Toward energy-efficient cold plasma sources: antenna-geometry effects in low-pressure argon inductively coupled plasmas

1 Introduction

Inductively coupled plasmas (ICPs) are widely used as high-density low-pressure plasma sources in materials processing, thin-film deposition, etching, surface modification, and plasma-assisted manufacturing. Their main advantage is that electromagnetic power can be coupled into the plasma through an external RF antenna without direct electrode contact with the discharge. This allows high plasma density to be produced while reducing electrode contamination and limiting direct ion bombardment from powered electrodes. ICP sources have therefore become an important class of RF plasma devices for both industrial processing and laboratory plasma studies [1–4].

As global manufacturing seeks to reduce environmental impact, plasma-based processes offer significant advantages over conventional wet-chemical methods by eliminating hazardous solvents, reducing chemical waste, and enabling dry processing at lower temperatures. However, the energy efficiency of plasma sources remains a critical concern for sustainable industrial adoption. RF power generators and matching networks consume substantial electrical energy, and inefficient power coupling leads to wasted energy, excessive heating, and reduced process throughput. Optimizing antenna geometry to maximize plasma density at lower applied power directly addresses sustainability goals by reducing electrical energy consumption per unit process output, minimizing electrode and chamber wear, and improving process yield all of which lower the environmental footprint and operational cost of plasma-assisted manufacturing. The development of energy-efficient plasma sources is therefore essential for advancing green manufacturing technologies and meeting international sustainability targets.

In an ICP source, the antenna geometry determines the spatial distribution of the RF magnetic field. Through Faraday induction, the time-varying magnetic field generates an electric field that drives plasma current and transfers energy to electrons. The resulting electron heating, ionization, diffusion, and wall losses then determine the final plasma-density distribution. Therefore, the antenna does not simply act as a power-delivery component; it is a key element controlling field topology, power deposition, and plasma uniformity.

Several studies have shown that antenna design can strongly affect plasma density and uniformity. Changes in antenna configuration, coil size, number of turns, operating frequency, and distributed capacitance can alter the balance between capacitive and inductive coupling. These effects become especially important in large-area or spatially extended plasma sources, where uniformity and downstream transport are critical [5–8]. However, direct comparison between antenna geometries is often difficult because measured plasma density depends not only on the vacuum RF field but also on plasma loading, matching-network behavior, antenna current, electron transport, and wall losses.

A further complication is the transition between low-density and high-density operating modes. ICP discharges can operate initially in a capacitively influenced mode, often referred to as an E mode, and then transition to a high-density inductively coupled H mode as RF power increases. This E-H transition may appear as an abrupt increase in plasma density, a reduction in RF plasma-potential oscillation, and a change in the RF electromagnetic-field structure. The transition mechanism depends on electron heating, sheath behavior, plasma conductivity, matching conditions, and antenna configuration [9–12].

RF magnetic-field penetration is also central to ICP behavior. In a simple local picture, increasing plasma conductivity reduces the electromagnetic penetration length and localizes power deposition near the source. However, low-pressure ICPs can exhibit more complex behavior, including anomalous skin effects, non-monotonic field penetration, phase reversal, and non-local electron heating. Experimental magnetic-field measurements and theoretical studies have shown that RF field penetration cannot always be described by a simple scalar skin-depth approximation [13–15].

Plasma-density uniformity is determined by more than the local RF field. Multidimensional fluid models and experimental studies have shown that electron heating, ionization, ambipolar diffusion, electron-energy transport, and wall losses can redistribute plasma density away from the primary power-deposition region. As a result, the maxima of RF magnetic field, induced electric field, absorbed power, electron temperature, and plasma density do not necessarily occur at the same spatial position [16–21]. Therefore, antenna performance should be evaluated using a combination of density measurements, RF potential measurements, magnetic-field diagnostics, and electromagnetic modeling.

More advanced numerical studies, including particle and particle-in-cell simulations, have further demonstrated the importance of electron kinetics, sheath effects, and capacitive coupling in ICP sources. These models are particularly useful when local conductivity or fluid assumptions become insufficient, especially at low pressure or in compact geometries where electron mean free paths are long compared with the characteristic dimensions of the discharge [22–25]. Nevertheless, such models are computationally demanding and require extensive validation against experimental diagnostics.

In the present study, three external antenna configurations are compared in the same low-pressure argon ICP system: a helical-type antenna, a planar spiral antenna, and a combined spiral-helical antenna. The comparison is based on spatially resolved measurements of plasma density, RF plasma-potential oscillation, and RF magnetic-field components. These measurements are used to identify how antenna geometry affects discharge transition behavior, plasma localization, downstream density distribution, and RF field structure. The practical objective is to identify an antenna configuration that maximizes plasma density and uniformity while minimizing the RF power required thereby improving the energy efficiency of the plasma source for sustainable processing applications.

To support the experimental interpretation, a three-dimensional vacuum-field Biot-Savart benchmark is also developed. This numerical benchmark isolates the effect of antenna geometry under equal-current conditions and provides a verified reference dataset for future plasma-loaded electromagnetic simulations. The benchmark does not replace a full plasma-loaded model, but it provides a controlled way to compare the intrinsic magnetic-field topology of the three antenna geometries. This vacuum-field, current-integration approach follows established practice for isolating antenna-geometry effects from plasma loading in ICP source design, and is used here strictly as a geometry-controlled reference; its verification and the resulting field topology are discussed in Section 5.2, and are used there to interpret the experimentally measured field structure of Section 4.

The aim of this work is therefore threefold. First, the experimental behavior of helical-type, planar spiral, and combined spiral-helical antennas is compared using density, RF potential, and magnetic-field diagnostics. Second, a verified geometry-based electromagnetic benchmark is used to interpret the observed differences and to define the requirements for a future plasma-loaded three-dimensional model. Third, the energy-efficiency implications of the optimized antenna configuration are discussed in the context of sustainable plasma processing. This combined experimental and numerical approach provides a basis for optimizing antenna geometry in energy-efficient, low-pressure ICP sources where both plasma density and spatial distribution are important.

2 Experimental setup and diagnostics

2.1 Plasma source and operating conditions

The experiments were carried out in a low-pressure radio-frequency inductively coupled plasma system operated with argon gas. The discharge was generated at the standard industrial RF frequency of 13.56 MHz, and the operating pressure was maintained at 3.0 mTorr, measured using a capacitance manometer. RF power was applied to external antenna structures positioned around or near the dielectric source region. The plasma generated in the source region expanded into a downstream stainless-steel chamber, where spatially resolved plasma and electromagnetic-field measurements were performed.

The aim of the experiment was to compare how different external antenna geometries influence plasma generation, discharge transition behavior, spatial plasma-density structure, RF plasma-potential oscillation, and RF magnetic-field distribution with the practical goal of identifying the most energy-efficient configuration for sustainable processing applications. Three antenna configurations were investigated: a helical-type antenna, a planar spiral antenna, and a combined spiral-helical antenna.

For each antenna configuration, the applied RF power was varied over the investigated operating range (20–200 W). Plasma density, RF plasma-potential oscillation, and RF magnetic-field components were measured as functions of both applied RF power and spatial position. This allowed the discharge behavior to be compared from both plasma-diagnostic and electromagnetic-field viewpoints, and the plasma-production efficiency to be evaluated for each antenna design.

2.2 Helical-type antenna

The first antenna configuration was a helical-type antenna wound around the dielectric source tube. The antenna consisted of three turns, with an approximate diameter of 5 cm and an axial length of approximately 12 cm. This antenna has an axially extended RF current path and is therefore expected to concentrate RF coupling along the source tube.

The helical-type antenna was used as the baseline configuration because it produced a comparatively smooth power dependence and a localized plasma source. Its geometry allowed the behavior of an axially distributed antenna to be examined before comparing it with the broader planar spiral geometry. The helical-type antenna configuration is shown schematically in Figure 1a.

2.3 Planar spiral antenna

The second antenna configuration was a planar spiral antenna positioned near the dielectric source boundary. The antenna consisted of three turns and had an outer diameter of approximately 12 cm. This type of antenna provides a broad planar RF current path and can generate a strong inductive field near the dielectric window.

In the present experiment, the spiral antenna was used to examine the development of a high-density inductively coupled discharge and to identify any abrupt transition from a low-density capacitively influenced state to a high-density inductive state. The spiral antenna configuration is shown schematically in Figure 1b.

2.4 Combined spiral-helical antenna

The third antenna configuration was a combined spiral-helical antenna. This antenna consisted of a helical section connected to a spiral section. The helical part provided an axially extended current path around the dielectric source tube, while the spiral part provided broader radial coverage near the downstream opening of the source region.

The combined configuration was designed to test whether adding a spiral section to a helical-type antenna could redistribute plasma production farther into the downstream chamber, thereby improving both plasma density and uniformity for more efficient processing. This configuration therefore combines the axial coupling characteristic of the helical-type antenna with the broader radial coupling characteristic of the spiral antenna. The combined spiral-helical antenna is shown schematically in Figure 1c.

2.5 Langmuir-probe density measurement

Plasma density was measured using a Langmuir probe. The probe was inserted into the plasma at selected axial and radial positions to obtain both power-dependent and spatially resolved density data. For power-dependent measurements, the probe was fixed at selected diagnostic positions while the applied RF power was varied. For spatial measurements, the probe was moved along the axial and radial directions to obtain density profiles in the source and downstream regions.

The axial coordinate was used to describe the distance from the antenna/source region into the downstream chamber, while the radial coordinate described the distance from the central discharge axis. These measurements provided the basis for comparing plasma localization, downstream expansion, and radial uniformity among the three antenna configurations, and for evaluating which geometry produces the most uniform and dense plasma per unit applied power.

Plasma density was extracted from the ion-saturation region of the probe characteristic using the orbital-motion-limited (OML) theory. Electron temperature and plasma potential were determined from the electron-retardation region and the inflection-point method, respectively. Typical electron temperatures in the investigated discharges were in the range of 2–5 eV.

Langmuir-probe diagnostics are widely used for measuring plasma parameters in low-temperature plasmas. However, probe interpretation in RF discharges requires particular care because RF fluctuations can distort the current-voltage characteristic. RF compensation and consistent probe-analysis procedures are therefore important when extracting plasma density from RF plasma measurements [26, 27]. Experimental uncertainties in plasma density are estimated at ±15%, based on probe reproducibility, RF compensation effectiveness, and analysis-method systematic error. This ±15% uncertainty applies to all reported density values and is shown as error bars in Figures 2, 3. RF plasma-potential measurements (Figure 4; Section 2.6) and RF magnetic-field measurements (Figure 5; Section 2.7) carry a smaller estimated uncertainty of ±5%, reflecting the higher reproducibility of these probe measurements; the corresponding error bars are shown in Figures 4, 5.

2.6 Emissive-probe measurement of RF plasma-potential oscillation

An emissive probe was used to measure the time-varying plasma potential. The crest and trough values of the RF plasma potential were denoted by V H and V L, respectively. The RF plasma-potential oscillation amplitude was calculated as Δ V RF = V H − V L. This parameter was used to assess the extent of RF potential modulation in the plasma. A larger Δ V RF indicates stronger RF potential oscillation, which is commonly associated with stronger capacitive influence and less effective plasma shielding. A smaller Δ V RF indicates stronger shielding by a high-density plasma and more inductive discharge behaviour, which is desirable for controllable and energy-efficient processing.

2.7 Magnetic-probe measurement of RF magnetic field

The RF magnetic field was measured using a magnetic probe. The axial and radial magnetic-field components were measured as B z and B r, respectively. Measurements were performed as functions of applied RF power and spatial position. The power-dependent measurements were used to examine how the local RF magnetic-field amplitude changed during discharge operation, while the spatial measurements were used to compare the field structure generated by each antenna.

2.8 Measurement strategy

The same diagnostic strategy was applied to all three antenna configurations. Four main types of measurement were obtained: plasma density as a function of applied RF power, spatial plasma-density profiles, RF plasma-potential oscillation as a function of applied RF power, and RF magnetic-field amplitude and spatial RF magnetic-field profiles.

This approach allowed each antenna to be evaluated using both plasma-response and electromagnetic-field measurements. The Langmuir-probe data show the resulting plasma density and spatial distribution. The emissive-probe data indicate the degree of RF plasma-potential oscillation and shielding. The magnetic-probe data provide information about the RF field structure associated with inductive coupling. Together, these diagnostics enable assessment of which antenna geometry provides the most efficient plasma production for sustainable processing applications.

The experimental results from these measurements are presented in Section 4.

3 Numerical methodology

3.1 Purpose of the numerical model

The numerical model was developed to support the experimental comparison of the helical-type, planar spiral, and combined spiral-helical antennas. The aim was to separate the geometrical effect of the RF current path from the plasma response. Experimentally, the measured plasma density, RF potential oscillation, and RF magnetic-field profiles depend on both antenna geometry and plasma loading. Numerically, the first step was therefore to calculate the intrinsic magnetic-field structure produced by each antenna under controlled equal-current conditions.

The numerical work was organized into two stages. First, a three-dimensional vacuum magnetic-field benchmark was calculated using the Biot-Savart law. This stage isolates the effect of antenna geometry and provides a verification dataset for later finite-element electromagnetic modeling. Second, a plasma-loaded frequency-domain electromagnetic model is required to include plasma conductivity, induced plasma current, field penetration, and absorbed-power density. This staged approach is consistent with previous experimental and numerical studies of inductively coupled plasma sources, where RF field structure, plasma loading, and power deposition are treated progressively before comparison with measured density and magnetic-field profiles [13, 17–21].

3.2 Antenna geometries used in the model

The three experimental antenna configurations were represented using their principal measured dimensions. The helical-type antenna was modeled as a three-turn external coil with a diameter of approximately 5 cm and an axial length of approximately 12 cm. The planar spiral antenna was modeled as a three-turn spiral with an outer diameter of approximately 12 cm. The combined antenna was represented as a helical section connected to a spiral section, reproducing the hybrid current path used experimentally.

In the first numerical stage, the antennas were represented as idealized current paths. This approach allows the intrinsic magnetic-field topology of each geometry to be compared without introducing additional uncertainty from conductor thickness, feed geometry, matching-network behavior, or plasma loading. In the later plasma-loaded electromagnetic model, the conductor diameter, feed structure, dielectric boundary, grounded chamber, and surrounding computational domain should be included to reproduce the experimental system more accurately.

Because the helical-type and combined antennas have intrinsically three-dimensional current paths, no axisymmetric approximation was used for the geometry comparison. This is important because two-dimensional axisymmetric models cannot fully represent the magnetic-field components generated by helical or hybrid antenna structures.

3.3 Vacuum magnetic-field calculation

The vacuum magnetic field generated by each antenna was calculated by direct numerical integration of the Biot-Savart law, B r = μ 0 I c 4 π ∫ d l × r − r ′ r − r ′ 3. In the discretized implementation, each antenna was divided into short current elements, and the magnetic-field contribution from each element was summed at every observation point. Here, μ0 is the permeability of free space, I c is the prescribed antenna current, dℓ is the vector current element, r′ is the midpoint of the current element, and r is the observation point.

3.4 Verification of the Biot-Savart implementation

The Biot-Savart calculation was verified against the analytical magnetic field of a circular current loop [28]. This verification step was performed before comparing the three antenna geometries. The maximum relative error between the numerical calculation and the analytical solution was approximately 5.6 × 10 − 6. This confirms that the discretized current-path method accurately evaluates the magnetic field for a known geometry.

3.5 Need for a plasma-loaded electromagnetic model

The vacuum Biot-Savart model is useful for comparing antenna geometry, but it cannot describe the electromagnetic response of the plasma. Once the discharge is formed, the finite plasma conductivity modifies the RF magnetic field, induces plasma current, changes field penetration, and redistributes absorbed power. A plasma-loaded electromagnetic model is therefore required for quantitative comparison with the measured ICP discharge. Such a model should calculate the complete electric and magnetic fields, E and B, rather than reconstructing the electric field using an axisymmetric approximation. This is necessary because the helical-type and combined antennas generate fully three-dimensional fields. A simple exponential damping of the vacuum field, such as B = B 0 ⁡ exp − z / δ, is not sufficient as a final plasma-loaded model. Such an expression is only a simplified approximation and cannot describe radial field redistribution, chamber-wall effects, dielectric boundaries, feed asymmetry, phase variation, or non-local electron response. Previous studies have shown that RF field penetration and absorbed-power deposition in low-pressure ICPs can be spatially complex [14, 15, 29].

3.6 Future plasma-loaded modeling requirements

The vacuum Biot-Savart benchmark isolates antenna geometry effects but cannot describe plasma loading. A future plasma-loaded frequency-domain electromagnetic model should solve the vector-potential equation using local plasma conductivity σ p, with prescribed electron densities or experiment-informed density profiles. Validation targets are the measured B z and B r profiles (Figure 8), plasma density (Figure 7), and RF potential oscillation. Such a model would allow quantitative comparison of absorbed power density and field penetration, but its development is beyond the scope of the present geometry-comparison study.

4 Experimental results

4.1 Experimental comparison strategy

The experimental part of this study compares three antenna configurations operated in the same low-pressure argon RF plasma system under identical external conditions: 13.56 MHz driving frequency, 3.0 mTorr argon pressure, and 20–200 W applied RF generator power. The same diagnostic approach, consisting of Langmuir-probe plasma-density measurements, emissive-probe RF plasma-potential measurements, and magnetic-probe RF field measurements, was applied to each configuration to enable a controlled comparison of antenna-geometry effects [13, 26, 27, 30–32]. The measurements were designed to address four related questions. First, does each antenna geometry support the formation of a high-density inductively coupled discharge, or does capacitive coupling remain significant? Second, where is the plasma produced spatially, and how effectively does it expand into the downstream region? Third, how sharply does the discharge change from low-density to high-density operation as RF power increases? Fourth, how are the RF magnetic-field structure and plasma-density distribution related?

The experimental dataset shows a consistent result: the combined spiral–helical antenna gives the strongest overall plasma-production behaviour among the three configurations. It produces the highest measured plasma density, the most favourable spatial uniformity, the broadest useful high-density region, and the strongest suppression of RF plasma-potential oscillation. This result is central to the manuscript. The combined antenna should therefore be described not only as producing a broader profile, but as the best-performing experimental configuration under the investigated conditions.

This conclusion must, however, be stated carefully. The phrase “highest measured density response” refers to the Langmuir-probe measurements obtained under the stated operating conditions. It should not be interpreted as proof of the highest intrinsic absorbed-power efficiency, because antenna current, antenna voltage, phase, reflected power, and net absorbed power were not measured for all configurations. The matching and plasma-loading conditions may differ among the antennas because of their different impedances. Therefore, the strongest justified conclusion is that the combined antenna gives the highest and most favourable observed experimental response under the investigated conditions.

4.2 Mode conversion from plasma-density power curves

Figure 2 compares the plasma density as a function of applied RF power at two axial positions, Z = 5 cm and Z = −10 cm, for the helical-type, planar spiral, and combined spiral–helical antennas. These two positions are important because they sample different parts of the source: Z = 5 cm represents the downstream region, whereas Z = −10 cm is closer to the antenna/source region.

At Z = 5 cm (Figure 2A), the helical-type antenna shows a gradual increase in plasma density with increasing RF power. No sharp density jump is observed at this downstream position, indicating that the helical-type antenna produces a more localised source-region plasma and does not generate a strong downstream E–H transition signature under these conditions. This behaviour is consistent with the geometry of the helical winding, which concentrates the RF current path around the narrow dielectric source tube.

The planar spiral antenna behaves differently. At low RF power, the density remains relatively low, consistent with a capacitively influenced discharge. Near the transition region, the density increases abruptly, indicating a change from a low-density state to a higher-density inductively coupled state. This abrupt density rise is characteristic of E–H mode conversion in low-pressure ICP sources, where increased seed plasma density enhances conductivity, improves inductive power absorption, and produces further ionisation [2, 9, 10].

The combined spiral–helical antenna gives the highest measured density response at Z = 5 cm over the investigated power range. Its density rises rapidly and remains above the values obtained with either antenna operated separately. This indicates that the hybrid geometry couples favourably to the downstream plasma region. The result is physically reasonable because the helical section can support plasma formation near the source tube, while the spiral section provides broader inductive coupling near the downstream/source-transition region. The combined antenna therefore produces a high-density state more effectively than either individual geometry.

At Z = −10 cm (Figure 2b), the comparison gives additional information about the location of plasma production and mode conversion. This position is closer to the antenna/source region, and the helical-type antenna shows a clearer local transition signature than it does at Z = 5 cm. This agrees with the interpretation that the helical antenna mainly produces a source-localised plasma. The spiral antenna, by contrast, is less effective at this upstream position because its coupling is concentrated closer to the planar source boundary. The combined antenna maintains the most favourable overall density response because it contains both the helical and spiral current paths.

Taken together, the two power curves show that antenna geometry controls both the threshold behaviour and the spatial location of the high-density plasma. The spiral antenna gives a clear downstream transition, the helical antenna gives a more localised source-region response, and the combined antenna gives the highest measured plasma density and the most favourable overall behaviour. These observations support the central conclusion that the combined spiral–helical antenna is the best-performing experimental configuration among the three designs tested.

4.3 Spatial plasma-density profile at 160 W

Figure 3 presents the axial plasma-density profiles at P RF = 160 W for the helical-type, planar spiral, and combined spiral–helical antenna configurations. The figure also includes an A + B reference curve, representing the simple superposition of the density profiles obtained from the separate helical and spiral antenna cases. This comparison is important because it shows whether the combined antenna behaves merely as the sum of two independent sources or whether physical integration of the two antenna geometries produces a more favourable plasma structure.

The helical-type antenna produces a source-localized density distribution. The density is relatively high near the upstream/source region, but it decreases rapidly toward the downstream processing region. This behaviour indicates that the helical winding mainly supports plasma production close to the narrow dielectric source tube, with limited axial extension into the chamber. The rapid downstream decay is consistent with localized RF coupling, axial diffusion, and particle losses before the plasma can expand effectively into the wider processing region [16–21].

The planar spiral antenna produces a different spatial response. Its density is lower in the upstream region but increases toward the downstream/source-exit region, reflecting the location and radial extent of the planar current path. Compared with the helical-type antenna, the spiral antenna provides a broader downstream plasma distribution, although the density still varies significantly along the axial direction. This behaviour is consistent with the stronger near-window inductive coupling expected from a larger-radius spiral geometry and with previous observations that antenna configuration strongly affects plasma-density formation and spatial uniformity in ICP sources [5–8, 13].

The combined spiral–helical antenna gives the highest measured plasma-density response over the main useful region of the discharge. The density reaches its maximum near Z ≈ 5 cm and remains high over an extended axial range. In particular, the combined antenna maintains a broad high-density region from approximately Z = 0 to Z = 10 cm, where it clearly exceeds the individual helical-type and spiral antenna cases. This confirms that the combined configuration is not only stronger in peak density, but also more favourable in terms of spatial plasma extension and uniformity.

Comparison with the A + B reference curve is consistent with a beneficial hybrid effect, although—as discussed below—this cannot yet be distinguished from a simple difference in absorbed power between configurations without antenna-current or absorbed-power measurements. In the central plasma-production region, the measured combined-antenna profile is higher than the simple A + B reference, indicating that the integrated spiral–helical geometry does not behave as a passive algebraic sum of two independent plasma sources. Instead, the physical combination of the two current paths appears to modify the discharge structure and plasma loading in a way that improves plasma production. This enhancement may arise from improved axial continuity of the inductive field, upstream plasma pre-conditioning by the helical section, stronger downstream inductive coupling from the spiral section, and more favourable RF power absorption in the combined configuration. This A + B curve should be regarded only as a qualitative visual reference for whether the combined-antenna response exceeds a naive superposition of the two individual profiles, and not as a rigorous, coupling-normalized baseline: it does not account for possible differences in electrical coupling, matching-network behaviour, or absorbed power between the individually operated and combined-antenna configurations. Attributing the enhancement specifically to genuine electromagnetic/plasma coupling effects, rather than to differences in absorbed power between configurations, would require matched antenna-current or absorbed-power measurements, which were not available in the present dataset.

These spatial-density data provide some of the strongest experimental evidence for the superiority of the combined antenna. The helical-type antenna is effective mainly near the source region, while the spiral antenna improves downstream coupling. The combined antenna integrates both advantages, producing the highest density and the broadest useful plasma region under the same external operating conditions. This behaviour is important for cold-plasma processing applications because a broader high-density region can improve treatment uniformity and may reduce the need for additional power, substrate motion, or complex reactor optimisation.

4.4 RF plasma-potential oscillation

Figure 4 shows the high and low values of the RF plasma potential, V H and V L, as a function of applied RF power at Z = 5 cm and R = 0 for the three antenna configurations. The RF plasma-potential oscillation amplitude is obtained from the separation between these two values, Δ V RF = V H − V L. This amplitude provides a useful diagnostic of the capacitive component of the discharge: larger potential oscillations indicate stronger RF voltage modulation of the plasma, whereas reduced oscillation indicates stronger plasma shielding and more inductive discharge behaviour [7, 9, 10, 30, 31].

For the helical-type antenna, the separation between V H and V L decreases gradually with increasing RF power. The oscillation amplitude is approximately 8–10 V at low power and decreases to about 4–5 V at high power. This gradual reduction is consistent with the gradual increase in plasma density shown in Figure 2. The helical-type antenna therefore behaves as a localized source in which the capacitive component is reduced progressively, but not abruptly suppressed, over the measured power range.

The planar spiral antenna shows a sharper change in RF plasma-potential behaviour. At lower RF power, the separation between V H and V L remains relatively large, indicating a stronger capacitive influence. Near the transition region, the oscillation amplitude decreases abruptly, consistent with the density jump observed in Figure 2. This simultaneous reduction in RF potential oscillation and increase in plasma density is characteristic of E-H mode conversion, where the discharge changes from a capacitively influenced low-density state to a more strongly inductively coupled high-density state [9,10].

The combined spiral-helical antenna gives the most favourable potential-oscillation response. As RF power increases, the separation between V H and V L becomes very small, especially in the high-density regime. This indicates strong suppression of measurable RF plasma-potential oscillation and suggests that the plasma more effectively shields the capacitive component of the RF field. This behaviour is consistent with the high plasma density produced by the combined antenna and supports the conclusion that the combined geometry gives the strongest overall experimental response.

The reduced RF potential oscillation in the combined case should be interpreted as evidence of improved discharge behaviour at the same applied RF generator power, rather than as a direct measurement of absorbed-power efficiency. A full efficiency comparison would require antenna current, voltage, phase, reflected power, and absorbed power measurements. Nevertheless, the simultaneous observation of high plasma density and strongly suppressed RF potential oscillation indicates that the combined antenna provides the most favourable plasma response among the three configurations tested.

4.5 Axial RF magnetic-field profile at 160 W

Figure 5 presents the axial profiles of the RF magnetic-field amplitude |Bz| at PRF = 160 W for the three antenna configurations, measured along the discharge axis at R = 0. The magnetic-probe amplitudes in this figure are reported in arbitrary units (a.u.) because the comparison is used to evaluate relative field topology and antenna-dependent field structure rather than calibrated absolute magnetic-field strength. The axial magnetic-field component provides an experimental indication of the RF field structure associated with inductive coupling. A larger time-varying magnetic-field amplitude can generate stronger induced azimuthal electric fields through Faraday induction and can therefore contribute to enhanced plasma current and electron heating [13, 32]. However, the measured field amplitude should be interpreted together with the plasma density, potential oscillation, and antenna-loading behaviour, because the local field magnitude alone does not determine the total absorbed power.

The helical-type antenna produces a source-localized |B z| profile. The field amplitude is high in the upstream/source region, with values approaching approximately 1.8–1.9 a. u. near Z ≈ −8 to −7 cm and then decreases steadily toward the downstream region. This spatial behaviour is consistent with the physical position of the helical winding around the narrow dielectric tube. The resulting field structure explains why the helical antenna produces a plasma-density profile that is concentrated near the source region and decays downstream.

The planar spiral antenna produces a different axial field distribution. Its |B z| amplitude increases from the upstream side and reaches a maximum of approximately 1.8–1.9 a. u. near Z ≈ −2 to −1 cm, before decreasing rapidly further downstream. The peak magnitude is therefore comparable to, rather than substantially higher than, the helical peak. The main difference between the two cases is not the absolute peak value, but the axial location and spatial distribution of the field. The spiral antenna shifts the strongest RF magnetic-field region closer to the source-exit/planar-antenna region, consistent with its broader downstream plasma-density response.

The combined spiral–helical antenna gives the strongest measured |B z| response among the three configurations. Its axial profile exhibits a pronounced hill-shaped distribution, with a peak amplitude of approximately 2.8–2.9 a. u. near Z ≈ −3 cm. This exceeds the peak amplitudes measured for the individual helical-type and spiral antennas; as discussed below in relation to Figure 8, absolute peak magnitudes from different scans should be treated as indicative of field topology rather than as precisely comparable calibrated values. The combined antenna also maintains a relatively strong field over a broader central axial region, reflecting the contribution of both the helical and spiral current paths. This enhanced and spatially redistributed RF magnetic-field profile is consistent with the experimentally observed high plasma density and improved spatial plasma extension produced by the combined antenna. These reported peak values (Figure 5, one-dimensional axial scan at R = 0) should be read as a spatial-topology comparison rather than as absolute calibrated field magnitudes; Figure 8, discussed below, was acquired as an independent two-dimensional Z–R map and is not directly interchangeable with Figure 5 on a point-by-point basis.

It is important to note that these measured |B z| profiles are plasma-loaded fields, not vacuum fields. In the discharge, finite plasma conductivity modifies the antenna-generated field through induced plasma currents and electromagnetic shielding, which affect field penetration and RF power deposition [14, 15, 29, 33]. Therefore, the profiles should not be interpreted as simple vacuum antenna fields. The fact that the combined antenna still produces the strongest measured |B z| under plasma-loaded conditions supports the conclusion that its hybrid geometry provides the most favourable experimental coupling behaviour among the three configurations.

4.6 Spiral-antenna spatial structure

Figure 6 shows the spatial structure of the planar spiral antenna at P RF = 160 W. The figure presents (a) the plasma-density distribution and (b) the RF plasma-potential variation as functions of axial position Z and radial position R. These measurements show that the spiral antenna produces a clear high-density inductive discharge, but that the plasma remains more spatially localized than in the combined spiral-helical case.

The plasma-density profile (Figure 6a) exhibits a hill-shaped distribution with its maximum located near Z ≈ 5 cm. The peak density is approximately 3.0 × 10 11 cm − 3, after which the density decreases gradually in the downstream direction. This profile reflects the planar geometry of the spiral antenna, where the RF current is distributed over a larger radial area near the dielectric window. The resulting inductive electric field is therefore strongest near the source-exit region, producing a high-density plasma close to the antenna plane. The downstream density decay is consistent with reduced RF power deposition, ambipolar diffusion, wall losses, and electron-energy relaxation as the plasma expands into the larger chamber volume [16–21].

The radial structure indicates moderate non-uniformity, with the highest density occurring near the central-to-intermediate radial region rather than being perfectly flat across the discharge. This behaviour is typical of planar ICP sources, where the annular current path and finite antenna radius can produce stronger induced electric fields at particular radial positions [5–8, 13]. Although the spiral antenna gives a stronger and broader downstream response than the helical-type antenna, its high-density region remains limited compared with the combined antenna. This radial description is presently qualitative; a quantitative radial non-uniformity indicator (e.g., a radial coefficient of variation, analogous to the axial FWHM criterion introduced in Section 4.9) was not computed here because it requires the full radially resolved density dataset underlying Figures 6, 7, rather than values that can be reliably extracted from the published three-dimensional surface plots. Reporting such an indicator for all three configurations is identified as a further improvement for future revisions of this analysis.

The RF plasma-potential profile (Figure 6b) shows that potential modulation is still present in the spiral-only case. The oscillation is strongest near the antenna/source region and decreases farther downstream. This indicates that capacitive coupling has not been fully suppressed, even though the discharge has entered a high-density inductively coupled regime. The coexistence of high density and measurable RF potential oscillation is consistent with partial capacitive coupling from the RF antenna structure, particularly near the dielectric window and source region [7, 9, 10, 30, 31].

Compared with the combined antenna shown in Figure 7, the spiral antenna produces a lower peak density, a narrower useful high-density region, and stronger residual potential oscillation. Therefore, the spiral antenna alone is effective in producing an inductively coupled discharge, but it does not provide the same overall plasma performance as the combined spiral–helical configuration. The combined antenna remains the best-performing configuration because it gives higher density, improved spatial extension, and stronger suppression of RF potential oscillation under the same operating conditions.

4.7 Combined-antenna spatial structure

Figure 7 shows the spatial profiles of (a) plasma density and (b) RF plasma-potential variation for the combined spiral-helical antenna at P RF = 160 W. This figure provides the clearest experimental evidence that the combined antenna gives the best overall plasma performance among the three configurations.

The plasma-density distribution (Figure 7a) shows a broad hill-shaped high-density region centred around Z ≈ 5 cm and R ≈ 0. The maximum density reaches approximately 5 × 10 11 cm − 3, which is higher than the peak values obtained with the individual helical-type and planar spiral antennas under the same operating conditions. More importantly, the high-density region extends over a relatively broad axial and radial volume rather than being confined to a narrow source region. This confirms that the combined antenna improves both peak plasma production and spatial expansion of the discharge.

The superior density profile can be understood from the hybrid antenna geometry. The helical section supports plasma formation near the source tube, while the spiral section provides broader inductive coupling near the source-exit region. Their physical combination therefore produces a more continuous plasma-production region than either antenna alone. This behaviour is consistent with the axial density comparison in Figure 3, where the combined antenna gives the highest measured density over the main useful plasma region and exceeds the simple A + B reference curve in the central discharge region.

The RF plasma-potential profile (Figure 7b) shows that the separation between the high- and low-potential surfaces, V H and V L, is relatively small over most of the measured region. This indicates that RF plasma-potential oscillation is strongly reduced in the combined antenna case. The reduced oscillation is physically consistent with the higher plasma density: as the discharge becomes more conductive, the plasma shields the capacitive component of the RF field more effectively, reducing the potential modulation associated with E-mode capacitive coupling [7, 9, 10, 30, 31].

Compared with the spiral-only case in Figure 6, the combined antenna produces a higher peak density, a broader useful high-density region, and weaker residual RF potential oscillation. These results show that the combined spiral–helical antenna does not simply merge the properties of the two individual antennas but produces a more favourable discharge structure. The combined configuration is therefore the best-performing experimental case in this study, providing high plasma density, improved spatial uniformity, and strong suppression of capacitive-coupling signatures under the same external operating conditions.

4.8 Axial and radial RF magnetic-field structure of the combined antenna

Figure 8 shows the experimental spatial profiles of the axial RF magnetic-field component B z and the radial RF magnetic-field component B r for the combined spiral-helical antenna at P RF = 160 W. These measurements provide the most direct electromagnetic evidence for the hybrid field structure produced by the combined antenna.

The axial component B z (Figure 8a) exhibits a pronounced hill-shaped distribution. The maximum amplitude reaches approximately 2.4–2.5 a. u. near the central/source region and then decreases with increasing axial distance from the antenna. The profile is not confined to a very narrow region, but extends over several centimetres in both axial and radial directions. This behaviour is consistent with the combined geometry, in which the helical section contributes to axial field penetration near the source tube, while the spiral section broadens the field distribution near the source-exit region.

The radial component B r (Figure 8b) shows a distinct M-shaped distribution, with two off-axis maxima and a reduced central value. The peak amplitude is approximately 1.4–1.5 a. u. This structure indicates that the combined antenna does not produce only an axial magnetic-field pattern, but also generates a strong radial field component. The off-axis enhancement of B r is consistent with the influence of the spiral section, where the planar current path naturally produces radial field spreading at intermediate radial positions. Figure 8 was acquired as a separate two-dimensional Z–R spatial map, using a different probe/amplifier configuration and spatial sampling procedure from the one-dimensional axial scan in Figure 5; consequently, the arbitrary-unit peak amplitudes reported in the two Figures 2.8–2.9a.u. in Figure 5 versus 2.4–2.5 a.u. here) are not directly interchangeable as absolute calibrated values, and the comparison between them should be restricted to the reproducible field topology (hill-shaped |Bz|, M-shaped |Br|) rather than to exact peak magnitude.

The physical importance of these two components is that they shape the induced electric-field structure responsible for inductive power deposition. In an RF discharge, the time-varying magnetic field induces an azimuthal electric field according to Faraday’s law. More precisely, the azimuthal induced electric field E_θ depends on ∂ B r / ∂ z − ∂ B z / ∂ r, so the spatial structure of both field components contributes to the distribution of inductive electric field, plasma current, and electron heating [13, 32]. The hill-shaped |Bz| profile supports axial power coupling, while the M-shaped |Br| profile promotes off-axis field structure and radial spreading. Together, these features help explain why the combined antenna produces a broader and denser plasma than the individual helical-type or spiral antennas.

These measurements are plasma-loaded RF magnetic fields, not vacuum fields. In the real discharge, finite plasma conductivity, induced plasma currents, electromagnetic shielding, and skin-depth effects modify the field penetration and redistribute RF power absorption [14, 15, 29, 33]. Therefore, the measured profiles should not be interpreted as simple vacuum antenna fields. Instead, they show how the combined antenna behaves under actual discharge conditions. The coexistence of a strong hill-shaped | B z | profile and an M-shaped B r profile supports the conclusion that the combined antenna produces a hybrid electromagnetic topology that favours both axial coupling and radial field spreading.

These results also provide useful constraints for future plasma-loaded electromagnetic modelling. A complete model should reproduce the hill-shaped |B z| profile, the M-shaped B r profile, the broad high-density plasma distribution, and the reduced RF potential oscillation observed experimentally. The vacuum Biot–Savart benchmark presented in Section 5 should therefore be regarded as a geometry-controlled reference, while Figure 8 represents the experimentally measured plasma-loaded field structure.

4.9 Direct experimental comparison of antenna behavior

The experimental results reveal three distinct antenna-dependent discharge behaviours. The helical-type antenna produces a gradual increase in plasma density, a gradual reduction in RF plasma-potential oscillation, and a source-localized density distribution. This behaviour identifies the helical-type antenna as the baseline localized-source case. The planar spiral antenna shows the clearest abrupt mode-transition behaviour, with a rapid increase in plasma density and a corresponding reduction in RF potential oscillation near the transition region. This confirms that the spiral geometry is more effective than the helical-type antenna in producing a high-density inductively coupled discharge in the downstream/source-exit region.

The combined spiral–helical antenna gives the most favourable overall experimental response. It produces the highest measured plasma density, the broadest useful high-density region, improved spatial uniformity, strong suppression of RF plasma-potential oscillation, and a hybrid axial–radial magnetic-field structure. The combined antenna should therefore not be described merely as producing a broader plasma profile; rather, it is the best-performing configuration among the three antenna geometries under the investigated operating conditions.

This conclusion should nevertheless be stated as an experimental performance comparison rather than as a definitive absorbed-power efficiency comparison. The antennas were compared at the same applied RF generator power, but antenna current, RF voltage, phase, reflected power, and net absorbed power were not measured for all configurations. Therefore, the strongest supported conclusion is that the combined antenna gives the highest and most favourable measured plasma response under the present experimental conditions.

To support these qualitative statements with an explicit quantitative criterion, we quantified the axial extent of the high-density region in Figure 3 for each antenna configuration using the full width at half maximum (FWHM), defined as the axial range over which the measured density remains at or above 50% of that configuration’s peak value. Based on the digitized profiles of Figure 3, the combined antenna exhibits a peak density of approximately 5.4 × 10¹¹ cm^-3 with FWHM ≈25 cm, compared with approximately 2.6 × 10¹¹ cm^-3 and FWHM ≈14 cm for the spiral antenna, and approximately 1.0 × 10¹¹ cm^-3 and FWHM ≈12 cm for the helical-type antenna. This quantitative comparison confirms that the combined antenna produces not only the highest peak density but also a high-density region roughly twice as broad as either individual antenna, supporting the statement that the combined configuration gives the broadest useful high-density region among the three configurations.

5 Numerical benchmark and experimental interpretation

5.1 Role of the numerical benchmark

The numerical part of the manuscript is positioned after the full experimental comparison summarized in Table 2. This is important because the experiment is the main result of the study, while the present numerical calculation is a supporting geometry benchmark. The completed calculation is a vacuum Biot-Savart field comparison under equal-current conditions. It does not include plasma loading, dielectric boundaries, grounded chamber currents, capacitive coupling, matching-network behavior, antenna-current redistribution, or the self-consistent density response of the plasma.

For this reason, Figures 7, 8 remain experimental figures because they show the actual density, potential-oscillation, and RF magnetic-field behavior of the combined antenna. Table 2 then summarizes the direct experimental comparison of all three antennas. The numerical matrix plots and extracted model profiles are presented afterward as Figures 9, 10, where they serve as supporting evidence for the geometry-dependent field interpretation rather than as replacements for the experimental results.

The purpose of the vacuum benchmark is to isolate how the current path of each antenna shapes the initial magnetic-field topology. By comparing the helical-type, spiral, and combined antennas at the same assumed current, the model shows the field structure imposed by geometry before the plasma modifies the field through conductivity and loading. Direct numerical integration of the Biot–Savart law for discretized antenna current paths is a standard approach for characterizing vacuum-field topology in ICP antenna design, and the verification of this implementation against the analytical field of a circular current loop (Section 5.2) confirms that the method accurately reproduces known geometries before it is applied to the more complex helical, spiral, and combined current paths considered here.

We also note that the equal-current assumption (Ic = 1 A for all three antennas, Figures 9, 10) is a simplification. The combined antenna’s conductor is substantially longer than either individual antenna (Table 1), giving it different self-inductance and impedance; in the real system, with a common matching network tuned at the same applied generator power, the actual antenna current is unlikely to be identical across the three configurations [34–36]. In addition, the physical proximity of the helical and spiral sections in the combined antenna may introduce mutual coupling between them, which could redistribute current between the two sections in a way that a simple equal-current superposition of independent current paths does not capture. The vacuum Biot–Savart benchmark should therefore be read as a controlled comparison of geometry-imposed field topology under a common reference current, not as a claim that the three antennas carry equal current in practice.

TABLE 1. Antenna specifications.

The combined antenna’s total wire length (∼0.94 m) is less than the sum of the individual helical (∼0.57 m) and spiral (∼0.72 m) lengths because, in the combined configuration, the end of the helical section connects directly into the start of the spiral section at a single shared junction, rather than each section retaining a separate terminal lead as in the two standalone configurations.

5.2 Verification of the Biot-Savart calculation

The Biot-Savart calculation was verified against the analytical magnetic field of a circular current loop [28]. This verification step was performed before comparing the three antenna geometries. The maximum relative error between the numerical calculation and the analytical solution was approximately 5.6 × 10 − 6. This confirms that the discretized current-path method accurately evaluates the magnetic field for a known geometry.

5.3 Vacuum-field matrix/surface comparison

Figure 9 presents three-dimensional color-map surface plots of the vacuum magnetic-field magnitude calculated for the three antenna geometries. The plots were generated from the corresponding matrix data and displayed using the same normalized scale, allowing the geometry-controlled field topology to be compared directly. For the helical-type antenna, the calculated field is mainly localized around the narrow source-tube region. For the planar spiral antenna, the field is distributed more broadly near the antenna plane, reflecting the extended radial current path. For the combined spiral–helical antenna, the field contains both localized axial features and broader radial components because the current path includes both helical and spiral sections.

This comparison provides a qualitative electromagnetic explanation for the experimental observations. The helical-type antenna tends to produce a more localized source-region plasma, whereas the spiral antenna produces stronger near-source planar coupling and clearer transition behaviour. The combined antenna provides a hybrid field structure that can support both localized inductive coupling and wider spatial field distribution, consistent with the experimentally observed high plasma density, improved uniformity, and reduced potential oscillation.

However, the calculated field should not be overinterpreted as a direct prediction of the measured plasma response. The calculation is performed in vacuum under equal-current conditions and does not include plasma conductivity, skin-depth effects, RF loading, sheath coupling, or possible differences in antenna current at the same generator power. Therefore, Figure 9 should be interpreted as a geometry-controlled Biot–Savart benchmark that helps explain the experimental trends, rather than as a plasma-loaded simulation of the measured magnetic field or density.

5.4 Extracted radial and axial vacuum-field profiles

Figure 10 shows the calculated radial and axial vacuum magnetic-field profiles extracted from the three-dimensional Biot–Savart benchmark for the three antenna geometries. The profiles are plotted on a common arbitrary-unit scale for direct comparison of the field topology and are not fitted or normalized to the experimental plasma-density data. Under the same reference-current condition, the combined spiral–helical antenna gives the strongest overall calculated response, particularly along the axial direction, where the field remains higher and broader than for the individual helical-type and planar spiral antennas.

The radial profile shows several narrow peaks that arise from the proximity of the sampling line to individual current-carrying antenna sections. These peaks should therefore be interpreted as geometry-related vacuum-field features rather than as direct predictions of measured plasma-loaded magnetic-field amplitudes. The helical-type antenna produces a more localized field contribution, while the spiral antenna produces a broader planar response. The combined antenna contains both contributions, giving a hybrid profile with enhanced field amplitude and broader spatial coverage. We note that this calculated radial profile shows several narrow, geometry-related peaks rather than the smoother two-lobed M-shaped distribution measured experimentally in Figure 8b; the correspondence between the two should therefore be read as a qualitative indication that both reflect a non-axisymmetric, off-axis radial field structure produced by the combined current path, not as a quantitative match of peak positions or shapes between the vacuum model and the plasma-loaded measurement.

These extracted profiles support the experimental observation that the combined antenna produces the highest plasma-density response and improved spatial uniformity. Nevertheless, the comparison remains qualitative. In the real discharge, plasma conductivity, skin-depth effects, RF loading, sheath coupling, and matching-network conditions modify the actual magnetic-field distribution. Therefore, Figure 10 should be interpreted as a geometry-controlled vacuum-field benchmark that explains the current-path topology, not as a direct quantitative simulation of the plasma-loaded experiment.

5.5 Connection between field topology and plasma-density formation

The experimental results show that the combined antenna produces the highest measured density and best spatial uniformity, while the vacuum benchmark shows that the combined current path produces a hybrid magnetic-field topology. These two observations are consistent, but they are not identical. Plasma density is not determined by magnetic-field magnitude alone. Electron heating depends on the induced electric field and plasma current, and the density profile is then shaped by ionization, ambipolar diffusion, electron-energy transport, and wall losses [17–21].

The correct physical sequence is therefore: antenna geometry determines the RF current path; the RF current path determines the magnetic-field topology; the time-varying magnetic field induces an electric field; the electric field drives plasma current and absorbed power; and particle creation plus transport produces the measured plasma-density profile. A model that stops at the magnetic-field stage can support interpretation, but it cannot by itself prove the density mechanism.

5.6 Requirements for a plasma-loaded electromagnetic comparison

The next modeling step should solve the frequency-domain electromagnetic problem using the measured antenna geometry, dielectric boundary, grounded chamber, and prescribed plasma conductivity. The calculated quantities should include E, B, plasma-current density, and absorbed-power density. These should be exported in OriginLab-compatible matrix and profile form so they can be compared directly with the experimental plots.

6 Discussion

6.1 Main experimental finding

The central finding of this work is that the combined spiral-helical antenna gives the best overall experimental plasma response among the three antenna configurations tested. It does not only broaden the density profile; it gives the highest measured plasma density, the best density uniformity, and strong suppression of RF plasma-potential oscillation in the high-density regime. This point is essential and has been strengthened throughout the revised manuscript.

6.2 Interpretation of the helical-type antenna

The helical-type antenna behaves as a localized source. It produces a gradual increase in plasma density and a gradual decrease in RF potential oscillation as RF power increases. Spatially, the density is concentrated near the dielectric source tube and decreases downstream. This behavior is consistent with the geometry of the helical winding, which concentrates the RF current path around a relatively narrow axial region.

The helical-type antenna is therefore useful as a baseline configuration and may be suitable when a compact source-localized plasma is required. However, it is less favorable when the application requires a broad downstream high-density region or high energy efficiency.

6.3 Interpretation of the spiral antenna

The spiral antenna shows the clearest transition behavior. The density increases abruptly with RF power, while RF potential oscillation decreases sharply. This simultaneous density rise and potential-oscillation suppression is consistent with a transition from a capacitively influenced low-density state to a more inductively coupled high-density state [2, 9, 10].

The spiral antenna also produces a broader field structure than the helical antenna, including radial field features that appear clearly in the magnetic-probe data. However, the spiral-only case does not produce the highest measured density or best uniformity. Its coupling remains strongly associated with the planar source region, whereas the combined antenna redistributes the plasma more favorably.

6.4 Interpretation of the combined spiral-helical antenna

The combined antenna is the most important configuration in the study. Experimentally, it produces the highest density and best spatial behavior. The original work explicitly indicates that the combined plasma production exceeds the simple separated-antenna comparison and that the combined case gives the best and highest plasma-density performance. The combined case also shows strong suppression of RF plasma-potential oscillation, indicating strong RF shielding by the high-density plasma.

The measured axial and radial magnetic-field profiles further support the interpretation that the combined antenna generates a hybrid field structure. The |Bz| profile has a hill-shaped distribution, while the |Br| profile has an M-shaped structure with off-axis maxima. These features show that the combined antenna changes the full spatial RF field topology rather than simply increasing field magnitude at one point.

This hybrid field structure provides a reasonable explanation for the improved plasma density and uniformity. However, the manuscript should not claim that the combined antenna has the highest intrinsic coupling efficiency unless absorbed power and antenna current are measured. The strongest justified claim is that the combined antenna gives the highest measured experimental plasma response under the investigated operating conditions.

6.5 Magnetic-field structure versus plasma-density structure

The measured magnetic-field and plasma-density profiles are self-consistent, but they are not identical. Magnetic-field profiles show the RF field structure associated with the antenna and plasma loading. Plasma density shows the outcome of electron heating, ionization, diffusion, and confinement. Therefore, the density maximum does not have to occur exactly at the magnetic-field maximum.

This distinction is important for the model interpretation. A vacuum magnetic-field calculation can explain why the three antennas impose different field topologies, but it cannot directly predict the measured density. A plasma-loaded electromagnetic model, followed by absorbed-power and transport analysis, is required for quantitative density prediction.

6.6 Significance of the vacuum benchmark

The vacuum Biot-Savart benchmark remains valuable because it provides a clean, reproducible comparison of antenna geometry under equal-current conditions. It separates geometry from plasma loading and allows the field topology of the helical, spiral, and combined current paths to be compared in a controlled way. Placing this benchmark after the experimental summary makes clear that Figures 9, 10 provide supporting physical interpretation rather than primary evidence. The experimental figures and Table 2 establish the main finding, while the numerical benchmark explains how the different current paths can impose different initial magnetic-field topologies.

TABLE 2. Summary of the experimentally observed behaviour of the three antenna configurations under the investigated operating conditions.

6.7 Implications for sustainable antenna design

The results suggest that antenna selection should be based on the required plasma objective and sustainability goals. The helical-type antenna is suitable for a compact, source-localized discharge where minimal power and simple geometry are priorities. The spiral antenna is suitable when a clear E-H transition and broad near-source coupling are desired. The combined spiral-helical antenna is most favorable when the goal is to obtain high density together with broader downstream plasma and reduced RF potential oscillation—all of which contribute to energy-efficient processing.

For sustainable manufacturing applications, the combined antenna may therefore be advantageous when high plasma density and improved spatial uniformity are both required. Higher density at the same applied power implies lower energy consumption per processed unit area, while improved uniformity reduces waste and rework. Nevertheless, final process optimization should also include ion flux, electron temperature, sheath voltage, absorbed power, antenna current, and process-uniformity measurements to fully quantify the energy-efficiency gains.

6.8 Limitations

The present comparison has several limitations. First, the antenna cases are compared using applied RF generator power rather than absorbed plasma power; therefore, the sustainability and energy-efficiency discussion should be interpreted as inferred performance potential, not as a quantified absorbed-power or carbon-footprint analysis. Second, antenna current, RF voltage, phase, reflected power, and net absorbed power are not available for all configurations, so differences in matching, impedance, and conductor losses cannot be separated from differences in plasma response. Third, the experiments were performed in argon at a single RF frequency of 13.56 MHz, so the results may not transfer directly to molecular or electronegative processing gases such as O2, CF4, or fluorocarbon mixtures, or to other driving frequencies. Fourth, the present numerical model is a vacuum-field benchmark and does not include plasma loading, capacitive coupling, dielectric boundaries, chamber-wall currents, or self-consistent particle balance. Fifth, the diagnostic results are limited by spatial resolution, probe positioning uncertainty, and possible perturbation of the local plasma by Langmuir, emissive, and magnetic probes. Sixth, the combined spiral–helical antenna was evaluated for a single set of geometric parameters (helical pitch/length, spiral radius/turns, and their relative axial spacing); the results establish that a favourable combined-antenna geometry exists and outperforms either individual configuration under the tested conditions, but do not establish that the specific dimensions used here are optimal, nor that the improvement generalizes across all possible combined geometries. A systematic parametric study varying these geometric parameters is identified as a necessary direction for future work to establish the general applicability of the combined-antenna strategy. The experiments were also carried out at a single operating pressure (3.0 mTorr); the results should accordingly be read as a case study of antenna-geometry effects under one representative low-pressure argon ICP condition, rather than as a generally optimized design, and pressure dependence is identified as an additional direction for future work.

These limitations do not weaken the experimental observation that the combined antenna gives the highest measured density and best overall behavior under the stated conditions. They only limit the type of mechanistic and sustainability claim that can be made. The paper should therefore claim superior observed experimental performance and inferred energy-efficiency potential, not proven universal efficiency or quantified environmental impact.

6.9 Overall interpretation

The overall interpretation is that antenna geometry controls the initial RF field topology, while plasma loading, induced electric field, power absorption, and transport convert that field topology into a measured density distribution. The combined antenna performs best because its hybrid current path combines axial coupling from the helical section with broader radial coupling from the spiral section. This produces a high-density plasma with improved spatial usefulness and strong suppression of RF potential oscillation.

From a sustainability perspective, these results indicate that thoughtful antenna design can improve the energy efficiency of plasma processing without requiring changes to the RF generator, matching network, or process chemistry. This geometry-based optimization approach is inherently low-cost and broadly applicable, making it an attractive strategy for green manufacturing.

7 Conclusion and future work

This study compared helical-type, planar spiral, and combined spiral–helical antennas in a low-pressure 13.56 MHz argon inductively coupled plasma source. Plasma-density measurements, RF plasma-potential measurements, and RF magnetic-field diagnostics were used to determine how antenna geometry affects discharge mode conversion, plasma production, and spatial plasma structure.

The helical-type antenna produced a gradual density increase and a source-localized plasma. The RF plasma-potential oscillation decreased gradually with increasing RF power, and the density remained concentrated mainly near the dielectric source region. This configuration therefore provides a useful baseline case for localized plasma generation.

The planar spiral antenna produced the clearest abrupt transition behaviour. The plasma density increased sharply as the discharge entered the higher-density regime, while the RF plasma-potential oscillation decreased near the same transition region. This behaviour is consistent with a change from a capacitively influenced low-density state to a more inductively coupled high-density state.

The combined spiral–helical antenna produced the strongest overall experimental response. It gave the highest measured plasma density, the best density uniformity among the three configurations, the broadest useful high-density region, and strong suppression of RF plasma-potential oscillation in the high-density state. The axial and radial RF magnetic-field profiles further showed that the combined antenna produces a hybrid electromagnetic structure rather than simply reproducing the behaviour of either individual antenna.

A verified three-dimensional vacuum-field Biot–Savart benchmark was developed to support the experimental interpretation. The benchmark showed that the helical-type, spiral, and combined current paths produce different magnetic-field topologies under equal-current conditions. The combined antenna produced a hybrid field structure, consistent with the experimentally observed improvement in density and spatial plasma extension.

The vacuum benchmark should be treated as a geometry-controlled supporting model, not as a plasma-loaded prediction. A fully quantitative model should include plasma conductivity, dielectric boundaries, chamber walls, antenna current, capacitive coupling, and ideally the external RF circuit. Future work should therefore compare calculated and measured |B z|, |B r|, field phase, plasma density, and RF plasma-potential oscillation under identical operating conditions.

Beyond the physics of antenna–plasma coupling, the results have practical implications for the design of more controllable and energy-efficient cold plasma sources. The combined antenna achieved higher plasma density and improved spatial uniformity at the same applied RF generator power, suggesting that optimized antenna geometry can improve plasma-source performance without changing the process gas or operating pressure. This may be useful for plasma-based deposition, etching, surface modification, and other cold-plasma processing applications where high density and uniformity are required.

Future work should quantify the energy-efficiency advantage more directly by measuring absorbed power, antenna current, RF voltage, phase, reflected power, and process throughput. Such measurements would allow the present applied-power comparison to be extended into a true absorbed-power efficiency analysis. Additional plasma-loaded electromagnetic modelling and application-specific testing would further clarify the potential sustainability benefits of hybrid antenna configurations.

The main conclusion is that, under the investigated conditions, the combined spiral–helical antenna is the most favourable of the three configurations for generating a high-density and spatially useful argon ICP. This conclusion is based on the measured plasma response and should be distinguished from a separate absorbed-power efficiency claim, which requires additional RF circuit and power-coupling diagnostics. Nevertheless, the improved density, spatial uniformity, and suppression of RF potential oscillation make the combined antenna a promising design for future cold plasma source optimisation.

Generative AI statement

The author(s) declared that generative AI was used in the creation of this manuscript. During manuscript preparation, OpenAI’s ChatGPT was used for language editing, grammar correction, and formatting assistance. The author reviewed, edited, and verified all scientific content, data interpretation, figures, references, and conclusions. No AI tool was used to generate scientific findings, analyze raw data, or replace author judgment.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Footnotes

Edited by: Prajwal Lamichhane, University of Antwerp, Belgium

Reviewed by: Youssef Lagmich, Abdelmalek Essaadi University, Morocco

Fengming Yang, Chengdu University of Technology, China

Mortaza Taheri, Urmia University, Iran