# Chemical Vapor Deposition of Longitudinal Homogeneous Parylene Thin-Films inside Narrow Tubes
## 4 Results and Discussion
### Deposition of Homogeneous PPX-N Thin-Films Inside Narrow Tubes  
Finally, a sticking coefficient curve for the generation of a homogeneous PPX-N film thickness for our tubes with \(\alpha=8.29\) was calculated according to Equation (22). The resulting temperature reference points for the temperature control were determined from the measurements of the relative sticking coefficient. As stated in Section 3, the exact temperature profile or sticking coefficient profile within the tube is not known, and is only accessible via a heat conduction equation (here using Comsol Multiphysics). The predicted temperature curve can in turn be transformed into a real sticking coefficient profile. This is shown for three experiments with slightly varying temperatures in Figure 4 (upper row) as a blue line. Here, the center column is to be considered as a reference, whereas the left or right course exhibits slight temperature differences at certain reference points. The temperatures measured from the experiment (at just these five reference points) were also converted into a sticking coefficient and are shown as empty black diamonds in Figure 4. A slight deviation from the blue curve, especially at the last reference point at 18 cm, can be seen. In particular, there are plateaus at the beginning and end of the tube for the sticking coefficients, which are caused by the limited geometry of the experimental setup. Thus, it should be noted that it is technically demanding to map the required theoretical sticking coefficient exactly along a long tube. The resulting film thicknesses (process parameters as at constant temperature), corresponding to the applied temperature fields, are shown in Figure 4 as black lines in the  
Figure 4: Upper row relative sticking coefficient vs. penetration distance \(x\). The black dashed line is ideal sticking coefficient. The blue line is the sticking coefficient calculated from the local temperature field and temperature measurement points are black diamonds. The lower row shows the film thickness with black line measurement, the blue line shows the simulation with all contributions (Equation (18)) and the red line shows the simple form of the boundary value problem (Equation (9)). bottom row. At first glance, it appears that all three temperature curves lead to homogeneous layer thicknesses with corresponding accuracy. The relative deviation from the mean value is no more than 20 % for all three experiments, and higher film thicknesses could even be obtained at the end of the tube when compared to the inlet. If the film thickness from the center column is considered as a reference, the slight temperature variations in the other experiments and their effect on the film thickness may be discussed. If the left experiment is taken into account, where the second and third temperature is increased by 5 \({}^{\circ}\)C, a layer thickness decrease of about 20-30% is found at this point. When examining the sticking coefficient at the second reference point, which is 47.4 \({}^{\circ}\)C on the left and 42 \({}^{\circ}\)C in the center, the sticking coefficient for the higher temperature is reduced by 20-25%. The same applies to the third temperature point. A comparison with the right experiment shows the contrary trend. Here, the temperatures at the third and fourth support points are reduced by 3 \({}^{\circ}\)C. This corresponds to an increase of the sticking coefficient by 10 and 20% (third and fourth point, respectively). The layer thickness increases correspondingly by approximately 15%, with a pronounced maximum in the center of the tube. Thus, it is straightforward to demonstrate that the expected change in film thickness within the tube approximately matches the relative change in the sticking coefficient. Using the specified sticking coefficient curves, the film thicknesses along the tubes were simulated. The solutions according to Equations (18) and (19) which correspond to the consideration of all terms and the simplified form of the boundary value problem, respectively, were examined.