# 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
The simulation of the monomer partial pressure was carried out analogously to the previous subsection. From this, the real film thickness can be calculated from the product of the local deposition rate according to Equation (1), multiplied by the corresponding process time. This is written as  
\[d_{\rm f}=\frac{\langle p_{\rm M}\rangle\tau}{\sqrt{\pi}\;\varrho_{\rm g}\; \rho_{\rm f}}\;S(X)\;P(X) \tag{24}\]  
with the density of the PPX-N layer \(\rho_{\rm f}=1.1\) g/cc [41]. The solutions of the simulation are given in the lower row of Figure 4, where the red curve belongs to the boundary value problem of Equation (9) and the blue curve includes all variable terms. The process parameters such as mean pressure \(\langle p_{\rm M}\rangle\) at the inlet of the tube and the process duration \(\tau\) are also given in the bottom row. It should be noted that initial results deviated more from the experiments, so we reduced the absolute value of the sticking coefficient by a factor of 1.75 for better comparison. Through this, the spatial response of experiment and simulation is in good agreement for all temperature gradients. Further, to better match the absolute value of the film thickness, we multiplied the pressure at the inlet of the tube by a factor of 0.7 in the simulation. As a result, the modeled absolute layer thicknesses only deviate from the experiment by a factor no larger than 1.2. It should be noted, however, that despite all approximations in the derivation of the boundary value problem, the simulations hit the same order of magnitude from the experiment without appropriate corrections. In general, we find a very good agreement between experiment and theory and distinctive points, such as the maximum layer thickness in the center of the tube of the right experiment, can be reproduced very well. Furthermore, the sloped bend at the inlet of the tube is correctly reproduced for all three experiments. We found that the origin of this is the finite size of the thermoelectric elements, and thus the sticking coefficient can only be mapped along the tube with limited accuracy. A comparison of the blue and red curves in Figure 4 also shows that the simple form of the DGL already gives good results. Especially in the first third of the tube, which is in good agreement with the analysis in the previous subsection. However, it can be seen that the full consideration of all terms leads to a better agreement between experiment and theory. In particular, it is shown that the simple form of Equation (9) somewhat overestimates the layer thickness in the second half of the tube. The relative deviations to each other, however, amount to only 5-10%, which is in good agreement with the analysis on the contributions of the individual terms in the previous subsection. Thus, it can be concluded that the detailed knowledge about the process parameters as well as the absolute sticking coefficient are rather more important than the inclusion of further correction terms in the physical modeling.