# Chemical Vapor Deposition of Longitudinal Homogeneous Parylene Thin-Films inside Narrow Tubes
## 4 Results and Discussion
### Measurement of the Temperature Dependence of the PPX-N Sticking Coefficient  
Next, the temperature dependence of the sticking coefficient was measured. The deposition experiments were obtained on soda lime glass microscope slides clamped on an aluminum slab. The surface temperature was linear between 10 \({}^{\circ}\)C and 70 \({}^{\circ}\)C at two distinct points. A temperature increment of 2 \({}^{\circ}\)C within this temperature interval was chosen, related to a spatial separation of thin-film interferometry measurement points on the substrates of 0.5 cm. When determining the sticking coefficient, it is clearly more convenient to specify the behavior relative to a given reference temperature. Thus, the pre-factor \((1-\Theta)\) was eliminated in the Langmuir isotherm description of \(S(T_{\text{s}})\), which is given by the product of a temperature-dependent function and the fraction of reactive surface cites via \(S(T_{\text{s}})=S_{0}(T_{\text{s}})(1-\Theta)\)[23]. Furthermore, the determination of the relative sticking coefficient was sufficient for our problem due to Equation (18), and a detailed investigation of the deposition kinetics is not aimed at in this work. Figure 2c showsthe evaluated relative sticking coefficient \(S_{\rm r}(T)=S_{0}(T_{\rm s})/S_{0}(T_{\rm ref})\), corresponding to a reference surface temperature of \(T_{\rm ref}=30\)\({}^{\circ}\)C (therefore \(S_{\rm r}(30\)\({}^{\circ}\)C) \(=1\) holds by definition). The data are given in Table 1 and depicted in Figure 2c (red line) with an almost exponential course of the relative sticking coefficient within our investigated temperatures. Above the ceiling temperature \(T_{\rm c}\) (see below for a precise identification), no film growth takes place. Just below the ceiling temperature, the relative sticking coefficient was determined to be \(S_{\rm r}=0.14(1)\), which then falls instantly to zero when exceeding \(T_{\rm c}\). Here, a smooth transition with a continuously decaying \(S_{\rm r}(T_{\rm s})\) is not found, as is the case in several deposition models [22; 23]. The minimum temperature in this study was 14 \({}^{\circ}\)C with \(S_{\rm r}=2.02(13)\). Thus, for the specification of the temperature gradient for the formation of a homogeneous PPX-N layer thickness inside narrow tubes, a maximum variation of the sticking coefficient by a factor of 15 was granted when working within our investigated temperature range. To compare our measured data with the Fortin model, a nonlinear curve regression was performed. The model is given with [23]  
\[S(T_{\rm s})=(1-\Theta)\;S_{0}(T_{\rm s})=(1-\Theta)\frac{1}{1+V\exp(-\Delta E /RT_{\rm s})} \tag{19}\]  
where \(\Delta E=E_{\rm d}-E_{\rm a}\) are the energy barriers to desorb \(E_{\rm d}\) and chemisorb \(E_{\rm a}\), \(V\) a probability constant and \(R\) the universal gas constant. The curve fit is shown in Figure 2a by the blue dotted line. We found the energy difference \(\Delta E=41.37\) kJ mol\({}^{-1}\) being in perfect agreement with [PERSON]'s value of \(\Delta E=39.4\) kJ mol\({}^{-1}\). The probability constant is, in our case, \(V=1.16\times 10^{8}\), where [PERSON] et al. report \(V=1.2\times 10^{8}\). For the absolute sticking coefficient at reference temperature an estimate can be obtained from fitting the loss coefficient \(\alpha\) to the constant temperature tube experiments. We found that \(S_{0}(T_{\rm ref})(1-\theta)\approx 0.44(9)\times 10^{-3}\) for our experimental data (see above) which deviates from the value calculated from the [PERSON] model. Although the model parameters are in good agreement, an increasing discrepancy towards the ceiling temperature between model and experiment becomes apparent. This mismatch is attributed to the insufficient accuracy of the chemisorption model for temperatures close to the ceiling temperature [10] (see also \(S_{0}(T_{\rm s})\), which falls off continuously in contrast to the observed abrupt drop).