## 4 Results and Discussion
### Sensitivity Analysis for the Electron Temperature and the Negative Ion Density  
As mentioned in Section 3.2.1, the theoretical determination of the charge density \(n_{\rm d}Z_{\rm d}\) and the transmittance \(T\) depends strongly on the assumed electron temperature through Equation (8) and the negative ion density through Equation (4). Both the electron temperature and negative ion density are difficult to determine experimentally or by modeling, and should therefore be assumed based on typical values found in the literature. In order to assess the sensitivity of the fitting procedure to these assumptions, the fitting procedure is also evaluated for different values for \(T_{\rm e}\) and \(n_{\rm i\cdots}\). Figure 6 shows the results of varying only the electron temperature \(T_{\rm e}\), while still using the same data set. The figure depicts the obtained dust particle radius and dust density as a function of time for \(T_{\rm e}=2\,\)eV, \(T_{\rm e}=3\,\)eV and \(T_{\rm e}=4\,\)eV. Variations in the electron temperature lead to relatively small changes; the average dust particle size variation over the measured time range is \(-7.0\,\)nm and \(+5.1\,\)nm, for \(T_{\rm e}=2\,\)eV and \(T_{\rm e}=4\,\)eV, respectively, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Author** & **Used Method** & **Precursor** & **Plasma Power** & **(Total)** & **Growth** & **Dust Particle Size** \\  & & **(W)** & **Pressure (Pa)** & **Time (s)** & **(nm)** \\ \hline [PERSON] et al. [50] & Ellipsometry & C\({}_{2}\)H\({}_{2}\) & 8 & 24 & 85 & 200 \\ [PERSON] et al. [51] & Ellipsometry & C\({}_{2}\)H\({}_{2}\) & 20 & 24 & 90 & 100 \\ [PERSON] et al. [73] & Ellipsometry + AFM & C\({}_{2}\)H\({}_{2}\) & 8 & 25 & 130 & 150 \\ [PERSON] et al. [74] & Ellipsometry & C\({}_{2}\)H\({}_{2}\) & 8 & 24 & 129 & 210 \\ [PERSON] et al. [23] & Ellipsometry & C\({}_{2}\)H\({}_{2}\) & 8 & 11.5 & 85 & 184 \\ [PERSON] et al. [75] & SEM & C\({}_{2}\)H\({}_{2}\) & 1 & 20 & 600 & 300 \\ [PERSON] et al. [61] & LII & C\({}_{2}\)H\({}_{2}\) & 7 & 10 & (a) & 100–165 (b) \\ [PERSON] et al. [76] & White light scattering & C\({}_{2}\)H\({}_{2}\) & 0.3 & 20 & 150 & 260 \\ [PERSON] et al. [57] & TiRe-LII & SiH\({}_{4}\) & 5 & 2.7 & 1000 & 200 \\ \hline \hline \end{tabular} \({}^{(a)}\): Continuous C\({}_{2}\)H\({}_{2}\) flow, switched off after 35 min, \({}^{(b)}\): Depending on the refractive index data set.  
\end{table} 
Table 1: Overview of the characteristics of low-pressure dust growth as reported in the literature. both with respect to the base case of \(T_{\rm e}=3\,\rm eV\). For the dust density, the average variation is found to be \(+0.50\times 10^{14}\,\rm m^{-3}\) and \(-0.26\times 10^{14}\,\rm m^{-3}\), with respect to the default case. This dependency can be explained as follows: From the OML theory, it can be derived that the dust floating potential \(V_{\rm d}\) increases with the increasing electron temperature \(T_{\rm e}\). Physically, this can be understood from the fact that a stronger potential barrier is necessary to repel more energetic electrons. For a constant or increasing \(a\), the dust charge \(Z_{\rm d}\) also increases with increasing \(T_{\rm e}\), which implies a larger Coulomb repulsion among the dust particles. Via Equation (5), it can be seen that \(n_{\rm d}\) must decrease for a (fixed) measured \(\Delta\hat{n}_{\rm e}\). Using the Lambert-Beer law in Equation (11), it can be seen that the dust particle radius \(a\) indeed must increase with the decreasing dust density \(n_{\rm d}\) for a fixed value of the measured transmittance. Figure 7 shows the effect of varying the negative ion density \(n_{\rm i-}\). Here, we see the dust particle radius and dust density as a function of time for \(n_{\rm i-}=2n_{\rm e0}\), \(n_{\rm i-}=4n_{\rm e0}\) and \(n_{\rm i-}=8n_{\rm e0}\).