Testing Conditions

These simulations are examined under the same conditions: a gas pressure of 20 mTorr, a CF4 flow rate of 230 sccm, and a deposited power of 200 W driven by 13.56 MHz frequency of current. The temperatures of the ion and the neutral species are assumed to be constant at 0.026 eV and 400 K respectively. The ion bombardment energy to the substrate is set at 100 eV at the substrate boundary. The grid resolution in both radial and axial directions is 1 mm. This grid size leads to approximately a total 2.5 million unknowns as considering 32 species, and this grid size has to perform via parallel computing to reduce running time within one day.

4.3.3 Spatial Profiles

Figure 58, Figure 59, Figure 60, Figure 61, and Figure 62 show the 2-D spatial profiles for n_e, streamline as well as a vector plot of CF₃⁺ flux and CF₃⁺ density, T_e, CF₄, and production rate of dissociative ionization respectively. In Figure 58, it is obvious that the concentration of electron accumulates near the gas inlet as gas inlet port located upon the top roof of chamber ((c), (d) and (e)), or n_e is peaked on axis as the inlet ring located beside the chamber ((a), (b), (f) and (g)). Because the uniformity of n_e known as discharge region strongly affect those fluxes to the SiO₂ substrate, it can be predicted that the etching uniformity in case of (b) must be the smoothest since n_e is peaked with a more extended and flatter region from center to edge as comparing to others. In contrast, for the cases ((c), (d) and (e)) of the gas inlet port set upon the root, n_e are constrained near region of gas inlet port because it can be find that the negative ions are mainly produced in gas inlet region where the electron temperature is relatively low so that electrons have to follow the positive and negative ions out of the system to

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maintain discharge, or the discharge will be collapsed. Later we will present that the discharge regions near the gas inlet port located upon the roof cause the etching uniformity rough in these case. In contrast, the discharge regions in the cases of dome-shaped reactor with gas inlet ring beside the chamber ((f) and (g)) are more extensive than the cases of typical cylindrical reactors ((a) and (b)), and they are deposited under similar power. Therefore, because of larger discharge region but the same power in series of dome-shaped reactor, we find that the plasma densities near the substrate in typical cylindrical reactors are richer than dome-shaped reactors. In this regard, it can predict that the etching rate of typical cylindrical reactors with side coils and top coils ((a) and (b)) will be higher than the etching rate of dome-shaped reactors ((f) and (g)). Before we show the comparison of etching uniformity and etching rate, we conclude that etching uniformity in case of (b) is must be the smoothest with relatively high etching rate. In the following, we will proof this point.

There are several effects that conspire to cause the density profile in Figure 58(b).

To understand these effects better, consider first the profile of ion flux streamline in Figure 59. The streamlines of ion flux also show that the discharge region is the widest and smoothest in Figure 59(b) as comparing to other cases. It is evident that the ion flux to the substrate is flat because the discharge extends from center to almost edge of substrate. Second, in Figure 60(b), electron temperature is peaked near the quartz region where the power is depositing beside the chamber and hence electron heating takes place off axis, but the electron thermal conductivity is relatively high in low pressure so that the plasma near center could obtain enough energy from off-axis region to discharge. Moreover, electron temperature is strongly relating to the dissociative ionization rate constant K(T_e) to affects the density profile. However, K(T_e) is not the main reaction to make the discharge region so extended and smooth, because the

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plasma discharge is strongly influenced by combination of K(T_e), n_e, and background gas feeding CF4. Next we will clearly discuss the spatial profile of CF4 and production rate of dissociative ionization that is the combination of n_e, CF₄ and K(T_e). In the Figure 61(b), the feedstock gas CF4 flow from inlet ring into the chamber. Then, CF4 is dissociated in the inlet region where the K(T_e) is relatively high, whose production rate is shown as Figure 62(b). It is evident that the dissociative ionization tends to peak off-axis to affect CF₃⁺ density profile most likely off-axis. In this case, the ion transport plays a more dominant role in determining the radial density profile. Now going back to the ion flux plot of Figure 59(b), it makes clear that ions born at large radius will preferentially flow to top and bottom surfaces of the reactor, thus making it difficult for ions to fill in the center of chamber.

On the contrary, Figures 59(c), 59(d) and 59(e) indicate that the discharge regions are constrained near the gas inlet, and the ion transport from discharge region to the SiO₂ is far and non-uniform. A reason that makes density profile in Figures 59(c), 59(d) and 59(e) first is the electron temperature is relatively low and CF₄ is relative high in that discharge region as comparing to other region, which are shown as Figures 60(c), 60(d) and 60(e). Negative ions tend to be generated in the low electron temperature from electron dissociatively attaching to CF₄. Therefore, more negative ions are produced, and these negative ions are difficult to transport in radial direction to extend the plasma discharge region. Another possible point is that the density of CF₄ fed from top inlet port (Figures 61(c), 61(d) and 61(e)) present higher approximately two order than those fed from side inlet ring (Figures 61(a), 61(b), 61(f) and 61(g)) under the same flow rate. Hence it is obvious that although K(T_e) is relatively low, the concentrations of electron and CF₄ are relatively high to make production rate so higher near top gas inlet in Figures 62(c), 62(d) and 62(e).

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On the other hand, for the cases of dome-shaped reactors with gas inlet ring beside chambers (cases of (f) and (g)), the streamlines in Figure 59 describe that the discharge regions in (f) and (g) are closer to substrate than those in (d) and (e). However, it is clear that the streamlines to the substrate show only the diffusion effect dominant in all dome-shaped reactors because the variation between positive and negative charged particles causes small electric field that can ignore the drift effect. The production rates in Figure 62(f) show higher rate than that in Figure 62(g) near the substrate. Therefore, it could be predicted that the etching rate of SiO2 in dome-shaped reactor with elliptic roof is higher than that in dome-shaped reactor with spherical roof.