# Chemical Vapor Deposition of Longitudinal Homogeneous Parylene Thin-Films inside Narrow Tubes
## 4 Results and Discussion
### Thin-Film Deposition in Narrow Tubes at Constant Surface Temperature  
The temperature along the temperature seesaw and tubes was set to 30 \({}^{\circ}\)C by means of thermoelectric elements for this experiment. The layer thicknesses along the tube were measured by thin-film interferometry and are shown in Figure 2a (black empty squares). The film thickness at the inlet of the tube is \(d(0)=2.55(6)\)\(\upmu\)m, which is about the same as the film thickness on a reference slide (placed at a similar position in the reactor) and decreases by 90% to roughly 300 nm at the tubes closing end. The choice of the evaporated precursor amount of 5 g, and the associated high layer thickness at the inlet of the tube, permitted high accuracy for the measurement by means of thin-film interferometry over the entire distance (occurrence of maxima and minima from a layer thickness of 200 nm in the reflectance spectrum may be observed). The \(\alpha\) factor was determined by fitting Equations (10) and (11) to 8.29(14) and 8.26(17), corresponding to whether we took into account or neglected the deposition at the tubes end, respectively. The similarity of the fitting values for both equations is due to the high aspect ratio of \(Ar=200\), which shows that the deposition at the closing surface relative to the total deposited PPX-N volume inside the tube may be neglected. Further, at first glance the simplification of Equation (14) in the form of Equation (11) predicts the experiment in an excellent manner (see Figure 2a red line), pointing out that the complex terms in the mathematical description of PPX-N deposition in tubes may be neglected. According to Equation (9), and the definition of the loss coefficient  
\[\alpha=\frac{2}{\sqrt{\pi}}\frac{L_{t}^{2}}{R_{t}^{2}}\frac{S(T_{\text{ref}}) }{\left<G_{p}\right>} \tag{17}\]  
the absolute sticking coefficient at our reference temperature of \(T_{\text{ref}}=30\)\({}^{\circ}\)C may be obtained. An analysis of the boundary value problem of Equation (13) should also provide deeper insight into the containing terms and the possibility of reducing the complexity until the simple form of Equation (9) is reached. Since the film growth rate is directly  
Figure 2: (**a**) Measured PPX-N film thickness along the tube for the condition of constant temperature (black squares). The red line results from the fit of Equation (11), while the blue line corresponds to the numerical solution of Equation (18). (**b**) Estimated Poiseuille coefficient from the spatial film thickness trend (black squares) and its mean value (black dashed line). The blue and red lines correspond to the numerical solution of Equation (18), with the blue line excluding the term containing \(dG_{p}/dX\). (**c**) The determined relative sticking coefficient of PPX-N with respect to a surface temperature of 30 \({}^{\circ}\)C is represented by the red line. A fit of the model of [PERSON] et al. to the data is shown as the blue dashed line (see Equation (19)). For comparison the measured ceiling temperature is also shown. (**d**) Relative change in optical reflectance of a coated slide at different temperatures compared to an uncoated slide. The ceiling temperature is determined to be between the highest temperature with \(\Delta R/R\
eq 0\) and the lowest temperature with \(\Delta R/R=0\). proportional to the pressure and sticking coefficient, with the latter being constant in this experiment, the mean Poiseuille coefficient may firstly be estimated. For this, the spatial pressure trend inside the tube during the experiment was determined by multiplying the measured relative film thickness by the average monomer partial pressure at the inlet of the tube. The mean pressure at the inlet was known from the capacitance manometer measurement (see Figure 1d) and the value was calculated as \(\langle p_{\text{M}}(0)\rangle=1.65\) Pa for a process time of approximately 17 min.