# Chemical Vapor Deposition of Longitudinal Homogeneous Parylene Thin-Films inside Narrow Tubes
## 5 Summary and Conclusions  
In this work, a formal basis for the generation of longitudinal homogeneous film thicknesses in narrow tubes, formed in a CVD process, is presented. As example, the Gorham process for the deposition of poly-para-xylylene (PPX-N) thin-films was considered. From the steady state mass flow equation in tubes, a generalized boundary value problem was derived yielding established models through corresponding approximations. Furthermore, the boundary problem was discussed for the special case of intermediately diluted gas mixtures which are required for a good conformity of the coating process. In order to achieve uniform layer thicknesses, a model that calculates the required local sticking coefficient was presented. As main result, a longitudinal homogeneous film can only be realized by partial suppression of the deposition at the beginning of the tube and vice versa. Thus, the gradient of the partial pressure of the reactant in the gas phase along the tube is less for a manipulated process than for deposition at constant temperature. This defines an upper limit on the relative film thickness of a manipulated process, which is referred to as the maximum deposition efficiency. For long aspect ratios, \(D<2/\alpha\) (with \(\alpha\) of the loss constant determined from experiments at constant temperature). An examination of the derived differential equation shows that neglecting complex terms distorts the theoretical result by only a few percent. This ensures that the applied theory can be kept as simple as possible. Furthermore, the relative sticking coefficient was accurately measured from room temperature up to the ceiling temperature where a deviation from a chemisorption model according to [PERSON] et al. was observed at temperatures just below the ceiling temperature. We report an experimentally determined value of 68 \({}^{\circ}\)C for the ceiling temperature which is in good agreement with a recently published value, but shows a larger deviation from quantities found in literature. Finally, by predicting a sticking coefficient curve, a temperature profile for our experimental setup for the so-called temperature seesaw and nearly homogeneous PPX-N film thicknesses in thin tubes of an aspect ratio of 200 were produced. The relative deviation along the entire tube in these experiments was less than 20% of the mean film thickness, with partially higher thicknesses at the end of the tube compared to the inlet. The experimental results match the modeled differential equation well. Due to the conception of this work, the given methodology is, in principle, independent of the reactant in the gas phase and can be adapted to various processes with the knowledge of a mean temperature-dependent sticking coefficient. We further expect our method to be applicable for related processes because our monomer resembles the simplest chain former with two radical functions, which are \(\mathrm{CH_{2}-CH_{2}}\), also known as ethylene. Therefore, PPX-N CVD may be seen as a prototype for polymerization, especially forced surface polymerization producing filamentous polymers.  
Conceptualization, D.R.; methodology, D.R. and M.B.; validation, D.R., M.B. and G.F.; formal analysis, D.R.; investigation, D.R. and M.B.; resources, G.F.; software D.R. and M.B.; writing--original draft preparation, D.R.; writing--review and editing, M.B. and G.F.; visualization, D.R.; supervision, G.F.; project administration, G.F.; funding acquisition, G.F. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Federal Secretary of Economy, grant number KF2527-5103 CR4.  
Not applicable.  
The data on which the figures in this paper are based are available on request from the corresponding author.  
The authors wish to thank [PERSON] for his technical assistance in fabricating the temperature seesaw.