Figure 10. The effective sticking coefficients (SE) of F, F2, SF3,

SF4, SF5 and SF6 on the walls of the reactor versus power. pOFF is 0.921 Pa and Tgas is 315 K. There is a net consumption of SF3, SF4 and F, and a net production of SF6, F2 and SF5 (after 150 W) at the

walls.

power show that in order to take into account the loss of a species at the walls in a global model, a constant value for the effective sticking coefficients may not be an adequate choice.

5.4. Sensitivity of the results on the rate coefficients

The sensitivity of the model outputs on uncertainties in the rate coefficients was made through a series of runs at specific conditions (2000 W, 2 Pa). At each run a coefficient was multiplied or divided by 10 while all others were kept constant. The effect of this change on the outputs of the model compared with the magnitude of the change was rather not significant: the great majority (>95% of 1800 values) of the values of outputs (densities, electron temperature and pressure rise) changed by a factor of less than 2. In particular, the changes in the rate coefficients for gas phase and surface reactions caused a change by a factor from 0.62 to 1.58 to F density, from 0.43 to 1.43 to SF6 density, from 0.27 to 1.69 to F2 density, from 0.27 to 2.73 to SF+5 density, from 0.39 to 2.57 to F− density, from 0.45 to 1.64 to the electron density, from 0.85 to 1.23 to the electron temperature, and from 0.50 to 1.65 to the pressure rise. Concerning the gas phase reactions, the outputs were found more sensitive to the coefficients of reactions (G1), (G6), (G8), (G13), (G35) and (G45). Concerning the surface reactions, the outputs were found more sensitive to the probabilities of reactions (S1), (S7), (S8) and (S35). In particular, the decrease in the probability of (S1) by a factor of 10 caused the decrease in F2 density and pressure rise by a factor of 2. The same decrease at the probability of (S7) caused the decrease in SF6 density and pressure rise by a factor of 2 and the increase in F density by a factor of 1.5. A similar decrease in the probability of (S8) caused the increase in SF6 density and pressure rise by a factor of 1.6 and the decrease in F2 density by a factor of 2. The increase in the probability of (S35) by a factor of 10 caused the decrease in the densities of SF6 and SF4 and pressure rise by a factor of 2. Finally, when the probabilities of surface reactions were multiplied and divided by 2 (instead

of 10), the change in all densities did not overcome 20%; all densities changed by a factor of 0.8–1.2.

6. Conclusions

A global (0D) model for the gas phase of SF6 plasmas consisting of a set of gas phase reactions (50) and a set of surface reactions (40) is formulated. The necessary cross sections and rate coefficients for the gas phase reactions are taken from the literature; a Druyvesteyn EEDF is used. The rate coefficients of the surface reactions are calculated by fitting the model to a set of available experimental measurements in an ICP reactor.

Deposition of SFx species on the reactor walls is found necessary to predict the experimental data. The subsequent growth of particles in the gas phase, onto nucleation sites ablated from the walls, cannot be excluded. SF6, F, F2 and SF4 are the dominant neutral species, SF+5 is the dominant positive ion and is followed by SF+3 ; the dominant negative ion is F−.

Both gas phase reactions between neutral species and surface reactions are found to be important for the production and consumption rates of the neutral species. There is a net consumption of F, SF4 and SF3 and a net production of F2, SF6 and SF5 (after 150 W) on the reactor walls. The effective sticking (surface loss) coefficient of F is calculated from 0.1 to 0.15.

This work has focused on the effect of wall-surface kinetics on the densities of species in the gas phase. A potential extension of the wall-surface kinetics would be to include reactions WITH the wall surface, and not only ON the wall surface (as in this work). The products originating by reactions of SF6 fragments with the wall surface, e.g. sputtered AlFx particles from AlO3 walls, even if they may not affect the pressure and the species densities in the gas phase, affect the formation of roughness of the Si etched surfaces [33, 72]. Another extension of the model would be to take into account wafer–surface kinetics; during etching of Si the consumption of F is very important and usually causes the loading phenomenon [73]. Potential applications of the model would be the simulation of the BOSCH process by coupling with a global model for C4F8 plasmas [36] and a feature scale module. Finally, the computational framework of the global model is complementary to our previous modelling works on feature scale etching [74, 75] and nanoscale etching [34] towards multiscale modelling of plasma etching processes.

Acknowledgments

The authors would like to thank Angeliki Tserepi for useful discussions and Paraskevi Geka for her work on the initial version of the computational framework. This work was supported by the project ‘Nanoplasma’ (IST-NMP-3, Contract No 016424).

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