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A schematic diagram for energy level and transition of Ar atom.: Argon atom energy levels of resonance states (4sr), metastable states (4sm), and 4p excited states are considered in this paper.
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Hysteresis, which is the history dependence of physical systems, is one of the most important topics in physics. Interestingly, bi-stability of plasma with a huge hysteresis loop has been observed in inductive plasma discharges. Despite long plasma research, how this plasma hysteresis occurs remains an unresolved question in plasma physics. Here, w...
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... evaluate the effect of the EEPF on the hysteresis, theoretical calculations of the ε c and the stable plasma density were investigated by using stepwise global model considering EEPF for the first time. In the stepwise model, we consider argon atom energy levels of resonance states (4s r ), metastable states (4s m ), and 4p excited states Fig. 5. To obtain the ε c , power and particle balance equations (eqs. (6) and (7)) are used. In the theoretical calculation, EEPF should be considered because the reaction rate con- stant is strongly dependent on the shape of the EEPF. The rate constants are obtained by using collision (Fig. 2a,d), while the EEPFs are the Maxwellian ...
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... details for plasma stability and hysteresis. The collisional energy loss ε c is obtained from the stepwise plasma balance equation. In this work, argon atom energy levels of resonance states (4s r ), metastable states (4s m ), and 4p excited states 42,43 are considered, as illustrated in following Table. 1 and Fig. 5. Then, the ε c is given ...
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... Moreover, they observed a smooth mode transition in He, and they concluded that hysteresis only existed in high pressure Ramsauer gas discharges, such as Ar. 20 More works about the E to H mode transition can be found in Refs. 3 and 21. ...
In this work, an analytical hybrid model, which consists of an analytical electromagnetic model and a global model, is developed to investigate the E to H mode transition in a planer inductively coupled plasma. By employing the hybrid model, the effect of discharge frequency, oxygen content, and gas pressure on the E to H mode transition is investigated. The results show that the electron density increases rapidly with coil current when the discharge shifts to the H mode, and the mode transition becomes smoother and occurs at lower current when the driving frequency is higher. As oxygen content increases, the electron density declines, and the threshold current for the mode transition exhibits a rising trend. The evolution of the threshold current with pressure is nonlinear; i.e., it decreases first and then increases, and the minimum value varies with discharge frequency. In addition, the plasma composition also changes during the E to H mode transition; i.e., all the charged species densities increase with coil current, except the O− density, which varies nonlinearly, and this indicates the decreasing electronegativity in the H mode. The results obtained in this work are helpful for understanding the effect of different discharAr/O2ge parameters on the E to H mode transition in Ar/O2 inductive discharges.
... For example, in inductively coupled plasma (ICP), it has been found that there is a hysteresis in the transition between the low-power, low-electron-density E mode and the high-power, high-electron-density H mode, which is thought to be related to the nonlinearity of the absorption power and dissipation power. [12][13][14] In addition, the hysteresis effect in discharge current vs applied voltage is a well-known phenomenon of DC glow discharge plasma, which is caused by the presence of negative differential conductivity in the current-voltage curve after the breakdown. 15,16 Another widely investigated topic in laboratory plasma is the appearance of instability phenomena of the equilibrium state, such as quasi-periodic, 17,18 period-doubling bifurcation, 19,20 and chaos. ...
As a typical highly nonlinear medium, laboratory plasmas can exhibit abundant nonlinear phenomena. It is well known that the presence of negative differential conductivity can cause the system to exhibit temporal chaotic oscillations when a DC glow discharge is operated in the subnormal glow discharge regime. In addition, for a nonlinear system, the hysteresis often occurs due to the coexistence of multiple attractors. In this work, a two-dimensional plasma fluid model based on the drift-diffusion approximation is developed to study the hysteresis phenomenon of the nonlinear dynamical behaviors of the low-pressure DC glow discharge. The results demonstrate that the initial discharge conditions selected in calculations will influence the nonlinear dynamical behaviors significantly that the system exhibits. Hysteresis can be observed from the voltage waveform when the applied voltage is altered to allow the system to work between the stationary discharge regime and the oscillatory discharge regime. In the hysteresis region, the system exhibits bi-stable characteristics. Near the critical point, the dynamical behaviors of the system will jump from the stationary state to the oscillatory state under small perturbations and the reverse adjustment of control parameters will not immediately restore the original stationary state, which is a typical characteristic of the subcritical Hopf bifurcation.
... This is because the electron distribution of the calculated ε T and measured ε T is the same as the Maxwellian distribution. When the gas pressure is 1.33 Pa (10 mTorr) at 300 W, the measured ε T is slightly smaller than the calculated ε T because the population of the high-energy electron in the bi-Maxwellian distribution is larger than that in the Maxwellian distribution [78,79]. When compared to the measured ε T in the N 2 plasma, the measured ε T in the Ar plasma is significantly lower (see figure 6(b)) and did not considerably increase with gas pressure. ...
The effect of the electron energy distribution function (EEDF) on the behavior of the electron density (ne) is investigated under various gas pressures of nitrogen (N2) in inductively coupled plasma (ICP) operated at low and high input powers. A Langmuir probe is used to measure the EEDFs and electron densities, and the antenna coil current is measured to obtain the absorbed power in the plasma (Pabs). At gas pressures above 2.67 Pa (20 mTorr) and 2500 W, Pabs increases continually with increasing the gas pressure, but the electron density slightly decreases. In this case, the EEDF has a Maxwellian distribution with a high-energy tail. On the other hand, at 300 W, Pabs decreases slightly with increasing gas pressure, but the electron density dramatically decreases, and the EEDF evolves from a bi-Maxwellian to a non-Maxwellian distribution with substantially highly depleted high-energetic part (high-energy tail). To analyze the difference in the behavior of the decrease rate in electron density, the total energy loss per electron-ion pair lost (εT) is measured through the probe diagnostics, and the measured electron density is compared with the calculated electron density from the global model. An additional experiment is performed in Ar plasma under the same discharge conditions as N2 plasma to compare the EEDF effect. This study provides experimental evidence that the EEDF has a decisive effect on the behavior of the electron density in plasmas.
... Furthermore, this interpretation suggests that the hysteresis may disappear by replacing the abscissa from gas pressure to neutral density, which is experimentally confirmed. It is worth noting that the origin and the detailed explanation of the hysteresis in this microwave-driven plasmas are different from those of the well-known hysteresis observed in inductively coupled plasmas during the E-H mode transition [20][21][22]. ...
We discovered a hysteresis in a microwave-driven low-pressure argon plasma during gas pressure change across the transition region between α and γ discharge modes. The hysteresis is manifested in that the critical pressure of mode transition depends on the direction of pressure change. As a corollary, the plasma would attain different discharge properties under the same operating parameters (pressure, power, and gas composition), suggesting a bi-stability or existence of memory effect. Analysis of the rotational and vibrational temperatures measured from the OH (A-X) line emissions shows that the hysteresis is mainly due to the fast gas heating in the γ -mode leading to a smaller neutral density than that of the α -mode. When increasing the gas pressure, the γ -mode discharge maintains a relatively higher temperature and lower neutral density, and thus, it requires a higher operating pressure to reach the α -mode. On the other hand, decreasing the pressure while maintaining α -mode, the transition to γ -mode occurs at a lower pressure than the former case due to a relatively higher neutral density of α -mode discharge. This interpretation is supported by the fact that the hysteresis disappears when the plasma properties are presented with respect to the neutral gas density instead of pressure.
... Furthermore, this interpretation suggests that the hysteresis may disappear by replacing the abscissa from gas pressure to neutral density, which is experimentally confirmed. It is worth noting that the hysteresis in the microwave-driven plasmas is different from the well-known hysteresis observed in the inductively coupled RF plasmas during the E-H mode transition [18,19]. ...
We discovered a hysteresis in a microwave-driven low-pressure argon plasma during gas pressure change across the transition region between $\alpha$ and $\gamma$ discharge modes. The hysteresis is manifested in that the critical pressure of mode transition depends on the direction of pressure change. As a corollary, the plasma would attain different discharge properties under the same operating parameters (pressure, power, and gas composition), suggesting a bi-stability or existence of memory effect. Analysis of the rotational and vibrational temperatures measured from the OH (A-X) line emissions shows that the hysteresis is mainly due to the fast gas heating in the $\gamma$-mode leading to a smaller neutral density than that of the $\alpha$-mode. When increasing the gas pressure, the $\gamma$-mode discharge maintains a relatively higher temperature and lower neutral density, and thus, it requires a higher operating pressure to reach the $\alpha$-mode. On the other hand, decreasing the pressure while maintaining $\alpha$-mode, the transition to $\gamma$-mode occurs at a lower pressure than the former case due to a relatively higher neutral density of $\alpha$-mode discharge. This interpretation is supported by the fact that the hysteresis disappears when the plasma properties are presented with respect to the neutral gas density instead of pressure.
... The I-V behavior of discharge in the magnetron sputtering technique is a significant factor for investigating the characteristics of the plasma and the deposition process. However, unusual behaviors observed in the hysteretic characteristics of I-V curves under non-reactive discharges [79], high-power impulse magnetron sputtering (HiPIMS) discharges, inhomogeneous magnetic fields, 'I-V curves with flat tails' noticed in weak magnetic fields [80], and so forth [81] causes the search for an analytic function properly fitting the empirical I-V data to be challenging. ...
In this paper, the incorporation of auxiliary grids/electrodes into the design of the sputtering method is scrutinized by studying the impact of factors such as grid size, grid position, grid bias voltage, electrode sheath design, substrate bias voltage, reactive gas partial pressure, and magnetic trap configuration on the discharge condition and thin-film growth. In this regard, utilizing the updated Berg model for reactive sputtering, the authors obtained a formulation for the reactive grid-assisted sputtering. By the newly-developed formulation, the sputtering rate and the reactive gas partial pressure were simulated as a function of the reactive gas flow rate for various grid-to-target distances, argon partial pressures (0.67, 1.6, and 3.6 Pa), and discharge current densities (0.01, 0.015, and 0.02 A/cm2). According to the computation results, with a grid being utilized, the width of the hysteresis loops can be modified in a broader range by changing either the grid-to-target distance, the argon partial pressure, or the discharge current, resulting in better control over the deposition process. Moreover, the novel configuration of anode-spot-assisted sputtering was proposed to significantly ionize sputtered/neutral atoms near the substrate and to simultaneously deposit sputtered species and products produced as the direct result of introducing dust into the dense plasma. Finally, diverse configurations of the grid-assisted co-sputtering method were introduced for two prime purposes: deposition of composite films in any desired ratios of constituents without significantly changing the other co-sputtering parameters, and favorable alternation of a hysteresis loop for one of the guns at shared gas flow rates.
... 9 This heating mode transition is accompanied by hysteresis, and the hysteresis loop can be changed by the discharge pressure, initial matching situation, electron density distribution, and multistep ionization. [15][16][17][18][19][20] In H-mode, in contrast to E-mode, the RF power is transferred to the plasma by the electric field induced by a timevarying magnetic field. In this regime, the capacitive coupling from the coil to the plasma causes additional ion energy loss and reduces the electron density. ...
The effects of capacitive coupling on electron and ion density profiles are studied in an argon inductively coupled plasma. Electron energy probability functions and two-dimensional ion density profiles were measured by changing the termination capacitance from 200 to 1000 pF. Experimental results show that a termination capacitor creates a virtual ground on a coil, and the virtual ground suppresses the local capacitive coupling. At 2 mTorr (non-local electron kinetics), there is little change in the azimuthal electron density distribution for different termination capacitances. However, at 50 mTorr (local electron kinetics), the virtual ground causes each mode (E-mode and H-mode) to have the maximum and minimum points in the azimuthal electron density distribution. As the termination capacitance increases, the virtual ground moves along the coil and the maximum and minimum points of the electron density also move with the virtual ground. These effects are explained by electron dynamics and the power transfer mechanism in each mode (E-mode and H-mode).
... The analysis of the EEPF is an efficient approach to reveal the mechanism of hysteresis formation [48]. To obtain the EEPF accurately, the ion current I i shall be subtracted from the total current, leaving only electron current I e . ...
... In this transition, the plasma emission intensity and the electron density increase abruptly, which is well known as the E-H mode transition in ICPs. [3][4][5][6][7][8] Other plasma characteristics, including the driven current flowing in the coil, 4,9-11 potential drop, 9,10 as well as the densities of the excited species, [12][13][14] would also suddenly change, and they have been comprehensively investigated in continuous wave (CW) driven ICPs. ...
In inductively coupled plasmas (ICPs), mode transition between capacitive coupling (E mode) and inductive coupling (H mode) is a key issue. Using an intensified charge-coupled device camera, the mode transition-related behaviors of the electron impact excitation of Ar(2p 1) are investigated under different discharge conditions in pulse-modulated radio-frequency (rf) Ar/O 2 ICPs. The initiation time of the E-H mode transition at the initial stage of a pulse period is examined under nanosecond time-resolution for the first time. It is found that the initiation time increases with increasing the applied power (300-600 W), while it decreases with raising the duty cycle (50%-80%) or gas pressure (20-80 mTorr). Besides, we also examined the spatial-temporal electron impact excitation rate over the whole pulse period (microsecond time-resolution), especially in the H mode when the discharge is operated at the steady state. We found that as the O 2 content/pressure increases, the electron impact excitation axially concentrates closer to the quartz window, and the bimodal structure becomes more prominent in the H mode. However, the excitation gets farther away from the window at higher power. In addition, the maximum value of the excitation rate appears earlier at the initial stage of a pulse period at higher pressure/O 2 content.
... Langmuir probes) with relevant theoretical models are available at low pressure. As considerable plasma parameters have been experimentally obtained via such simple diagnostics, they have allowed for further insights into plasma physics, including electron kinetics [27][28][29] and electron heating mechanisms [30,31]. Compared with low-pressure plasmas, limited experimental informa- tion is available for free electrons in atmospheric-pressure plasmas, which are difficult to measure, and this lack of data is troublesome. ...
Weakly ionized plasmas at or near 1 atm pressure, or atmospheric-pressure plasmas, have received increasing attention due to their scientific significance and potential for use in a variety of applications, particularly for medicine, agriculture, and food. However, there is a large imbalance between scientific research on plasma physics and applications, which is partly due to the considerable differences in the characteristics of these plasmas compared with those of low-pressure plasmas. This discrepancy is particularly related to the difficulty in performing plasma diagnostics for highly collisional plasmas. Information on electrons (such as the electron density and temperature) is essential since electrons play a dominant role in the generation of active species related to the physical and chemical processes inside the plasma. So far, limited diagnostics have been available for electrons such as Thomson scattering and optical emission diagnostics based on equilibrium models. Here, we review the available diagnostic methods along with their merits and limitations for characterizing electrons in weakly ionized collisional plasmas. Particular attention is paid to continuum radiation-based spectroscopy, which facilitates multidimensional imaging of electron density and temperature. The future impact of these plasmas on relevant fields (i.e. laboratory and industrial plasmas and their applications) is also addressed.
