Jump and hysteresis of plasma density in the spatial afterglow of inductively coupled plasmas Open Access

Inductively coupled plasma (ICP) sources have been widely used in etching,^1–5 material surface modification,⁶ film deposition,^7–10 and neutral beam ion source for negative hydrogen ions^11,12 due to low discharge pressure, high plasma density, and simple device structure.^13,14 One of the characteristics of the ICP source is the E–H mode transition, that is, the change of mode from capacitive discharge to inductive discharge. In practical applications, ICP sources are generally required to remain in the H mode due to the low efficiency of the E mode discharge. With the development of semiconductors, photovoltaics, and negative ion sources, the control of plasma transport and chemical reactions in industry has become more demanding.

An effective method is to use a remote plasma source (RPS).¹⁵ This type of plasma device generally consists of two parts: the active plasma, generated by a solenoid-type coil ICP source in which the coil is wound around the quartz tube, and the spatial afterglow is formed away from the driver source and connected to the end of the active plasma.¹⁶ The feed gas is transported to the spatial afterglow to participate in the gas phase reaction after being excited in the active plasma.¹⁰ Sometimes, with the special design of the reactor, lower temperature of electrons and higher concentration of free radicals can be obtained at the bottom of the spatial afterglow.¹⁷ These radicals are generally in a ground state or excited state and have strong chemical reactivity that allows thin film deposition, material processing, and synthesis of nanoparticles with unusual properties in the spatial afterglow.^6–10,18 In hydrogen discharges, low energy electrons favor the formation of negative hydrogen ions in the spatial afterglow.^19,20

In addition to the spatial afterglow, there is also a temporal afterglow. What both have in common is that there is no RF power feed-through.^18,21–23 The difference is that the temporal afterglow occurs after turning off the power supply that maintains the plasma glow discharge.¹⁸ As the power is off, the energetic electrons are cooled rapidly and the plasma density is gradually decreased, leading to the change of the plasma from ambipolar diffusion to free diffusion. The dynamics of temporal plasma afterglow have recently been reviewed by Couëdel, in which the basics of temporal afterglow are discussed in detail and experimental and theoretical results are given.²⁴ In this case, the electron flux out of the plasma is greater than the ion flux. The faster electron loss causes the plasma afterglow to no longer obey quasi-neutrality.^18,21,24 This property makes it possible to reverse the polarity of particle charges in dust plasma to positive charges. In a new approach, Chaubey and Goree found that switching the polarity of a DC voltage to positive at a specific time in the afterglow can control the resulting residual charge of dust particles.²⁵ van Huijstee et al. found that the residual charge of microparticles in a spatiotemporal afterglow plasma is strongly related to the local characteristic diffusion length of the system, i.e., the location of the particles at the moment of plasma termination influences their residual charge.²⁶ These applications include ultra-clean low-pressure systems for pollution control and plasma-enabled nanocontamination control strategies, among other applications.^21–23,26

The spatial afterglow has also been investigated in the application of negative hydrogen ion sources. Gao et al. studied the hydrogen discharge in a ICP source,²⁷ and they found that the electron energy probability function (EEPF) evolved from the two-temperature Maxwellian distribution in the active plasma to the Maxwell distribution in the spatial afterglow at 0.5 Pa. Averkin et al. performed a simulation study of a novel micropore RPS,^19,20 and the results showed that when the pressure was below 10 Torr, H⁻ ions were mainly generated by electrons attached to the high-energy vibrational hydrogen, and the vibration distribution function of the hydrogen molecule was approximated to be the Bray distribution. By contrast, when the pressure was above 10 Torr, H⁻ ions were mainly generated by electrons attached to low-energy vibrational hydrogen, and the vibration distribution function of hydrogen molecule was approximated to be the Boltzmann distribution. In this novel RPS, the active plasma and the spatial afterglow are connected by a micropore with diameters on the order of millimeters, which has the advantage that the pressure in both regions can be controlled independently by two vacuum systems. This design is very meaningful, but the simulation results have some limitations. Although much work has been done by Averkin et al. on this new structure of the RPS, it has been limited to a single chamber simulation study of the active plasma and to providing experimental data on the flow of negative hydrogen ions in the extraction region. Experimental studies of the active plasma and spatial afterglow in such a plasma source with a micropore structure have not been given. Therefore, it is necessary to systematically study the discharge characteristics of this particular structure of the RPS and to investigate the mechanism of plasma generation and transport.

This paper discusses the effects of RF power, micropore diameter, and pressure on the plasma evolution laws in argon, hydrogen, nitrogen, and argon–hydrogen mixed gas discharges in the active plasma and spatial afterglow. We found that larger micropore diameters lead to higher plasma densities in the spatial afterglow for fixed active plasma discharge parameters. The plasma density in the spatial afterglow increased slightly with rising pressure in the spatial afterglow at a micropore diameter of less than or equal to 3 mm. However, at the micropore diameter of 4 mm, the plasma density first increased slightly with rising pressure, then there was a “jump” increase, and finally a slow increase, i.e., the plasma density in the spatial afterglow showed a jump from LD to HD with increasing pressure in the spatial afterglow. This LD–HD jump phenomenon is different from the E–H mode transition in ICP. The E–H mode transition is essentially a conversion of the plasma from generation and maintenance by the electrostatic field (E mode) to maintenance by the electromagnetic field (H mode). However, in this work, the discharge condition of the active plasma is kept constant (fixed RF power, coil voltage, and coil current) when the LD–HD jump occurs in the spatial afterglow. This may be due to the fact that the plasma is injected through the micropore into the spatial afterglow to generate a “new” plasma. In addition, by adjusting the spatial afterglow pressure back and forth with a micropore diameter of 4 mm, it was observed that the trajectory of the plasma density jumping from LD to HD did not overlap with that from HD to LD, indicating the trajectory of the plasma density forms a hysteresis loop.

The paper is organized as follows: Section II presents the experimental devices. The LD–HD mode transition and the hysteretic loops, which are different from the E–H mode transition and are found in the spatial afterglow, are introduced in Sec. III, and the reasons for this phenomenon are emphatically analyzed. Finally, a brief summary is given in Sec. IV.

Figure 1 illustrates the schematic diagram of an ICP driven by a solenoid-type coil. The device consists of a quartz tube with a 20 mm diameter and 230 mm length, divided into two parts by a quartz micropore with a diameter ranging from 2 to 4 mm. The upper part, known as the active plasma, is with a height of 150 mm, while the lower part, referred to as the spatial afterglow, is 80 mm in length. Vacuum flanges are present in both regions for the attachment of double probes.

To achieve specific pressure conditions, the top of the active plasma is connected to a mechanical pump via bellows, while the bottom of the spatial afterglow is linked to a molecular pump and a mechanical pump. When the difference in pumping rate between the two regions is large, the micropore can create a pressure difference by restricting gas flow. This configuration allows for control of high pressure in the active plasma and low pressure in the spatial afterglow. In this experiment, the pressures in the upper and lower regions are almost independently controlled by the valves of the corresponding vacuum pumps, while the stable pressures in the upper and lower regions are obtained through dynamic equilibrium processes. To ensure the upper region (active plasma) always being at the constant pressure, one needs to adjust the valves in both regions to change the pressure in the lower region (spatial afterglow). Testing reveals that a smaller micropore diameter maintains a larger pressure difference between the two regions. Vacuum gauges are provided at the top of the active plasma and at the bottom of the spatial afterglow to monitor the pressures in both regions.

Three-turn coils surround the upper part, with one side grounded and the other side connected to an RF power supply operating at a frequency of 13.56 MHz through an automatically adjustable $Γ$-type matching network. A VI Probe (Impedans Octiv PolyTM) is installed between the matching box and the power supply to monitor the applied power, which is equal to the difference between forward power and reflected power. Air-cooling system directly opposite the RF shield vents to cool coils and stabilize wall temperature. The working gases employed include argon (99.999%), nitrogen (99.999%), hydrogen (99.999%), as well as various proportions of argon–hydrogen mixtures. The working gases are fed into the chamber through the inlet at the top of the tube, at a total flow rate of 10 SCCM by means of the mass flow controller. Additionally, a metal shielding box, grounded like the system, encloses the quartz tube.

The effect of the micropore diameter on the plasma was first studied, followed by measurements of the effect of the pressure, input power, gas type and gas mixture ratio on plasma density, effective electron temperature, plasma light intensity, and excitation rate at a fixed micropore diameter of 4 mm.

To further investigate this plasma density jump, the effects of the input power, operating pressure, gas type, and gas mixture ratio on the plasma parameters in both regions were systematically studied at a micropore diameter of 4 mm.

The plasma afterglow density and active plasma density vs the spatial afterglow pressure at a fixed input power of 200 W and micropore diameter of 4 mm are shown in Fig. 3(a). As can be seen, the plasma afterglow density first increases slowly with the pressure at the active plasma pressure of 7 Pa and then it shows an obvious “jump” increase in about five times as the pressure rises from 0.6 to 0.8 Pa, i.e., there is a jump of the plasma density from the LD to the HD as the spatial afterglow pressure increases, and the plasma density in the HD increases slightly as the pressure continues to rise; conversely, as the pressure gradually decreases, the plasma density in the HD decreases slightly until it “jumps” to the LD at 0.3 Pa. With the cyclical pressure variation in the spatial afterglow, the jump trajectory of the plasma density from the LD to the HD does not coincide with the one from the HD to the LD, forming a “hysteresis loop.” This jump and hysteresis of plasma density in the spatial afterglow also occur at active plasma pressures of 12 and 16 Pa. However, the plasma afterglow density gradually decreases as the active plasma pressure rises, and the pressure threshold for LD to HD conversion gradually increases. The active plasma density increases gradually with increasing active plasma pressure, but varies little with spatial afterglow pressure.

Figure 3(b) shows the evolution of the effective electron temperature (T_eff) in afterglow and active plasma region vs spatial afterglow pressure at different active plasma pressure. As can be seen, the T_eff in the afterglow also undergoes a jump. The T_eff in active plasma region decreases gradually with increasing active plasma pressure, but varies little with spatial afterglow pressure. There is an interesting situation. That is, for the same afterglow pressure, the higher afterglow plasma density corresponds to the lower active plasma density in both LD and HD. Although this phenomenon is rather counterintuitive, it is easy to understand by comparing Fig. 3(b) that there is a good agreement between the variation of the plasma afterglow density with the active plasma pressure in Fig. 3(a) and that of the T_eff in active plasma region with the active plasma pressure in Fig. 3(b). It indicates that the electron temperature has a greater influence on the afterglow than the plasma density in argon discharges. More frequent collisions due to the increased active plasma pressure result in a severe loss of electron energy; thus, the electrons diffusing into the afterglow are of lower energy and the collisions are weakened, in other words, the increased plasma density may not be able to compensate for the decrease in ionization caused by the loss of electron energy. Therefore, this may weaken the collision ionization process in the afterglow, reducing the afterglow density and leading to plasma density conversions at higher pressures, as shown in Fig. 3(a), e.g., a critical afterglow pressure of 0.6 Pa at an effective plasma pressure of 7 Pa, and a critical afterglow pressure of 1.2 Pa at an effective plasma pressure of 16 Pa.

This conversion is different from the well-known E–H mode transition and hysteresis in ICPs.^31–35 The E–H mode transition occurs in the active plasma, which is essentially a conversion of the plasma from being driven by the electrostatic field generated by the coil voltage (E mode) to being maintained by the electromagnetic field induced by the coil current (H mode).^34,35 However, in this experiment, when the plasma afterglow undergoes a jump, the input power and pressure are fixed in the active plasma, i.e., the voltage and current across the coil are constant, so the variation of the plasma density with the pressure in the spatial afterglow is not the same as the E–H mode jump.

The electrons diffuse into the afterglow region through the micropore and are in LD at low pressure of the spatial afterglow, because the collision frequency between the electrons and the background gas is too low to cause direct collision ionization or collision excitation. As the spatial afterglow pressure rises, more frequent collisions increase ionization and excitation, resulting in a slow increase in plasma density and light intensity. When the spatial afterglow pressure rises to the critical value, the collision frequency further increases and the collisional ionization is enhanced, as can be seen in Fig. 4, resulting in an abrupt increase in plasma density, where the plasma density jumps from the previous LD to the HD. Conversely, as the spatial afterglow pressure decreases, the collision ionization weakens and the plasma density decreases until the certain pressure where collision ionization cannot be maintained. Finally, the plasma density in the spatial afterglow jumps from the HD back to the LD.

The plasma density and light intensity in the spatial afterglow and the afterglow T_eff vs the afterglow pressure at different input power are shown in Fig. 5. The constant active plasma pressure is 7 Pa, and the micropore diameter is 4 mm. At the RF power of 100 W, the plasma density initially increases slowly as the pressure rises in the spatial afterglow. When the pressure rises to 0.8 Pa, the plasma density in the spatial afterglow undergoes a jump from the LD to the HD, and the plasma density in the HD increases slightly as the pressure continues to rise. In contrast, the plasma density in the HD slowly decreases as the pressure gradually drops, and the plasma jumps from the HD to the LD when the pressure drops to 0.3 Pa. Along with the conversion of the plasma density and the hysteresis loop, the plasma light intensity vs the spatial afterglow pressure will also have a “jump” variation, and vice versa; at the same time, the trajectory of the plasma light intensity also appears “hysteresis loop,” as shown in Fig. 5(b). The afterglow T_eff also jumps, as shown in Fig. 5(c), and gradually decreases with increasing power, which is consistent with the results of other researchers.³⁹ This phenomenon also occurs at input powers of 150 and 200 W, but as the discharge power increases, the plasma converts from LD to HD at lower pressures due to the gradually enhanced ionization in the spatial afterglow as the power increases, as shown in Fig. 6.

In the active plasma, as can be seen in Fig. 7, the plasma density and effective electron temperature increase significantly with the RF power, which enhances the ionization in the afterglow, allowing the plasma density jump to occur at lower pressures, e.g., a critical pressure of 0.8 Pa for a 100 W discharge and 0.6 Pa for a 200 W discharge [see Fig. 5(a)]. This is also the reason why the hysteresis loop becomes smaller as the RF power increases.

To further investigate the mechanism of plasma density jump and hysteresis in the spatial afterglow, experimental diagnostics are also performed on nitrogen, hydrogen, and argon–hydrogen gas mixtures. As shown in Fig. 8(a), when the discharge gas is argon, the critical pressure for the plasma to jump from the LD to the HD is about 1 Pa, and the plasma in the HD has a higher density. When the discharge gas is nitrogen, the jump and hysteresis of plasma density still exist, but the critical pressure is higher, about 2.5 Pa, and the plasma density is lower compared to the argon discharge in the HD. For the hydrogen discharge, however, the jump is not obvious and the hysteresis loop almost disappears. This phenomenon may be determined by the discharge characteristics of the gas itself.

In the active plasma, when the discharge gases are argon, nitrogen, and hydrogen, the plasma densities are roughly 10¹², 10¹¹, and 10¹⁰ cm⁻³, respectively, the ionization collision cross sections of the three kinds of gases gradually decrease, as can be seen from Fig. 8(b). It indicates that the argon discharge has a higher plasma density for the same RF power and pressure, resulting in more electrons being ejected through the micropore into the afterglow region, making it easier to initiate LD–HD conversion at lower pressures. The lower plasma density produced by the nitrogen discharge and the lower number of electrons ejected into the spatial afterglow allow conversion to occur at higher pressures, resulting in a larger hysteresis loop for nitrogen compared to argon. The hydrogen discharge produces the lowest plasma density and fewer electrons are ejected into the afterglow, resulting in less significant LD–HD jump and nearly disappeared hysteresis loop.

Figure 9 shows the active plasma density and effective electron temperature vs the hydrogen content in the Ar/H₂ discharge at RF power of 200 W and active plasma pressure of 16 Pa. As expected, the active plasma density decreases rapidly and then slowly with the hydrogen content. This is because the electrons consume some of the energy for collision dissociation and excitation with hydrogen molecules and atoms after adding hydrogen. According to the conservation of energy, the effective electron temperature increases gradually with increasing hydrogen content. This agrees with what other researchers have found.⁴² 

The plasma density and light intensity vs pressure in the spatial afterglow at RF power of 200 W and active plasma pressure of 16 Pa are shown in Fig. 10. In the case of the pure argon discharge, there is a significant LD–HD jump and a hysteresis loop. At 1% hydrogen, as the spatial afterglow pressure rises, the plasma density gradually increases and the plasma passes into the HD at 1 Pa. Continuing to rise the pressure, the plasma density remains almost constant. Compared to the pure argon discharge, the plasma afterglow density in Ar/H₂ discharge increases significantly, by about four times. On the contrary, as the pressure gradually drops, the plasma density initially stays almost constant and then decreases slightly, but eventually no jump from the HD to the LD is observed. This trend also occurs at 10% and 20% hydrogen, but as the hydrogen content grows, the plasma density gradually decreases and the critical pressure for the plasma to be in the HD gradually rises. Along with the variation of the plasma density with the hydrogen content, the plasma light intensity shows a similar pattern, as shown in Fig. 10(b). This is somewhat different from the afterglow evolution characteristics of pure Ar discharges. For Ar discharges, the plasma afterglow density decreases with increasing active plasma pressure and density. However, with the addition of H₂, both the active plasma density and the afterglow density decrease with increasing H₂ content. It indicates that the addition of hydrogen enhances the effect of the active plasma density on the spatial afterglow.

The diffusion coefficient of the neutral gas is given by these equations $D = 1 3 υ λ ¯$⁠, $υ ¯ = 8 k B T π m$⁠, $λ ¯ = 0.677 n π d 2$⁠, where $D$ is the diffusion coefficient of the neutral gas, $υ ¯$ is the mean speed of molecules, $λ ¯$ is the mean free path of molecules, $T$ is the temperature of the neutral gas, $m$ is the mass of molecules, $n$ is the number density of molecules, and $d$ is the effective diameter of the gas molecule. The mean free path of molecules is related to the state of the gas. In standard temperature and pressure (STP), the mean free path of hydrogen molecules is about 1.123 × 10⁻⁷ m, with an effective diameter of about 2.7 × 10⁻¹⁰ m, and the mean free path of argon molecules is about 0.666 × 10⁻⁷ m, with an effective diameter of about 3.2 × 10⁻¹⁰ m. Thus, the diffusion coefficients of hydrogen and argon in the standard state can be estimated to be about 6.38 × 10⁻⁵ and 8.34 × 10⁻⁶ m²/s, respectively.

The mass and collision cross section of hydrogen molecules is much smaller than that of argon atoms, so the diffusion coefficient of hydrogen is about an order of magnitude higher than that of argon. Although the active plasma density decreases with the addition of hydrogen, as shown in Fig. 9, the diffusion of the neutral gas into the spatial afterglow is greatly enhanced due to the higher diffusion coefficient of hydrogen, which simultaneously brings in a large amount of plasma and promotes collision ionization in the afterglow region, causing the plasma afterglow density to increase and the critical pressure to decrease. As the hydrogen content continues to rise, the active plasma density further decreases, which reduces the number of electrons flowing into the afterglow region, resulting in a lower plasma afterglow density and a higher critical pressure, as shown in Fig. 10(a), where the critical pressures are 1 Pa at 1% hydrogen and 1.2 Pa at 20% hydrogen. This indicates that there is a competition between the enhancement of neutral gas diffusion and the reduction of active plasma density as increasing the addition of hydrogen.

In this paper, we have presented the jump and hysteresis of plasma density in the spatial afterglow of ICPs. The pressure between the active plasma and the spatial afterglow is independently controlled by using a micropore between them. The plasma parameters in both regions, including density, effective electron temperature, light intensity, and excitation rate, have been measured. At a micropore diameter of 4 mm, the plasma density converts between LD and HD with the spatial afterglow pressure rising and falling, which agree well with variations of light intensity and excitation rate. The variation of the plasma density from the LD to HD is inconsistent with that from the HD to LD, thus forming a hysteresis loop.

For pure argon discharges, it is easier for plasma density jump in the spatial afterglow. Nitrogen is harder to ionize than argon, and the critical pressure at which the plasma density in the spatial afterglow undergoes a jump is higher, creating a larger hysteresis loop. For pure hydrogen discharges, the jump of plasma density in the spatial afterglow is less pronounced and the hysteresis loop almost disappears, because it is more difficult to ionize hydrogen than argon and nitrogen at the same conditions.

For argon–hydrogen mixed gas discharges, there is no hysteresis loop in plasma density. The addition of hydrogen can result in a competition between enhanced diffusion of the neutral gas from the active plasma to the spatial afterglow and reduced the active plasma density. As the hydrogen concentration increases from 0% to 1%, the addition of hydrogen enhances the diffusion of the neutral gas and thus the collision ionization in the spatial afterglow. At this point, the diffusion enhancement of neutral gases plays a dominant role. As the hydrogen concentration increases from 1% to 20%, the further decrease in active plasma density weakens the collision ionization in the afterglow, leading to a gradual increase in the critical pressure for plasma density jump. In this case, the reduction of the active plasma density has a greater effect than neutral gas diffusion.

The ICP source is capable of enhancing the spatial plasma afterglow density by controlling the pressure in two regions. In the future, this property may have promising applications in materials synthesis and processing, dust plasma pollution control, negative hydrogen ion sources, etc. However, the present study is limited by the existing means of diagnosis. Even if the measured excitation rate shows the plasma density jump is due to the increased ionization, the exact cause of the enhanced ionization in the spatial afterglow requires further detailed studies. The simulation that can provide information on the electron energy distribution function and the ionization rate in both regions may help to better explain these phenomena.

This work is financially supported by the National Natural Science Foundation of China (NSFC) (Nos. 12075049 and 12105041), the National Key R&D Program Projects (No. 2017YFE0300106), and the Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, Dalian 116024, China (No. KF2302).

The authors have no conflicts to disclose.

Yu Zhang: Data curation (equal); Formal analysis (equal); Validation (equal); Writing – original draft (equal). Wei Yang: Formal analysis (equal); Writing – review & editing (equal). Fei Gao: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). You-Nian Wang: Project administration (equal); Writing – review & editing (equal).

The data support the findings of this study are available from the corresponding authors upon reasonable request.