Ion motion above a biased wafer in a plasma etching reactor Open Access

The almost universal dependence of consumer products on microelectronics components necessitates innovative research on improving efficiency and stability of semiconductor fabrication. Recently, plasma etching for fabrication of microelectronics components is challenged by three-dimensional device geometries, such as 3D NAND and 3D DRAM memory, having aspect ratios exceeding 100. The high aspect ratio (HAR) stacks of 3D DRAM memory are typically composed of conductor materials (Si, SiGe) whose plasma etching processes are conducted using radio frequency (RF) inductively coupled plasmas (ICPs) having a substrate bias. Etching of HAR features requires ions incident onto the wafer, which activates the etch, to arrive with near normal angles with narrow angular spread (< a few degrees) and high energy (> several kilo-electron volt).^1–3 

The ion energy and angle distributions (IEADs) incident onto wafers are determined by their acceleration from the bulk plasma, through the presheath into (and through) the sheath produced by the RF bias on the wafer.⁴ Elastic momentum transfer collisions along this path can broaden the angular distribution arriving at the substrate as these collisions create transverse components of the ion velocity at the sheath edge. Inelastic collisions in the sheath can reduce the ion energy at the wafer in addition to broadening the angular distribution. In spite of the importance of the ion trajectory from bulk plasma to wafer, there have been few direct measurements of the ion velocity and angle on this path.

In experiments, ion incident angles can be directly inferred from the etch profile, usually obtained by cutting the etched wafer and taking scanning electron microscope (SEM) image of the cross section.^5,6 Probes sensitive to ion flux and energy better parameterize the plasmas, but often find difficulty in isolating the signal from the background RF. Retarding field energy analyzer, modified to be used in the presence of high voltage RF bias, has been a popular way to measure the ion energy distribution function.^7–13 Specie-resolved measurement can be obtained by further combining the energy analyzer with a mass filter or mass spectrometer.^11–13 Laser based non-intrusive diagnostics, such as cavity ringdown spectroscopy^14,15 and laser induced fluorescence (LIF),^16–22 captures velocity information of a single ion species through Doppler shift and broadening.

LIF has the advantage of providing good spatial resolution with the use of a high resolution camera and temporal resolution with the use of a short-pulsed laser. Direct images of the ion motions can be obtained, making LIF an ideal tool for studying ion transport in small regions. However, LIF measurement is only effective in low density plasma that has enough population of metastable ions.

In this paper, we report on the direct LIF measurement of the transverse and perpendicular velocity components of argon ions in Ar/ $O 2$ mixtures on their path from the bulk plasma, through the presheath and sheath in an ICP with substrate bias. The results from accompanying numerical simulations are also presented. The plasma chamber is an industrial ICP etching tool as used in HVM modified to enable three-dimensional probe motion and optical access for LIF experiments.

The ICP source and the wafer bias can be pulsed independently at different frequencies, using matchless RF sources with a rise time of approximately 50  $μ s$⁠. Pulse-power modulation of etching reactors provides an additional parameter space for customizing fluxes to the wafer^23,24 and maintaining the symmetry.²⁵ In this investigation, the ICP coil was 2 MHz, while the bias was 1 MHz, both pulsed at 10 Hz to match the laser pulse rate. We found that different combinations of pulsed operation of ICP and bias have a significant effect on IEADs. The IEAD is more mono-energetic and more uniform around the wafer edge when the bias switched on in the plasma afterglow. Sheath variation, ion drift, and simulation results are also presented and discussed.

LIF provides a non-intrusive diagnostic to investigate ion transport in low density plasma. In an LIF event, a photon is absorbed from a metastable state to a higher state, which then decays and emits a fluorescence photon. The ion velocity distribution can be measured by scanning a narrowband tunable laser across a range of wavelengths and recording the fluorescence line shape.^16,18 At each scanned wavelength, ions having a velocity component whose Doppler shift corresponds to the shifted wavelength of the interrogating laser, absorb the photon. The line shape of the optical emission from the resulting higher states is Doppler broadened and proportional to the velocity distribution of the absorbing species.

With the probability of absorption scaling with $| k → · v → |$ (⁠ $k →$ is the photon wavevector, and $v →$ is the ion velocity), the LIF line shape mainly corresponds to the 1D velocity component parallel to the interrogating laser. Multi-dimensional spatially resolved measurement can be achieved with the use of multiple laser entry angles and a fast, high resolution camera.

In this work, we utilized a tunable dye laser^18,20 centered at λ₀ = 611.661 nm. It pumps $Ar +$ from the metastable state 0 (⁠ $3 d 2 G 9 / 2$⁠) to the metastable state 1 (⁠ $4 p 2 F 7 / 2$⁠), which then optically radiates at 460.957 nm to state 2 (⁠ $4 s 2 D 5 / 2$⁠), as shown in Fig. 1. State 0 is 19.2 eV above the ion ground state and is populated by electrons in the tail of the distribution function directly impacting ground state ions. After being pumped by the laser, state 1 ions have a 67% branching probability of decaying to state 2 and emitting a photon at 460.957 nm, easily distinguishable from the pumping laser. A laser tuned to $λ = 611.661$ nm excites metastable ions at rest, while the moving ions are excited by the appropriate Doppler shifted wavelength. During our experiment, the tunable laser was shifted in increments of 0.001 nm, typically across a range of λ₀ ± 0.15 nm, which corresponds to an ion energy range of roughly ± 1600 eV.

The laser excited state 1 (⁠ $4 p 2 F 7 / 2$⁠) has a measured lifetime of 8.5 ns²⁶ and stays relatively free from collisional loses in the low temperature background plasma (T_e = 4 eV). On the other hand, the lifetime of state 0 (⁠ $3 d 2 G 9 / 2$⁠) was measured to be $≳$17  $μ s$ in comparable experiment conditions,²⁷ and so can be quenched by collisions, dominantly charge exchange, at frequencies greater than $6 × 10 4 s − 1$⁠. Goeckner et al.²² experimentally found that significant quenching occurs at pressures above about 0.7 mTorr. We observed a significant drop in the LIF signal above a neutral pressure of 1 mTorr and chose to perform the experiments at around 0.5 mTorr.

The ion energy distribution (IED) is constructed from the LIF signal corresponding to the absorbing laser wavelength. The ion velocity $v ∥$ parallel to the laser propagation is related to the Doppler shifted absorbing wavelength by $λ − λ 0 = v ∥ / c$⁠.

The cylindrical ICP chamber was constructed of anodized aluminum with an internal diameter of 52 cm. The chamber has an RF biased substrate, which was covered by a 30 cm diameter Si wafer. The axial distance between the wafer and the ceramic lid was 17.2 cm. The bottom of the antenna is set 1 cm above the top surface of the lid and consists of a 1.5 turn flat spiral. The antenna is powered at 2 MHz that, when pulsed, has a power rise time of 50 μs and an adjustable maximum power of 300 W–1 kW. The silicon wafer was clamped on a electrostatic chuck, which was biased at 1 MHz. The chamber pressure was set at 0.5 mTorr. The feedstock gas was a mixture of Ar/ $O 2$ of ratio 95/5 (purity 99.999%). The applied bias produced sputtering of the Si. The small amount of $O 2$ was needed to etch sputtered Si that coated the optical windows. In a previous work, the plasma density, electric potential, internal magnetic field, and electron temperature in pulsed plasmas were measured in full three dimensions.²⁸ 

The plasma reproducibly reignited when the ICP was pulsed on and off at pressures greater than 5 mTorr but had difficulty igniting for the first time at 0.5 mTorr. To overcome this, we started at a higher pressure to ease breakdown and then decreased the pressure to the desired value. The ICP was pulsed between high and low powers (typically 550 and 125 W) so that the plasma was never completely extinguished. There was no visible breakdown during the low power interval, which we treated as plasma afterglow. Measurements were performed with the wafer bias either on or off, when ICP was at high power or in the afterglow.

The optical setup and triggering scheme are shown in Fig. 2. The laser light was produced by a dye laser (Sirah CSTR-D-532) pumped by a Nd:YAG laser (Spectra Physics Pro-230) with a center wavelength of 611.661 nm, linewidth of 0.000 136 nm, and pulse length of 8 ns. It was transmitted via an optical fiber from the laser room to the adjacent ICP reactor room and made into a sheet of light through a combination of cylindrical lenses. A 461 ± 0.5 nm narrow bandpass filter and a CCD fast camera (PCO Dicam C1) are used to capture the LIF signal from a window on the side of the chamber transverse to the beam path.

Figure 3 details how the laser enters the chamber, either horizontally (parallel to the wafer) or vertically (toward the wafer). A photograph of the setup is shown in Fig. 4. Alternate data runs using either horizontal or vertical beams allowed for measurement of ion transport and calculation of ion flow patterns in two dimensions. Optical access limited the field of view to a maximum of 2.5 cm vertically × 5 cm horizontally. To capture LIF data above both the edge and the center of the wafer, separate data runs were conducted and the camera was re-positioned accordingly.

LIF data were acquired at three different setup conditions as follows:

1. when the 2 MHz ICP was on high power (i.e., in the plasma glow) and the 1 MHz wafer bias was switched on;

2. when the ICP was on high power and wafer bias was off;

3. when the bias was switched on after the ICP switched to low power, i.e., in the plasma afterglow.

Figure 5 illustrates the timing of case (1), while (2) and (3) only differ in the start time of the bias and laser. Each ICP high power pulse had a duration of 12 ms, at a 10 Hz repetition rate. The bias voltage on the wafer plate turned on at 7 ms after the start of the ICP high power and continued for 4 ms in case (1). For both cases (1) and (2), the 8 ns laser pulse fired at 10 ms. Figure 6 is a timing diagram for the afterglow experiment. For case (3) in the afterglow, the bias turns on 10  $μ s$ after the ICP high power pulse, and the laser fires 30  $μ s$ after the high power pulse. The time axis is relative to the laser firing. The photodiode integrates the incident laser light, and its derivative gives the laser intensity in arbitrary units. On the timescale of the laser pulse, the photodiode signal immediately rises, allowing us to determine the exact timing of the laser firing.

On top of the main trigger, the laser firing time can be fine-tuned with respect to the bias voltage, and therefore, the LIF measurement can be phase resolved with a resolution of 8 ns out of the 1  $μ s$ RF bias period. The camera exposure lasted 60 ns and was triggered in such a way that the LIF emission resulting from the entire laser pulse was captured.

The raw camera data were automatically binned over four adjacent pixels that were then averaged into a single pixel. A typical image has 752 pixels along the wafer and 551 pixels above the wafer. Each pixel contains a 12 bit number. At each scanned wavelength, data consisting of about $2.0 × 10 5$ photons per acquired image at the peak wavelength were collected and averaged over 500–1000 acquired images. All the raw camera images were stored in HDF5 files as groups of 2D arrays and then read into Python for further image processing using NumPy with SciPy image processing.

It was key to subtract the background light at every laser wavelength, which was performed as follows and is illustrated in Fig. 7. After acquiring the LIF signal, the camera was triggered to capture an image 200 ns later, well beyond the laser pulse (8 ns) and the lifetime of the excited state (8.5 ns). This image recorded background noise including photons from the metastable state due to population of state 1 by electron impact, camera heat noise, and any other background plasma light that entered the bandpass filter at an angle. A 500 shot averaged background was acquired at every wavelength, and this signal was subtracted pixel-by-pixel from the LIF signal. A typical data run spanned 450 wavelengths taking approximately 10 h. The background subtracted LIF images were smoothed with a Gaussian filter over four pixels, and then, a Butterworth filter was applied to remove high frequency noise.

A photograph of a 2D graticule placed at the location of the laser sheet was used to determine that each (x, y) square pixel was 0.018 cm wide in the image plane. The images in Fig. 7 document the processing of a raw LIF signal taken with a horizontal laser beam at the line center wavelength (corresponding to zero parallel velocity) in one representative case.

The applied bias voltage has a sinusoidal waveform $V ( t ) = 1 2 V p p sin ( 2 π f t ) + V d c$⁠, where V_pp is the peak-to-peak voltage, f is 1 MHz, and V_dc is the self-generated DC bias on series capacitance with the substrate.²⁹ To track the wafer voltage, a metal plate was placed at the center of the wafer and its voltage was measurement with a high voltage probe attached to a coaxial feedthrough. The metal plate was taken out from the chamber during the laser experiment to avoid interfering with the LIF signal and boundary conditions. The applied voltage and the voltage at the surface of the wafer voltage are shown in Fig. 8.

In this reactor, V_dc is approximately 90% of the RF amplitude: $V d c ≈ − 0.9 ( 1 2 V p p )$⁠. The maximum potential during the peak of the cathodic portion of the RF cycle reaches $− 0.82 V p p$ as shown in Fig. 8. The ion transit time across the sheath is estimated to be $τ i = 3 s m i / ( 2 e V s h ) ≈ 0.14$ ns, where s is the sheath thickness, m_i is the ion mass, and V_sh is the sheath voltage. Our bias condition is close to the low RF regime (⁠ $2 π f τ i ≪ 1$⁠), and therefore, ions entering the sheath are largely able to follow the instantaneous voltage waveform as opposed to responding to the time averaged sheath potential.³⁰ Therefore, the most energetic ions are expected to strike the wafer with an energy level approaching $0.82 V p p ≈ 980$ eV.

In Secs. III A–III C, the experiments were designed and triggered according to the applied voltage V_pp, since voltage on the wafer was measured by an intrusive electrode and therefore could not be monitored simultaneously with the LIF measurement.

Ar⁺ ions undergo charge exchange collisions with $O 2$ having a cross section for energies of a few electron volt of $2 – 4 × 10 − 16 cm 2$ with rate coefficients of $10 − 10 cm 3 s − 1$⁠.³¹ For a gas pressure of 0.5 mTorr, the mean free path between charge exchange collisions of Ar⁺ with $O 2$ for a gas temperature of 600 K is above 10 m. Given the size of the chamber, Ar⁺ ions are likely not being depleted by charge exchange collisions with $O 2$⁠. The symmetric charge exchange collision of Ar⁺ with Ar at a few eV is about $20 × 10 − 16 cm 2$⁠, which produces a mean free path of about 70 cm,³² increasing to about 150 cm at 100 eV. One might then expect some mild amount of charge exchange that would contribute to thermalizing the low energy part of the velocity distribution.

Representative IEDs for setup case (1) and (2), i.e., with or without bias during the plasma glow, are shown in Fig. 9, highlighting the side of the function corresponding to ions moving toward the wafer. The positions z = 0 and x = 0 correspond to the surface of the wafer at the edge of the wafer.

The distribution functions of ion velocity parallel (horizontal) to the wafer, $f H ( E )$⁠, are shown at a height of z = 0.69 cm (at the edge of the sheath) and z = 4.03 cm (in the bulk plasma) in Fig. 9(a). $f H ( E )$ at both heights is essentially the same with and without a wafer bias. This is as expected since the bias mainly effects vertical ion motion. We only show the no bias case here. Beyond −40 eV, $f H ( E )$ falls completely below the noise level (blue region), indicating an absence of high energy ions.

$f H ( E )$ entering the sheath sets a lower limit on the angular spread of ions striking the substrate. The minimum angle is $θ = E T / q V s$⁠, where E_T is the transverse energy and V_s is the substrate bias voltage. $f H ( E )$ is symmetric in both negative (inward moving) and positive (outward) moving directions, implying an isotropic distribution. The FWHM (full width half maximum) of $f H ( E )$ is 0.3 eV, which is commensurate with the computed ion temperature for similar conditions.

The vertical IEDs, $f V ( E )$⁠, without a bias at z = 0.67 and z = 4.09 cm are shown in Fig. 9(b). The FWHM of the no bias $f V ( E )$ is 0.3 eV, similar to that of $f H ( E )$⁠, which again implies a largely isotropic distribution. Unlike $f H ( E )$⁠, however, $f V ( E )$ s show an asymmetry with a velocity component commensurate with the sheath voltage drop directed downwards toward the wafer.

When the bias is applied, $f V ( E )$ broadens and shows distinct feature near the sheath region. Figure 9(c) shows a case of $f V ( E )$ with a V_pp = −1200 V bias for heights of z = 0.345 cm (sheath), 1.38 cm (sheath edge), and 3.11 cm (bulk plasma), acquired when the applied bias is at the most cathodic phase. At the height of z = 3.11 cm, which is well above the sheath edge, $f V ( E )$ contains ions that are accelerated down the plasma potential toward the sheath. In this reactor, the plasma potential is at its most positive value near the middle of the chamber (z = 9.5 cm).²⁸ Close to the sheath edge, $f V ( E )$ extends to higher energies. At z = 0.345 cm, the maximum ion energy (above noise) directed toward the wafer is up to 660 eV.

To further illustrate the effect of RF bias, a 3d contour map of $f V ( E )$ with V_pp = −1200 V at all z is plotted in Fig. 10, from which Fig. 9(c) can be viewed as cross-sectional slices at selected z values. The presence of the high energy ions is visualized as a “ridge” extending to negative energy (directed toward the wafer) as high as 820 eV. The thickness of the “ridge” in z is 0.3 cm, indicated by the yellow double arrow on the axis, which we approximate as the sheath thickness.

Figure 8 shows that the maximum ion energy for acceleration from the sheath edge is 980 eV. In our experiment, no significant LIF signal was obtained beyond 820 eV at the most cathodic phase of the applied bias. This is likely due to the low plasma density very close to the wafer (1–2 mm) and ion density scales inversely with ion speed for a collisionless sheath in which ion flux is conserved. A phase delay between the applied bias voltage and the ion motion is also observed, illustrated in Fig. 13. The maximum energy might be easier to detect at a phase other than the most cathodic.

For case (3) in the plasma afterglow, measurements are particularly difficult as there must be sufficient number of electrons to populate state 0 (⁠ $3 d 2 G 9 / 2$⁠) with an excitation energy of 19.2 eV (Fig. 2). Collecting a sufficient number of photons to be above noise requires that the electrons in the afterglow are still warm. It was experimentally determined that there was sufficient signal to perform LIF 30  $μ s$ after the ICP switched to low power (i.e., 20  $μ s$ after the initial bias pulse), and no later than that. The wafer bias pulse was turned on 10  $μ s$ after the ICP switched to low power.

$f V ( E )$ as a function of height in afterglow is shown in Fig. 11 at x = 4.6 cm. The applied bias of V_PP = −1200 V is at the most cathodic phase. As with measurements when the ICP is on high power, $f V ( E )$ is dominated by a low energy component in the bulk plasma (z $≫$ 0.5 cm). At distances less than 0.5 cm, there is gradual acceleration to about 175 eV. Upon entering the sheath proper (<0.3 cm), $f V ( E )$ has a high energy component peaked at 880 eV and extending to 985 eV. This value is near the expected maximum energy of about 1 keV.

Compared to case (2), $f V ( E )$ in Fig. 11 has a distinctive high energy feature. The fast ions in the sheath region are concentrated in a small band of energies close to the wafer bias, instead of having a smooth tail extending to high energy, as seen in $f V ( E )$ during ICP high power (Fig. 10).

Apart from the energy-resolved data obtained at the most cathodic phase of the applied bias, the phase-resolved LIF signal was obtained at a fixed excitation laser wavelength.

Ions enter a collisionless sheath at the Bohm velocity, $c B = k T e / m i$⁠, where kT_e is the electron temperature and m_i the ion mass.³⁰ An RF compensated Langmuir probe measured the background T_e to be 4 eV (⁠ $c B = 3.1 × 10 3$ m/s). The dynamics of the sheath is sensitive to various parameters, such as surface bias and ion species, to satisfy the boundary conditions. In the simpler case of a DC bias, Child–Langmuir law predicts the sheath size to have a 3/4 power dependence on the bias voltage with appropriate assumptions, while analytical approach often shows a thicker sheath.^4,33 For low frequency RF bias (⁠ $2 π f τ i ≪ 1$⁠) reported in this paper, the sheath dynamics is able to keep up with the bias waveform, and therefore, the thickness should also vary at the same frequency, as shown by various numerical models.^30,34

Figure 12 shows the LIF signal from an excitation wavelength of 611.6547 nm in the vertical direction, corresponding to $v ion = 3.08 × 10 3$ m/s. The time steps are 100 ns apart and cover one complete bias cycle (t = 0 is at the most cathodic phase).

The sheath is represented as the dark area where the LIF signal significantly drops and falls below the noise level. The sheath edge at the most cathodic phase of the applied bias (t = 0) agrees well with the sheath seen in Fig. 10.

The motion of the sheath along the RF cycle is clearly visible, and its height varies from δz = 0.32 to 0.17 cm. The thickness of the sheath as a function of time in one RF cycle is shown in Fig. 13. The motion is observed to respond to the instantaneous potential change, yet not completely in phase with the wafer voltage.

The net drift speed is inferred by locating the peak of the velocity distribution function relative to λ₀ (E = 0 eV). The technique to determine the bulk drift is illustrated in Fig. 14 where the vertical LIF signal shows a shift of the main peak to the blue, corresponding to ions drifting toward the wafer. The smaller peak to the red side is due to light reflected from the wafer and is symmetric with the main peak. In cases where ions drift upward, the largest peak is to the red side of λ₀.

The ion motion with and without wafer bias near the edge of the wafer (x = 0) and near the center (x = 15) is shown in Figs. 15 and 16, respectively. The data in both plots indicate only the drift motion and do not include the kilo-electron volt ions accelerated in the sheath. In the cases for which there was no bias, the laser was triggered at one phase point in the coil current so that the figures are not an average over an ICP cycle. When bias was applied, the laser was fired at the most cathodic part of the applied bias waveform, which is also phase locked to the coil current. There were 414 352 locations in the x–z plane at which an LIF signal was acquired. For visual clarity, 1% of the arrows at randomly selected positions are drawn.

In region beyond the edge of the wafer (x < 0) over the electrostatic chuck, LIF measurements indicate net drift of Ar ions vertically upward.

When viewing the background ion drift in these and other cases, the largest vertical drifts are close to the surface of the wafer. They are far higher, of course, when the wafer is biased (e.g., Fig. 9). With and without bias, there is an abrupt change in the drift pattern near the wafer edge. When the wafer is unbiased, the edge drifts are smaller. In this case, the maximum drift of 6 eV is about three times the sound speed (based on $T e$ = 4 eV). In the biased case, the maximum drift near the wafer edge is three times larger than the unbiased case and very little upward drift is observable past the wafer edge. The ion drift in the afterglow with and without bias is shown in Fig. 17. Here, the highest energy ions are included.

The vorticity $ω →$ is given by $ω → = ∇ × v →$⁠. We calculated the vorticity near the wafer edge from vector data as shown in Figs. 15(a) and 17(a). The vorticity in energy units is plotted for case (1) in Fig. 18(a) and case (3) in Fig. 18(b). During the glow, the downward drift near the edge is about twice as large close to the wafer when it is biased. Unlike the edge, the drifts are uniform over the 2 cm viewed near the center. In comparison, Fig. 18(b) in the afterglow shows more uniformity across the wafer with less activity near the edge.

The total velocity close to the wafer is determined by the horizontal drift velocity v_x and the downward velocity -v_z imposed by the RF bias. For a −1200 V bias, v $z = 5.4 × 10 4$ m/s or 17.5 times the sound speed for 4 eV electrons.

A contour map of the ion angles in velocity space is shown in Fig. 19. Away from the edge (x > 1 cm), ion angles just above the wafer in case (1) [Fig. 19(b)] are at most $θ ≃ 0.5$°, which corresponds to a horizontal energy of order of 0.1 eV and vertical energy of 1 keV. For case (3), the incident angle is $θ ≃ 0.2$° across the surface [Fig. 19(a)]. In the bulk plasma, the ion angle is mostly zero for case (3) and about 0.25 for case (1).

The numerical simulations were conducted for conditions that closely approximated the experiment (0.5 mTorr $Ar / O 2$⁠: 95/5, 530 W). In all cases of the simulations, the ICP power was continuous with 2 MHz RF due to the low repetition rate and long power-on time in the experiments. With 10 Hz and 12% duty cycle, 530 W antenna power was on 10⁴ μs during the power-on part of the pulse. The numerical simulations were run up to 500 μs in which it is ensured that charged particles reach quasi-steady state. The applied bias on the electrode under the wafer is $V ( t ) = 1 2 V p p sin ( 2 π f t )$⁠, where V_pp is the peak-to-peak amplitude and f is the frequency. V_pp is 1.2 kV peak-to-peak at 1 MHz. The cylindrical geometry used in the simulations is shown in Fig. 20, which is a best-case representation of the experiment. The ceramic window has a relative permittivity of $ε r = 3.9$⁠. The electrode is covered by the Si wafer having a conductivity of $σ = 0.05 ( Ω c m ) − 1$ and relative permittivity of $ε r = 11.8$⁠. The electrode is surrounded by a ceramic chuck and focus ring having $ε r = 9.3$ and negligible conductivity. Gas is injected from the dielectric layer with a flow rate of 100  sccm and pumped annularly around the substrate. The 3-turn antenna is offset from the window by a gap of 3.5 mm. With the exception of the feed to the electrode, the outer boundary of the mesh (top, right side, and bottom) is grounded metal. The RF bias is applied to the metal electrode, connected serially to the power supply through a block capacitor on which the DC bias, V_DC, appears. Unlike the experiment, the ICP chamber is connected to the power generator via a matchbox.

The computational investigations were conducted using the Hybrid Plasma Equipment Model (HPEM).³⁵ For low pressures (<10 mTor), the conventional continuum approach might be questionable due to the highly nonequilibrium transport of particles and nonlocal heating. For the given operating pressure, the particle methods are accurate but computationally expensive.^36,37 By calculating transport coefficients, distribution functions kinetically and solving the conservation equations with fluid approach improves accuracy with a reasonable computational cost.³⁸ The HPEM is a two-dimensional modeling tool with several modules addressing different physical processes coupled using hierarchical structure. The modules that were used in this investigation are the Electromagnetics Module (EMM), Electron Energy Transport Module (EETM), Fluid Kinetics Module (FKM), and Plasma Chemistry Monte Carlo Module (PCMCM). The EMM module calculates the electromagnetic fields produced by the RF driven antenna as they propagate into plasma and dielectric materials. The frequency domain wave equation is solved using the method of successive-over-relaxation. An impedance matching network is implemented in the circuit model to minimize mismatch between the ICP reactor and the power supply.³⁹ Electron impact rate coefficients and source terms are calculated in the EETM using a Monte Carlo simulation including electron–electron collisions based on these electromagnetic fields from the EMM and electrostatic fields produced in the FKM. These coefficients are transferred to FKM. In the FKM, densities, velocities, and temperatures of heavy particles are calculated with densities of electrons. Poisson's equation solved for the electrostatic potential. Based on source functions for ion production and the electromagnetic and electrostatic fields, pseudo-particles for ions launched and tracked as they move through the plasma in the PCMCM to calculate the phase resolved energy and angular distributions at locations in the plasma and when striking a surface.³⁵ The reaction mechanism used for $Ar / O 2$ plasmas is the same as that described by Huang et al.⁴⁰ Data in the computational studies are averaged over 1 RF bias cycle unless otherwise is stated. In the experiment, the IEAD's were measured over a very short (⁠ $≈$ 20 ns) interval of time when the bias is most cathodic. Also, in the simulation, the wafer was divided into four equal pieces and IEADs were collected on the third innermost piece, 3–7 cm from the wafer edge. In the experiment, measurements were made at specific radial (x) locations.

At sufficiently high pressures, the coupling between electromagnetic fields and the plasma is achieved through Ohm's law where power deposition is largely local. At low pressures, less than 10 mTorr, non-collisional heating might become significant or outweigh the collisional heating.^41,42 The increased mean free path of electrons at lower pressures allows electrons to traverse regions with different electric fields between collisions. To account for these non-local effects, the following procedure is used, described by Rauf and Kushner.³⁸ In the EETM, electron trajectories are computed based on accelerations provided by the electromagnetic fields from the EMM and electrostatic fields produced in the FKM. This is a kinetic calculation that accounts for non-local effects. The electron trajectories in the plane of the antenna produced electric fields (the azimuthal direction here) are binned according to position and phase. The total kinetically derived power deposition is computed by summing the product individual pseudo-particles of $E → . v →$⁠. These statistics are Fourier analyzed at the antenna frequency to provide harmonic currents, which are then used in the wave equation solved in the EMM. To ensure proper power normalization, the antenna currents are normalized so that the inductive power equals the kinetically delivered power.

As in most of the RF-powered systems, an impedance matching network (IMN) between the ICP reactor and the power supply was used in this study, as described by Qu et al.⁴³ The load impedance seen by the IMN includes inductance, capacitance, and resistance from plasma, antenna, and chamber. The IMN matches the load impedance with the power supply impedance to reduce the reflected power due to mismatch between the power supply and the plasma filled chamber. The impedance of the chamber depends on the capacitance of the window capacitance, and inductance and resistance of the antenna. The plasma impedance depends on the conductivity and sheath thickness. Some portion of the power from the supply is dissipated as resistive losses of the antenna and components of the IMN. The remaining power deposited into the plasma has both capacitive and inductive modes contributions. Since perfect impedance matching is assumed in this study, the reflected power due to mismatch is zero. The antenna delivers the capacitive power to the plasma through the electric fields along r and z. On the other hand, inductive power is delivered to electrons through the azimuthal fields. The capacitively coupled power is the time average of the displacement current and antenna voltage product, whereas inductively coupled is calculated through a cycle averaged $j · E$⁠. The nonlocal heatings are coupled to the power deposition with the current density.

Although it is challenging to analyze LIF measurements at high pressures, the effects of pressure on ion energy angle distributions and sheath thickness are investigated for 1 and 5 mTorr in addition to 0.5 mTorr. The decrease in the pressure causes a reduction in the electron density, causing a larger skin depth and resulting in less inductive power coupling. The inductive powers at steady state are 379, 406, and 505 W for 0.5, 1, and 5 mTorr, respectively. On the other hand, the capacitive powers are 48, 26, and 2.5 W for 0.5, 1, and 5 mTorr, respectively. The remaining powers are dissipated as resistive losses; the total deposited power is 530 W. The averaged IEADs onto the wafer (z = 0 cm) are plotted for three pressures over one bias cycle, as shown in Fig. 21(a). The maximum value of each plot is obtained from corresponding ion energy distributions (IED), angle integrated IEADs, as shown in Fig. 21(b). Due to larger capacitive coupling at 0.5 mTorr, ions have higher energies with broader angle distributions. This indicates that at more industrial relevant operating pressures, IEADs are expected to be more bimodal and have even smaller incident angles than the LIF measurements presented in this paper.

The energy delivered to ions depends on the RF bias amplitude, DC bias from the blocking capacitor under the electrode, and the capacitive coupling from the antenna. Since the sheath above the wafer also acts as a capacitor, there are slight changes in the DC bias from the blocking capacitor. For each case, the DC bias from the blocking capacitor is almost the same, 370–380 V. The remaining differences in the energy are mainly caused by power coupling. At 1 MHz RF frequency, ions are fast enough to see the instantaneous electric field, which causes two distinct peaks at IEDs for low and high energies, as shown in Fig. 21(b).

The computational investigations of ion energies for afterglow were tested similarly. In the simulation, the antenna with average power of 530 W was operated until 0.5 ms, and then, the antenna power decreased to one-eighth of its peak. After 10  $μ s$⁠, the bias is applied to the electrode for 20  $μ s$ and ion energy and angle distributions were collected. The modifications in operation conditions were made to achieve similar conditions in the experiments, as in Fig. 11. The computational results are shown in Fig. 22. The cycle averaged peak ion energies are dropped up to 300 eV in afterglow simulations compared to the glow case, Fig. 21(a) 0.5 mTorr case. When the bias is most negative, the ion energies at various z locations are shown in Fig. 22(b). At the wafer surface, z = 0.00 cm, the ions energies are in the range of 650–800 eV. The ions hit the wafer anisotropically with energies higher than 700 eVs. The accelerations of ions can be estimated as 100 eVs per mm from 0.25 and 0.5 cm distributions. The anisotropy holds until 10 mm into the sheath. The ions are accelerated toward the wafer through the sheath potential. Near the plasma core in the middle of the chamber, 10 mm, ion energies gets closer to the thermal ion energies with broad-angle distributions. The sheath thickness for the afterglow is increased due to the lower charged densities from low-power operating antenna. The capacitive power coupling from the antenna is achieved with ions. Since the portion of ion energies from the power coupling is decreased, the lesser ion energies are observed for the afterglow simulations. At the experimental measurements, the ion energies reach up to 850 eVs at 3 mm above the wafer observed at the most cathodic part of the cycle (Fig. 11).

The measured ion energies are slightly larger than the computational ones. This discrepancy could arise from the differences between the actual and simulated antenna powers delivered to the plasma. Although the capacitive coupling from the antenna is low with the inclusion of nonlocal heating in the simulations, the discrepancies were expected in the deposited power due to the possible differences in the chamber conditions, matching conditions, etc. The computational methods observe the energetic ions; however, their densities are small, requiring 5–6 decades of plotting. There was not enough LIF signal in the experiment to plot angles over this many decades, and the experimental angles were close to the highest values (red and orange) in Fig. 22. The measurements and computations were done at the most cathodic part of the cycle; however, there could be a slight shifts at the temporal location of the RF cycle.

The cycle-averaged ion energies are collected at various locations on top of the wafer, Fig. 23 for glow (antenna power is 530 W) and afterglow (antenna power is reduced to 66 W). There are more high energy ions at z = 0.1 mm [Fig. 23(c)] in the glow case compared to the afterglow. When the antenna is running with reduced power, the capacitive power coupling with ions is decreased. The maximum cycle-averaged ion energy decreased from 975 eV for the glow case to 725 eV in the afterglow case at 0.1 mm above the wafer due to the change in the capacitive coupling from the antenna. The reduction in the ion energies can be seen at other z locations. The afterglow simulations peak around 700 eV at 1 mm above the wafer, whereas the experimental values are up to 800 eV, as shown in Fig. 10.

The computational ion energy and angle distributions at three z locations, as in Fig. 9, with and without bias, are shown in Fig. 24. When there is no bias applied to the electrode, there is still a potential difference between the wall and plasma reaching up to 60 V. The plasma potential starts to decrease around 0.6 cm above the wafer. At z = 0.2 cm above the wafers, ions experience the potential difference and accelerate toward the wafer at the sheath edge. However, ion energies are getting closer to the primarily thermal at higher distances, and angular distributions get broader.

Figure 24(b) shows the simulated IEADs at three z locations, averaged over 1/10 of the bias cycle (0.1 μs) during the most cathodic part in the attempt to match the experimental condition in Fig. 9. z = 1.38 and z = 3.11 cm are above the sheath, and ion energies are low as in the no bias case.

For z = 0.35 cm, the simulated data are shown with two- and five-decade variations. While two two-decade plots, as in the measured data plots, show ion energies from 300 to 500 eV, ion energies expanded to 50–750 eV with five-decade plots. The five-decade plots show the high energy tail of the ions, which is in better agreement with the experimental data. However, the 400 eV peaks in the five-decade plots were not observed in the experimental measurements, which have almost monotonic distributions on a logarithmic scale from low energies to high energies. This could be the result of different time spans of the computational data (0.1 μs time step) and experimental data, which was practically collected for ∼16.5 ns (laser pulse length + state 1 decay time). Since the ion response is not completely in phase with the bias waveform as shown experimentally in Fig. 13, the sheath is still expanding to its maximum during the 0.1 μs time step. The simulated data at z = 0.35 cm possibly include more ions that are not yet close to the sheath. The cycle-averaged glow simulations at the same z location [Figs. 23(a) and 23(c)] show the similar monotonic profiles on a log scale and match better with the experiments.

LIF has been used to map the energy distribution and drift of ions in a plasma etch tool with a biased or unbiased wafer, during the plasma glow or in the plasma afterglow. The ability to independently pulse the ICP current and wafer bias opens a range of parameter space for plasma etch previously unavailable when these were operated in steady state. Recent progress on advanced RF sources makes rapid turn on/off available (τ < 50 μs). Donnelly and Kornblit⁴⁴ speculates that superior plasma etch is possible when the plasma is pulsed and better if the wafer bias is pulsed on in the plasma afterglow. We have studied both cases in this work. The high energy peak of the bimodal distribution function was shown to be more mono-energetic when the wafer bias was switched on during the plasma afterglow (Fig. 11). Ions at energy close to the wafer bias potential and at background low energy were observed, while the detection of ion energies in the middle range falls below the noise level. When the bias was switched on with the ICP on high power (during the plasma glow) [Fig. 9(c)], the vertical ion distribution had a long tail with a continuum of particles with energies out to the bias voltage. In the afterglow, high energy ions have smaller incident angles and strike the wafer more uniformly near the edge of the wafer (Figs. 18 and 19). Sheath expansion in relation to the RF bias voltage was also captured by the LIF signal (Fig. 13). We observed that the sheath followed the instantaneous bias voltage on the wafer, and the maximum sheath size of 0.32 cm was achieved about 70 ns later than the most cathodic moment of the bias voltage.

Experimental results were acquired at chamber pressure of 0.5 mTorr, and LIF ceases to work at higher pressures. The simulations were done at this pressure and two higher ones (5 and 10 mTorr), showing that the angles the ions struck the wafer were smaller at higher pressures. Industrial processing occurs at higher pressures generally in the range of 10–50 mTorr. This indicates the experimentally observed angles are an upper bound. Simulated energy distributions in the glow and the afterglow case were compared. The plasma operating at 0.5 mTorr requires a kinetic approach to capture physics correctly. Due to the high computational cost and efforts, the hybrid solver, HPEM, was used in this study. The expected peak ion energies were around 1100 eVs. Although the calculated highest ion energies onto the wafer (z = 0 cm) are close to the expected, the ion energies measured as high as 820 eV at z = 0.2 cm. The cycle averaged IEADs peak around 900 eV at z = 0.1 cm for the glow case, as shown in Fig. 23. The differences between experiments and computations are elevated when IEADs are compared at specific z when the bias is most cathodic. The discrepancy might be the results of the low plasma density at the sheath for LIF measurements and not capturing ion transport accurately at low pressures with hybrid approaches. The takeaway from this study is that superior etch can be achieved with non-simultaneous pulsing of the ICP and bias. This, coupled with the huge parameter space, associated with independent bias frequency, and perhaps, multiple pulsing can usher a new age in the industry.

The authors thank Professor Mark Kushner for many valuable discussions and editorial suggestions. We also wish to thank Zalton Lucky, Marvin Drandell, and Ty Lai for their expert technical assistance. The work was funded with an NSF-GOALI Award No. NSF-PHY-2010558. We also want to thank Dr. Vyacheslav Lukin for his advice and guidance, and LAM Research Corporation for equipment donations. Finally, we wish to thank the Basic Plasma Science facility at UCLA for technical support.

The authors have no conflicts to disclose.

Yuchen Qian: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (lead); Methodology (equal); Visualization (equal); Writing – original draft (lead). Walter Gekelman: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal). Patrick Pribyl: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). Tugba Piskin: Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – original draft (equal). Alex Paterson: Conceptualization (equal).

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