The influence of surface properties on the plasma dynamics in radio-frequency driven oxygen plasmas: Measurements and simulations

Non-equilibrium low pressure capacitively coupled plasmas (CCP) are well-established for technological applications, in particular, for etching and deposition processes in the semiconductor industry. The energy transport mechanisms in the plasma-surface interface region are of special importance. Without detailed comprehension of power dissipation mechanisms under industrially relevant conditions, plasma processes can only be optimized empirically, but not predictively on a scientific basis. The measurement of in-situsurface conditions,which strongly affect the plasma-surface interaction processes, is therefore of key importance but extremely challenging. New concepts for process control and plasma monitoring have been developed based on the combination of numerical simulations and advanced plasma diagnostics.^1–3 

The influence of surface condition on the plasma dynamics is investigated by means of numerical simulations of a capacitively coupled oxygen rf discharge. The surface loss probability of singlet delta molecular oxygen (SDO) is varied to investigate the corresponding impact on the plasma parameters and associated excitation features.

The plasma and electrode dimensions are assumed to be large compared to the discharge gap, allowing one-dimensional (1D) treatment. The applied self-consistent 1D fluid model includes a semi-kinetic treatment of electrons and an improved treatment of ion mobilities, see Ref. 4. This approach combines accounting for a local non-Maxwellian electron energy distribution function (EEDF) and a computationally efficient treatment of heavy-particles. The two-term approximation Boltzmann solver BOLSIG+ (Ref. 5) is used to calculate, in advance, electrontransport coefficients and electron-impact reactionrates on the basis of recommended cross-section data for the elastic and dominant inelastic collision processes. The resulting data is then implemented in the form of look-up tables into the fluid model to account for the individual spatial and temporal dependence of each quantity.

The 1D numerical simulation aims to describe a geometrically asymmetric capacitively coupled rf plasma across a 40 mm electrode gap. This geometry is based on an inductively coupled Gaseous Electronics Conference (GEC) reference cell⁶ with a modified electrode configuration. The top coil is grounded (normally powered) and the standard (not extended) lower electrode is powered (normally grounded). The asymmetry is given by the ratio of both electrodesurface areas(S₁, S₂) and was determined to be S₂/S₁ = 36. This ratio is a reasonable assumption for the standard GEC reference cell based on the actual chamber geometry and the experimental observations.

The governing equations are the continuity equation for electrons, ions, and neutrals employing the drift diffusion approximation, electronenergy conservation, and Poisson equation for the electric field. Detailed information on the asymmetric 1D simulation and the set of equations as well as the used boundary conditions can be found in Ref. 4 and references therein.

A total of five species are accounted for in the model, namely, electrons (e), molecular oxygen background gas (O₂), positive molecular oxygen ions $(O2+)$⁠, negative atomic oxygen ions (O^–), and metastable singlet delta molecular oxygen $(O2(1Δ))$⁠. Depletion of the background gas density can be neglected in this type of discharge.⁷ The secondary electron emission coefficient γ is set to 0.05,⁸ unless otherwise stated. The background gas temperature is assumed to be 300 K.

The used reaction scheme results from an analysis of several detailed reaction schemes,^9,10 and is purposely kept as simple as possible to allow insight into the fundamental impact of changing surface conditions on plasma dynamics.

The reactions describe electron momentum transfer(e + O₂ → e + O₂), dominant charged heavy particles volume production processes through ionization $(e+O2→2e+O2+)$ and dissociative attachment (e + O₂ → O + O^–) as well as their destruction induced by collisions with electrons$(e+O2+→2O,e+O−→2e+O)$⁠. Heavy particle interaction is described by ion neutralization $(O−+O2+→O+O2)$ and associative detachment $(O−+O2*→e+O3)$⁠. To account for the SDO formation, electron momentum transfer, the main volume production reaction through electron excitation of the background gas $(e+O2→e+O2(1Δ))$⁠, and several volume destruction reactions induced by collisions with electrons are added $(e+O2(1Δ)→M)$⁠. The latter set of reactions includes the production of negative atomic oxygen ions,positive molecular oxygen ions, as well as de-excitation and dissociation into atomic oxygen ground and excited states. Although, atomic oxygen has a slightly higher rate constant for the loss channel of negative atomic oxygen ions than SDO,¹¹ it is justified to neglect atomic oxygen in the model considering reported atomic oxygen number densities of at least one order of magnitude lower than for SDO in a very similar experimental set up.¹² 

For the SDO surface loss, the thermal flux of SDO towards the chamber walls is considered as: $Γ→·n→=sSDO·14vthn$⁠. Here, s_SDO is the SDO surface loss probability, v_th the thermal velocity, and n the density of SDO.

Simple calculations in a global volume averaged model, introduced in Ref. 13, have shown a SDO content of 12% of the ground-state density. These calculations are based on a-priori assumptions for the surface-to-volume ratio and the SDO surface loss probability, although the real value for the latter is in most cases rather insufficiently known.

An actual value for the SDO surface loss probability at the chamber walls is very difficult to assess both experimentally and theoretically. Generally, the loss probability for any species hitting the chamber walls depends not only on the considered species itself, but also on the surface material, the surface temperature, the surface roughness,and the actual surface condition, which can vary substantially. The literature value for the SDO surface loss probability ranges over several orders of magnitude from 1 × 10⁻⁵ (Ref. 14) to 7 × 10⁻³ (Ref. 15).

In the investigated parameter regime (p = 10–100 Pa, V_rf = 200–500 V amplitude, f = 13.56 MHz) qualitatively equivalent trends are observed. For the following analysis,a pressure of 40 Pa and a voltage amplitude of 300 V is exemplarily chosen. Consequences of the SDO surface loss probability are revealed on the basis of global particle densities and excitation dynamics. Similar to the global volume averaged model, it is found that the SDO distribution across the discharge gap is practically homogeneous, slightly dropping near the electrodes. However, the total density depends strongly on the actual surfacecondition.

Often, it is assumed that SDO, due to its natural radiative lifetime of 64.4 min (≈ 3900 s), is a long living metastable species that has no effect on and is not affected by the fast plasma dynamics or the surface condition.¹⁶ However, the effective SDO lifetime is significantly lower in such plasmadischarges, allowing SDO to react to surface condition changes on industrially relevant timescales in the order of seconds to minutes.

The effective SDO lifetime has been determined using volume destruction processes, wall losses,and the gas residence time. Its value, averaged over the total volume, lies in the range of 1 s,based on the average electron and negative ion densities responsible for the volume destruction of SDO. Similar observations of a significant metastable lifetime reduction due to volume processes have been reported previously in a helium-oxygen atmospheric plasma.¹⁷ At the surfaces, the effective SDO lifetime varies over a range of several milliseconds to seconds because it is mainly governed by the SDO surface loss probability, which can vary significantly. The gas residence time in the plasma region is estimated to be in the order of 0.5 s, based on an oxygen mass flow rate of 50 sccm.

From this follows, that the effective SDO lifetime is still long enough (thousands of rf cycles)to allow a build-up of significant SDO metastable densities in O₂ discharges as observed experimentally¹² and theoretically.¹⁸ Nevertheless, due to the reduced effective SDO lifetime, SDO can actually respond to changes in surface condition on a time scale below seconds that are likely to occur in plasmaprocessing applications, and consequently it is important to take this into account.

Figure 1 shows the major impact of the SDO surface loss probability on the charged particle densities, and consequently on the global electronegativity (en),which is defined here as the ratio of time and space averaged negative atomic oxygen ion density versus time and space averaged electron density $(⟨n−⟩x,t/⟨ne⟩x,t)$⁠, as well as on the global SDO concentration. The SDO surface loss probability was varied from 1 × 10⁻⁵ to 8 × 10⁻³ in the simulations, while keeping all other parameters fixed.

The SDO content shows a clear dependence on the SDO surface loss probability, dropping from about 15% to below 1%. The electronegativity shows an oppositional, so increasing trend, since SDO dominates the volume destruction of O^–, whereas the electron density stays approximately constant.

Typically, the SDO content is assumed to be in the range of about 12%–17% for stainless steel electrodes on the basis of an SDO surface loss probability of (4–7) × 10⁻³ (Ref. 15). In contrast, our simulations imply an SDO surface loss probability of 1 × 10⁻⁵, which is supported by the experimentally observed excitation dynamics, as will be shown.

Generally, the time averaged electron density profile is found to be rather flat and almost independent of the SDO surface loss probability, whereas the negative ion density increases with increasing surface loss probability. The overall increased negative net charge density is accordingly balanced by an increased positive molecular oxygen ion density. Since the electron density remains almost unaffected, while the charged heavy particle densities increase, the electronegativity of the system increases correspondingly. The global electronegativity values are found to be in good agreement with independent measurements^12,19,20 in view of the differences in discharge design and operational parameters.

The electron excitation dynamics is probed by observing the phase resolved optical emission.²¹We demonstrate this approach on the atomic oxygen emission line at λ = 844.6 nm, from which the excitation is calculated, and correlated with the numerical simulations.

Figure 2 shows the measured phase resolved excitation of theλ = 844.6 nm optical emission line along the radial center axis of the discharge on a normalized false color scale (a, c) and the corresponding simulated excitation pattern (b, d), for two different electrodematerials, namely stainless steel and Teflon.

The 844.6 nm optical emission line is spectrally separated by a spectrograph (Andor Shamrock 500)and detected by an intensified charge-coupled device (ICCD) camera (Andor DH334T-series). The phase and space resolved emission signal is captured with 2 ns phase resolution and 42 μm spatial resolution. To compare the calculated excitation to simulations, only dissociative excitation is taken into account, because this is known to be the dominant excitation processes under the investigated conditions,²² since the atomic oxygen density is small.²³ 

The abscissa covers one full rf cycle ( ≈ 73.75 ns) and the ordinate only shows the lower part (0 mm–25 mm) of the total discharge gap of 40 mm to facilitate the comparison. The powered electrode is located at the bottom. The roman letters in Figure 2 denote the expected two distinct excitation features associated with: (I) sheath expansion and (II) sheath collapse. The sheath edge positions, as obtained according to the equivalent sharp electron step criterion,²⁴ are indicated by white dashed lines.

For both electrodematerials, there is a very good agreement both qualitatively in position and shape, and quantitatively between simulation and experiment for excitation features I and II. In particular,the weighting of the two excitation features during the sheath expansion and sheath collapse phases, apart from their individual spatio-temporal shapes, strongly depends on the SDO surface loss probability. For low SDO surface loss probability, the dominant excitation takes place during the sheath expansion phase (feature I). With increasing SDO surface loss probability the magnitude of the sheath expansion feature (I) remains almost constant, while the sheathcollapse feature (II) becomes more pronounced. This trend reflects our predictions of an increased global electronegativity according to the explanation stated in Refs. 25 and 26, which also confirms a correspondingly deeper extension of the excitation features into the plasma bulk.

The simulation matching the experimental observation for the stainless steel electrode indicates a relatively low SDO surface loss probability (s_SDO = 1 × 10⁻⁵), which corresponds to an SDO content of 15% and an electronegativity of en = 1.2. While, for Teflon as electrode material the best match result is an SDO surface loss probability of s_SDO = 3 × 10⁻³,which is more than two orders of magnitude higher. Thereby, the SDO content drops to less than 1%and the discharge becomes more electronegative (en = 12.5). From this, we can conclude that Teflon appears to be much more efficient in de-exciting SDO than stainless steel. The secondary electron emission coefficient is negligible, because no excitation from secondary electrons is observed.

The change in shape, in case of the higher SDO surface loss probability, can be explained due to the increased electronegativity in the bulk.^27–29 This creates relatively high electric fields in the quasi-neutral bulk, in which the electrons are significantly accelerated enhancing excitation in this region. The same applies for the sheath collapse phase (II), where a stronger electric field reversal can be identified due to the higher electronegativity.³⁰ 

We showed that surface loss probabilities of SDO in low-pressure electronegative oxygen capacitively coupled radio-frequency plasmas have a major influence on the plasma dynamics, thus representing a sensitive indicator for the actual surfacecondition.

An increasing SDO surface loss probability evokes in the first place a reduction of the total SDO concentration in the system, which induces an increasing negative atomic oxygen ion density. The negative ions on their part affect other charged particles. In order to compensate the increased negative net charge in the plasma, the positive ion density increases. On time average, electron densities are only minorly affected by the SDO surface loss properties, thus leading to an increasing electronegativity in the system, to an extend that O^– becomes successively more dominant over electrons.

Time and space resolved electron excitation dynamics is more critically governed by changing the SDO surface loss probability. It is revealed that the increasing loss of SDO at the surfaces leads to a successively more pronounced excitation during the sheath collapse phase. This is verified experimentally for two different electrode materials. Thus, conclusions on the surface condition are drawn by means of assigning absolute values for the SDO surface loss probability to the experimental observations.

The authors would like to thank Intel Ireland (Ltd.) for financial support, and in particular G. J. Ennis and N. MacGearailt for valuable discussions. The authors acknowledge the UK Engineering and Physical Sciences Research Council (EPSRC) for supporting this research through the EPSRC Manufacturing Grant (EP/K018388/1) and the EPSRC Career Acceleration Fellowship (EP/H003797/1).