Even though interactions between the influences of the single settings are expected to occur, a fractional factorial design was used to get as much information on the deposition process as possible with a minimum experimental effort. Heater temperature (

t_{H}), RF power, targeted thickness (

t_{th}) and ratio between nitrogen and argon gas flow (N

_{2}/Ar ratio) were varied in three levels each.

Table A1 in

Appendix B gives an overview of the experimental design. The

t_{H} varies between room temperature and 300 °C and the RF power between 300 and 500 W. In a preliminary experiment, the deposition rate was determined using different values of applied RF power for a short deposition time of 5 min at room temperature and pure argon gas flow. These rates were the base for the calculation of the

t_{th} in the range between 0.3 µm to 1.7 mm. The N

_{2}/Ar ratio in this study varies between 0% and 10%, whereby the argon gas flow in the chamber has a constant value of 80 sccm.

All layers on LTCC and silicon samples were analyzed with X-ray diffraction (XRD) (D5000, Siemens/Bruker, Karlsruhe, Germany) in Bragg–Bretano mode. The curves of a reference measurement of the uncoated substrates were subtracted in order to obtain only the information on the deposited film. All patterns are provided in

Figure S1 (on ceramics) and

Figure S2 (on silicon),

supplementary material. The relative texture coefficient (RTC) of the respective (

hkl) orientation was calculated from the intensity of the measured curves using Equation (1) [

31,

32]:

I_{hkl} is the intensity of the measured peak determined from the XRD patterns and

I^{0}_{h}_{kl} the theoretical intensity of the respective peak. In total, eight peaks are considered leading to a RTC value of 12.5% for a poly-crystalline material. Each crystalline orientation with a RTC higher than 12.5% can be considered as preferred orientation. The bar charts for all RTC calculations are given in

Figure S3 for ceramic and

Figure S4 for silicon in the

supplementary material. The RTC

_{(002)} values for all experiments are summarized in

Table A1,

Appendix B. They served as criterion for the DoE evaluation. Two samples have amorphous character, for those a RTC

_{(002)} value of 0.5 was set in order to perform the analysis of means (ANOM) fulfilling the valid parameter range. The analysis was carried out for each substrate type separately using the software Minitab (Minitab 18.1, Minitab GmbH, Munich, Germany). The target value in this study is a maximum RTC

_{(002)} as index for pronounced

c-axis orientation. The mean plots of RTC

_{(002)} resulting from ANOM are depicted in

Figure 1. They allow the assessment of single parameters: If a factor change leads to a strong shift of the target value, it influences the process target strongly. The ANOM allows thus a factor weighting. Further, the best settings for the factors can be derived. A low shift of the target value can be attributed to a no-significant influence of the parameter. A supporting measure, the analysis of variances (ANOVA) allows a reliable assertion that the factor has significant influence. It correlates the variances of single factor levels with the total process variance and compares the result with the fisher-distribution (

F-test). It allows thus the judgement of the factor significance on a chosen confidence level. In the present study, the analysis of variances (ANOVA) was carried out at confidence level of 99% and 99.95% to evaluate the significance of parameter influences.

The mean size of ordered domains

d, which is related to grain size, was calculated for the respective strongest orientation using Scherrer method, see Equation (2) [

33]:

In this equation, λ is the wavelength of copper radiation, β is the line broadening at half the maximum intensity, θ is the Bragg’s angle, and

K a dimensionless shape factor, which was set to 1. These calculation results are also summarized in

Table A1,

Appendix B.