Ion energy distribution function measurements by laser-induced fluorescence in a dual radio frequency sheath

Plasmas are used extensively in several of the processes in the fabrication of microelectronic devices. One such process, ion etching, typically utilizes radio frequency (rf) biasing of the substrate in order to accelerate ions in the plasma to bombard the substrate at high energies. The region of the plasma where these ions experience the largest acceleration is a narrow (millimeter to submillimeter) region above the surface of the wafer called the sheath. The acceleration in this region will largely determine the ion energies, flux, and angle of impact at the surface of the substrate.¹ These parameters are critical in determining etch selectivity, etch rates, and etch anisotropy. The control of these parameters is thus important in achieving high quality etching. Unfortunately, ions in the sheath are difficult to study directly using traditional probe diagnostic techniques due to the size of the sheath and its transient nature caused by the rf biasing. Furthermore, analytic studies prove extremely difficult due to the highly nonlinear physics of the sheath.

Several experimental and computational studies have investigated ion properties in plasmas with single frequency rf sheaths.^2–25 Ion energy distribution functions (IED) have been found to be extremely dependent on the ratio of the bias frequency to the ion transit frequency, $ωrf/ωion$⁠. The time-averaged IEDs are found to be bimodal, with the separation between the peaks, $ΔEi$⁠, dependent on bias frequency regime.¹ For low frequency (LF) biases $(ωrf/ωion≪1)$⁠, the ions traverse the sheath more rapidly than the sheath potential changes. This results in a broad IED. The sheath is essentially an ensemble of dc sheaths and can be modeled using the Child-Langmuir law.¹ Conversely, for high frequency biases (⁠$ωrf/ωion≫1)$⁠, ions respond to the time-averaged potential and the peaks in the IED converge (⁠$ΔEi→0$⁠), resulting in a monoenergetic distribution.

With a single frequency rf bias, however, it is difficult to achieve independent control of the ion energies and flux.¹ Many novel bias configurations have been investigated in order to solve this issue and achieve greater control of the ion energy and angular distribution functions. For example, one such technique is to use nonsinusoidal waveforms to bias the substrate.¹² Studies into these bias configurations have included slow voltage ramps,²⁶ pulsed dc bursts,²⁷ tailored waveforms calculated using computation techniques.⁹ Pulsed plasmas have also been investigated as a method of controlling ion energy distribution functions.^2,28

One of the most widely used methods to attempt to control the ion energy distribution function in the sheath is to use a dual frequency bias.^1,12 By using both a LF and high frequency bias together, it can be possible to achieve independent control of the ion energy and flux.^29–31 In such a configuration, the goal is that the LF power controls the ion energy while the high frequency (HF) controls the ion density, and hence the ion flux bombarding the surface of the wafer or substrate.¹ Several experiments performed till date, however, have shown some degree of coupling between high and LF biases and hence some coupling between the ion energies and flux.^32–35 

Most investigations into dual frequency sheaths have been computational.^30,31,36,37 Kim et al.³⁰ developed an analytic model for dual frequency sheaths using an effective frequency and compared the results to particle-in-cell (PIC) simulations. Using the approximation of an effective frequency, the authors obtained several other effective plasma parameters, such as plasma density, plasma potential, and particle currents. The authors also found that the reduction in the size of the bulk plasma due to expansion of the sheath can be significant and needs to be taken into consideration. Boyle et al.³¹ used a PIC simulation to show that is possible to achieve independent control of the ion energy and flux in a capacitively coupled plasma (CCP) reactor by using two frequencies that are sufficiently different. However, for their simulations, in order for this independent control to be achieved, the sheath size must be comparable to the size of the bulk plasma. These conditions are not typical for etch tools. Kim and Lee³⁸ confirmed this assertion as they found that with a larger bulk plasma size (∼20 times larger than the sheath), the plasma density increases with LF power rather than decreasing.

Investigations of the ion energy distribution in a dual frequency sheath have also been performed using computational techniques.^7,37 Lee et al.⁷ performed PIC simulations to calculate IEDs, plasma potential, self-bias, and densities in a CCP reactor. The authors found the IED to be multipeaked. With increasing LF voltage, the shape of the IEDs changed such that the peaks in the distribution smoothed out. The sheath width, plasma potential, and self-bias also increased with increased LF voltage while the plasma density decreased. Zhang et al.³⁷ used a hybrid model to calculate ion energy and angular distributions in a CCP reactor. The authors found the IEDs to be bimodal and multipeaked in between. The relative heights of the bimodal peaks, and hence the ion flux, could be controlled by changing the input high frequency power. The authors also investigated effects from changing the relative phases between the low and high frequency powers. They found that by alternating between disparate phases in the high frequency power, the smaller peaks between the broad bimodal peaks were smoothed out.

Several experimental investigations into dual frequency sheaths have also been performed.^{32,33,35,39,40} Booth et al.³² measured electron density and ion flux in a 50 mTorr Ar/O₂ CCP using a hairpin resonator probe and ion flux probe, respectively. Measurements were taken in the bulk plasma at several combinations of 2 and 27 MHz bias powers. The investigators found that both electron density and ion flux increased with both increasing low and high frequency power and the ratio of the two to be relatively constant. This demonstrated that the plasma density and flux can still be strongly coupled to the LF bias in a dual frequency bias configuration. The authors also speculated that the effect from the LF power could be caused by enhanced ionization caused by secondary electron emission from the oxidized silicon wafer. As there is oxygen present in the plasma, the surface of the silicon wafer will oxidize to SiO₂, which has a much larger (16 times) secondary electron yield than Si.⁴¹ 

Electron density measurements have been performed in the plasma bulk in dual frequency CCP reactors by using rf compensated Langmuir probes.^33,34 Yuan et al.³⁴ found in a plasma driven with 60/13.56 MHz biases, at lower pressures (10 mTorr), the electron density did not change appreciably with varying LF power, suggesting that independent control of the ion energy and flux can be achieved in these conditions. At higher pressures (30–100 mTorr), this was not the case as increasing the LF power also increased the plasma density. Measurements performed by Ahn and Chang³³ in a 2/27.12 MHz dual frequency capacitive discharge were consistent with these results, because at higher pressures (50 and 300 mTorr), increasing the 2 MHz power simultaneously increased the electron density.

Liu et al.³⁵ measured argon and oxygen ion energy distribution functions on a grounded electrode in a dual frequency CCP using an energy resolved mass spectrometer. The authors investigated the dependence of the bimodal shape of the IED on a LF bias frequency and power. The measurements showed a strong dependence of the high energy peak on frequency and power. As the frequency of the LF bias increased, the separation between the two peaks of the distribution decreased as the high energy peak approached the lower energy peak. The low energy peak remained at relatively the same energy, corresponding to approximately the floating potential, at all frequencies. The size of the peak increased with frequency, suggesting that the sheath remains collapsed for a longer time. The opposite dependence was observed with increasing bias power.

In the work described in this article, direct measurements of ion velocity distributions (IVDs) in a dual frequency (2.2 and 19 MHz) rf sheath are described. The measurements are taken using planar laser-induced-fluorescence (LIF) in a commercial inductively coupled plasma (ICP) sustained in an Ar/O₂ gas mixtures of a few mTorr pressure with the dual frequency rf bias on the substrate. IVDs are measured from the bulk plasma, into the presheath and through the sheath. The biases used in this experiment place this experiment in the intermediate regime, $ω2 MHz/ωion=0.5$⁠, $ω2 MHz/ωion=0.76$⁠, and $ω19 MHz/ωion=5.5$⁠. The results are compared to measurements taken previously²⁵ above a single frequency biased wafer in the same etch tool.

Laser-induced fluorescence is a noninvasive plasma diagnostic that has been used to measure various ion and plasma properties, such as densities, drift velocities, and energy distribution functions.^42–44 By using cylindrical optics, a planar sheet of laser light can be produced to measure these quantities at multiple spatial positions simultaneously. Of interest to the fabrication of microelectronic devices, LIF has been used to measure ion properties within dc and rf sheaths.^22,45–54 LIF-dip, a two-step LIF process, has also been used to measure the electric field within an rf sheath.^55,56

The particular scheme used in this experiment uses the 3d′ ²G_9/2–4p′ ⁷F_7/2 transition in argon, shown in Fig. 1. In this scheme, a metastable ion state (state 1, 3d′ ²G_9/2) absorbs a 611.492 nm (2 eV) photon to transition to an excited state (state 2, 4p′ ⁷F_7/2). State 2 is extremely short lived (on the order of nanosecond) and will radiatively relax to the original state 1 or to a new state 3 (4s′ ²D_5/2). In this process, a photon corresponding to the energy transition will be emitted. The 461 nm photon emitted from the state 1 to state 3 transition is the desired LIF signal. This signal can be measured by using an imaging device, such as a CCD camera, with an appropriate narrow band-pass 461 nm filter to mask out the laser pump beam and any light from background radiation. The measured signal will be proportional to the metastable ion (state 1) density, which well represents the ground state density.⁵⁷ 

By probing the metastable state with a range of laser frequencies (such as with a tunable dye laser), it is possible to measure the ion velocity distribution function. From the frame of reference of the ion, the incident laser light will be Doppler shifted by amount dependent on the ion of the velocity. By using the Doppler equation $2πΔν=2π(νL−ν0)=v→ ⋅k→=ν∥k$⁠, where $νL$ is the laser frequency, $ν0$ is the excitation frequency, $v→$ is the ion velocity, and $k→$ is the laser wavevector, one can solve for the ion velocity component parallel to the incident laser light. By scanning over a range of laser frequencies, one can thus obtain the ion velocity distribution function.

The plasma source (Fig. 2) used in this experiment is a modified commercial ICP reactor donated by the Intevac Corp. The chamber is approximately cylindrical with a diameter of 50 cm and a height of 40 cm. Windows and ports have been added to chamber sides for the purpose of diagnostics. The ICP coils are situated on top of the chamber and secured onto a ceramic in a “top hat” configuration. The coils are driven at 440 kHz at 500 W continuous wave. Gas is fed in through the top of the chamber via gas inlets in an aluminum top. An Ar/O₂ gas (80% Ar, 20% O₂) is used at a 0.6 mTorr fill pressure. Oxygen is added to the argon gas primarily as an in situ cleaning method. The sputtering of silicon was found to quickly coat the chamber windows and interfere with optical measurements. The added oxygen reacts with the sputtered silicon forming quartz allowing the quartz windows to remain transparent for the CCD camera measurements. In addition, the added oxygen better emulates the electronegative gasses typically used in processing plasmas. The fill pressure is artificially lower than what is typically used in industry (10–100 mTorr) as higher pressures would result in neutral quenching of the metastable ions and hinder LIF data acquisition. The bulk plasma parameters were measured using a Langmuir probe. For these measurements the plasma was pulsed and measurements taken in the afterglow 50 μs after shutoff. This was determined to be a short enough time that plasma parameters did not change appreciably. For this study, T_e ≈ 2 eV (δT_e/T_e ∼ 0.3) and n_i ≈ 2 × 10¹⁰cm⁻³ (δn/n ∼ 0.35).

A 30 cm diameter silicon wafer was electrostatically clamped to the chuck located at the bottom of the chamber. The wafer was surrounded by a dielectric focus ring. LIF measurements were taken over a volume of the outer 4 cm of the wafer and from the surface to 3 cm above the surface. Measurements focused on the outer edge of the wafer in order to observe any potential radial variation in the energy distribution functions and calculated moments.

The wafer bias was powered by a 2.2 MHz and a tunable 10–20 MHz source. In order to reduce the wafer etch rate, the bias was operated at a 10% (10 ms on) duty cycle. Measurements were taken during the last 1 ms of the bias. This was sufficiently long enough for the bias waveform to stabilize. A function generator output sinusoidal voltage waveforms at 10 ms pulse duration (10% of the experiment repetition rate) to the tunable high frequency source. This output was amplified to the kilowatt level, and in this setup, maximum power transfer to the pedestal was found to occur at 19 MHz driving frequency. Peak to peak voltage at maximum power (1930 W) was measured to be 600 V at the base of the pedestal. The 2.2 MHz source was fixed and output a peak power of 1960 W at 2500 V peak to peak. A separate tank circuit was constructed for each bias individually. The rf power was delivered to the chuck via a low inductance (∼10 nH) copper tube.

For the LIF scheme outlined previously, a tunable Sirah Cobra-Stretch dye laser was used to probe wavelengths around the 611.492 nm excitation. The laser was pumped by a Spectra Physics Quanta-Ray Nd:YAG laser frequency doubled to 532 nm. The laser repetition rate was 10 Hz with each pulse lasting 10 ns with an energy of 450 mJ. The dye used was a mixture of Rhodamine B and Rhodamine 101, resulting in a pulse energy of 80 mJ per pulse. The dye laser bandwidth, measured by a Fabry-Perot interferometer, was Δλ = 1.36 × 10⁻³nm.⁴⁸ Glan-Thompson polarizers were used to reduce the laser power to 200 μJ per pulse so as to not damage the fiber optic cable that delivered the laser beam to the processing chamber. The laser power (≈10⁴kW/m² entering the reactor per laser pulse) was measured at the reactor-side of the fiber optic cable. This laser intensity is large enough that power broadening, which has been shown to occur at intensities of <10³kW/m² for low temperature ions, will greatly affect the width of the observed spectra.⁵³ The implications of this broadening are addressed in the experimental results. For each data run, the laser wavelength was stepped form 611.250 to 611.750 nm using 1 pm increments. The laser wavelength was monitored continuously using a high precision High Finesse wavelength meter accurate to within 0.5 pm (or in units of ion velocity, to within 3 × 10² m/s).

The beam exiting the fiber on the reactor side was collimated onto a planoconvex lens by aspherical lens. Two cylindrical lenses were then used in order to create a planar sheet of laser light that allowed fluorescence to be measured at thousands of spatial positions simultaneously. The laser sheet entered the chamber through a rectangular window located at the top of the machine. The beam was oriented perpendicular to the surface of the wafer in order to measure the perpendicular velocity component of the ions traversing the sheath. Laser light reflected from the surface of the wafer will also contribute to the observed LIF signal corresponding to ions directed away from the sheath and toward the plasma bulk. These data were not considered, and only results from the ions moving toward the wafer are presented.

The LIF measurements were taken using a fast (30 ns exposure), 12 bit DiCam-Pro Intensified CCD camera, which recorded images 1280 pixels wide by 1056 pixels tall. The camera was centered vertically along the top edge of the wafer and was positioned to capture the fluorescence above the outer 10 cm of the wafer. Images were averaged over 1000 shots and 2 × 2 pixel bins twice, once by the acquisition software and again before the final analysis resulting in a final resolution of 320 × 256 pixels. The absolute spatial calibration was performed by imaging an aluminum plate with gridded with 1 × 1 cm squares, which was placed in the laser path inside the plasma chamber. The resulting spatial resolution for each pixel was 0.4 × 0.4 mm.

The repetition rate of the experiment was 10 Hz. Timings are shown in Fig. 3. Both the 2 and 19 MHz sources are triggered simultaneously (at t = 0) and are on for 10 ms. The laser flash lamps and a phase lock are triggered at t = 9 ms. The phase lock receives a signal from the 2 MHz bias and outputs a trigger once the voltage waveform undergoes a zero-crossing. This allows the laser Q-switch to be phase locked to the LF bias. The Q-switch timing is variable, depending on the desired LF bias phase for LIF measurements. The camera is triggered 500 ns after the Q-switch fires.

A photodiode was used to observe the laser light immediately before the laser sheet entered the plasma chamber. The phase calibration was performed by comparing the photodiode signal with the measured waveform. The phase could be adjusted by changing the delay between the phase lock and the laser Q-switch.

The voltage delivered to the wafer was measured at the base of the copper pedestal using a resistive voltage divider. A network analyzer was used to measure the frequency response of the voltage divider to ensure voltage measurements in the desired 2–19 MHz frequency range were correct. These results showed the response to be comparable to a dc signal, as desired. During a separate single frequency operation, the calibrated peak-to-peak voltage measurements of the 2 MHz bias were measured to be 2500 V and the 19 MHz to be 900 V. During dual frequency operation, the high frequency voltage remained at 900 V while the 2 MHz component of the measured voltage dropped to 1900 V.

The 2 MHz bias was phase-locked to the laser Q-switch. Phase-locking the experiment to the 2 MHz bias resulted in a time-averaged 19 MHz voltage added to the LF bias, the upper and lower bounds of which are shown along with the filtered 2 MHz. LIF measurements were taken at two disparate phases of the LF rf cycle, denoted by $ΦLF=π$ and $ΦLF=0$⁠, corresponding to the most negative (⁠$ΦLF=π$⁠) and least negative (⁠$ΦLF=0$⁠) phases. Due to the highly asymmetric geometry of the capacitive discharge and the blocking capacitor, the dc self-bias across the sheath is approximately half of the applied peak-to-peak voltage. In other words, the maximum potential drop across the sheath would be approximately 2800 V with a dc bias of −1400 V.

Using the Child sheath approximation,⁵⁸ the calculated sheath widths of the low and high frequency sheath separately are s_LF = 7.8 mm and s_HF = 4.5 mm, where s_LF is the LF sheath width and s_HF is the high frequency sheath width. The sheath width is thus controlled primarily by the LF bias. As the LF bias is phase-locked in this experiment, the sheath front during data acquisition can be thought of as slowly moving LF sheath with oscillations due to the high frequency time-averaged sheath.

The ion transit parameters for the two biases are $ω2MHz/ωion=0.76$ for the LF bias and $ω19MHz/ωion=5.5$⁠.¹² This places the lower frequency sheath in the intermediate frequency (⁠$ωrf/ωion≈1$⁠) regime, meaning the sheath will change substantially as the ion traverses the region. The 19 MHz sheath is closer to the high frequency approximation (⁠$ωrf/ωion≫1$⁠), but still low enough that the phase at which the ion enters the sheath is important to the evolution of the ion energies through the sheath.

For previous experiments in this plasma chamber,^22,25 a deconvolution algorithm was used to obtain the IVD from the broadened LIF measurements. For this experiment, however, a deconvolution was not performed. Measurements of cold ions in the plasma bulk show power broadening of 20 eV. The observed distributions in this experiment had peak widths ranging from 150 to 400 eV, corresponding to uncertainties in the peak widths of 13% and 5%, respectively. Furthermore, peaks less than 20 eV in width and spaced by less than this amount thus cannot be resolved. This broadening is acceptable for this study as the location of the peak centers in the IEDs is of much more interest than the width of the peaks. The LIF signal corresponding to the high energy ions was sufficiently small such that the deconvolution algorithm would suppress the high energy peaks and leave only the central peak corresponding to the cold ions. The decrease in LIF signal for this experiment can be explained by a lower bulk plasma density (26% lower than in previous experiments) and lower densities of high energy ions within the sheath due to the substantially larger bias voltages. From flux conservation, larger ion velocities will result in a corresponding drop in the ion density. This lower density will in turn result in a lower LIF signal at higher velocities.

Ion energy distribution functions at a height of 0.8 mm for the phase $ΦLF=π$ are shown in Fig. 4(a). Measurements are shown only up to 2000 eV as the LIF signal was unreliable above this point due to the aforementioned decrease in ion densities. The energy distribution functions shown are normalized to the maximum of each distribution. A large low energy peak at 20 eV was well observed in the ion energy distributions into the sheath. This peak was removed to further emphasize the high energy ions responsible for etching. The large low energy peak could result from ionization or charge exchange within the sheath. While the mean free path for collisions exceeds the sheath width, a small number of charge exchange collisions are still possible. At a distance of r = 13 cm, the density 4 mm above the wafer was observed to about 6% of the plasma bulk. Using the measured sheath width and the ion charge exchange mean free path $λce=6.7 cm$⁠, we estimate the proportion of collided ion flux to be 5.7%.¹ This is consistent with the observed density. Booth et al. have also observed enhanced ionization near a silicon wafer in a 50 mTorr Ar/O₂ plasma, possibly due to SiO₂ secondary electron emission from oxygen ions bombarding the wafer.³² Secondary emission is not likely to be significant in this experiment, however, as the fill pressure is much lower. As such, the electron ionization mean free path is ∼1 m. Contributions from charge exchange are on the order of ten times larger than the contributions from second electron ionization collisions. Toward the edge of the sheath, the distribution function is comparatively flat and higher energy peaks emerge as the ions approach the wafer surface. The observed peaks are rather broad, which can partially be attributed to the aforementioned broadening of the LIF measurement. Notably, the ion energy distribution functions close to the surface of the wafer are multipeaked. If there is ionization within the sheath, these peaks would arise due to the rf modulation of the high frequency bias, as described in Wild and Koidl.²³ The number of high frequency periods that an ion would experience as it traverses the sheath is given by the ratio of the ion transit time across the expanded LF sheath to the period of the high frequency bias. This ratio is 6.6, meaning that we would expect to see up to six peaks in the distribution function. As measurements in this experiment were not reliable up to the expected maximum energy of 2950 eV, it is not certain if the observed results agree completely with the theoretical prediction. Additional peaks above 2000 eV could be present.

A comparison of the IEDs in Fig. 4(a) at two different radial positions (r = 12.1 and r = 14.6 cm) show differences between the IED peaks in the two cases. Similar peaks such as those seen closer to the midwafer are observed in the distribution function at the wafer edge, including the multipeaked structure. The location of the peaks is similar to those observed at the smaller radial position.

Distribution function measurements for the collapsed sheath phase (⁠$ΦLF=0$⁠) for two different radii are shown at the same height of 0.8 mm in Fig. 4(b). For this less negatively biased phase, fewer high energy ions are observed as compared to the $ΦLF=π$ phase. The multipeak structure observed in the expanded sheath case is also not present for this case. If the peaks are caused by rf modulation from the higher frequency source, fewer peaks would be expected in this phase. A smaller sheath width would result in a shorter ion transit time across the sheath and thus an ion would experience fewer cycles of the high frequency bias. This would result in few peaks in the energy distribution function. The cold peak was once again removed.

For a purely high frequency sheath, one would expect to see a single peak in the distribution function corresponding to the time-averaged potential drop across the sheath. In this experiment, that would correspond to an energy peak around 450 eV. Closer to the intermediate frequency regime, a bimodal structure would be expected. Broadening of the LIF signal, however, might prevent resolution of the peak separation. As LF bias is also present, the value of the peak energy will change depending on the sheath potential for this particular phase. It is difficult to determine the exact effect from the LF bias in this experiment, however, as the sheath is changing substantially as the ion traverses the sheath. Single peaks are observed in the distribution function at 450 eV at the wafer edge and approximately 600 eV more toward midwafer. These values agree with the expectation of a peak near the time-averaged value of the 19 MHz bias. The larger energy toward the midwafer suggests a more significant contribution from the changing sheath width and potential as compared to larger radial positions.

After removal of the cold central peak, the remaining peaks in the distribution functions are very well approximated by the sum of several Maxwellian distributions centered around different velocities. The ion velocity distribution functions for both the midwafer and wafer edge case presented in Fig. 4(a) were each fit to a sum of four Maxwellian distribution functions. The resulting ion energy distributions are shown in Figs. 5 and 6. In Figs. 5(a) and 6(a), the sum of the Maxwellian fits are shown to compare favorably with the measured data. The IEDs corresponding to the four separate ion energies are shown in Figs. 5(b) and 6(b) along with the overall sum. For the midwafer case (Fig. 5), the four peaks were centered at 110, 370, 780, and 1600 eV. Energies at the wafer edge were larger (Fig. 6), with peaks centered at 130, 610, 1030, and 1800 eV. It is difficult to say whether any individual peak is due solely to any specific bias as opposed to the combination of the two. A single peak might be expected near 2350 eV corresponding to the 1900 V peak-to-peak 2 MHz bias in addition to the 450 V time-averaged 19 MHz. Measurements did not extend to this energy range, however.

Integrating the ion distribution functions over all measured velocities yields the spatial dependence of the ion density (⁠$n(r,z,t)=∫f(r,z,vz,t)dvz$⁠), as shown in Fig. 7. For these calculations, data corresponding to ions moving away from the wafer surface were once again ignored as it was not possible to distinguish between an ion moving upwards and fluorescence resulting from reflected light off the surface of the wafer. The data presented are normalized to maximum density of the three separate cases (⁠$ΦLF=π$⁠, $ΦLF=0$⁠, and unbiased), approximately 2 × 10¹⁰ cm⁻³. The bulk plasma density was the same for each case. For the dual frequency $ΦLF=π$ (expanded sheath) phase shown in Fig. 7(a), the density is shown to be highly radially nonuniform. At the wafer edge, densities are a factor of two lower than those seen toward the middle of the wafer. This trend continues even several centimeters above the wafer, well outside the sheath region. Densities for the dual frequency $ΦLF=0$(collapsed sheath) case are shown in Fig. 7(b) and compared with measurements from a case with a single frequency bias [Fig. 7(c)] and an unbiased case [Fig. 7(d)]. The densities for the latter three cases are essentially the same and are much more radially uniform than the dual frequency expanded sheath (⁠$ΦLF=π$⁠) case. This discrepancy in radial uniformity could possibly be due to effects from ponderomotive forces. By approximating the amplitude of the electric field from the sheath potential drop, the ponderomotive potential from the 1900 V 2 MHz bias was approximately 180 V. Using this potential, the ratio of the energy stored in the ponderomotive electric field to the thermal energy of the ions, $ϵE2/nkT$⁠, is approximately 5. This suggests that one would expect this electric field to move the density outward. The effects from the ponderomotive potential due to the 2 MHz bias are substantially larger than the effects from the high frequency bias (a ponderomotive potential of a few volts). The ponderomotive potential in the dual frequency case is also approximately twice as large as the potential from the single frequency case where a 650 V bias was used. The gradient of the electric field would also be most pronounced near the edge of the wafer, which is consistent with the shape of the density profile. Zhang et al.³⁷ have reported similar measured and computed density radial profiles in a capacitively coupled device. Densities were radially uniform with a single high frequency (60 MHz) bias, but the addition of a LF bias resulted in a decreased plasma density toward the wafer edge.

Calculated fluxes (⁠$Γi(r,z,t)=∫vzf(r,z,vz,t)dvz$⁠) are shown for the two phases $ΦLF=π$ and $ΦLF=0$ in Fig. 8 as a function of radial position and height above the wafer. The calculated ion flux from measurements taken at the time of the most negative phase of a single frequency bias experiment is also shown for comparison. In the dual frequency expanded sheath case, the flux increases as the ions move from the plasma bulk toward the presheath. As the ions approach the sheath, the flux reaches a maximum and remains relatively constant through the sheath and to the surface of the wafer. Fluxes observed in the dual frequency collapsed sheath case are much lower, as expected. The flux in this case is relatively constant in the presheath and decreases as the ion traverse the sheath toward the wafer, in contrast to the dual frequency expanded sheath $ΦLF=π$ phase. In both cases, the flux was seen to be relatively radially uniform, which would be desired for processing plasmas. This is in stark contrast to observations made during a single frequency operation. The ion fluxes observed under these conditions were extremely nonradially uniform, as shown in Fig. 8(c).

Planar laser-induced fluorescence has been used to measure the ion velocity distribution functions above a dual rf biased silicon wafer in an industrial plasma etch tool. Measurements were phase locked to the 2 MHz LF bias while the 19 MHz high frequency bias was time-averaged. Multipeaked IEDs were observed in the sheath for the most strongly biased phase. While the exact locations of the peaks varied with radius across the surface of the wafer, the overall structure was similar. These results and the number of peaks are consistent with other experiments and simulations.^23,37 For a disparate collapsed sheath phase of the 2 MHz bias, the measured IEDs exhibited few peaks. One peak roughly corresponded to the time-average of the high frequency bias with the exact position again depending on the radial position.

Densities, velocities, and ion fluxes were calculated from the measured IVDs. The radial dependence of the ion density differed substantially between the two phases investigated. For the strongly biased LF case, the density was highly dependent on the radial position with densities decreasing substantially toward the wafer edge. This decrease in ion density was not observed in the disparate low bias phase where the density was relatively radially uniform and similar to the density profile above an unbiased wafer. These trends are consistent with other experiments and simulations.³⁷ Velocity profiles exhibited less radial variation, though mean velocities at the edge of the wafer were observed to be slightly larger. A comparison of the maximum velocity measured in the two phases is consistent with the expectations, given the peak-to-peak voltage of the applied biases. Ion fluxes showed no strong radial dependence, a characteristic which would be desired in an industrial setting. This is in stark contrast to the single frequency case where measured fluxes were extremely radially nonuniform. Uniformity in the flux would provide a more uniform etch radially across the wafer. It appears that for this dual frequency case, the desired uniformity in the flux is a trade off with the potentially undesirable multipeaked structure observed in the ion energy distribution functions.

The results from this study have provided insight into the ion dynamics within both a single and dual rf sheath in an industrial etch tool. Such results are important to both the improvement of existing processing techniques and the validation of simulations and models. A comparison of the experimental results with results from computer simulations can help to improve the underlying models, which can then in turn be used to help guide further progress in processing techniques.

This work was performed at the UCLA Basic Plasma Science Facility and was supported by the National Science Foundation PHY-1004203. The authors would like to thank Mark Kushner for his advice and guidance, Zoltan Lucky, Marvin Drandell, and Tai Ly for their technical assistance, and the Intevac Corporation for donation of the plasma etch tool.