Many different gas discharges and plasmas exhibit bistable states under a given set of conditions, and the history-dependent hysteresis that is manifested by intensive quantities of the system upon variation of an external parameter has been observed in inductively coupled plasmas (ICPs). When the external parameters (such as discharge powers) increase, the plasma density increases suddenly from a low- to high-density mode, whereas decreasing the power maintains the plasma in a relatively high-density mode, resulting in significant hysteresis. To date, a comprehensive description of plasma hysteresis and a physical understanding of the main mechanism underlying their bistability remain elusive, despite many experimental observations of plasma bistability conducted under radio-frequency ICP excitation. This fundamental understanding of mode transitions and hysteresis is essential and highly important in various applied fields owing to the widespread use of ICPs, such as semiconductor/display/solar-cell processing (etching, deposition, and ashing), wireless light lamp, nanostructure fabrication, nuclear-fusion operation, spacecraft propulsion, gas reformation, and the removal of hazardous gases and materials. If, in such applications, plasma undergoes a mode transition and hysteresis occurs in response to external perturbations, the process result will be strongly affected. Due to these reasons, this paper comprehensively reviews both the current knowledge in the context of the various applied fields and the global understanding of the bistability and hysteresis physics in the ICPs. At first, the basic understanding of the ICP is given. After that, applications of ICPs to various applied fields of nano/environmental/energy-science are introduced. Finally, the mode transition and hysteresis in ICPs are studied in detail. This study will show the fundamental understanding of hysteresis physics in plasmas and give open possibilities for applications to various applied fields to find novel control knob and optimizing processing conditions.

Many different physical systems, such as plasmas (Sivis and Ropers, 2013; Lee and Chung, 2015a; Schweigert, 2004; Chabert et al., 2005; Turner and Lieberman, 1999; and Lee et al., 2013; 2010a), electronic devices (Prodromakis et al., 2012; Strukov et al., 2008; Asamitsu et al., 1997; and Yang et al., 2013), and magnetic materials (Provenzano et al., 2004 and Crespo et al., 2004), can exhibit more-than-two stable (bistable or more) states under a given set of conditions. This property manifests itself in the history-dependent hysteresis of an intensive observable quantity of the system upon variation of an external parameter, e.g., the input power (Lee and Chung, 2015a; 2015b). This phenomenon, which arises from an excitation memory that is intrinsic to the system, is one of the most important effects in the fundamental and applied natural sciences and has been extensively studied in the context of gas-plasma formation (Schweigert, 2004; Chabert et al., 2005; Turner and Lieberman, 1999; Lee et al., 2013; 2010a; Prodromakis et al., 2012; Merlino and Cartier, 1984; Malkov and Diamond, 2008; Itoh and Itoh, 1988; Ding et al., 1994; Taniguchi and Kawai, 1999; Bortolon et al., 2006; El-Fayoumi et al., 1998; Xu et al., 2000; Daltrini et al., 2007; Kortshagen et al., 1996; Xu et al., 2000; Lee et al., 2007; Ding et al., 2008; Gao et al., 2010; Lee et al., 2006; Lee and Chung, 2015a; and Sivis and Ropers, 2013).

Recently, the hysteresis phenomena have become a great attention to gas discharges or plasmas because thorough understanding of the microscopic plasma excitation mechanisms is critical for stable plasma operation, in such diverse fields as plasma etching in industrial nanodevice fabrication (Lee and Chung, 2015a), fusion reactors (Evans et al., 2006), bio-medical plasmas (Lu et al., 2014), and extreme-ultraviolet (EUV) light generation in plasmonic nanostructures (Ostrikov et al., 2016; Peng et al., 2012; Nie and Emory, 1997; Sivis et al., 2012; Sivis and Ropers, 2013; and Sivis et al., 2013 and references therein). Importantly, the discharge mode transition and its huge hysteresis phenomena have been extensively reported in radio-frequency (RF) plasmas, especially inductively coupled gas-discharge plasmas (ICPs) (Fig. 1), which are characteristically nonlinear and display hysteresis loops (Lee and Chung, 2015a and references in therein). When the discharge power increases, the plasma density increases suddenly from a low- to high-density mode, whereas decreasing the RF power maintains the plasma in a relatively high-density mode, resulting in significant hysteresis (Fig. 1). To date, a comprehensive description of plasma hysteresis and a physical understanding of the main mechanism underlying their bistability remain elusive, despite the many experimental observations of plasma bistability conducted under RF ICP excitation (Merlino and Cartier, 1984; Malkov and Diamond, 2008; Itoh and Itoh, 1988; Ding et al., 1994; Taniguchi and Kawai, 1999; Bortolon et al., 2006; El-Fayoumi et al., 1998; Xu et al., 2000; Daltrini et al., 2007; Kortshagen et al., 1996; Xu et al., 2000; Lee et al., 2007; Ding et al., 2008; and Gao et al., 2010).

FIG. 1.

Inductively coupled plasma: plasma parameters and nano-applications.

FIG. 1.

Inductively coupled plasma: plasma parameters and nano-applications.

Close modal

This work, entitled “Review of Inductively Coupled Plasmas: Nano-Applications and Bistable Hysteresis Physics” comprehensively reviews both the current knowledge in the context of various nanoscience applications and the global understanding of the bistability and hysteresis physics in various systems of the ICPs. Because ICPs have been widely used not only for semiconductor-device fabrication processes and nanostructure fabrication (Fig. 1) but also for nuclear-fusion operation, spacecraft propulsion, discharge lamps, gas reformation, and the removal of hazardous gases and materials, this study will be of great relevance to various applications and give optimizing conditions and fine control, as well as the fundamental understanding of the discharge mode transition and hysteresis physics.

This review, which describes nano-applications and bistable hysteresis physics of the ICPs, consists of three parts: Sec. II—Fundamental understanding of ICPs, Sec. III—Applications of ICPs to various fields of nano/environmental/energy science, and Sec. IV—Mode transition and hysteresis in ICPs.

The ICP was first applied to light lamp, called wireless plasma lamp generated by Faraday's law. This means that the ICP can be thought to be a transformer circuit with single circular plasma as secondary circuit part of the transformer. The ICP has a variety of configurations: cylindrical, planar, and ferrite immersed types, etc. These fundamental aspects of the ICPs will be discussed in Sec. II.

There have been a number of applications of the ICP, such as industrial plasma processing for memory-device fabrication, plasma propulsion for spacecraft and satellite, nanostructure fabrication, and environmental/energy science applications. This is dealt in Sec. III. In the industrial processing, the plasmas are widely used for etching, deposition, ion implantation, and ashing. Recently, line widths (the critical feature size) decreased less than 10 nm and high aspect ratio etching technique is strongly needed (Sec. III A). The ICPs perform well high aspect ratio etching in semiconductor plasma process, and the detailed techniques, such as Bosch process, high aspect ratio etching technique, and cryoetching, are introduced. On the other hand, there is a high demand for atomic-layer etching technique, which uses extremely low ion energies (Sec. III A). Nowadays, ICPs have become widely used in various fields (nanostructure fabrication in the nano/bio sciences, nuclear-fusion operation, spacecraft propulsion, and plasma torches for gas reforming and the removal of hazardous gases and materials) beyond industrial plasma processing for memory-device fabrication. These are shown in Sec. III B.

In Sec. IV, the discharge mode transition and hysteresis in ICPs are discussed in detail. The term “inductively coupled plasma” signifies that the plasma is generated by inductive coupling, which means that enough plasma density to make a closed plasma circle-loop is needed. But, the plasma is sustained at extremely low plasma density regime below 1×109−10 cm−3. This plasma sustainment at very low plasma density implies that there is a different plasma heating mechanism, so called capacitive mode. Thus, with the increasing external parameter such as radio-frequency power, transition from capacitive to inductive mode occurs. There has been much effort on the discharge-mode transition from the capacitive to inductive mode in ICPs in terms of both experimental and theoretical approaches, and these are shown in Sec. IV A.

Many physical systems can exist in either of two different configurations under a given set of conditions, depending on the system history. This phenomenon is generally called hysteresis. (Sec. IV B) It is noteworthy that ICP shows significantly huge hysteresis and bistability characteristics than other plasmas. The potential for hysteresis and bistability in ICPs to provide insights into plasma physics, in general, has motivated many experimental studies of ICP characteristics (Sec. IV C). Hysteresis mechanisms in ICPs are indicated in Sec. IV D. There is open question on the hysteresis, and it is illustrated in Sec. IV E.

Finally, conclusions and outlook are given in last part, and studies on the hysteresis and bistability in such plasmas (ICP) should help to deepen the fundamental understanding of hysteresis physics in plasmas and to open possibilities for applications.

RF ICPs have been widely studied for over 130 years. The basic concept for generating an ICP stems from Faraday's law, ×E=B/t. An RF current flowing into an antenna coil induces a time-varying magnetic field. This magnetic field produces an induction field, which generates and sustains the plasma. This system can be thought of as a transformer circuit in which the antenna coil acts as the primary circuit, while the plasma forms the secondary circuit with a single circular loop, as shown in Fig. 2 (Piejak et al., 1992).

FIG. 2.

(a) Inductively coupled plasma reactor. (b) Electrical-circuit representation of an inductive RF discharge as the secondary circuit of an air-core transformer. I1 is the current flowing in the antenna induction coil (with resistance R0 and inductance L0). I2 is the current of the plasma that is inductively coupled through L2, the plasma resistance R2, and the plasma inductance j(ω and2 by electron inertia. Figure 2(b) was redrawn from an original (Piejak et al., 1992). Reproduced with permission from Piejak et al., Plasma Sources Sci. Technol. 1, 179 (1992). Copyright 1992 Institute of Physics.

FIG. 2.

(a) Inductively coupled plasma reactor. (b) Electrical-circuit representation of an inductive RF discharge as the secondary circuit of an air-core transformer. I1 is the current flowing in the antenna induction coil (with resistance R0 and inductance L0). I2 is the current of the plasma that is inductively coupled through L2, the plasma resistance R2, and the plasma inductance j(ω and2 by electron inertia. Figure 2(b) was redrawn from an original (Piejak et al., 1992). Reproduced with permission from Piejak et al., Plasma Sources Sci. Technol. 1, 179 (1992). Copyright 1992 Institute of Physics.

Close modal

Hittorf (1884) first proposed that plasma lamp could be produced by wireless inductive coupling to an antenna coil surrounding the tube. The plasma was then named an “electrodeless RF lamp,” and it overcame the drawbacks of conventional fluorescent and discharge lamps with electrodes (Godyak, 2002). Since the filing of patents for the ICP lamp by Hewitt (1907) [Fig. 3(a)] and by Bethenod and Claude (1936) [Fig. 3(b)], much effort has sought to improve the ICP lamp design (Anderson, 1970; Shinomiya et al., 1991; Coaton and Marsden, 1997; and Lister et al., 2004).

FIG. 3.

(a) First patent on the radio-frequency inductive lamp filed by Hewitt (1907), involving a spherical glass bulb filled with mercury vapor. (b) Radio-frequency inductive lamp with a reentrant cavity (Bethenod and Claude, 1936). The inductive antenna-coil is immersed in the lamp body to prevent light shading and reduce EM wave radiation.

FIG. 3.

(a) First patent on the radio-frequency inductive lamp filed by Hewitt (1907), involving a spherical glass bulb filled with mercury vapor. (b) Radio-frequency inductive lamp with a reentrant cavity (Bethenod and Claude, 1936). The inductive antenna-coil is immersed in the lamp body to prevent light shading and reduce EM wave radiation.

Close modal

In the 1970s, applications of ICPs were extended to new fields such as plasma torches in material processing and plasma sources used in semiconductor/display processes. Plasma torches were operated in the high- or atmospheric-pressure regime (Eckert, 1974), whereas plasma sources for semiconductor and display processing were used at low pressures below a few hundred millitorr (mTorr) due to the need of clean environment. The use of plasmas in semiconductor processing stems from their novel characteristics, namely, the directional motion of ions and synergetic effects between the ions and radicals (Coburn and Winters, 1979). In particular, ICPs were actively developed and applied to semiconductor processes because high-density plasma generation over a large area is possible without the need to insert an electrode. In early semiconductor processes, ICPs were used mainly for plasma etching but are now actively used for other processes, including ashing, ion implantation, and deposition process, as well as the etching. The decrease in semiconductor linewidth requires a new structure of the plasma source in which an RF bias is applied to the ICP (Lee et al., 2010c). ICPs have also served various applications (e.g., nanostructure fabrication, plasma-driven biosensors and bio-applications, nuclear-fusion operation, and spacecraft propulsion), beyond plasma lamps and the industrial plasma processing for memory-device fabrication.

ICP structure can be of several types: cylindrical-coil, planar-coil, or ferrite-core, as outlined in Fig. 4. A cylindrical ICP consists of a helical coupler and a helical resonator, while the planar ICP consists of a conventional transformer-coupled plasma (TCP) installed in the chamber periphery and an immersed ICP installed in the vacuum chamber (Hopwood, 1994). The ferrite-core ICP has a closed magnetic path formed by wrapping the ferrite material around the antenna to improve discharge performance, as measured by the significant power-transfer efficiency, which results in a high plasma density (Godyak, 2013).

FIG. 4.

Schematic diagram of ICP types: (a) cylindrical, (b) planar (Lieberman and Lichtenberg, 2005) [Reproduced with permission from Lieberman and Lichtenberg, Principle of Plasma Discharges and Materials Processing, 2nd ed. Copyright 2005 John Wiley and Sons Inc.], and (c) ferrite immersed types (Godyak, 2011). Reproduced with permission from Godyak, Plasma Sources Sci. Technol. 20, 025004 (2011). Copyright 2011 Institute of Physics.

FIG. 4.

Schematic diagram of ICP types: (a) cylindrical, (b) planar (Lieberman and Lichtenberg, 2005) [Reproduced with permission from Lieberman and Lichtenberg, Principle of Plasma Discharges and Materials Processing, 2nd ed. Copyright 2005 John Wiley and Sons Inc.], and (c) ferrite immersed types (Godyak, 2011). Reproduced with permission from Godyak, Plasma Sources Sci. Technol. 20, 025004 (2011). Copyright 2011 Institute of Physics.

Close modal

In the ICP system, an additional RF bias can be applied to the substrate or electrode where the wafer is placed. The structure is then called an RF-biased ICP or reactive ion etcher. The upper antenna coil controls the plasma density while the lower RF bias controls the ion energy independently. However, Lee et al. (2010c) and Sobolewski and Kim (2007) found that the electron temperature, plasma density, and electron energy distribution function (EEDF) change with the RF bias power. Since then, the effect of RF bias power on ICPs has been intensively investigated, both experimentally and theoretically (Kwon et al., 2011; Lee et al., 2011a; 2011b; Schulze et al., 2012; Wen et al., 2016; Zaka-ul-Islam et al., 2015; Lee and Chung, 2014; 2015a; Lee and Chung, 2012b; and Lee et al., 2012a). The combination of an ICP and RF bias provides a way to understand, fundamentally, the heating mechanism that underlies plasma sustainment via the combined capacitive and inductive fields, for the purpose of application to nanomaterial fabrication.

When the plasma is sustained, a non-neutral region called the sheath is formed at the plasma boundary to balance electron and ion losses for the quasi-neutral characteristic (Bohm, 1949; Riemann, 1997; and Hershkowitz, 2005). The ions are accelerated through the sheath, and the ions reaching to the surface or the wafer are then vertically incident. This behavior is a prerequisite for semiconductor processes involving vertical etching. An important feature of semiconductor processes is the synergy of ions and radicals. In a notable 1979 study, Coburn and Winters (1979) showed two ways to etch a wafer surface, involving a chemical reaction (radicals) and a physical reaction (ions sputtering), as depicted in Figs. 5(a) and 5(b). The chemical reaction is isotropic, whereas the physical reaction is anisotropic. Their combined application [Fig. 4(c)] yields an etch rate that is one order of magnitude greater than the sum of their individual effects, as shown in Fig. 4(d). This synergetic effect highlights the benefits of using plasmas for device fabrication (Graves, 1994; Poulsen, 1977; Winters, 1977; and Somekh, 1976).

FIG. 5.

Basic etching mechanisms: (a) chemical etching, (b) sputtering, (c) plasma etching combined with chemical etching and sputtering (Abe, 2008). (d) Example of plasma etching (also called ion-assisted etching) of Si using Ar ions (Coburn and Winters, 1979). Etching rates are significantly enhanced when the Ar ions and XeF2 gas are irradiated together. Reprinted with permission from J. Appl. Phys. 50, 3189 (1979). Copyright 1979 AIP Publishing LLC.

FIG. 5.

Basic etching mechanisms: (a) chemical etching, (b) sputtering, (c) plasma etching combined with chemical etching and sputtering (Abe, 2008). (d) Example of plasma etching (also called ion-assisted etching) of Si using Ar ions (Coburn and Winters, 1979). Etching rates are significantly enhanced when the Ar ions and XeF2 gas are irradiated together. Reprinted with permission from J. Appl. Phys. 50, 3189 (1979). Copyright 1979 AIP Publishing LLC.

Close modal

The semiconductor industry has strived to increase device yield and performance, in particular, by shrinking line widths (the critical feature size) to below a few nanometers. There is also increasing demand for new structured devices with a three-dimensional (3D) architecture (e.g., FinFET and vertical (V) NAND flash memory) (Wu et al., 2010; Lee et al., 2014; Burke et al., 2015; Marchack and Chang, 2011; and Donnelly and Kornblit, 2013). However, lithography, which forms the initial step of semiconductor processes, still makes use of existing light sources (ArF-I 193 nm light) (Stamm, 2004) (Kim et al., 2012), and the conversion to EUV light sources (13.5 nm wavelength) is also being delayed. Even if an EUV light source was to become available, several problems would still need to be solved, e.g., low light efficiency, low production yield, high levels of roughness in the photo resistor, and chamber contamination by metals arising from the use of the metal droplet. Presently, the limits of lithography are overcome by plasma-etching techniques, such as multi-patterning [called the double patterning technique (DPT) and the quadruple patterning technique (QPT)] (Kim et al., 2012). Plasma-etching techniques become more important as the critical feature size decreases to below a few nanometers. Besides, in the case of a DRAM memory device, a capacitor structure with an extremely narrow spacing must be fabricated. Also, new structures for cell-array transistors (CATs) are needed to reduce leakage currents and to enhance device performance, e.g., buried-gate (BCAT) and vertical-channel (VCAT) structures. This requires an etch process with a high aspect ratio (HAR), where a strong ion energy is essential. Flash memory devices now employ 3D V NAND flash memory structures owing to the processing challenges associated with reducing line widths in planar NAND flash and the need to avoid high leakage currents (Lu, 2012). However, achieving a HAR hole etch remains a challenge for 3D V NAND flash memory.

An ICP has been used as the plasma source for HAR etching by applying an RF bias to the substrate. Jo et al. (2005) described the deep silicon etching technique in an SF6/C4F8 ICP with an RF bias by using the modified Bosch-type process shown in Figs. 6(a) and 6(b). This method is originally based on the Bosch method described by Laermer and Schilp (1996), which uses a time-multiplexed process with etching and polymerization steps [Fig. 6(a)], while they controlled the etching/passivating time, the process transition step, and the ion energy [Fig. 6(b)]. The Bosch etching method is illustrated in Figs. 6(c)–6(f). Ayón et al. (1999) showed that the most critical parameters in the Bosch process are the gas flow rate, pressure, and applied RF power. Morton et al. (2008) achieved sub-40 nm HAR silicon pillar arrays, as shown in Figs. 6(g)–6(i).

FIG. 6.

Schematic illustration of (a) the standard Bosch process and (b) the modified Bosch process (Jo et al., 2005). Reprinted with permission from J. Vac. Sci. Technol. A 23, 905 (2005). Copyright 2005 AIP Publishing LLC. The Bosch process involves alternating etch and deposition steps. Whereas, in the standard Bosch process, C4F8 gas is used to provide the fluorocarbon for coating the entire upper surface of the silicon with polymer, in the modified Bosch process, SF6 gas is used to provide the fluorine to etch the silicon isotropically. (c)–(f) Examples of the Bosch process flow: (c) sidewall passivation using C4F8 gas, (d) isotropic silicon etching using SF6 gas, (e) SEM image of a deep trench etched by deep reactive-ion etching, and (f) magnified SEM image of the sidewall with the silicon microstructure (Kang et al., 2008). Reproduced with permission from Kang et al., J. Micromech. Microeng. 18, 075007 (2008). Copyright 2008 Institute of Physics. (g)–(i) Etching results showing arrays of vertical silicon (100) nanopillars achieved using deep reactive-ion etching with an antireflection-coating-layer etch mask. (g) Array of vertical silicon nanopillars with a diameter as small as 40 nm and a height of 1.5 μm, ordered on a grid of 235 nm pitch. (h) Higher magnification showing a peak-to-peak sidewall roughness of less than 10 nm. (i) Wide-angle view of a large-area array with long-range order (Morton et al., 2008). Reproduced with permission from Morton et al., Nanotechnology 19, 345301 (2008). Copyright 2008 Institute of Physics. (j) Principle of the physical and chemical mechanisms involved in cryoetching. (k) Typical trench profile obtained in silicon cryoetching (Dussart et al., 2014). Reproduced with permission from Dussart et al., J. Phys. D: Appl. Phys. 47, 123001 (2014). Copyright 2014 Institute of Physics.

FIG. 6.

Schematic illustration of (a) the standard Bosch process and (b) the modified Bosch process (Jo et al., 2005). Reprinted with permission from J. Vac. Sci. Technol. A 23, 905 (2005). Copyright 2005 AIP Publishing LLC. The Bosch process involves alternating etch and deposition steps. Whereas, in the standard Bosch process, C4F8 gas is used to provide the fluorocarbon for coating the entire upper surface of the silicon with polymer, in the modified Bosch process, SF6 gas is used to provide the fluorine to etch the silicon isotropically. (c)–(f) Examples of the Bosch process flow: (c) sidewall passivation using C4F8 gas, (d) isotropic silicon etching using SF6 gas, (e) SEM image of a deep trench etched by deep reactive-ion etching, and (f) magnified SEM image of the sidewall with the silicon microstructure (Kang et al., 2008). Reproduced with permission from Kang et al., J. Micromech. Microeng. 18, 075007 (2008). Copyright 2008 Institute of Physics. (g)–(i) Etching results showing arrays of vertical silicon (100) nanopillars achieved using deep reactive-ion etching with an antireflection-coating-layer etch mask. (g) Array of vertical silicon nanopillars with a diameter as small as 40 nm and a height of 1.5 μm, ordered on a grid of 235 nm pitch. (h) Higher magnification showing a peak-to-peak sidewall roughness of less than 10 nm. (i) Wide-angle view of a large-area array with long-range order (Morton et al., 2008). Reproduced with permission from Morton et al., Nanotechnology 19, 345301 (2008). Copyright 2008 Institute of Physics. (j) Principle of the physical and chemical mechanisms involved in cryoetching. (k) Typical trench profile obtained in silicon cryoetching (Dussart et al., 2014). Reproduced with permission from Dussart et al., J. Phys. D: Appl. Phys. 47, 123001 (2014). Copyright 2014 Institute of Physics.

Close modal

As another etching method to achieve HAR in silicon, cryogenic etching process can be used, shown in Figs. 6(j) and 6(k). The cryogenic etching, first introduced by Tachi et al. in 1988 (Ayón et al., 1999), involves cooling the substrate from -70 °C to -140 °C and applying an additional RF bias to the substrate. The chemical reactions on the trench sidewalls then become frozen so that only the bottom is etched by ion bombardment. Strictly speaking, the mechanism of the cryogenic etching process is to use both the ion bombardment and the chemical reaction at the bottom layer. Many studies have investigated ICP cryogenic etching with an RF-bias system (Dussart et al., 2014; Plank et al., 2003; Aachboun et al., 2000; and Craciun et al., 2002).

When performing HAR hole etching, Kim et al. (2015) showed that the contact pattern is critically distorted by increasing the aspect ratio of the etched oxide in the ICP, as shown in Fig. 7(a). An HAR etch generally requires a high bias power to provide high ion energies. However, Imai (2008) observed that, with an ICP, decreasing the bias power from 1300 to 700 W significantly improves the aspect ratio from 27 to 133. This result implies that there is a critical sheath voltage at which ions are accelerated and surface charging is reduced or damage of the hard mask is minimized. The choice of an appropriate hard mask that is robust to high ion energies and chemical reactions is also required to ensure a high etch selectivity. As achievable HARs are approaching values near 100 in 3D V NAND flash memory, higher sheath voltages will soon become necessary. Many issues, such as surface charging, twisting, hole distortion, not-open, and tilting, will then become major obstacles to plasma etching, as evidenced in Fig. 7(b). The optimization of process protocols is therefore crucial for ICP HAR etch systems operating at high ion energies.

FIG. 7.

(a) Degree of contact-hole distortion in HAR etching, as a function of the aspect ratio, for an amorphous silicon mask. HAR etching was carried out using a C4F8/C4F6/O2/Ar gas mixture at 10 mTorr, 1500 W of source power, 4800 W of bias power, and 300 K of substrate temperature (Kim et al., 2015) Reprinted with permission from J. Vac. Sci. Technol. A 33, 021303 (2015). Copyright 2015 AIP Publishing LLC. (b) Channel-hole etching for 3D V NAND flash memory, illustrating issues such as clogging, hole-shape distortion, and not-open (Kim et al., 2012). Reproduced with permission from Kim et al., Proc. SPIE 8326, 832605 (2012). Copyright 2012 SPIE.

FIG. 7.

(a) Degree of contact-hole distortion in HAR etching, as a function of the aspect ratio, for an amorphous silicon mask. HAR etching was carried out using a C4F8/C4F6/O2/Ar gas mixture at 10 mTorr, 1500 W of source power, 4800 W of bias power, and 300 K of substrate temperature (Kim et al., 2015) Reprinted with permission from J. Vac. Sci. Technol. A 33, 021303 (2015). Copyright 2015 AIP Publishing LLC. (b) Channel-hole etching for 3D V NAND flash memory, illustrating issues such as clogging, hole-shape distortion, and not-open (Kim et al., 2012). Reproduced with permission from Kim et al., Proc. SPIE 8326, 832605 (2012). Copyright 2012 SPIE.

Close modal

On the other hand, there is a high demand for atomic-layer etching, involving extremely low ion energies (Donnelly and Kornblit, 2013 and Kanarik et al., 2015). On length scales below 10 nm, transistor-device performance is highly sensitive to the etch-process result and to the surface conditions. For example, transistor-gate dimensions are smaller than a few nanometers and such gates require careful etching. Surface morphology and roughness also affect device performance critically. There is therefore a need for a new etching technology that can remove the few damaged layers remaining after an HAR etch. In this perspective, atomic-layer etching (ALE) technology is a promising candidate. Originally called “digital etching” by Meguro et al. in 1990 ALE involves using self-limiting surface reactions, as shown in Fig. 8. When a clean Si surface is exposed to a reactant gas, the surface is modified (chemisorption step) and Si-Si bonds are weakened by the absorbed reactant gas. The reported absorption time for complete saturation is order of a few or tens of seconds (i.e., 30 s). After the reactant gas is purged, the layer is etched by precisely controlled ion bombardment, where the ion energy is sufficient to desorb the weakened Si-Si bonds. However, these ion energies are too low to etch the bottom layer, which does not absorb the reactant gas. The ALE is similar to atomic-layer deposition (ALD) in the way indicated in Fig. 8. The ALE etching is a promising technique for fabricating transistor devices with critical feature sizes below 10 nm, such as 3D NAND flash memory, logic devices, and FinFETs.

FIG. 8.

(a) Generic concept for ALE. (b) ALE process applied to silicon. (c) Comparison with ALD. ALE is similar to ALD but differs in that ALE involves the removal of material while ALD involves adsorption in Reaction B (Kanarik et al., 2015). Reprinted with permission from J. Vac. Sci. Technol. A 33, 20802 (2015). Copyright 2015 AIP Publishing LLC.

FIG. 8.

(a) Generic concept for ALE. (b) ALE process applied to silicon. (c) Comparison with ALD. ALE is similar to ALD but differs in that ALE involves the removal of material while ALD involves adsorption in Reaction B (Kanarik et al., 2015). Reprinted with permission from J. Vac. Sci. Technol. A 33, 20802 (2015). Copyright 2015 AIP Publishing LLC.

Close modal

ICPs can be used successfully as plasma sources for ALE because they allow a low plasma potential with minimal RF fluctuations and a precise control of ion energies. Athavale and Economou (1996) performed ALE of silicon using an ICP involving chlorine gas (chemisorption step) and argon-ion bombardment (desorption step). Kanarik et al. (2013) showed that surface roughness is significantly improved and a vertical flat etch without micro-trenching structures is achieved by using ICP ALE. Metzler et al. (2014) demonstrated the ALE of SiO2 in Ar/C4F8 ICP. In addition, pulse-power-modulated ICP is also a good candidate for atomic-layer etching because radicals and ion energies can be controlled via the duty ratio and driving frequency of the pulse power, and surface-charging damage is significantly reduced.

Nowadays, ICPs have become widely used in various fields beyond industrial plasma processing for memory-device fabrication. Examples include nanostructure fabrication in the nano/bio sciences, nuclear-fusion operation, spacecraft propulsion, and plasma torches for gas reforming and the removal of hazardous gases and materials. This section discusses the variety of ICP applications.

The main mechanisms involved in plasma treatment in various applications are illustrated in Fig. 9 (Lee and Chung, 2014). When RF power is applied to the chamber, a plasma is generated and maintained by electron heating (Kaganovich et al., 1996; Godyak and Kolobov, 1998; Godyak et al., 1998; Evans and Chen, 2001; Kolobov and Economou, 1997; Ramamurthi et al., 2003; Turner, 2009; Lee et al., 2010d; and Lee and Chung, 2012b). The electrons generated in the plasma collide with the neutral gases and particles. Under these circumstances, the discharge characteristics are remarkably dependent on the plasma parameters (plasma density, electron temperature, and EEDF). The radicals, which react strongly with the nanosurface, are created by collision reactions with electrons above a certain threshold energy. Thus, the density and the composition of these radicals depend on the plasma parameters. Since plasma generation occurs through collisions with electrons participating in ionization reaction, the density of ion species that react physically with the surface are also determined by the plasma parameters. The sheath potential, which accelerates ions so that they transfer their high kinetic energy to the surface, is determined by the electron temperature and the EEDF. In conclusion, as the external variables (pressure, power, and gas composition) are changed, the plasma parameters and the discharge property are also changed, thereby influencing and allowing the control of the nanoparticle shape and surface characteristics. This low-temperature plasma application where the gas temperature is close to room-temperature has clear benefits when compared to conventional methods like the thermal method, which usually causes material damage.

FIG. 9.

Correlation between the plasma parameters and the processing results in nanomaterial fabrication using plasma. When RF power is applied to the plasma reactor, electrons are heated by phase-breaking processes such as wave-electron interactions or collisions between electrons and neutral gas particles. The electrons have an energy distribution and undergo different kinds of collision above a certain threshold energy, resulting in dissociation (εth,1) and ionization (εth,2). The ions are accelerated across the sheath and participate in the physical reaction on the wafer or nanomaterial surface. The radicals produced by dissociation react chemically with the surface, and atoms excited by electron impacts also emit ultraviolet radiation upon de-excitation. The plasma parameters (plasma density, electron temperature, and the EEDF),which affect the process results, are therefore crucial for controlling surface modification (Lee and Chung, 2014). Reproduced with permission from Lee and Chung, Plasma Sources Sci. Technol. 23, 062002 (2014). Copyright 2014 Institute of Physics.

FIG. 9.

Correlation between the plasma parameters and the processing results in nanomaterial fabrication using plasma. When RF power is applied to the plasma reactor, electrons are heated by phase-breaking processes such as wave-electron interactions or collisions between electrons and neutral gas particles. The electrons have an energy distribution and undergo different kinds of collision above a certain threshold energy, resulting in dissociation (εth,1) and ionization (εth,2). The ions are accelerated across the sheath and participate in the physical reaction on the wafer or nanomaterial surface. The radicals produced by dissociation react chemically with the surface, and atoms excited by electron impacts also emit ultraviolet radiation upon de-excitation. The plasma parameters (plasma density, electron temperature, and the EEDF),which affect the process results, are therefore crucial for controlling surface modification (Lee and Chung, 2014). Reproduced with permission from Lee and Chung, Plasma Sources Sci. Technol. 23, 062002 (2014). Copyright 2014 Institute of Physics.

Close modal

Many studies have exploited the synergetic effect in ICPs to fabricate nanostructure materials. A vertically aligned single-crystalline nanostructure was produced on Si (100) wafer in the Ar/H2 ICP shown in Fig. 10 (Xu et al., 2011). This simple ICP method achieved a high performance with a conversion efficiency of approximately 11.9%, a short-circuit photocurrent intensity of up to 32 mA/cm2, an open-circuit voltage of 530 mV, and a fill factor reaching 70% of the value achieved in Si solar cells. These results are significant improvements over earlier similar nanostructure-enhanced solar cells.

FIG. 10.

(a) Schematic experimental setup of the ICP. (b) Photograph of the plasma glow. (c) Outline of the deposition process. (d) Representative SEM image of a Si nanostructure array. (e) Outline of a nanoarray-based solar cell (Xu et al., 2011). Reproduced with permission from Xu et al., Adv. Energy Mater. 1, 373 (2011). Copyright 2011 Wiley-VCH Verlag GmbH & Co. KGaA.

FIG. 10.

(a) Schematic experimental setup of the ICP. (b) Photograph of the plasma glow. (c) Outline of the deposition process. (d) Representative SEM image of a Si nanostructure array. (e) Outline of a nanoarray-based solar cell (Xu et al., 2011). Reproduced with permission from Xu et al., Adv. Energy Mater. 1, 373 (2011). Copyright 2011 Wiley-VCH Verlag GmbH & Co. KGaA.

Close modal

ICPs have also been applied to graphene synthesis because they operate at low temperatures, are readily controllable, and catalyst-free method (Li et al., 2016). The direct growth of graphene on transition-metal substrates, such as Ni, Cu, or Co, was achieved (Peng et al., 2013; Kim et al., 2013; Terasawa et al., 2012; Wang et al., 2010; and Kato and Hatakeyama, 2012). Those results are interesting because conventional thermal chemical vapor deposition (CVD) requires high temperatures in the range of 800 °C–1000 °C, which can damage devices and is inapplicable to flexible device. The low-temperature growth of graphene using an ICP was also performed on dielectric substrates (Zhang et al., 2011 and Wei et al., 2013). Recently, vertically oriented graphene (VG) nanosheets displayed unique functional properties such as a high electrical conductivity and surface area, compared to flat nanosheets. An ICP can be used to fabricate VG nanosheets. Yang et al. showed that the vertical growth of graphene can be controlled via the ICP power and process temperature (Yang et al., 2013). When the plasma power was increased from 50 to 200 W, denser VG nanosheets were obtained, as shown in Figs. 11(a)–11(c). For a plasma power of 300 W, VG nanosheets were grown even when the growth temperature was decreased [Figs. 11(d)–11(f)] (Yang et al., 2013). When the CH4 concentration was increased in a CH4/H2 mixture plasma, the VG nanosheets became smaller and denser [Figs. 11(g)–11(i)] (Wang et al., 2004). It was also observed that, when the Ar flow increased in the ICP, the VG nanosheets also became smaller and produced denser graphene walls [Figs. 11(i) and 11(j)] (Jain et al., 2011). This Ar-flow effect is similar to that of the ICP power shown in Figs. 10(a)–10(c) because an enhanced Ar flow increases the densities of the plasma and radicals. A uniform carbon nanocone array was also self-organized in an Ar/H2/CH4 ICP in the presence of a DC-biased substrate stage (Tsakadze et al., 2007).

FIG. 11.

(a)–(c) SEM images of graphene walls grown directly on SiO2 substrates with an ICP power of (a) 50 W, (b) 100 W, or (c) 200 W, at 900 °C, or with an ICP power of 300 W at (d) 600 °C, (e) 700 °C, or (f) 800 °C (Yang et al., 2013). Reproduced with permission from Yang et al., J. Mater. Chem. A 1, 770 (2013). Copyright 2013 Royal Society of Chemistry. SEM images of carbon nanosheets grown on Si substrates with CH4 concentrations of (g) 10%, (h) 40%, or (i) 100% (Other deposition conditions were 900 W ICP power, 680 °C, ∼12 Pa, 20 min) (Wang et al., 2004). Reproduced with permission from Wang et al., Carbon 42, 2867 (2004). Copyright 2004 Elsevier. Comparison of wall sizes in the ICP at a constant temperature of 665 °C and for argon gas flows of (j) Ar-27  sccm, (k) Ar-45  sccm, and (l) Ar-55  sccm. The films were deposited on a steel substrate (Jain et al., 2011). Reproduced with permission from Jain et al., Carbon 49, 4987 (2011). Copyright 2011 Elsevier.

FIG. 11.

(a)–(c) SEM images of graphene walls grown directly on SiO2 substrates with an ICP power of (a) 50 W, (b) 100 W, or (c) 200 W, at 900 °C, or with an ICP power of 300 W at (d) 600 °C, (e) 700 °C, or (f) 800 °C (Yang et al., 2013). Reproduced with permission from Yang et al., J. Mater. Chem. A 1, 770 (2013). Copyright 2013 Royal Society of Chemistry. SEM images of carbon nanosheets grown on Si substrates with CH4 concentrations of (g) 10%, (h) 40%, or (i) 100% (Other deposition conditions were 900 W ICP power, 680 °C, ∼12 Pa, 20 min) (Wang et al., 2004). Reproduced with permission from Wang et al., Carbon 42, 2867 (2004). Copyright 2004 Elsevier. Comparison of wall sizes in the ICP at a constant temperature of 665 °C and for argon gas flows of (j) Ar-27  sccm, (k) Ar-45  sccm, and (l) Ar-55  sccm. The films were deposited on a steel substrate (Jain et al., 2011). Reproduced with permission from Jain et al., Carbon 49, 4987 (2011). Copyright 2011 Elsevier.

Close modal

ICPs have also had other important applications, for example, as neutral-beam injector (NBI) sources for nuclear-fusion operation, spacecraft-propulsion sources (Sun et al., 2005), plasma sources for gas reforming, and hazardous gas/material removal (Georges et al., 2013). Figure 12(a) shows an ICP system used for negative-hydrogen-ion production for the purpose of an NBI system of fusion devices (Kraus et al., 2012). A high-density plasma is generated by the ICP source and negative hydrogen ions are formed by surface production and volumetric collision process. Because of the long distance from the ICP region to the expansion region, the electrons are cooled and negative-ion production is favored. The electrons are diverted by a magnet, while the negative hydrogen ions can reach the grid region. The hydrogen ions are then accelerated before becoming neutralized. Recently, the concept of photo-neutralization was also studied in an NBI (Simonin et al., 2016 and Cousineau et al., 2017).

FIG. 12.

(a) Inductively coupled negative-hydrogen-ion sources designed for neutral-beam-injection (NBI) systems in a fusion device (Kraus et al., 2012). Reprinted with permission from Rev. Sci. Instrum. 83, 02B104 (2012). Copyright 2012 AIP Publishing LLC. (b) Geometry of the helicon source for plasma propulsion and ion-beam formation in a current-free double layer (Sun et al., 2005). Reproduced with permission from Sun et al., Phys. Rev. Lett. 95, 025004 (2005). Copyright 2005 American Physical Society. (c) Schematic diagram of the Destruction of Organo-Halogenated Liquids process system (Kamgang-Youbi et al., 2013). Reproduced with permission from Kamgang-Youbi et al., J. Hazard. Mater. 244, 171 (2013). Copyright 2013 Elsevier.

FIG. 12.

(a) Inductively coupled negative-hydrogen-ion sources designed for neutral-beam-injection (NBI) systems in a fusion device (Kraus et al., 2012). Reprinted with permission from Rev. Sci. Instrum. 83, 02B104 (2012). Copyright 2012 AIP Publishing LLC. (b) Geometry of the helicon source for plasma propulsion and ion-beam formation in a current-free double layer (Sun et al., 2005). Reproduced with permission from Sun et al., Phys. Rev. Lett. 95, 025004 (2005). Copyright 2005 American Physical Society. (c) Schematic diagram of the Destruction of Organo-Halogenated Liquids process system (Kamgang-Youbi et al., 2013). Reproduced with permission from Kamgang-Youbi et al., J. Hazard. Mater. 244, 171 (2013). Copyright 2013 Elsevier.

Close modal

Figure 12(b) depicts a magnetized ICP that is applicable to spacecraft propulsion (Sun et al., 2005). The magnetized ICP can produce a high plasma density with helicon-wave modes (Chen, 2012). There is a double layer region between the plasma and the diffusion chamber, which accelerates the ions (Charles, 2007). Much effort has been devoted to the study of helicon plasmas (magnetized ICPs with a helicon wave mode). A large helicon discharge was produced by Chen et al. (1995), Lynn et al. (2009), Chen (2015), and Shinohara et al. (2010). On the other hand, a mini-thruster was made by Charles (1993), Carter and Khachan (1999), Batishchev (2009), Takahashi et al. (2016), and Sheehan et al. (2014).

An ICP can be used for gas reforming and for removing hazardous gases, water, or other materials. Figure 12(c) (Kamgang-Youbi et al., 2013) is an example of an application to energy and environmental science. This study reported the noteworthy performance of an ICP torch in the degradation of chlorinated hydrocarbon waste. The ICP was generated by high-voltage power supply coupled with a high-frequency (64 MHz) transmitter. The plasma was confined to a quartz tube. Three stages (refractory wall, afterburner, and quenching) were connected to the ICP torch. Chlorinated acids were found to be successfully trapped in a scrubber and transformed into mineral salts. The final off-gas composition comprised only CO2 and H2O, when the liquid-type chlorinated hydrocarbon waste was introduced into the ICP torch system. The detailed results for gas reforming and hazardous gas, water, and material removals can be found in the papers (Bruggeman et al., 2016; Jiang et al., 2014; Wang et al., 2012; and Tatarova et al., 2014).

ICPs display mode transition characteristics. At a low plasma density, the ICP is maintained in a capacitive mode (the “E mode”) by the voltage formed between the antennas, while the discharge is transited into an inductive mode (the “H mode”) at a high plasma density regime. When the external power is lowered, the plasma density decreases and the discharge mode evolves from the H to the E mode. Interestingly, hysteresis occurs during the E-to-H and H-to-E mode transitions, where the plasma density remains relatively high, even when the H-to-E mode transition occurs at a low power. Hysteresis can occur through a variation in external parameters, such as the power, pressure, or gas mixture, etc. Although there have been many experimental observations and a few theoretical studies, much research remains to be done to explain this behavior.

Despite the widespread use of ICPs in various fields, a fundamental understanding of mode transitions and hysteresis is lacking. As mentioned, ICPs are widely used not only for semiconductor-device processes, discharge lamps, and nanostructure fabrications but also for nuclear-fusion operation, spacecraft propulsion, and plasma torches for gas reforming and hazardous gas and material removal. If, in such applications, plasma undergoes a mode transition and hysteresis occurs in response to external perturbations, the process result can be strongly affected by changes in the plasma parameters, such as the plasma density, the electron temperature, the radicals, and the EEDF. [Consider the correlation between the plasma parameters and the process results. The number density and energy flux of charged particles (ions or electrons) critically affects physical reactions at a surface. Furthermore, radicals, which react strongly with the surface, are governed by the plasma parameters (Lee and Chung, 2014).] Accordingly, an understanding of the mode transition of the plasma parameters and its bistability and hysteresis are very important, not only to gain a fundamental understanding of the physical phenomenon but also for the purpose of applications. This section therefore concerns the experimental and theoretical understanding of mode transitions and hysteresis.

The term “inductively coupled plasma” signifies that the plasma is generated by inductive power coupling, following Faraday's law (see Fig. 2 for the electrical-circuit representation of an inductive RF discharge, as described also in the literature (Piejak et al., 1992 and El-Fayoumi and Jones, 1998). However, at low RF power, the electron density in the plasma is very low, and it is therefore difficult to maintain the inductively coupled discharge. In the discharge regime, plasma generation and electron heating are governed by the electrostatic field, which is produced between the powered antenna and the grounded antenna or the grounded wall. This discharge mode is the E mode. A low plasma density and a weak light emission are characteristic of the E mode. Figure 13 shows an electrical-circuit representation of an inductively coupled RF discharge that also includes capacitive coupling (El-Fayoumi et al., 1998) (see the difference between Figs. 2 and 13).

FIG. 13.

Circuit representation of an ICP, which allows for both inductive and capacitive couplings of the RF power to the plasma. The blue and orange rectangles indicate the inductive and capacitive couplings, respectively (El-Fayoumi et al., 1998). Reproduced with permission from El-Fayoumi et al., J. Phys. D: Appl. Phys. 31, 3082 (1998). Copyright 1998 Institute of Physics.

FIG. 13.

Circuit representation of an ICP, which allows for both inductive and capacitive couplings of the RF power to the plasma. The blue and orange rectangles indicate the inductive and capacitive couplings, respectively (El-Fayoumi et al., 1998). Reproduced with permission from El-Fayoumi et al., J. Phys. D: Appl. Phys. 31, 3082 (1998). Copyright 1998 Institute of Physics.

Close modal

As the RF power increases, the electrostatic field becomes suppressed because of the wave-cutoff via an increase in the plasma density. On the other hand, the electromagnetic field starts to increase. Electron power absorption from the electromagnetic field is therefore enhanced and becomes maximized when the skin depth is comparable to the chamber characteristic length. In this regime, inductive power absorption exceeds capacitive power absorption. As the plasma density is increased by the RF power, inductive power absorption decreases because the skin depth becomes shorter than the chamber characteristic length. This is because the electrons reaching to the skin depth only participate in the electron-heating mechanism. [Note that most cold electrons are confined in the plasma bulk due to the ambipolar potential barrier (Lee and Chung, 2012a).] Figure 14 (Lee et al., 2006) clearly identifies the relevant electron-power absorption mechanism in the ICP, depending on the plasma density.

FIG. 14.

Calculated power transferred by the capacitive (dotted curve) and inductive couplings (dashed curve), and the total transferred power (solid curve), at 50 mTorr argon pressure and 0.3 A coil current. In regions I and II, power is predominantly transferred by the capacitive coupling and is proportional to the electron density (I) and inversely proportional to the electron density (II). In regions III and IV, power is predominantly transferred by the inductive coupling and is proportional to the electron density (III) and inversely proportional to the electron density (IV) (Lee et al., 2006). Reprinted with permission from Phys. Plasmas 13, 063510 (2006). Copyright 2006 AIP Publishing LLC.

FIG. 14.

Calculated power transferred by the capacitive (dotted curve) and inductive couplings (dashed curve), and the total transferred power (solid curve), at 50 mTorr argon pressure and 0.3 A coil current. In regions I and II, power is predominantly transferred by the capacitive coupling and is proportional to the electron density (I) and inversely proportional to the electron density (II). In regions III and IV, power is predominantly transferred by the inductive coupling and is proportional to the electron density (III) and inversely proportional to the electron density (IV) (Lee et al., 2006). Reprinted with permission from Phys. Plasmas 13, 063510 (2006). Copyright 2006 AIP Publishing LLC.

Close modal

The stable discharge regime, where inductive power absorption exceeds capacitive power absorption, is the H mode. The main discharge characteristics of the H mode are a high plasma density, usually in excess of 1 × 1010 cm−3, and a bright light emission. Notably, even though the discharge regime is in the H mode, there is a little capacitive coupling where the RF plasma potential fluctuates. Godyak and Piejak (1990) showed that the RF plasma potential can be minimized by installing a Faraday shield. Also, the capacitive field is essential for the discharge breakdown, even though the enough RF power is applied in the ICP chamber.

Several studies have considered the E mode. It was reported that the pressure dependence of the EEDF in the E mode is similar to the evolution of the EEDF in a capacitively coupled plasma (Chung and Chang, 2002). It was found that the EEDF in the E mode changes from a bi-Maxwellian to a Druyvestein-like structure with increasing Ar gas pressure. This result corresponds to the result of the capacitively coupled plasma obtained by Godyak and Piejak (1990). Lee and Chung (2014) investigated low-energy electron heating by applying the E mode power from the ICP coil when the background plasma was sustained (Fig. 15). This method is significant for the following reasons. The reduction in critical device dimensions to below 20 nm has recently made it crucial to control the plasma. The independent control of the plasma density and electron temperature is a promising technique for plasma etching technology in 3D transistor device fabrication because the electron temperature controls radical composition, while the plasma density affects the surface physical reactions. Lee and Chung (2014) applied an additional pulse-modulated E-mode power in the background plasma sustained by a capacitively coupled power and found that the electron temperature was controlled with little change in the plasma density. This method was applied to the ashing process of the photoresistor (Lee and Chung, 2015b). The ashing rate was found to increase substantially by controlling the EEDF, even though the ion density and energy flux were not enhanced. The E-mode power also improved the cleaning of polymer resist residues on few-layer graphene without damaging the device. Lim et al. (2012) showed that the performance of a graphene field-effect-transistor, measured in terms of the carrier mobility, and the charge-neutrality point are restored to their defect-free state when an E-mode plasma is irradiated onto the graphene.

FIG. 15.

Measured EEDFs and plasma parameters resulting from the addition of a small amount of pulse-modulated inductive power (20 W) in the background plasma. The background plasma was produced by a capacitively coupled plasma (CCP) power of 80 W. The effective electron temperature (Teff) was abruptly increased with an increase in the temperature of the low-energy electrons during the pulse-on time of the ICP power of 20 W. When only the CCP power was applied, the plasma density ne was 7.05 × 108 cm−3 and Teff was 1.37 eV. When a pulse-modulated ICP power of 20 W was applied to the CCP, ne was 6.65 × 108 cm −3 and Teff was 1.84 eV. Thus, ne and Teff changed by 5.5% and 34.3%, respectively. This significant increase in Teff with little variation in the plasma density is due to the fact that, with the small additional pulse-modulated ICP power, the inductive field heats up the low-energy electrons predominantly, while the high-energy electrons that participate in the inelastic collisions are still produced by the CCP power. When the pulse modulated ICP power was switched off, Teff decreased abruptly and returned to its initial value. This work can therefore be applied to the control of the EEDF and Teff without varying ne. It is also expected that, by controlling Teff by changing the duty ratio of the pulse-modulated ICP power, the radical compositions can be controlled in real time without a large variation in the ion energy flux impinging on the wafer (Lee and Chung, 2014). Reproduced with permission from Lee and Chung, Plasma Sources Sci. Technol. 23, 062002 (2014). Copyright 2014 Institute of Physics.

FIG. 15.

Measured EEDFs and plasma parameters resulting from the addition of a small amount of pulse-modulated inductive power (20 W) in the background plasma. The background plasma was produced by a capacitively coupled plasma (CCP) power of 80 W. The effective electron temperature (Teff) was abruptly increased with an increase in the temperature of the low-energy electrons during the pulse-on time of the ICP power of 20 W. When only the CCP power was applied, the plasma density ne was 7.05 × 108 cm−3 and Teff was 1.37 eV. When a pulse-modulated ICP power of 20 W was applied to the CCP, ne was 6.65 × 108 cm −3 and Teff was 1.84 eV. Thus, ne and Teff changed by 5.5% and 34.3%, respectively. This significant increase in Teff with little variation in the plasma density is due to the fact that, with the small additional pulse-modulated ICP power, the inductive field heats up the low-energy electrons predominantly, while the high-energy electrons that participate in the inelastic collisions are still produced by the CCP power. When the pulse modulated ICP power was switched off, Teff decreased abruptly and returned to its initial value. This work can therefore be applied to the control of the EEDF and Teff without varying ne. It is also expected that, by controlling Teff by changing the duty ratio of the pulse-modulated ICP power, the radical compositions can be controlled in real time without a large variation in the ion energy flux impinging on the wafer (Lee and Chung, 2014). Reproduced with permission from Lee and Chung, Plasma Sources Sci. Technol. 23, 062002 (2014). Copyright 2014 Institute of Physics.

Close modal

The significant changes in the plasma parameters and the need to understand the physics of the discharge during the E-to-H mode transition have motivated several theoretical and experimental studies. The theoretical critical coil current required for sustaining the H mode was calculated by Kortshagen et al. (1996). Yoon et al. (1998) developed a theoretical formula for the transition power for the E-to-H mode transition based on non-local heating theory (Yoon et al., 1997). The mechanisms for this transition were studied in an ICP in the continuous-wave power mode (Turner and Lieberman, 1999) and the pulsed-power mode (Cunge et al., 1999). Lee et al. (2006) calculated the total power absorption transferred to the plasma using Maxwell's equations and a global model. It was found that the E-to-H and H-to-E mode transitions occur at critical electron densities. Zhao et al. (2009) studied the E-to-H mode transition using a hybrid fluid/Monte-Carlo model. Takao et al. (2012) conducted two-dimensional axisymmetric particle-in-cell simulations to investigate the effect of capacitive coupling in a miniature ICP with RF frequencies in the range of 100–1000 MHz. Xu et al. (2015) developed a two-dimensional fluid model that considered the effect of the circuit-matching network. Guittienne et al. (2017) used analytic expressions to interpret a planar ICP with a large area.

More intensive experimental studies have focused on the E-to-H mode transition. Amorim et al. (1991) and Suzuki et al. (1998) observed a jump in plasma density in an Ar ICP. Cunge et al. (1999) investigated plasma features such as the spatial ion-density profile, the EEDF, and optical emission at 750 nm in the continuous power mode. The time evolution of the antenna-coil current, the plasma impedance, and the magnetic field were also studied in a pulsed-power mode Ar ICP with an RF frequency of 13.56 MHz. Seo et al. (1999) measured the electrical characteristics of the antenna and the plasma potential at the E-to-H mode transition of an Ar ICP with RF frequencies of 6.5 and 19 MHz. It was found that the sudden drop in the plasma potential can serve as an indicator of the change in power coupling from the E mode to the H mode (Seo et al., 1999 and Lee et al., 2010a). Miyoshi et al. (2002; 2010) applied optical emission spectroscopy and tomography to study the E-to-H mode transition in ICPs consisting of Ar or Ar–CF4 mixtures at 13.56 MHz. They observed the spatial evolution of the excited-state densities for the Ar 2p1 level. Lee et al. (2011c) measured the two-dimensional plasma density in an Ar ICP at 13.56 MHz. They found that, at the high gas pressure where the electron-energy relaxation length λε is shorter than the characteristic plasma length L, the peak plasma density, initially in the region between the powered antenna coil and the grounded coil in the E mode, moves to the vicinity of the circular antenna coil in the H mode. This dramatic change originates from the transition in electron kinetics from nonlocal to local (Lee et al., 2010d; Lee and Chung, 2013; and Lee et al., 2011b). Razzak et al. (2004; 2005) captured this discharge dynamics connected to electron kinetics and electron-heating mechanism by using high-speed imaging in a cylindrical ICP under atmospheric pressure. As shown in Fig. 16, cumulative ionizations (like the multiple streamer-like discharge) take place along the electrostatic-field direction in the early stage of the discharge, while the ring-shaped azimuthal discharge is formed over a period of time (1.7 ms in Fig. 16). Lee et al. (2010a) observed a dramatic evolution of the EEDF in a 100 mTorr N2 ICP [Fig. 17(a)]. In the E mode, the measured EEDF was unusual, displaying a flat region, or a dip, at electron energies near 3 eV, but evolved into a Maxwellian distribution in the H mode. The dip on the EEDF is attributed to vibrational excitation collisions and a similar result was found earlier in a N2 capacitively coupled plasma (Turner and Hopkins, 1992). The evolution of the EEDF into a Maxwellian distribution is due to electron-electron collisions, and is governed by the electron-electron collision frequency during the electron residence time (Seo et al., 2000 and Lee et al., 2010a). Figure 17(b) shows the calculated electron-electron collision frequency and the total electron bounce frequency. The result indicates that the electron-electron collision frequency increases significantly during the E-to-H mode transition and exceeds the total electron bounce frequency, resulting in electron-energy thermalization. Many studies on the E-to-H mode transitions have also been done in ICPs. Those results are covered together with hysteresis in Secs. IV B and IV C in greater detail.

FIG. 16.

Observation of E-to-H mode transition dynamics by high-speed imaging under atmospheric pressure (Razzak et al., 2004). Reprinted with permission from J. Appl. Phys. 96, 4771 (2004). Copyright 2004 AIP Publishing LLC.

FIG. 16.

Observation of E-to-H mode transition dynamics by high-speed imaging under atmospheric pressure (Razzak et al., 2004). Reprinted with permission from J. Appl. Phys. 96, 4771 (2004). Copyright 2004 AIP Publishing LLC.

Close modal
FIG. 17.

(a) Measured EEPFs for increasing ICP power in N2 gas. (b) Electron-electron collision frequency and total electron bounce frequency. In the E-mode region, the measured EEDF shows an unusual dip near 3 eV, but the EEDF evolves into a Maxwellian distribution and the dip disappears in the H mode. This evolution in the EEDF occurs as the electron-electron collision time decreases below the electron residence time (Lee et al., 2010a). Reprinted with permission from Phys. Plasmas 17, 033506 (2010). Copyright 2010 AIP Publishing LLC.

FIG. 17.

(a) Measured EEPFs for increasing ICP power in N2 gas. (b) Electron-electron collision frequency and total electron bounce frequency. In the E-mode region, the measured EEDF shows an unusual dip near 3 eV, but the EEDF evolves into a Maxwellian distribution and the dip disappears in the H mode. This evolution in the EEDF occurs as the electron-electron collision time decreases below the electron residence time (Lee et al., 2010a). Reprinted with permission from Phys. Plasmas 17, 033506 (2010). Copyright 2010 AIP Publishing LLC.

Close modal

Many physical systems, including plasmas (Thomas et al., 1998; Sivis and Ropers, 2013; Lee and Chung, 2015a; Prodromakis et al., 2012; Merlino and Cartier, 1984; Steinberg et al., 2001; Zaplotnik and Mozetic, 2011; and Francis, 1948 and references in there-in), electronic devices (Prodromakis et al., 2012; Strukov et al., 2008; and Yang et al., 2013), magnetic materials (Provenzano et al., 2004 and Crespo et al., 2004), and even the northern hemisphere ice sheets (Abe-Ouchi et al., 2013), can exist in either of two different configurations under a given set of conditions, depending on the system history. This phenomenon is generally called hysteresis.

A recent study noted the interest in the discharge-mode transitions and hysteresis observed in plasmas, due to the versatile use of plasmas in the nano- and biosciences, energy science, and the semiconductor and display industries. Examples taken from that study are reproduced in Fig. 18 and show the hysteresis observed in various plasmas. Schweigert (2004) simulated the transitions between the discharge regimes of a capacitively coupled plasma in methane with a combined particle-in-cell Monte Carlo collision algorithm [Fig. 18(a)]. She showed that the discharge has two distinct regimes. One of these regimes is dominated by the discharge volume at low plasma densities, whereas the “active sheath” regime features at high plasma densities. Hysteresis occurs as the discharge current varies either upward or downward, as shown in Fig. 18(a). Jiang et al. (2009) investigated the effect of the gap length on the properties of capacitive discharges using particle-in-cell Monte Carlo simulations [Fig. 18(b)]. They observed hysteresis in the plasma density as the gap length was varied. Ghanashev et al. (1997) reported hysteresis in the power with respect to the plasma density hysteresis in surface-wave sustained microwave discharges [Fig. 18(c)]. Greiner et al. (1993) investigated a period-doubling route to chaos in a modulated low-pressure thermionic argon plasma [Fig. 18(d)] and found hysteresis in the current-voltage characteristics (Greiner et al., 1993; Ding et al., 1994; Sun et al., 1995; and Chaubey et al., 2016). Musschoot et al. (2008) experimentally showed that hysteresis in the discharge current with respect to the voltage occurred above a certain Ar gas pressure in a magnetron discharge [Fig. 18(e)]. Kortshagen et al. (1996) observed hysteresis in the Ar emission of the 419.8 and 420.0 nm lines during the E-to-H and H-to-E mode transitions in the ICP [Fig. 18(f)].

FIG. 18.

Hysteresis displayed in different plasmas. (a) Simulated time-averaged electron energy and electron density, plotted as functions of the current j for a pressure 0.075 Torr and distance 6 cm in a capacitively coupled plasma in methane. These results were simulated with a combined particle-in-cell Monte Carlo collision algorithm. The dashed and solid curves correspond to increasing and decreasing current, respectively (Schweigert, 2004). Reproduced with permission from Phys. Rev. Lett. 92, 155001 (2004). Copyright 2004 American Physical Society. (b) Simulated dependence of the maximum bulk electron density on the discharge gap length, in a capacitively coupled plasma with an Ar pressure of 1.2 Pa (Jiang et al., 2009) Reproduced with permission from Jiang et al., J. Phys. D: Appl. Phys. 42, 102005 (2009). Copyright 2009 Institute of Physics. (c) Measured plasma density hysteresis at P = 36 Pa (solid line), labeled with azimuthal and radial mode numbers (m,n), in the observed light-emission patterns. For comparison, the computed resonance densities of the TMmno modes in surface-wave sustained microwave discharges are shown by the dashed lines. The electron density was measured at a distance z = 10 mm from the dielectric window, 50 mm off-axis (Ghanashev et al., 1997). Reprinted with permission from J. Appl. Phys. 36, 4704 (1997). Copyright 1997 AIP Publishing LLC. (d) Experiment on current-voltage hysteresis curve and chaos characteristics in a filament cathode discharge (Greiner et al., 1993). Reproduced with permission from Greiner et al., Phys. Rev. Lett. 70, 3071 (1993). Copyright 1993 American Physical Society. (e) Voltage-current characteristics in magnetron discharge at different Ar pressures. If the pressure increases, the jump in discharge current occurs at a lower discharge voltage (Musschoot et al., 2008). Reproduced with permission from Musschoot et al., Plasma Sources Sci. Technol. 17, 015010 (2008). Copyright 2008 Institute of Physics. (f) Light-emission from the Ar 419.8 and 420.0 nm lines in the ICP during a transition from the E- to the H-mode in a pure argon discharge at 0.1 Torr, plotted as a function of the RF coil-current amplitude. The arrows indicate the time evolution of the trace, starting from the E mode at low RF coil currents (Kortshagen et al., 1996). Reproduced with permission from Kortshagen et al., J. Phys. D: Appl. Phys. 29, 1224 (1996). Copyright 1996 Institute of Physics.

FIG. 18.

Hysteresis displayed in different plasmas. (a) Simulated time-averaged electron energy and electron density, plotted as functions of the current j for a pressure 0.075 Torr and distance 6 cm in a capacitively coupled plasma in methane. These results were simulated with a combined particle-in-cell Monte Carlo collision algorithm. The dashed and solid curves correspond to increasing and decreasing current, respectively (Schweigert, 2004). Reproduced with permission from Phys. Rev. Lett. 92, 155001 (2004). Copyright 2004 American Physical Society. (b) Simulated dependence of the maximum bulk electron density on the discharge gap length, in a capacitively coupled plasma with an Ar pressure of 1.2 Pa (Jiang et al., 2009) Reproduced with permission from Jiang et al., J. Phys. D: Appl. Phys. 42, 102005 (2009). Copyright 2009 Institute of Physics. (c) Measured plasma density hysteresis at P = 36 Pa (solid line), labeled with azimuthal and radial mode numbers (m,n), in the observed light-emission patterns. For comparison, the computed resonance densities of the TMmno modes in surface-wave sustained microwave discharges are shown by the dashed lines. The electron density was measured at a distance z = 10 mm from the dielectric window, 50 mm off-axis (Ghanashev et al., 1997). Reprinted with permission from J. Appl. Phys. 36, 4704 (1997). Copyright 1997 AIP Publishing LLC. (d) Experiment on current-voltage hysteresis curve and chaos characteristics in a filament cathode discharge (Greiner et al., 1993). Reproduced with permission from Greiner et al., Phys. Rev. Lett. 70, 3071 (1993). Copyright 1993 American Physical Society. (e) Voltage-current characteristics in magnetron discharge at different Ar pressures. If the pressure increases, the jump in discharge current occurs at a lower discharge voltage (Musschoot et al., 2008). Reproduced with permission from Musschoot et al., Plasma Sources Sci. Technol. 17, 015010 (2008). Copyright 2008 Institute of Physics. (f) Light-emission from the Ar 419.8 and 420.0 nm lines in the ICP during a transition from the E- to the H-mode in a pure argon discharge at 0.1 Torr, plotted as a function of the RF coil-current amplitude. The arrows indicate the time evolution of the trace, starting from the E mode at low RF coil currents (Kortshagen et al., 1996). Reproduced with permission from Kortshagen et al., J. Phys. D: Appl. Phys. 29, 1224 (1996). Copyright 1996 Institute of Physics.

Close modal

It is noteworthy that an ICP [Fig. 18(f)] shows significantly huge hysteresis and bistability characteristics than other plasmas (Lee and Chung, 2015a). The potential for hysteresis and bistability in ICPs to provide insights into plasma physics, in general, has motivated many experimental and theoretical studies of ICP characteristics. In summary, significant hysteresis and bistability are observed in the ICPs used in various industrial fields. Further studies on the hysteresis and bistability in such plasmas (ICP) should help to deepen the fundamental understanding of hysteresis physics in plasmas and to open possibilities for applications.

Many experiments have investigated the effect on hysteresis in ICPs of various external parameters. El-Fayoumi et al. (1998) measured the large hysteresis in the plasma resistance and reactance in a low-frequency (560 kHz) ICP and suggested that the nonlinearity of the absorbed power may result from the difference in sheath thickness during the E-to-H mode transition. Xu et al. investigated the plasma parameters and electrical characteristics in a low-frequency (500 kHz) planar-coil ICP in terms of the Ar gas pressure (Xu et al., 2000). They found that the plasma resistance, power, density, and potential and the optical emission all displayed hysteresis during the mode transitions. They suggested that step-wise ionization via the excited states of Ar atoms may be responsible for the hysteresis.

Lee et al. (2007) measured coil currents and the plasma density during the E-to-H and H-to-E mode transitions in a 13.56 MHz cylindrical ICP with Ar gas pressures ranging from 8 to 175 mTorr (Fig. 19). They observed hysteresis at high gas pressures above 55 mTorr and concluded that the step-wise ionization may be a dominant contributor to hysteresis in the E-H transitions. Hayashi et al. (2011) measured the 2 D spatial profile of the net-excitation rate of Ar (2p9) at 300 mTorr in an Ar ICP driven at 13.56 MHz and found that the H-to-E transition and hysteresis are strongly influenced by metastable atoms. Daltrini et al. (2007) observed hysteresis in the Ar 750.4 nm intensity in ICPs at Ar and Ar/N2 mixtures and noted the influence of metastable Ar atoms on the shape of the EEDF.

FIG. 19.

Measured plasma densities, plotted as functions of the coil current in 13.56 MHz ICP with Ar gas at (a) low and (b) high pressures. Hysteresis in E-H transitions is clearly observed at the higher pressures and is absent at the lower pressures (Lee et al., 2007). Reprinted with permission from Appl. Phys. Lett. 90, 191502 (2007). Copyright 2007 AIP Publishing LLC.

FIG. 19.

Measured plasma densities, plotted as functions of the coil current in 13.56 MHz ICP with Ar gas at (a) low and (b) high pressures. Hysteresis in E-H transitions is clearly observed at the higher pressures and is absent at the lower pressures (Lee et al., 2007). Reprinted with permission from Appl. Phys. Lett. 90, 191502 (2007). Copyright 2007 AIP Publishing LLC.

Close modal

Daltrini et al. (2008) also conducted an experiment on argon-plasma behavior near the E-to-H transition in an ICP (Fig. 20). They considered the effect of impedance matching on the E-to-H mode transition. There was no hysteresis in the plasma density and Ar metastable emission line in the ICP at an Ar pressure of 120 mTorr, when plotted as functions of the plasma power (absorbed power to plasma). They emphasized that hysteresis had previously been observed when varying the coil current or input power, but did not take into account the power dissipated in the coil and matching network. They suggested that the hysteresis in the E-to-H mode transition may be due to the neglected inherent power loss of the antenna coil and matching network. Subsequently, some researchers (Ding et al., 2008 and Gao et al., 2010) investigated the effect of impedance matching on hysteresis and found that the hysteresis loop size is critically affected by the matching conditions.

FIG. 20.

Observed effect of the matching conditions on hysteresis in an ICP. (a) Dependence of light emission at 750.4 nm and at different gas pressures on the applied power (forward power minus reflected power). (b) Dependence of the ion density, plasma-emission intensity at 750.4 nm, and relative metastable density on the plasma power at 120 mTorr (16 Pa). The ion density and emission intensity are shown on a logarithmic scale, while the metastable density is shown on a linear scale (Daltrini et al., 2008). Reprinted with permission from Appl. Phys. Lett. 92, 061504 (2008). Copyright 2008 AIP Publishing LLC.

FIG. 20.

Observed effect of the matching conditions on hysteresis in an ICP. (a) Dependence of light emission at 750.4 nm and at different gas pressures on the applied power (forward power minus reflected power). (b) Dependence of the ion density, plasma-emission intensity at 750.4 nm, and relative metastable density on the plasma power at 120 mTorr (16 Pa). The ion density and emission intensity are shown on a logarithmic scale, while the metastable density is shown on a linear scale (Daltrini et al., 2008). Reprinted with permission from Appl. Phys. Lett. 92, 061504 (2008). Copyright 2008 AIP Publishing LLC.

Close modal

Lee et al. (2013) carefully reproduced the hysteresis experiment by considering the external circuit effect, as shown in Fig. 21. At an Ar pressure of 100 mTorr (where hysteresis had previously been observed), there was no hysteresis with respect to the coil current, input power, or absorbed power, when impedance matching was considered. From these results (Daltrini et al., 2008 and Lee et al., 2013), it may be concluded that impedance matching produces a hysteresis loop at relatively low gas pressures. However, hysteresis was clearly apparent with varying the input power and the absorbed power, when the gas pressure was increased to 350 mTorr (Lee et al., 2013). This indicates that hysteresis at such high pressure is not caused by impedance matching itself, but by the nonlinearity of the plasma. In fact, in real industrial plasma processing, RF power is usually delivered via an automatically tuned matching network. Thus, clarifying the mechanism underlying hysteresis and identifying the dominant effect on the plasma nonlinearities are essential, both for achieving a fundamental understanding and for industrial applications.

FIG. 21.

Hysteresis experiment in an ICP at an argon gas pressure of 100 mTorr. (a) Measured plasma density under different impedance matching conditions. (b) Hysteresis of the plasma density with respect to the input power and absorbed power at an argon gas pressure of 350 mTorr, under well-matched conditions (Lee et al., 2013). Reprinted with permission from App. Phys. Lett. 102, 234104 (2013). Copyright 2013 AIP publishing LLC.

FIG. 21.

Hysteresis experiment in an ICP at an argon gas pressure of 100 mTorr. (a) Measured plasma density under different impedance matching conditions. (b) Hysteresis of the plasma density with respect to the input power and absorbed power at an argon gas pressure of 350 mTorr, under well-matched conditions (Lee et al., 2013). Reprinted with permission from App. Phys. Lett. 102, 234104 (2013). Copyright 2013 AIP publishing LLC.

Close modal

To bring together the vast array of hysteresis studies, Lee and Chung (2015a) conducted a full quantitative experiment and developed a model to provide a global understanding of plasma hysteresis (Fig. 22). They suggested that the evolution of the electron-energy distribution produces strong hysteresis. Their experiment was performed in an ICP driven at 13.56 MHz, with the RF power being applied to the antenna coil through an automatically controlled impedance-matching network to consider the effect of impedance matching. To observe plasma-mode transitions and hysteresis, the input power was increased or decreased in 1 W increments. In Ar gas at 40 mTorr, the plasma density followed the same trajectory when undergoing the E-to-H or H-to-E mode transitions, i.e., displaying no hysteresis. However, a large hysteresis loop in the plasma density was observed in Ar gas at 250 mTorr [Fig. 22(b)]. Notably, there was no hysteresis under a high He pressure (300 mTorr) plasma, either. Interestingly, a crucial difference between the discharges for Ar 250 mTorr and other plasmas is the shape of the EEDF. This difference is due to the quantum-mechanical effect of the Ar gas called the Ramsauer-Townsend scattering minimum.

FIG. 22.

Hysteresis experiment performed with Ramsauer and non-Ramsauer gases. Plasma density versus plasma power for Ar gas at (a) 40 mTorr and (b) 250 mTorr. (c) Plasma density versus plasma power for He gas at 300 mTorr. Hysteresis is observed only in a high-pressure Ramsauer gas. In Fig. 22(b), when applying a low plasma power (input power Pin= 23 W, plasma power Pp= 5.87 W, see Methods section), a capacitive E-mode plasma is sustained, showing faint emission and with a very low plasma density (1.48 × 108 cm−3). A slight increase in Pin from 26 W (Pp = 7.18 W) to 27 W (Pp = 17.43 W) results in an inductive H-mode discharge with an abrupt jump in the plasma density from 1.78 × 108 cm−3 (region I) to 8.18 × 1010 cm−3 (region II). When Pin decreases to 23 W (Pp= 12.56 W), the plasma density remains high at 5.49 × 1010 cm−3 (region III). A further decrease in Pin to 22 W (Pp= 6.1 W) changes the discharge characteristics abruptly from H-mode (region III) to E-mode (region IV). Thus, there is clear hysteresis with respect to the plasma power in Fig. 22(b) (Lee and Chung, 2015a) Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

FIG. 22.

Hysteresis experiment performed with Ramsauer and non-Ramsauer gases. Plasma density versus plasma power for Ar gas at (a) 40 mTorr and (b) 250 mTorr. (c) Plasma density versus plasma power for He gas at 300 mTorr. Hysteresis is observed only in a high-pressure Ramsauer gas. In Fig. 22(b), when applying a low plasma power (input power Pin= 23 W, plasma power Pp= 5.87 W, see Methods section), a capacitive E-mode plasma is sustained, showing faint emission and with a very low plasma density (1.48 × 108 cm−3). A slight increase in Pin from 26 W (Pp = 7.18 W) to 27 W (Pp = 17.43 W) results in an inductive H-mode discharge with an abrupt jump in the plasma density from 1.78 × 108 cm−3 (region I) to 8.18 × 1010 cm−3 (region II). When Pin decreases to 23 W (Pp= 12.56 W), the plasma density remains high at 5.49 × 1010 cm−3 (region III). A further decrease in Pin to 22 W (Pp= 6.1 W) changes the discharge characteristics abruptly from H-mode (region III) to E-mode (region IV). Thus, there is clear hysteresis with respect to the plasma power in Fig. 22(b) (Lee and Chung, 2015a) Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

Close modal

In the low-plasma-density mode (E mode) with an Ar gas pressure of 250 mTorr, where the electron-neutral collision frequency νm is much higher than the driving angular frequency, low-energy electrons are more efficiently heated than the high-energy electrons in a Ramsauer gas. Thus, the EEPF displays a Druyvesteyn rather than a Maxwellian distribution under the high gas pressure [Fig. 23(a)]. On the other hand, the EEPF evolves into a Maxwellian distribution in the high-plasma-density mode (H mode), as shown in Fig. 23(b), owing to the heating-mode transition and the enhancement of electron-electron collisions. The evolution of the EEPF over the heating-mode transition can result in hysteresis in plasma discharges, as follows. The enhanced electron heating and electron-electron collisions replenish the high-energy electron regime of the EEDF, which had originally been depopulated by inelastic collisions under the high gas pressure. These replenished electrons then enhance plasma production, which causes a significant reduction in the collisional energy loss εc, the energy required to create an ion-electron pair. Thus, the ionization efficiency is strongly increased as the EEDF evolves during the E-to-H mode transition. Consider now the EEDF during the H-to-E transition. When the plasma power decreases to some threshold regime such as region (III) in Fig. 22(b), the EEDF remains a Maxwellian distribution (Fig. 23). This indicates that the ionization efficiency is sufficiently high to produce a high-density plasma. Thus, the H-to-E transition occurs at a relatively lower plasma power than for the E-to-H transition. Hysteresis therefore appears with the change in the EEDF. It should be noted that hysteresis was not observed under other conditions [Figs. 22(a) and 22(c)], for example, in plasmas with a high He pressure (300 mTorr) or a low Ar pressure (40 mTorr), where the EEDFs for both the E and H modes have a Maxwellian distribution (Lee and Chung, 2015a).

FIG. 23.

Evolution of the electron-energy probability function (EEPF) due to the heating-mode transition in the Ar Ramsauer gas. (a)–(d) Measured EEPFs in each region (I)-(IV) in the Ar gas discharge at 250 mTorr of Fig. 22(b). The EEPFs display a Druyvesteyn distribution in the low-plasma-density mode [Figs. 23(a) and 23(d)], and a Maxwellian distribution in the high-density-plasma mode [Figs. 23(b) and 23(c)]. The Druyvesteyn distribution results from energy-dependent electron heating in a Ramsauer gas. (e) Elastic-collision cross sections in Ar and He. The cross section for Ar is minimal for collisions between electrons and neutral atoms at a certain electron energy, a quantum-mechanical effect referred to as the Ramsauer-Townsend scattering minimum (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

FIG. 23.

Evolution of the electron-energy probability function (EEPF) due to the heating-mode transition in the Ar Ramsauer gas. (a)–(d) Measured EEPFs in each region (I)-(IV) in the Ar gas discharge at 250 mTorr of Fig. 22(b). The EEPFs display a Druyvesteyn distribution in the low-plasma-density mode [Figs. 23(a) and 23(d)], and a Maxwellian distribution in the high-density-plasma mode [Figs. 23(b) and 23(c)]. The Druyvesteyn distribution results from energy-dependent electron heating in a Ramsauer gas. (e) Elastic-collision cross sections in Ar and He. The cross section for Ar is minimal for collisions between electrons and neutral atoms at a certain electron energy, a quantum-mechanical effect referred to as the Ramsauer-Townsend scattering minimum (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

Close modal

An early study by Turner and Lieberman (1999) suggested that hysteresis can be caused by nonlinearity in either the power absorption or power dissipation, or in both. They mentioned the matching effect and two power coupling modes in the nonlinearities of the absorbed power, while nonlinearities of the dissipated power can be caused by the multistep ionization and electron-electron collisions, etc. Emphasis was placed on the need for a full quantitative experiment and an improved model to find the dominant factor and to provide a basis for a global understanding of the physics underlying hysteresis.

Lee and Chung (2015a) reported an improved ICP model to investigate the origin of hysteresis. They used stepwise plasma balance equations that include the EEDF and stepwise effects to identify the dominant factor controlling hysteresis, as follows. The collisional energy loss εc was calculated from the plasma balance equation

iKiz,inineεc=iKiz,inineεiz,i+jKex,jnjneεex,j+kKel,knkne3mMTe,
(1)

where Kiz,i, Kex,j, and Kel,k, are the rate constants for ionization, excitation, and elastic collision, and the last term reduces to Kelngne (3m/M)Te (Lee et al., 2005).

As shown in Fig. 24, the Ar energy levels for the resonance (4sr), metastable (4sm), and 4p excited states (Lee et al., 1995; 2005) are considered in the calculation. In Eq. (1), the EEDF should be considered because the rate constant K for collisions between a and b is strongly EEDF-dependent

Kab=0σab(ε)2εmege(ε)dε,
(2)

where σ is the collision cross section for each reaction process in Fig. 24. Data for σ for Ar gas are available in the literature (Gargioni and Grosswendt, 2008; Dasgupta, 1999; Schappe, 1994; McGuire, 1979; Deutschdag et al., 1999; Ton-That et al., 1977; and Deutsch et al., 2004). The generalized EEDF is written (Ren et al., 2008) as

ge(ε)=xε3/2[Γ(2.5/x)]3/2[Γ(1.5/x)]5/20ε1/2exp(1εx[Γ(2.5/x)Γ(1.5/x)]xεx)dε,
(3)

where ⟨ε⟩ is the mean electron kinetic energy. We therefore obtain two EEDFs referring to the Maxwellian distribution, ge,Maxw(ε) = 1.128Te−3/2ε1/2exp(−ε/Te), and the Druyvesteyn distribution ge,Druy(ε) = 0.565Te−3/2ε1/2exp(−0.243ε2/Te2). The particle-balance equation can then be written as

iKiz,inineV=(Kging+Kminm+Krinr+Kpinp)neV=neUBAeff,
(4)

where Kgi, Kmi, Kri, and Kpi are the rate constants that take into account the EEDF, as expressed in Eqs. (2) and (3). The power-balance equation is expressed as

Pdiss[=eneuB(εc+εi+εe)Aeff]=Ptrans,
(5)

where Aeff= 2πR[0.86 R(3 + h/2λi)−1/2+0.8 h(4 + R/2λi)−1/2] (Lee et al., 1995) is the loss area, εi is the loss in ion energy, εe is the loss in electron kinetic energy, Pdiss is the dissipated power, and Ptrans is the total transferred power.

FIG. 24.

Schematic diagram for the energy levels and transitions in an Ar atom, used for modeling an Ar plasma and hysteresis. The resonance (4sr), metastable (4sm), and 4p excited states are considered in this work (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

FIG. 24.

Schematic diagram for the energy levels and transitions in an Ar atom, used for modeling an Ar plasma and hysteresis. The resonance (4sr), metastable (4sm), and 4p excited states are considered in this work (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

Close modal

Equations (4) and (5) yield the εc curves self-consistently, as shown in Fig. 25. The collisional energy loss εc decreases with the plasma power (or the plasma density) because the step-ionization enhances plasma production. The dependence of εc on the EEDF is of particular interest. When considering only a Maxwellian EEDF, εc,Maxw decreases slightly from 71.2 to 60.1 V. This means that the step-ionization process makes non-linearity of the power absorption and can make a hysteresis. However, such a small variation in εc,Maxw may be insufficient to explain the jump in plasma density and the strong hysteresis in Fig. 22(b).

FIG. 25.

Calculated loss in collisional energy and hysteresis during the E-to-H and H-to-E mode transitions. The dashed-dotted and dotted lines represent the collisional energy losses (εc,Maxw, εc,Druy) for the Maxwellian and Druyvesteyn distributions, respectively. The forward and backward arrows refer to the experimental conditions of Fig. 22(b). Strong hysteresis occurs only when the evolution of the EEDF is considered (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

FIG. 25.

Calculated loss in collisional energy and hysteresis during the E-to-H and H-to-E mode transitions. The dashed-dotted and dotted lines represent the collisional energy losses (εc,Maxw, εc,Druy) for the Maxwellian and Druyvesteyn distributions, respectively. The forward and backward arrows refer to the experimental conditions of Fig. 22(b). Strong hysteresis occurs only when the evolution of the EEDF is considered (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

Close modal

When the modification of the EEDF is considered in the model, εc changes dramatically and the origin of the hysteresis becomes clearly apparent. In the E mode with the Druyvesteyn EEDF, εc,Druy = 165.2 V. When the E-to-H mode transition occurs by varying the plasma power, the plasma acquires a Maxwellian EEDF, which results in a remarkable reduction of εc to εc,Max = 61 V in region (II). When the plasma power decreases, the EEDF retains its Maxwellian shape until a certain threshold where the H mode is sustained. At this point, εc = εc,Max = 61.6 V. With a further decrease in the plasma power, the H-to-E mode transition occurs in conjunction with the evolution of the EEDF from Maxwellian to Druyvesteyn. In this case, εc increases substantially to εc,Druy = 148.5 V. Therefore, εc displays a strong hysteresis with the E-to-H and H-to-E mode transitions (Fig. 25), consistent with the plasma hysteresis seen in Fig. 22(b).

The stable plasma density was calculated with detail by using the E- and H-mode power couplings (Pcap, Pind) (Lee and Chung, 2015a). The total transferred power Ptrans, combining Pcap and Pind, is derived from Maxwell equations and by integrating the Poynting vector over the surface area of the interface of the plasma and dielectric wall

Ptrans=Pind+Pcap=Re[i(πhωμ0N2I2lα)(J1(αh)J0(αh))]+Re[i(πhlμ0)(Vc2ωλκd2lc2λκp)(J0(λh)J12(λh)J1(λR)J02(λ(h+d)))],
(6)

where α = [(ωpe/c)2/(−1 + m/ω)]1/2, J0 and J1 are the zero- and first-order Bessel functions, Vc/l is the voltage difference, λ = κp1/2ω/c, κp= 1 − (ωpe/c)2/(1−m/ω), and λ′=κd1/2ω/c. The stable plasma is determined from the balance between the transferred power Ptrans and the power dissipation Pdiss in Eqs. (1)–(6). At the stable working point of the plasma density, the intersection of Ptrans and Pdiss should satisfy Ptrans/ne< Pdiss/ne. Figure 26 shows the stable points (▪: evolution of the EEPF considered and □: only Maxwellian EEPF considered).

FIG. 26.

Stable plasma density and the presence of hysteresis, obtained by considering the EEDF. Transferred power and dissipation power calculated during (a) the E-to-H mode transition and (b) the H-to-E mode transition. Solid lines (—) indicate the power Ptrans transferred to the plasma. The dashed curves (- - - -) and dashed-dotted curves (— + + —) denote the power dissipations for the Maxwellian (Pdiss,Max) and Druyvesteyn distributions (Pdiss,Druy). Pdiss are nonlinear functions of the plasma density and are strongly EEDF-dependent. Ptrans is also a nonlinear function of the plasma density, and shows two maxima, due to the E and H power-coupling modes. The filled (▪) and unfilled squares (□) denote the stable working points between Ptrans and Pdiss for which, respectively, the variable EEPF or only the Maxwellian distribution are considered (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

FIG. 26.

Stable plasma density and the presence of hysteresis, obtained by considering the EEDF. Transferred power and dissipation power calculated during (a) the E-to-H mode transition and (b) the H-to-E mode transition. Solid lines (—) indicate the power Ptrans transferred to the plasma. The dashed curves (- - - -) and dashed-dotted curves (— + + —) denote the power dissipations for the Maxwellian (Pdiss,Max) and Druyvesteyn distributions (Pdiss,Druy). Pdiss are nonlinear functions of the plasma density and are strongly EEDF-dependent. Ptrans is also a nonlinear function of the plasma density, and shows two maxima, due to the E and H power-coupling modes. The filled (▪) and unfilled squares (□) denote the stable working points between Ptrans and Pdiss for which, respectively, the variable EEPF or only the Maxwellian distribution are considered (Lee and Chung, 2015a). Reproduced with permission from Lee and Chung, Sci. Rep. 5, 15254 (2015). Copyright 2015 Nature Publishing Group.

Close modal

A conventional analysis that assumes only the Maxwellian EEDF in the stepwise model (i.e., neglecting changes in the EEDF) shows little hysteresis during the E-to-H and H-to-E transitions, as indicated in trajectory B (a→b→c→II→III→d→e) in Fig. 26. In contrast, there is clear hysteresis once the EEDF is fully considered, as reflected in trajectory A (I→II→III→IV) of Fig. 26 This result demonstrates that the remarkable plasma hysteresis results from the evolution of the EEDF. Because EEDFs in plasmas are not usually at thermal equilibrium, this EEDF effect can be regarded as a universal phenomenon in plasma physics. This kind of hysteresis can also be observed in various gas discharges, where the EEPF is modified by transitions in the electron-heating (e.g., bounce-resonance heating, secondary-electron acceleration by a high voltage, or wave-electron resonant heating resulting from transit-time resonance and Landau damping) or electron-cooling mechanisms.

The detailed physics of the E-H mode transition and hysteresis through a number of theoretical and experimental results were discussed with external parameters (matching effect and power coupling) and internal parameters (EEDF effect, stepwise ionization, etc.) in Sec. IV. It is now an open question as to how hysteresis can be controlled or whether a general interpretation of the hysteresis in various plasmas is possible from the phenomena observed in ICP. For example (1) there was no hysteresis in the ICP with helium gas as a non-Ramsauer gas, and this implies that the mode transition and hysteresis can be controlled with helium addition. Conversely, other rare gases (Kr, Xe) with the Ramsauer effect as well as Ar can make hysteresis in ICPs because the strong non-Maxwellian EEDF is expected (Aleksandrov et al., 1996; Dyatko et al., 2003; 2006; Dyatko, 2007; Dyatko et al., 2006; and Dyatko and Donkó, 2015) at low plasma density regime, and the evolution of the EEDF may occur with the discharge mode transition. However, studies on the hysteresis in the plasmas with other rare gases have not been explored. It is also question that the hysteresis will be generated and controlled with external parameters, such as the RF bias or additional inductive coil power with different driving frequency because the power absorption and/or power dissipation curve varies more nonlinearly.

(2) It was shown experimentally and theoretically that evolution of the EEDF makes a strong plasma hysteresis in the ICP. This can be thought to the generalized plasma physics phenomenon, not limited to the ICP, because electrons in various plasmas are not in a thermal equilibrium and they usually have non-Maxwellian distributions. Thus, following is a question: Can this EEDF effect on the hysteresis be considered a universal phenomenon in plasma physics or other plasma sources, such as capacitively coupled plasma, helicon plasma, magnetron plasma, fusion plasma, and space plasmas? The CCP may have the hysteresis with alpha (α)-to-gamma (γ) mode transition where the EEDFs are significantly different between the discharge modes. Due to the gamma mode effect, the hysteresis will be shown in the CCPs even at helium gas where the EEDF is strongly non-Maxweliian.

(3) This EEDF-effect on the hysteresis can be significant in plasma processing (etching, deposition, ashing, etc.) where molecular gases are frequently used because the EEDF is strongly non-Maxwellian in molecular gas discharges. This non-Maxwellian EEDF at the molecular gases is originated from many electron-neutral excitation collision processes even at low electron energy range due to vibration collisions, dissociation collisions, dissociative attachment, and ionization collisions, as well as the momentum transfer collisions. For example, the collision cross section for the vibrational excitation sharply peaked near the electron energy of 3 eV at N2. From this vibrational excitation collision, the complex deformations of the EEDF were reported in N2 plasmas (Dyatko et al., 1993; 2000; 2002; Dyatko and Napartovich, 2003; Dyatko et al., 2010; Gorbunov and Mel'nikov, 1999; Gorbunov et al., 1999; 2000; 2001; and Lee et al., 2010a). Thus, the hysteresis at plasma processing gases can be occurred.

(4) It was very recently reported that nanoplasmas excited with high-repetition-rate femtosecond laser sources can exhibit bistable hysteresis behavior (Sivis and Ropers, 2013). The nanoplasmas are generated under spatial confinement volumes, e.g., in the near fields at surfaces or in plasmonic nanostructures (Ostrikov et al., 2016), and the paper (Sivis and Ropers, 2013) showed the hysteresis of the optical excitation depending on the gas type and pressures. In the nanoplasmas, is the modeling or qualitative analysis similar to ICP possible to the nanoplasmas? There are a few key clues for the questions as follows: (i) the generated peek-plasma-density will be higher than that in conventional RF plasmas. This is because the plasma length in the nanostructured-waveguide with hundreds nanometer should be longer than sheath length or Debye length. Thus, there should be the plasma ignition/sustainment mechanism with discharge dynamics in such nanoscale structures. (ii) There are strong nonlinear effects in terms of internal (plasma generation and loss, photon induced secondary electron emission from the nano-structure wall, gas, and plasma diffusion scale depending on the nano-structure shape, etc.) and external parameters (high-repetition-rate femtosecond laser time, laser intensity, etc.). The above mentioned items in Sec. IV E have not yet been explored and it is open questions.

The ICP that the plasma is sustained by inductive power coupling following Faraday's law, has many advantages, such as high plasma density, low ion damage, possibility of the scale-up, wide window for stable plasma sustainment, tailored control of the plasma density and ion energy by additional RF bias, and combination effect between the RF bias and ICP. Due to these reasons, the ICP is in great attention in semiconductor/display/solar-cell plasma processing (etching, deposition, and ashing). Recently, the critical feature size of the device decreased less than 10 nm, and the high aspect ratio etching technique is essentially needed due to 3D structure memory devices, such as 3D NAND flash, 3D DRAM, and FinFET. Also, there is much demand for the atomic layer etching in ultrathin film process. The ICPs are believed to a novel volunteer in the next generation technique of the plasma processing and have been actively used in the state-of-art plasma processes to achieve the novel processing results and high quality of the device.

Beyond the industrial plasma processing for memory and display device fabrication, the ICP have become widely used in various applied fields, such as nano-structure fabrications, nuclear-fusion operation, spacecraft propulsion, and plasma torches for gas reforming and the removal of hazardous gases and materials. Many studies have exploited the synergetic effect in ICPs to fabricate nanostructure materials, such as vertically aligned single-crystalline nanostructure applicable to solar cells, readily controllable, and catalyst-free graphene synthesis at low temperatures, etc. The ICP has been also applied to spacecraft propulsion. Compared to conventional gas propulsion, the ICP propulsion has novel characteristics, like highly efficient fuel consumption and high propulsion force due to ion acceleration and thus, this makes that the space flight time can be dramatically extended. There have been much efforts on the study of the ICP propulsion from the large helicon discharge to miniaturized-thruster. Besides, the ICPs are being actively used for neutral-beam injector sources for nuclear-fusion operation and plasma sources for gas reforming and hazardous gas/material removal.

It should be noted that if, in such various applications, plasma undergoes a mode transition and hysteresis occurs in response to external perturbations, the process result could be strongly affected. In other words, if we know well and can use the mode transition to the plasma processing in the various applications, it becomes a novel control method to achieve high performance of the processing results. Interestingly, the ICP shows discharge mode transition characteristics. At a low plasma density, the ICP is maintained in a capacitive mode (the “E mode”) by the voltage formed between the antennas, while the discharge is transited into an inductive mode (the “H mode”) at a high plasma density regime. When the external power is lowered, the plasma density decreases and the discharge mode evolves from the H to the E mode. More importantly, hysteresis occurs during the E-to-H and H-to-E mode transitions, where the plasma density remains relatively high, even when the H-to-E mode transition occurs at a low power. Hysteresis can occur through a variation in external inputs, such as the power, pressure, or gas mixture. The detailed physics of the E-H mode transition and hysteresis through a number of theoretical and experimental results were discussed with external parameters (matching effect, power coupling) and internal parameters (EEDF effect, stepwise ionization, etc.).

This review will find the fundamental understanding of the mode transition and hysteresis physics in plasmas and give open possibilities for applications to various applied fields to find novel control knob and optimizing processing conditions.

The author (H. Lee) thanks to Dr. Murat Sivis at University of Göttingen for helpful discussion to the nanoplasmas. This research was supported by Korea Research Institute of Standard and Science (KRISS), Ministry of Trade, Industry and Energy (10077629), and the R&D Convergence Program (1711062007, CAP-17–02-NFRI-01) of National Research Council of Science and Technology (NST) of Republic of Korea.

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