Cl2 inductively coupled plasma

IOP PUBLISHING

JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 41 (2008) 065207 (14pp)

doi:10.1088/0022-3727/41/6/065207

Simulation of an Ar/Cl2 inductively coupled plasma: study of the effect of bias, power and pressure and comparison with experiments S Tinck1,2 , W Boullart2 and A Bogaerts1 1

Research Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, B-2610 Antwerp, Belgium 2 IMEC, Kapeldreef 75, B-3001 Leuven, Belgium E-mail: [email protected]

Received 11 November 2007, in final form 29 January 2008 Published 27 February 2008 Online at stacks.iop.org/JPhysD/41/065207 Abstract A hybrid model, called the hybrid plasma equipment model, was used to study Ar/Cl2 inductively coupled plasmas used for the etching of Si. The effects of substrate bias, source power and gas pressure on the plasma characteristics and on the fluxes and energies of plasma species bombarding the substrate were observed. A comparison with experimentally measured etch rates was made to investigate how the etch process is influenced and which plasma species mainly account for the etch process. First, the general plasma characteristics are investigated at the following operating conditions: 10% Ar 90% Cl2 gas mixture, 5 mTorr total gas pressure, 100 sccm gas flow rate, 250 W source power, −200 V dc bias at the substrate electrode and an operating frequency of 13.56 MHz applied to the coil and to the substrate electrode. Subsequently, the pressure is varied from 5 to 80 mTorr, the substrate bias from −100 to −300 V and the source power from 250 to 1000 W. Increasing the total gas pressure results in a decrease of the etch rate and a less anisotropic flux to the substrate due to more collisions of the ions in the sheath. Increasing the substrate bias has an effect on the energy of the ions bombarding the substrate and to a lesser extent on the magnitude of the ion flux. When source power is increased, it was found that, not the energy, but the magnitude of the ion flux is increased. The etch rate was more influenced by a variation of the substrate bias than by a variation of the source power, at these operating conditions. These results suggest that the etch process is mainly affected by the energy of the ions bombarding the substrate and the magnitude of the ion flux, and to a lesser extent by the magnitude of the radical flux. (Some figures in this article are in colour only in the electronic version)

processes are inductively coupled plasma (ICP) reactors where the plasma is generated by a radio frequent (rf) inductively coupled electric field. A frequently used ICP reactor geometry, also called a transformer coupled plasma (TCP), is where the rf field is generated by a planar coil on top of the reactor [2]. To optimize these etch processes, it is necessary to understand the effect of operating conditions such as gas pressure, source power and substrate bias on the plasma characteristics since the etch process is strongly dependent on the plasma composition and the characteristics of the ion and radical fluxes to the substrate. To investigate the influence

1. Introduction The shallow trench isolation (STI) process for isolating active areas, for the fabrication of electronic devices, is an attractive technology in the microelectronics industry [1]. In STI, trenches are etched in Si with a high aspect ratio (depth/width > 10) at a high etch rate. Therefore, it is necessary that these processes are as efficient as possible in terms of anisotropy, uniformity, selectivity and etch rate. Ar/Cl2 is a common gas mixture used for the etching of Si. The most widely used reactors for these highly anisotropic etch 0022-3727/08/065207+14$30.00

1

© 2008 IOP Publishing Ltd

Printed in the UK

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

of these conditions on the plasma within the reactor volume, we use numerical simulations that provide us with detailed information of the plasma. These simulation results will be compared with experimentally measured etch rates to study the effect of the plasma characteristics on the etch process itself. There are already several experimental studies and numerical simulation results reported on inductively coupled Ar/Cl2 plasmas and their surface reactions used for etching applications. Mahony et al [3] measured Cl and Cl− densities in a 13.56 MHz and 14 MHz Ar/Cl2 inductively coupled processing plasma, for powers up to 200 W, in the pressure range 0.5–12 Pa with Cl2 fractions up to 50%. They used laser induced fluorescence to measure atomic Cl and probe based photodetachment for Cl− . In their experiments, a Langmuir probe was applied to measure the electron energy distribution functions and calculate the rate coefficients for electronheavy particle reactions. They found for 5% Cl2 that the Cl density rises with power or pressure, and that the Cl− fraction decreases as power is increased. Their experimental results were compared with results from a kinetic model. Lee, Shin and co-workers [4, 5] performed etch experiments of Ta with Ar/Cl2 plasmas at varying process parameters such as Cl2 /Ar gas mixing ratio, source power and substrate bias. They measured the relative change in the densities of Cl and Ar by optical emission spectroscopy (OES) as a function of Cl2 percentage. X-ray photoelectron spectroscopy was used to investigate the chemical states of the etched surface with mixing ratios. The authors found that with a ratio of 60% Cl2 and 40% Ar, a Ta etch rate of 230 nm min−1 could be obtained under the following conditions: 500W source power, 500 W substrate bias power, 18 mTorr gas pressure and 13.56 MHz frequency. Their results suggest that Cl radicals have a major effect on the etch rate of Ta and that the density of Cl radicals is greatly affected by the percentage of Ar. Okpalugo et al [6] have measured coil currents and voltages using derivative close coupled I–V sensors, subsequent Fourier analysis and probe transforms. From this, the authors determined the delivered rf source power, minus the transmission and matching network losses. The operating conditions were 14 MHz applied frequency, source powers from 5 to 80 W, a pressure of 2.7 Pa and both pure Ar and 95% Ar with 5% Cl2 . Their results suggest that the measured power deposition is different for pure argon and the Ar/Cl2 mixture. Dong-Pyo et al [7] investigated the etching behaviour of Bi4−x Lax Ti3 O12 (BLT) films in inductively coupled Ar/Cl2 plasma in terms of etch parameters. They found that the etching rate as a function of mixing ratio showed a maximum of 50.3 nm min−1 for a mixture of 80% Ar and 20% Cl2 and that the increase of source power or substrate bias caused an increase in BLT etch rate under any fixed gas composition. They performed Langmuir probe measurements that indicate that an increase of Ar ratio leads to monotonic changes of both electron density and total density of positive ions. The same tendencies were found for chlorine atoms and molecules, using OES.

Sung-Mo et al [8] studied the etching characteristics of MgO thin films using Cl2 /Ar plasmas. They measured the etch rate by varying the etching parameters such as source power, substrate bias and chamber pressure. Using Langmuir probe and OES for plasma diagnostics, they found that the maximum etch rate of 85 nm min−1 was obtained at a gas mixture of 30% Cl2 and 70% Ar. Efremov et al [9–11] investigated the etching mechanism of SrBi2 Ta2 O9 (SBT) thin films using Cl2 /Ar by varying the gas mixing ratio. Their results suggest that an increase in the Ar mixing ratio leads to an increase of the SBT etch rate, which reaches a maximum of 97 nm min−1 at 80% Ar. They also reported results on the influence of gas mixing ratio, gas pressure (0.26–3.3 Pa) and source power (400–900 W) on the Cl2 /Ar plasma parameters by applying a Langmuir probe and quadrupole mass-spectroscopy for plasma diagnostics, combined with plasma simulation, given by a selfconsistent global zero-dimensional model with Maxwellian approximation for the electron energy distribution function. Fuller et al [12] have used trace gases OES in Ar/Cl2 ICPs to measure the electron temperature, at 18 mTorr, as a function of the source power and the Ar fraction. Finally, Kushner and coworkers [13–19] have applied a hybrid model, called the hybrid plasma equipment model (HPEM), to study Ar/Cl2 ICPs under varying conditions. In Reference [13], the electron density and temperature were calculated for a 80% Ar 20% Cl2 gas mixture for source powers of 200–800 W and rf bias powers of 50–400 W. The electron density, Cl− density and electron temperature were investigated as a function of time in [14], for pulsed 80% Ar 20% Cl2 electron cyclotron resonance (ECR) plasmas. In [15], the ion energy distribution, as well as the ion and radical fluxes were calculated and discussed for a 70% Ar 30% Cl2 plasma at source powers of 150–1000 W, pressures of 5–20 mTorr and substrate rf bias amplitudes of 0–150 V. Furthermore, the electron production rates, power deposition, electron temperature and density, as well as the ion fluxes were calculated for a 70% Ar 30% Cl2 plasma at 700 W and 5 mTorr, where coil configuration, reactor chamber aspect ratio and wall materials were varied. The electron density and power deposition were also investigated as a function of source power and dc bias. The goal in this paper is to make a detailed study of the effect of chamber pressure, source power and substrate bias on the plasma characteristics, as well as on the ion and radical fluxes to the substrate, for an Ar/Cl2 ICP with a relatively high fraction of Cl2 (90 %) used for etching applications. Since only the reactive chlorine particles can chemically etch Si (forming etch products such as SiCl4 ), the etch rate is increased at a higher percentage of Cl2 . A low pressure is applied and a small percentage of Ar is added for allowing a highly anisotropic ion assisted chemical etching process. The simulation results will be compared with etch experiments in order to determine the effects of the ion and radical fluxes on the etch process.

2. Description of the model In this paper, the HPEM, developed at the University of Illinois by Kushner and coworkers [13–19], is used to study the effect 2

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

of different operating conditions on the plasma characteristics. The HPEM is able to calculate plasma properties within the reactor volume as well as substrate level processes such as an etch process or a deposition process in a self-consistent manner. The HPEM consists of a series of modules through which the calculation iterates. In this paper, only a brief description of the relevant modules is given. More detailed information on this model can be found in [13–19], which are publications from Kushner et al, the developers of the HPEM. For calculating the plasma properties within the reactor volume itself, the HPEM uses three main modules. After defining the reactor geometry and initial operating conditions, the first module, called the electromagnetics module (EMM), calculates the electromagnetic fields within the reactor volume by solving Maxwell’s equations. The next module, called the electron energy transport module (EETM) computes the electron density, electron temperature, electron energy distribution function and electron impact reaction rates with a Monte Carlo procedure or the Boltzmann equation, based on the electromagnetic fields calculated in the EMM. From these rates, the fluid kinetics simulation (FKS), which is the third module, calculates the heavy particle densities and fluxes with continuity equations, and the electrostatic field with Poisson’s equation. This electrostatic field is used as input again in the EMM. This cycle is iterated until convergence. An optional module, called the plasma chemistry Monte Carlo simulation (PCMCS), is used to calculate plasma species fluxes and energy distributions to the substrate to produce detailed information at the substrate level. Ten different species are included in the model, as listed in table 1. Ar* and Cl* are the excited Ar and Cl atoms, respectively. The Ar* species comprises the sum of the 4s[3/2]2 , 4s[3/2]1 , 4s
[1/2]0 and 4s
[1/2]1 excitation levels with a threshold of 11.60 eV. The Cl* species comprises the sum of the 4s, 4p, 3d, 5f , 4d and 5d electronic excitation levels.

The inelastic electron impact reactions and heavy particle reactions are listed in tables 2 and 3, respectively. The cross sections for the electron impact reactions can be found in figures 1(a) and (b). The recombination probabilities of the Cl radical on the reactor walls (anodized Al) and on the dielectric window (quartz) were implemented based on experimental results [21–23]. Values of 0.15 and 0.02 were assumed for the reactor walls and the dielectric window, respectively.

3. Results and discussion 3.1. Calculated general plasma characteristics Calculations were performed for a 10% Ar 90% Cl2 plasma in a TCP reactor as shown in figure 2 under the following operating conditions: 5 mTorr total gas pressure, 100 sccm gas flow rate, 250 W source power, −200 V dc bias at the substrate electrode and an operating frequency of 13.56 MHz applied to the coil and to the substrate electrode. Figure 3 shows the calculated density profiles of the different plasma species in the reactor volume, averaged over one rf cycle. The gas species (Cl2 and Ar) and the Cl radicals are mainly present in the reactor. The Cl2 and Ar densities have a maximum at the inlet and their profiles spread out more or less uniformly throughout the reactor volume. Their densities reflect well the 90% Cl2 10% Ar gas ratio. The calculated gas flow lines are also indicated in the figure. The density profile of the Cl radical is also fairly uniform in the reactor. Comparing the Cl radical density with the Cl2 density in the main region of the plasma, we find that Cl2 dissociates for almost 50% into radicals, at the conditions under study. This is mostly due to electron impact dissociation of Cl2 . (table 2, label 10). The Cl+2 ion is the most abundant positive ion present in the plasma and so the flux of positive ions to the substrate mainly consists of Cl+2 ions. The maximum density of the Cl+2 ion is at the nozzle in the centre of the reactor chamber because it is mostly formed from Cl2 by electron impact ionization (table 2, label 11). The maximum Cl+2 density is still roughly 100 times smaller than the radical or gas species densities because it easily dissociates into radicals by dissociative recombination (table 2, label 8). Cl+ and Ar+ are mainly formed from the excited species Cl* and Ar* by electron impact ionizations (table 2, labels 4 and 7) since these reactions have a lower

Table 1. Overview of species included in the model. Species e, Ar, Ar+ , Ar∗ , Cl2 , Cl+2 , Cl+ , Cl*, Cl, Cl−

Table 2. Overview of the inelastic electron impact reactions included in the model, with references. The labels correspond to the curves in figure 1. Labels 1 2 3 4 5 6 7 8 9 10 11 12

Reactions ∗

e + Ar → Ar + e e + Ar → Ar + + 2 e e + Ar ∗ → Ar + e e + Ar ∗ → Ar + + 2 e e + Cl → Cl∗ + e e + Cl → Cl+ + 2 e e + Cl∗ → Cl+ + 2 e e + Cl+2 → Cl + Cl e + Cl2 → Cl + Cl− e + Cl2 → 2 Cl + e e + Cl2 → Cl+2 + 2 e e + Cl− → Cl + 2 e

Reaction types

References

Electronic excitation Ionization Electronic de-excitation Ionization Electronic excitation Ionization Ionization Dissociative recombination Dissociative attachment Dissociation Ionization Neutralization

[20] [24] [14] [25] [26] [26] [26] [14] [26] [26] [26] [26]

3

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Table 3. Overview of heavy particle reactions included in the model, with rate coefficients and corresponding references. Nos 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Rate coefficients (cm3 s−1 )

Reactions ∗

∗

Ar + Ar → Ar + Ar + e Ar + Ar + → Ar + + Ar Cl+2 + Cl− → 3 Cl Cl2 + Cl+ → Cl+2 + Cl Cl+ + Cl− → 2 Cl Cl+ + Cl → Cl + Cl+ Cl2 + Cl+2 → Cl+2 + Cl2 Cl∗ → Cl + hv Cl + Cl + Cl → Cl2 + Cl Cl + Cl + Cl2 → Cl2 + Cl2 Cl2 + Ar ∗ → Cl+2 + Ar + e Cl− + Ar + → Cl + Ar Cl + Ar ∗ → Cl∗ + Ar Cl2 + Ar + → Cl+2 + Ar Cl2 + Ar + → Cl + Cl+ + Ar Cl + Ar + → Cl+ + Ar Cl + Cl + Ar → Cl2 + Ar +

−10

5.00 × 10 5.66 × 10−10 1.00 × 10−7 [Tgas /298 K]0.5 5.40 × 10−10 [Tgas /298 K]0.5 1.00 × 10−7 [Tgas /298 K]0.5 1.00 × 10−9 [Tgas /298 K]0.5 0.80 × 10−9 [Tgas /298 K]0.5 1.00 × 105 1.28 × 10−32 cm6 s−1 5.40 × 10−32 cm6 s−1 7.00 × 10−10 [Tgas /298 K]0.5 1.00 × 10−7 [Tgas /298 K]0.5 7.00 × 10−11 [Tgas /298 K]0.5 0.84 × 10−10 [Tgas /298 K]0.5 0.64 × 10−10 [Tgas /298 K]0.5 2.00 × 10−10 [Tgas /298 K]0.5 1.28 × 10−32 cm6 s−1

References [14] [14, 27] [14] [14, 28] [14] [14] [14] [14] [29] [29] [14] [14] [14] [28] [28] [28] [28]

(a)

Figure 2. Two-dimensional TCP reactor geometry used in the model. The reactor is cylindrically symmetric, so only a half plane of the reactor is shown.

threshold than the direct ionization from Cl or Ar. Therefore, the maximum densities of Cl+ , Ar+ , Cl* and Ar* are in the same location within the reactor volume, where the electron temperature is the highest due to the highest power deposition (see below). The Ar* density is not presented in this figure, since it has a very similar density profile as the Cl* species, although a factor 3 lower, which is explained by the lower Ar fraction in the gas mixture. In analogy, this explains why the Ar+ density is lower than the Cl+ density in this case. The density of the negative ion Cl− is higher than the electron density and is highest at the inlet because it is only formed from Cl2 by electron impact dissociative attachment (table 2, label 9). These results are well compared and validated with results from literature. Dong-Pyo et al [7] have measured an electron density with a Langmuir probe of 1.7×1011 cm−3 for an Ar/Cl2 plasma with 90% Cl2 at 700 W applied power, 2 Pa pressure and −200 V dc bias. This density is higher because the applied power is increased to 700 W. They also found with OES that the densities of Cl and Cl2 species are in the same order of

(b)

Figure 1. Electron impact cross sections as a function of electron energy. The labels of the curves refer to table 2. (a) shows all electron impact reactions with Ar, Ar*, Cl and Cl* (labels 1–7). The solid lines represent collisions with Cl and the different dashed lines represent collisions with Ar, Ar* and Cl*. Ar* has one thin solid line for clarity (Label 3). Figure (b) shows all electron impact reactions with Ar+ , Cl+2 , Cl− and Cl2 (labels 8–12). The solid lines represent collisions with Cl2 and the different dashed lines represent collisions with the ions.

4

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Figure 3. Overview of the calculated 2D plasma species density profiles for a 90% Cl2 and 10% Ar gas mixture. The operating conditions are: 5 mTorr total gas pressure, 100 sccm gas flow rate, 250 W source power, −200 dc bias at the substrate and 13.56 MHz operating frequency at the coil and at the substrate electrode.

magnitude, with the radical density slightly higher than the density of Cl2 due to the relatively easy dissociation of Cl2 into radicals, which is also found in our simulation results, SungMo et al [8] also determined nearly identical relative densities of the Cl and Cl2 species with OES at operating conditions of 10 mTorr, 700 W applied source power and −300 V dc bias. Efremov et al [9] have applied a zero-dimensional model to calculate plasma species densities under the following input parameters: 15 mTorr, 700 W applied power, −200 V dc bias. They found for a 90% Cl2 and 10% Ar mixture that the chlorine ion densities were in the order of 1011 cm−3 and that the Ar+ density was in the order of 109 cm−3 . This is in good agreement with our results taking into account that the applied power is only 250 W in our simulations. They also found with OES that, under the same conditions, the Cl density is slightly higher that the Cl2 density.

In another paper, Efremov et al [10] calculated a Cl density in the order of 1014 cm−3 for a 90% Cl2 and 10 % Ar mixture at 2 Pa and 700 W applied power, by means of their zero-dimensional model. This is also in good agreement with our results taking into account that the pressure is roughly three times higher in their experiment and Cl2 easily dissociates into radicals. Their calculated results also show that the total positive ion and electron densities are in the order of 1011 cm−3 which is again in good agreement with our results since they use a much higher power deposition of 700 W. Collison et al [19] calculated a Cl− density of 2 × 1010 cm−3 , for an 50/50 Ar/Cl2 ICP, with inlet flow rate of 100 sccm, 500 W source power at 10 mTorr and 13.56 MHz, which is slightly lower than our results since our Cl2 fraction in the gas mixture is higher. 5

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Grapperhaus et al [13] investigated a 50/50 Ar/Cl2 discharge, with inlet flow rate of 50 sccm, 400 W source power, 100 V rf bias amplitude at 10 mTorr, and measured a peak electron density of 4.6 × 1011 cm−3 . This value is slightly higher than our results because their ICP reactor has a thinner dielectric plate, resulting in a higher power deposition. Calculations performed by Hoekstra et al [17] resulted in a maximum Ar+ density of 6.2 × 1011 cm−3 for a pure Ar gas at 5 mTorr gas pressure, 800 W source power and 100 V rf bias amplitude. The numerical simulations of Ventzek et al [18] predicted a maximum plasma density of 2.3×1011 cm−3 for an Ar plasma at 13.56 MHz operating frequency and 10 mTorr gas pressure with 500 W source power. Subramonium et al [14] investigated 80/20 Ar/Cl2 pulsed ECR plasmas at 30 mTorr, 300 W source power, 10 kHz pulse frequency and 20 sccm. The electron density as well as the Cl− density was calculated to be in the order of 1010 cm−3 , where the Cl− density was slightly lower than the electron density. This reversed trend is explained by the different Ar/Cl2 ratio. Hoekstra et al [15] discussed for a 70/30 Ar/Cl2 plasma at 10 mTorr, 500 W source power and 100 V rf bias amplitude that the positive ion density was in the order of 3 × 1011 cm−3 . This is in good agreement with our results keeping in mind that the applied source power and the gas pressure in our basic case are 250 W and 5 mTorr, respectively. These authors predicted a maximum radical density of 3.7 × 1013 cm−3 at these conditions. Ventzek et al [16] studied a 70/30 Ar/Cl2 plasma, at 700 W source power, 5 mTorr pressure and 80 sccm and found that the electron density is in the order of 1011 cm−3 , but they also discussed that at a higher percentage of Cl2 , the electron density becomes lower. They also observed that the timeaveraged Cl2 density was 1.9 × 1013 cm−3 and the Cl density 1.8 × 1013 cm−3 , which is in good agreement with our results keeping in mind that they only use 30% Cl2 in their gas mixture. The negative ion density was found to be 7.7×1010 cm−3 under these conditions. Finally, Vasenkov et al [30] measured for an Ar/C4 F8 ICP at 3 mTorr, 400 W and 3.39 MHz that the maximum electron density was 6 × 1010 cm−3 which is in good agreement with our calculated results keeping in mind the different operating conditions. The potential distribution in the reactor volume, averaged over time in the rf cycle, is shown in figure 4. It is fairly uniform throughout the reactor volume and in the order of 50 V, except in the sheath at the substrate, where the potential drops significantly towards the substrate, over a distance of ≈0.6 mm. Here, the ions are accelerated to bombard the substrate. The time-averaged (or dc) bias at the substrate is ≈−200 V. Note that the rf amplitude of the applied voltage at the substrate was used as input in the simulations and that the dc substrate bias is self-consistently calculated from this rf amplitude. However, for comparison with experimental etch data, a specific rf bias amplitude was chosen to obtain the desired dc bias of ≈−200 V, as applied in the experiment. The variation of the plasma potential and the potential at the substrate electrode as a function of time during one rf cycle is plotted in figure 5.

Figure 4. Calculated potential distribution in the reactor volume, time-averaged over one rf cycle at 13.56 MHz (≈74 ns) and operating conditions as described in figure 3.

Figure 5. Calculated potential in the plasma and at the substrate electrode, as a function of time, during one rf cycle (≈74 ns) under the operating conditions as described in figure 3.

The rf amplitude of the substrate electrode is around 250 V and varies from ≈−450 to ≈80 V creating a negative timeaveraged dc bias of ≈−200 V. The plasma potential remains positive during the rf cycle, varying between 1 and 110 V, resulting in a time-averaged plasma potential of ≈50 V. Our results concerning the plasma potential are in reasonable agreement with results from the literature. Subramonium et al [14] observed that the maximum plasma potential was 42 V for a 80/20 Ar/Cl2 pulsed plasma at 20 mTorr, 300 W source power and 20 sccm at a pulse frequency of 20 kHz. The average plasma potential in the reactor volume that was calculated by Hoekstra et al [17] was nearly 30 V for a pure Ar plasma at 5 mTorr gas pressure, 800 W source power and 100 V rf bias amplitude. Similar calculations were performed by Ventzek et al [18] who found a maximum plasma potential of 13.8 V for an Ar plasma at 13.56 MHz operating frequency and 10 mTorr gas pressure with 500 W source power. Ventzek et al [16] also observed for a 70/30 Ar/Cl2 plasma, at 700 W source power, 5 mTorr pressure, 75 V rf bias 6

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

source power and 100 V rf bias amplitude, a temperature of about 600–700 K for the neutral species when hitting the substrate. Dong-Pyo et al [7] have measured an electron temperature with a Langmuir probe of about 4 eV for an Ar/Cl2 plasma with 90% Cl2 at 700 W applied power, 2 Pa chamber pressure and −200 V dc bias. The electron temperature is slightly higher because their applied power is 700 W instead of 250 W used in our simulations. Similarly, Efremov et al [9], [10] also applied a Langmuir probe to measure an electron temperature of about 3–4 eV for a 90% Cl2 and 10% Ar mixture under the following input parameters: 15 mTorr, 700 W applied power, −200 V dc bias, which is again in good agreement with our simulation results. A peak electron temperature of roughly 10 eV was calculated by Subramonium et al [32] for a purely Cl2 pulsed ECR plasma at 10 mTorr, 300 W source power, 10 kHz pulse frequency and 100 sccm gas flow rate. Finally, Fuller et al [33] used emission spectroscopy to measure the electron temperature in Ar/Cl2 plasmas at a pressure of 18 mTorr and a source power of 600 W. They found that the electron temperature increased from about 4 eV for pure Cl2 plasmas to about 6 eV for pure Ar plasmas. 3.2. Experimentally measured etch rate A series of 300 mm blanket p-silicon wafers was etched in a TCP reactor (LAM Research 2300 Versys Kiyo; see figure 2) for 15 s after a stabilization step of 5 s. The wafer consisted of 200 nm p-silicon on top of a 100 nm SiO2 layer. The thickness of the wafers was measured with ellipsometry (KLA-Tencor SCD100) at 21 different locations on the wafer before and after the etch process to calculate the etch rate. Measurements were performed for a range of operating conditions as described below. First, a blanket p-Si wafer was etched for 15 s under the same operating conditions as defined in the simulations: 5 mTorr total gas pressure, 10% Ar 90% Cl2 gas mixture, −200 V dc substrate bias, 250 W source power, 100 sccm gas flow rate and 13.56 MHz frequency at the coil and the substrate electrode. The etch rate, obtained by measuring the thickness of the Si wafer before and after the etch experiment, is shown in figure 7. It is clear that the etch rate reaches a maximum at the centre of the wafer, due to higher ion fluxes at the centre, which is shown below. The etch rate was found to be in the order of 160–180 nm min−1 at the operating conditions under study (table 4). The measured etch rate as a function of position from the centre to the edge on the wafer, compared with the ion fluxes, is shown in figure 8. The uniformity of the etch process is clearly dependent on the uniformity profiles of the ion fluxes. The Cl+2 flux is highest due to the fact that its density is highest in the bulk plasma. The radical flux to the substrate is not shown in the figure, but was found to be very uniform, with a value in the order of 1018 cm−2 s−1 and did not significantly vary at different locations on the wafer.

Figure 6. Calculated gas (a) and electron (b) temperature profiles for the operating conditions as described in figure 3.

amplitude and 80 sccm that the maximum plasma potential was around 30 V and the maximum electron temperature around 5 eV. In an other paper, Ventzek et al [31] investigated a 85/12/3 Ar/CF4 /O2 plasma at 15 mTorr, 75 V rf bias and 900 W source power, and found that the plasma potential was in the order of 10–30 V and the electron energy ≈3 eV. The calculated gas and electron temperature profiles are shown in figure 6. The gas temperature reaches a maximum of 700 K, i.e. clearly above room temperature, due to the energy transfer of high-energetic plasma species to the background gas. The electron temperature is highest where the power deposition is at maximum, i.e. directly under the quartz plate, between the coil windings. Our calculated electron temperature can be well compared with results from the literature. Indeed, Ventzek et al [18] found an average electron temperature of 4 eV for an Ar plasma at 13.56 MHz operating frequency and 10 mTorr gas pressure with 500 W source power and Subramonium et al [14] observed that the average electron temperature was roughly 4 eV for a 80/20 Ar/Cl2 pulsed plasma at 20 mTorr, 300 W source power, 10 kHz pulse frequency and 20 sccm. Similar calculations were performed by Hoekstra et al [15] who measured, for a 70/30 Ar/Cl2 plasma at 10 mTorr, 500 W 7

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Figure 7. Measured etch rate (nm min−1 ) profile of a 300 mm blanket Si wafer. The local etch rate was obtained from the experimentally measured thickness at various points on the wafer. The operating conditions are the same as in figure 3.

Figure 8. The thick solid line represents the measured etch rate as a function of position on the wafer, referring to the left vertical axis. The thin lines represent the calculated ion fluxes as a function of position on the wafer, referring to the right vertical axis. The calculated radical flux was very uniform from centre to edge on the wafer and around 8 × 1018 in value. The operating conditions are the same as in figure 3.

Table 4. Experimentally measured minimum and maximum etch rates on the wafer at operating conditions as described in figure 3 where pressure, substrate bias and source power are varied. Gas pressure (mTorr)

Minimum etch rate (nm min−1 )

Maximum etch rate (nm min−1 )

5 10 20 40 80 Substrate bias (V) −100 V −150 V −200 V −250 V −300 V Source power (W) 250 300 500 700 1000

163.6 148.2 123.6 80.2 95.0

180.7 168.7 141.6 93.1 108.4

133.1 164.6 163.6 175.8 186.1

144.5 150.6 180.7 193.9 204.8

163.6 180.2 206.0 235.3 265.7

180.7 197.7 223.0 247.3 272.9

3.3. Effect of pressure Calculations were performed for the same operating conditions as described in section 3.1, but now the pressure was varied from 5 to 80 mTorr. It was found that at higher pressure, the radical density in the bulk plasma is increased due to the easy dissociation of Cl2 into radicals by electron impact (table 2, label 10). This effect is also observed in the magnitude of the radical flux to the substrate at different pressures, as shown in figure 9(a). The Cl radical flux as a function of position on the wafer for different pressure values is illustrated in figure 9(b) and is spatially very uniform. On the other hand, our calculations predict that the magnitude of the total ion flux to the substrate did not change significantly with pressure, as shown in figure 10. This is because at higher pressure, the formation as well as the neutralization of the ions is increased due to more collisions,

Figure 9. The calculated Cl radical flux to the substrate: (a) as a function of pressure. The error bars are a measure for the uniformity of the flux from centre to edge of the substrate. (b) as a function of position on the wafer, for different pressure values. The other operating conditions are the same as described in figure 3.

8

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Figure 10. The ion flux to the substrate as a function of pressure. The error bars are a measure for the uniformity of the flux. The other operating conditions are the same as noted in figure 3.

Figure 12. Measured etch rate as a function of position on the wafer at different pressure values. The etch rate seems to stop at a minimum at 40 mTorr or higher under these conditions. The other operating conditions are the same as described in figure 3.

Figure 11. Calculated fractional fluxes of the Cl+2 , Cl+ and Ar+ ions to the substrate. The other operating conditions are the same as in figure 3.

Figure 13. The calculated Ar+ energy and angular distributions obtained at different pressure values. The energy and angular distributions of the other ions were found to be very similar, and are therefore not shown. However, the energy distribution of the Cl+2 ions is slightly narrower since the Cl+2 ion has a higher mass. The other operating conditions are the same as in figure 3.

resulting in a non-significant change of the total ion density in the reactor volume and hence of the total ion flux to the wafer. However, the composition of the ion flux changes slightly with pressure. At higher pressure, the charge exchange reactions of Ar+ and Cl+ with Cl2 to form Cl+2 (table 3, Nos 4 and 14) are favoured, resulting in a higher fractional flux of Cl+2 as plotted in figure 11. For a gas mixture of 90% Cl2 and 10% Ar, the total ion flux consists mainly of Cl+2 ions, from about 80% at lower pressure (5 mTorr) to 90% at 80 mTorr. This effect was also found by Hoekstra et al [15], although more pronounced since these authors studied a 70% Ar 30% Cl2 gas mixture. Experimentally, it was found that the etch rate decreases with increasing pressure, as plotted in figure 12, in contrast with the calculated trend in the radical fluxes to the substrate. However, at higher pressure, the mean energy of the ions bombarding the substrate is lower due to more collisions. Moreover, the angle distribution in which the ions hit the substrate is also broadened. This results in a less anisotropic ion flux to the substrate at higher pressure. This effect is also discussed by Collison et al [33] for a N2 plasma, where it was

found that the electron temperature decreases with increasing pressure. The same effect was also observed by Sung-Mo et al [8] who experimentally investigated the dependence of the pressure on the etch rate and of MgO thin films with Ar/Cl2 plasmas. They found that the etch rate decreased with increasing pressure. The calculated energy and angular distributions of the Ar+ ions at 5, 20 and 80 mTorr are plotted in figure 13. The energy and angular distributions of the other ions were found to be very similar. However, the energy distribution of the Cl+2 ions is slightly narrower since the Cl+2 ion has a higher mass and therefore a longer transit time through the sheath. This effect is discussed in more detail below. It is clear that at lower pressure, the mean value of the energy is significantly higher what explains the higher etch rate. The mean value of the angle in which the ions hit the wafer is also lower at lower pressure, resulting in a more anisotropic flux to the substrate. 9

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Figure 15. Calculated Ar+ ion energy distributions at the wafer at different values of the substrate bias. The energy distributions of the Cl+ and Cl+2 ions are comparable with the distributions of Ar+ and are therefore not shown. However, the distribution of Cl+2 is slightly narrower since Cl+2 has a larger mass and hence a longer transit time. The other operating conditions are the same as described in figure 3.

in figure 14(b). Furthermore, increasing the substrate bias has a distinct influence on the energy of the ions hitting the substrate as illustrated in figure 15. Indeed, the energy (in eV) of the ions hitting the substrate is roughly in the same order as the dc bias (in V). The bimodal character of the energy distributions is due to the fact that the transit time, of the ions going through the sheath before hitting the substrate, is shorter than one rf cycle. At 13.56 MHz, an rf cycle takes ≈ 74 ns. The transit time of the ions is typically
30 ns which is shorter than the rf cycle due to a fairly thin sheath (≈ 0.06 cm), which is due to a relatively high plasma density. Hoekstra et al [15] found for a 70/30 Ar/Cl2 plasma at 10 mTorr, 500 W source power and 100 V rf bias amplitude a sheath thickness of about 0.05 cm, which is in good agreement with our results. This means that the ions do not only feel the time-averaged dc bias but also a time specific bias depending on the phase within the rf cycle when the ions enter the sheath. Therefore, the energy distributions have two maxima, which correspond to the highest and lowest values of the substrate rf bias amplitude. The sheath thickness is increased when the substrate bias becomes more negative. However, at the same time, the ions are more accelerated, which results in an overall decrease of the transit time in the sheath and hence an increasing width of the energy distribution [15]. Therefore, at larger substrate bias, the rf frequency should be increased if a smaller energy distribution width is desired. These results are in good correlation with observations made by Ventzek et al [18], who calculated an energy distribution of Ar+ ions hitting the substrate ranging from 50 to 55 eV at a dc bias of also 50–55 V for an Ar plasma at 13.56 MHz operating frequency and 15 mTorr gas pressure with 500 W source power. Similarly, in [16] these authors found for a 85/12/3 Ar/CF4 /O2 plasma at 15 mTorr, 75 V rf bias and 900 W source power, that the dc bias was −53 V and that the energy of the ions was calculated in the vicinity of 50–55 eV.

Figure 14. Calculated average radical (a) and ion (b) fluxes as a function of position on the substrate at different values of the dc bias. The other operating conditions are the same as in figure 3.

The range of angles of incidence of the bombarding ions seems to be in reasonable agreement with the theoretical predictions of Hoekstra et al [15]. These authors observed for a 70/30 Ar/Cl2 plasma at 10 mTorr, 500 W source power and 100 V rf bias amplitude that the average angle of incidence of Cl+2 ions was ≈8◦ and that the ion energy distribution slightly broadened with increasing pressure. Comparing our calculated results with the measured etch rates, we can conclude that the etch rate of Si by an Ar/Cl2 plasma is mainly dependent on the energy of the ions bombarding the substrate and seems not to be significantly affected by the radical flux. 3.4. Effect of substrate bias Calculations were performed for the same operating conditions as described in section 3.1, with the dc bias now varied from −100 to −300 V. It was found that a variation of the substrate bias at these operating conditions has no significant effect on the plasma characteristics within the reactor volume itself. As a consequence, the radical flux to the substrate was found to be nearly constant for different values of the dc bias, as shown in figure 14(a). The total ion flux to the wafer increases however, more pronounced with dc bias as illustrated 10

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Figure 16. Measured etch rates at different values of the substrate bias. The uniformity is comparable to the uniformity profiles of the ion fluxes to the substrate. The other operating conditions are the same as in figure 3.

Figure 17. Calculated plasma species densities in the bulk plasma as a function of source power. The other operating conditions are the same as noted in figure 3.

gas temperature from roughly 600 to 1800 K. The fact that the electron and background gas temperature both increase with source power, is expected because there is more electric heating of the electrons and ions, and consequently, more energy transfer from energetic plasma species to the background gas. Our results are in good agreement with results from Ventzek et al [16] who found for a 70/30 Ar/Cl2 plasma, at 5 mTorr pressure and 80 sccm that the peak electron density increased from 1.4 × 1010 to 8.2 × 1011 cm−3 when source power is increased from 100 to 2000 W. Moreover, Rauf et al [34] calculated that for a pure Ar plasma, the maximum Ar+ density at 5 mTorr and 600 W was in the order of 1011 cm−3 and that for a 70/30 Ar/Cl2 at 5 mTorr and 600 W source power the peak electron density was in the order of 1010 cm−3 . Finally, Efremov et al [10] have applied a zerodimensional self-consistent model to investigate the effect of the source power on the electron density for a 20% Cl2 and 80% Ar mixture at 2 Pa. They observed a similar effect where the electron density increases with applied source power, which is in agreement with our simulation results. The increase in ion density in the bulk plasma results in an increase of the calculated ion fluxes to the substrate, while the radical flux appears not to change significantly with source power. This can be seen in figure 18(a). The Cl radical flux is, however, still much higher than the ion fluxes even at relatively high source power. Important to notice is that the total ion flux changes from roughly 80% Cl+2 at 250 W to 50% Cl+2 (with 50% Cl+ and Ar+ < 1%) at 1000 W. This is due to the fact that at higher source power, and hence higher electron energy, the ionization of Cl radicals into Cl+ by electron impact (table 2, label 6) is more favoured than the ionization of Cl2 into Cl+2 by electron impact (table 2, label 11). Subsequently, the Cl+ ions are more easily formed at higher electron energy and source power. (table 2, labels 6 and 7). In figure 18(b), the total ion fluxes are plotted as a function of position on the wafer, for different values of the source power. Again, it is clear that the ion fluxes increase with source power and that they are fairly uniform.

Finally, Hoekstra et al [15] found that the energy distributions of the Ar+ , Cl+ and Cl+2 ions have minima and maxima of roughly 20 and 80 eV for a dc bias of −32 V, for a 70/30 Ar/Cl2 plasma at 10 mTorr, 500 W source power and 100 V rf bias amplitude. This is also in agreement with our calculated results. Experimentally, it was found that the etch rate increases when the substrate bias becomes more negative, as is plotted in figure 16. The variation of the etch rate with dc bias, as well as the uniformity, are in good agreement with the calculated ion fluxes plotted in figure 14. This indicates that the etch rate is strongly determined by the ions bombarding the wafer, rather than by the radicals. A similar effect was experimentally observed by Sung-Mo et al [8] who investigated the etch rate and selectivity of MgO thin films with Ar/Cl2 plasmas at different substrate bias. They found that the etch rate increased with substrate bias. 3.5. Effect of source power Calculations were performed for the same operating conditions as described in section 3.1, where the source power was varied between 250 and 1000 W. All calculated species densities (except for Cl* and Ar*) in the bulk plasma are plotted as a function of applied source power in figure 17. It is clear that the neutral species (Cl2 , Cl and Ar) decrease in density, whereas all ion species densities increase, when a higher source power is applied. This increasing trend of the ion densities is due to the fact that the average electron temperature is increased from roughly 3.5 to 4.2 eV, increasing the formation of ions by electron impact reactions. The Cl radical density decreases slightly due to the fact that at higher electron temperature the direct ionization and excitation of Cl by electron impact reactions is slightly more favoured than the formation of Cl radicals from Cl2 by electron impact dissociation (table 2, labels 5–7). The drop in background gas densities is attributed to the increased loss by ionization and excitation and especially to the increased average background 11

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

Figure 19. Calculated Ar+ energy distributions at different values of source power. The other operating conditions are the same as in figure 3.

Figure 18. (a) calculated ion and radical fluxes to the substrate as a function of source power. (b) total ion fluxes as a function of position on the substrate at different values of the source power. The other operating conditions are the same as described in figure 3. Figure 20. Measured etch rates at different values of source power. The other operating conditions are the same as described in figure 3.

These results can be well compared with reported calculation results at higher source power. Indeed, Grapperhaus et al [13] found for a 50/50 Ar/Cl2 discharge, with inlet flow rate of 50 sccm, 400 W source power, 100 V rf bias amplitude at 10 mTorr, an average total ion flux of 4 × 1016 cm−2 s−1 . This value is still somewhat higher than our results because their ICP reactor has a thinner dielectric plate, resulting in a higher power deposition. Subramonium et al [14] investigated 30/70 Ar/Cl2 pulsed plasmas at 30 mTorr, 300 W source power, 10 kHz pulse frequency, 20 sccm with no substrate bias and found that the average total ion flux to the substrate was roughly 6 × 1015 cm−2 s−1 . Hoekstra et al [18] obtained for a 70/30 Ar/Cl2 plasma at 10 mTorr, 500 W source power and 100 V rf bias amplitude that the resulting dc bias was −32 V and the ion fluxes in the order of 1016 cm−2 s−1 . The radical flux was in the order of 1017 cm−2 s−1 . This is lower due to the fact that the use only 30% Cl2 . Similarly, Ventzek et al [16] predicted for a 70/30 Ar/Cl2 plasma, at 700 W source power, 5 mTorr pressure and 80 sccm that the ion fluxes as well as the radical flux were in the order of 1016 . This is in reasonable agreement with our results since they applied a 700 W source power, increasing the ion fluxes, and they used a 30% Cl2 gas, resulting in a lower radical flux than

for a 90% Cl2 gas. Finally, it was also shown by Grapperhaus et al [13] that the magnitude of the ion flux is more strongly dependent on the applied source power and to a less extent on the substrate bias. The calculated energy distributions of Ar+ ions hitting the substrate at different values of source power are plotted in figure 19. The Cl+2 and Cl+ energy distributions are comparable with the distributions of Ar+ and are therefore not shown. At higher source power, the plasma density is increased, resulting in the formation of a thinner sheath. As a consequence, the transit time is shorter, resulting in a broader energy distribution for the ions. This effect was also discussed by Hoekstra et al [15, 17]. Experimentally, it was found that the etch rate increases with source power, as is shown in figure 20. This is due to the fact that the ion flux to the substrate is higher at increased source power. Indeed, comparing the measured etch rates in figure 20 with the total ion fluxes in figure 18(b) clearly illustrates that the trend in etch rates, upon variation of the source power, is very similar to the trend in calculated ion fluxes as a function of source power. Also the uniformity of 12

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

the etch processes can be well compared with the calculated ion fluxes. This suggests again that the etch process is mainly determined by the ion fluxes rather than by the Cl radical flux, at the operating conditions under study. Collison et al [33] experimentally measured an etch rate of 250 nm min−1 for a pure Cl2 ICP at 10 mTorr pressure and 800 W source power, what is in good agreement with our etch rate measurements. Finally, the same trend, where the etch rate increases with source power, was also experimentally found for other substrates. Sung-Mo et al [8] observed an increasing etch rate of SiO2 and MgO with source power for an Ar/Cl2 plasma.

Acknowledgments We would like to thank IMEC for financial support as well as the CalcUA computing facilities of the University of Antwerp. S Vanhaelemeersch, D Samyrian, V Paraschiv, S De Gendt and J Wouters are acknowledged for experimental support and interesting discussions. Finally we are very grateful to M Kushner and group members for providing the HPEM and useful advice.

References [1] Boufnichel M, Aachboun S, Grangeon F, Lefaucheux P and Ranson P 2002 J. Vac. Sci. Technol. B 20 1508–13 [2] Liebermann M A, Lichtenberg A J 1994 Principles of Plasma Discharges and Materials Processing (New York: Wiley) [3] Mahony C M O, Escoffier C N, Maguire P D, Corr C S, Gomez S, Costa E, Bricha I and Graham W G 2001 American Physical Society, 54th Annual Gaseous Electronics Conf. (Pennsylvania State University, State College, PA, 9–12 October 2001) (Pennsylvania Meeting ID: GEC01, abstract #JWP.026) [4] Lee Y S, Na S W, Song S G, Kim Y M, Lee N E and Ahn J H 2003 Proc. Int. Symp. Dry Process 3 167–72 [5] Shin M H, Na S W, Lee N E and Ahn J H 2006 Thin Solid Films 506–507 230–4 [6] Okpalugo O A, Laverty S, Maguire P D, Mahony C M O and Graham W G 2000 American Physical Society, 53rd Annual Gaseous Electronics Conf. (Houston, TX, 24–27 October 2000) (Houston Texas Meeting ID: GEC00, abstract #JWP.017) [7] Dong-Pyo K, Kyoung-Tae K, Chang-Il K and Efremov A M 2004 Thin Solid Films 447–448 343–8 [8] Sung-Mo G, Dong-Pyo K, Kyoung-Tae K and Chang-Il K 2005 Thin Solid Films 475 313–7 [9] Efremov A M, Dong-Pyo K and Chang-Il K 2005 Thin Solid Films 471 328–35 [10] Efremov A M, Gwan-Ha K, Jong-Gyu K, Bogomolov A V and Chang-Il K 2007 Microelectron. Eng. 84 136–43 [11] Efremov A M, Dong-Pyo K and Chang-Il K 2004 Plasma Sci. IEEE Trans. 32 1344–51 [12] Fuller N C M, Donnely V M and Herman I P 2002 J. Vac. Sci. Technol. A 20 170–3 [13] Grapperhaus M J and Kushner M J 1997 J. Appl. Phys. 81 569–77 [14] Subramonium P and Kushner M J 2002 J. Vac. Sci. Technol. A 20 325–34 [15] Hoekstra R J and Kushner M J 1996 J. Appl. Phys. 79 2275–86 [16] Ventzek P, Grapperhaus M and Kushner M J 1994 J. Vac. Sci. Technol. B 12 3118–37 [17] Hoekstra R J and Kushner M J 1995 J. Appl. Phys. 77 3668–73 [18] Ventzek P, Hoekstra R J and Kushner M J 1994 J. Vac. Sci. Technol. B 12 461–77 [19] Collison W Z and Kushner M J 1996 Appl. Phys Lett. 68 903–5 [20] Tachibana K 1986 Phys. Rev. A 34 1007–15 [21] Kota G P, Coburn J W and Graves D B 1998 J. Vac. Sci. Technol. A 16 270–7 [22] Kota G P, Coburn J W and Graves D B 1999 J. Appl. Phys. 85 74–86 [23] Kota G P, Coburn J W and Graves D B 1999 J. Vac. Sci. Technol. A 17 282–90 [24] Rapp J D and Englander-Golden P 1965 J. Chem. Phys. 43 1464 [25] McFarland R H and Kinney J D 1965 Phys. Rev. A 137 1058 [26] Rogoff G L, Kramer J M and Piejak R B 1986 IEEE Trans. Plasma Science 14 103–11

4. Conclusions An ICP reactor with 10% Ar 90% Cl2 gas mixture used for the etching of Si was investigated by means of hybrid plasma simulation. Also the effect of total gas pressure, substrate bias and source power on the calculated ion and radical fluxes to the substrate and on experimentally obtained etch rates was studied. It was found that at increased pressure, the radical density and flux to the substrate is increased due to the easy dissociation of Cl2 into radicals. The magnitude of the total ion flux was found to be fairly independent of the gas pressure. However, the composition of the ion flux changes with pressure. At the investigated pressure range from 5 mTorr to 80 mTorr, the fraction of Cl+2 is increased from 80% to about 90% due to a favoured charge exchange reaction from Cl+ and Ar+ to Cl+2 . Experimentally, it was found that the etch rate decreases when pressure is increased. This is due to the fact that the mean energy of the ions hitting the substrate is decreased at higher pressure due to more collisions, as confirmed by the model. Moreover, the width of the angle distribution in which the ions hit the substrate becomes larger at higher pressure, resulting in a less anisotropic flux. At increased bias, the energy and fluxes of the ions hitting the substrate are higher, resulting in an increase in the etch rate which is also observed experimentally. The energy distribution of the ions at the substrate becomes broader when the substrate bias is increased due to a smaller transit time of the ions through the sheath. At higher source power, it was found that the gas and electron temperature increase as well as the ion densities, resulting in an increase of ion fluxes to the substrate, while the radical flux did not change significantly. The composition of the ion flux changes drastically with source power, from ≈ 80% Cl+2 at 250 W to 50% Cl+2 at 1000 W due to a favoured formation of Cl+ than Cl+2 . The energy distribution of the ions hitting the substrate becomes broader at higher source power due to a thinner sheath. Our calculations suggest that, under the investigated operating conditions, the etch rate is more strongly affected by the energy and flux of the ions bombarding the substrate and in less extent by the magnitude of the radical flux, even though the radical flux is roughly 100 times higher than the total ion flux. 13

J. Phys. D: Appl. Phys. 41 (2008) 065207

S Tinck et al

[31] Ventzek P, Sommerer T J, Hoekstra R J and Kushner M J 1993 Appl. Phys. Lett. 63 605–7 [32] Subramonium P and Kushner M J 2001 Appl. Phys. Lett. 79 2145–7 [33] Collison W Z, Ni T Q and Barnes M S 1998 J. Vac. Sci. Technol. A 16 100–7 [34] Rauf S and Kushner M J 1997 J. Appl. Phys. 81 5966–74

[27] Ellis H W, Pai R Y, McDaniel E W, Mason E A and Viehland L A 1976 At. Data Nucl. Data Tables 17 177 [28] Ikezoe Y, Matsuoka S, Takabe M and Viggiano A 1987 Gas Phase Ion–Molecule Reaction Rate Constants Through 1986 (Tokyo: Mass Spectroscopy Society of Japan) [29] NIST Chemical Kinetics Database 17, Version 2Q98, http://kinetics.nist.gov/index.php [30] Vasenkov V and Kushner M J 2003 J. Appl. Phys. 94 5522–9

14