# Effect of Substrates on the Dynamic Properties of Inkjet-Printed Ag Thin Films
## 1 Introduction  
With the interest in alternatives to traditional photolithography, inkjet printing has attracted considerable attention in various printed electronics applications such as flexible displays, electronic skins, flexible solar cells, and thin-film transistors [1; 2; 3; 4; 5; 6]. Inkjet printing has the advantages of lowering material waste, manufacturing cost, and manufacturing process steps due to the integrated circuit pattern fabrication in flexible electronics. Moreover, inkjet technologies allow printing of precise amounts of various materials with electrical, optical, and chemical functionalities [7; 8]. In addition, high precision, stability, user customization, and rapid production have encouraged the technology to expand into new applications such as patch antenna emitters, bio-sensing, biomimetic devices for providing water, and vibrational energy harvesting [9; 10; 11; 12]. Electric circuits are produced through printing and sintering processes of liquid ink droplets on a substrate. The densification and electrical performance are affected by various factors during sintering. Proper sintering conditions allow the design of printed devices for high performance. In previous studies, temperature was the major factor, which improved the quality of the film and determined the complete densification process [13; 14]. Pressure was used to reduce the temperatures required to improve the conductivities during the sintering process [15]. The thickness of the film increased in proportion to the number of overprints. It was determined that the Young's modulus and the hardness of the film are dependent on the film thickness [16; 17]. The electrical performance of thin film transistors was optimized by adjusting the thickness of the film [18]. The electrical resistivity and physical deformations of the film after sintering were also related to the substrate [19; 20]. Since mechanical properties directly affect the performance of flexible electronic products, the Young's modulus and loss factor of the thin film should be identified to make highly reliable products. The nanoindentation test was developed to measure the properties of thin films. [21; 22]. When the indenter is pressed into the specimen, the Young's modulus is obtained from the load-displacement curves. This method using an indenter causes damage to the specimen due to plastic deformations [23]. The accuracy of the measurement is not guaranteed for hard films on soft substrates [14]. Modal analysis is a common method to measure the dynamic properties of a beam. The cantilever beam is widely used for measuring due to the clear implementation of boundary conditions associated with accuracy [24; 25]. Methods based on modal properties utilize the resonance frequencies of the vibrating system. The measured resonance frequencies generally encounter assorted unwanted conditions such as noise and nonlinear responses. These aspects require complicated signal processing to accurately measure the properties of the beams. In this study, flexural wave propagation was utilized to estimate the dynamic characteristics of inkjet-printed Ag thin films. The surface morphology of the inkjet-printed Ag thin film was measured using a 3D optical profiler. Experiments were conducted with the inkjet-printed Ag thin film on varied substrates. The effects of the substrate on the dynamic properties of the film were investigated. The wave approach was presented to analyze vibrations of the thin film on the substrates. The Young's modulus and loss factor of Ag thin films with the substrates were represented by the combined bending stiffness of the bilayer beam. Vibration transfer on the bilayer beams was measured. The dynamic properties of the thin film were obtained numerically using the vibration transfer with regard to the properties of the substrates. The proposed method allows the dynamic properties of the thin film on arbitrary substrates to be determined.