used to simulate the plasma transport in and out of the cylindrical cathode with different currents in the electromagnetic coils, respectively. The simulation results reveal that different electromagnetic fields can achieve different plasma density distributions, resulting in different accumulated positions and different diffusion paths. When the coil current is positive, the resistance to axial motion of electrons is small but the resistance to radial motion is large, so that the hollow cathode effect is weakened and the plasma beam tends to output uniformly. When the coil current is negative, the resistance to axial motion of electrons is large but the resistance to radial motion is small, so that the hollow cathode effect is enhanced and the plasma tends to gather on the central axis and then diffuses outward. To verify the simulation results, Ar/Cr HiPIMS discharge experiments are carried out with the cylindrical cathode in a homemade vacuum system. The experiment results indicate that the threshold voltage, the plasma flow shape, the optical emission spectrum (OES) intensity, and the deposition distribution are determined by the electromagnetic coil current. The variation tendency is in coincidence with the prediction of the simulation. Consequently, by adding an expanding electromagnetic field, the plasma discharge in the cylindrical cathode can be easily controlled and the deposition rate is greatly enhanced. This electromagnetic control strategy not only realizes the enhancement and effective control of plasma, but also improves the homogeneity and the deposition rate of the coatings, thus laying a foundation for the industrial application of HiPIMS.

Comparative studies of capacitively coupled radio-frequency discharges in helium and argon at pressures between 10 and 80 Pa are presented applying two different fluid modeling approaches as well as two independently developed particle-in-cell/Monte Carlo collision (PIC/MCC) codes. The focus is on the analysis of the range of applicability of a recently proposed fluid model including an improved drift-diffusion approximation for the electron component as well as its comparison with fluid modeling results using the classical drift-diffusion approximation and benchmark results obtained by PIC/MCC simulations. Main features of this time- and space-dependent fluid model are given. It is found that the novel approach shows generally quite good agreement with the macroscopic properties derived by the kinetic simulations and is largely able to characterize qualitatively and quantitatively the discharge behavior even at conditions when the classical fluid modeling approach fails. Furthermore, the excellent agreement between the two PIC/MCC simulation codes using the velocity Verlet method for the integration of the equations of motion verifies their accuracy and applicability.

We present numerical kinetic modeling of generation and evolution of the plasma produced as a result of resonance enhanced multiphoton ionization (REMPI) in Argon gas. The particle-in-cell/Monte Carlo collision (PIC/MCC) simulations capture non-equilibrium effects in REMPI plasma expansion by considering the major collisional processes at the microscopic level: elastic scattering, electron impact ionization, ion charge exchange, and recombination and quenching for metastable excited atoms. The conditions in one-dimensional (1D) and two-dimensional (2D) formulations correspond to known experiments in Argon at a pressure of 5 Torr. The 1D PIC/MCC calculations are compared with the published results of local drift-diffusion model, obtained for the same conditions. It is shown that the PIC/MCC and diffusion-drift models are in qualitative and in reasonable quantitative agreement during the ambipolar expansion stage, whereas significant non-equilibrium exists during the first few 10 s of nanoseconds. 2D effects are important in the REMPI plasma expansion. The 2D PIC/MCC calculations produce significantly lower peak electron densities as compared to 1D and show a better agreement with experimentally measured microwave radiation scattering.