The present ed work shows a load-deflection bulge test method to characterize mechanical parameters of thin films by mean s of a numerical model ling approach. A methodology based on the combination of finite element analysis and classical analytical equations is presented and discussed. F inite element model ing was conducted for monolayer (Si 3N4) and bi-layer ( Si3N4/Al) membranes with the aim to determine a set of elastic parameters (Young ’s modulus and Poisson ’s ratio) which satisf ied the load-deflection curves experimentally measured by the bulge test method . It is well known that in a traditional bulge test analysis only biaxial elastic modulus, i.e. combination of Young’s modulus and Poisson’s ratio, can be determined . It is due to the mechanical coupling that exists between the two elastic parameters . However, in this study both mentioned elastic constants can be determined independently through a proposed numerical procedure that includes error functions for minimizing the displacement with a specific set of optimal elastic parameters . Resu lts shows that t he estimated Young’s modulus (Al 64 GPa and Si 3N4 236 GPa) agree with corresponding values determined by other methods in the literature of the studied thin films . Keywords: Bulge test, thin film, finite element analysis, elastic properties 1. Introduction Thin film manufacturing requires precise instrumentation to achieve the geometric and mechanical conditions necessary for each industrial application in which are microelectronics, nano -devices, coating applications, biomedical devices among others [1]. However , the evaluation of mechanical properties is important to predict the mechanical behaviour of thin films since these are subjected repeatedly to deformations by bending, folding, rolling, twisting, stretching , thermal cycling or compression . Therefore , to identify these properties with traditional material testing, it seems as a difficult task. Several experimental techniques have been developed to overcome challenges in the identification process of the properties ; in which we can mention nano indentation, diffraction -based techniques, Raman spectroscopy, deflection techniques among others [2-3]. The relative advantages and limitations of all the mentioned techniques have been discussed in the literature [3], which prefers the bulge test (deflection technique) because is easy to implement it. The bulge test consists in applying gas pressure on a free standing thin film and measuring the deflection over the bulged region [4-5]. This relation is called l oad-deflection curve and it is analy sed by means of different methods that permits to determine the elastic parameters from the experimental data. For example , the fitting of analytical equations and finite element analysis [6-10] are the most used . This paper shows that elastic parameters (Young’s modulus and Poisson’s ratio) of a bi -layer Si3N4/Al film can be determined by combining finite element analysis with the classical method to identif y properties . 2. Methods 2.1 Experimental setup for bulge tests in thin films A bulge testing apparatus was constructed in-house with an adequate instrumentation and uses interferometric techniques to evaluate bi -layer (Si 3N4/Al) membranes as shown in the scheme of Figure 1 . Two important variables are measured in the bulge test, pressure and membrane deflection. The principle of the test is to app ly a differential pressure on a free -standing membrane and to measure the membrane shape in form of displacement field for each pressure increment. The differential pressure is applied using an industrial grade piston that presses the air by computer -controlled syringe pump. Pressure is measured by the pressure transmitter (A) with maximal error of 60 Pa which is connected to a data acquisition system. The shape of the membrane is measured using an interferometric system (Twyman -Green interfer ometer) in which the light source is a fiber -coupled HeNe laser with wave -length of 633 nm. The beam is split into a measuring beam that reflects off the measured sample and a reference beam that reflects off a reference mirror with high surface flatness o f λ/10. The interferometric system uses a Nikon 50mm f/1.4 NIKKOR G lens to image the sample onto a camera that captures the interferograms that are used to determine the displacement field of the bulged film at the z position . In Figure 1a experimental setup is shown , and in Figure 1b, the interferometric system is illustrated with a reconstructed shape of a tested membrane Figure 1 c. A complete description of the exposed bulge test apparatus is described in details in [9], basic working principles of bulge test can be found also in [2,4,6 -7]. Figure 1 . a) Experimental setup. b) Scheme of the experimental test. c) Reconstructed bulged bi -layer film of 22 2 mm 2.2 Numerical strategy for determination of elastic parameters of bi-layer thin films In this study, a numerical procedure is performed to determine Young’s modulus and Poisson’s ratio of bi-layer thin films combining finite element analysis with the following classical analytical solution [7] 3 00 12 24( ) ,rtw EtwP C C vaa=+ (1) Figure 2. a) Segmente d finite element model for bi-layer membrane s (Si3N4/Al). b) Application of residual stress and load pressure in the finite element model. where 1C and 2()Cv are constants that depend on geometric and material parameters, r is the residual stress , t is the thi ckness , E is Young’s modulus and v is Poisson’s ratio. Equation 1 was initially proposed for monolayer membranes subjected to bulge test , but it can be extended to more than one layer [11-12]. A combination of numerical solutions and experimental data permit s the determination of all elasti c properties of bi-layer films in this study . In this process, w e can highlight that finite element analysis is a powerful tool to simulate bulge test ing technique with the aim to estimate the properties of thin films as demonstrated in different studies [2-7]. There are several challenges in the estimations of elastic properties until nowadays, as for example elastic coupling between Poisson’s ratio and Young’ s modulus as it was evidenced by [10]. We propose estimat ion of the elastic properties in two stages; first stage , applying the procedure proposed by [10] in a monolaye r. In a second stage , to determine the elastic properties of the studied membrane (knowing properties of the support membrane) by an iterat ive process with finite element analysis in bi-layer membranes . For modelling of mono -layer and bilayer membranes by means of finite element analysis , a segmented geometry is considered to approximate re al conditions in the simulation . The geometry is define d by the membrane f (real domain corresponding to experiments ) and a virtual boundary  (numerical boundary). f is composed by two layer s which in our study are Si3N4 and Aluminium . With only the imposition of the residual stress r on ( 3 4)f Si N is possible estimate the residual stress of the Aluminium by bending conditions with a proposed numerical strategy . Figure 2 show s the geometrical considerations for the finite element model and the application of the residual stre sses, also details of this type of modelling can be reviewed in [10]. In this study, finite element solutions were obtained with ANSYS 16.1 on an ASUS ROG Strix GL553VE (Intel Core (TM) i7 -7700HQ CPU @ 2.8 GHz, 16 GB RAM) notebook which was ran in Windows 10 environment in order to verify the proposed numerical procedures. 3. Results Experimental bulge tests on Si 3N4 (monolayer) and Si 3N4/Al (bi -layer) of 2 2 mm (square) with thicknesses of 500 nm (Si3N4) and 1760 nm (Al) were carried out to be used as fitting database in the proposed method ology . These were tested with the experimental setup shown in Section 2.1 . In Figure 3 , the results (elastic properties) obtained for Si 3N4 ( 236.22 2 , 0.264E GPa  =  = ) and Aluminum ( 64 2 , 0.3E GPa  =  = ) are shown . The comparison between load- deflection curves ( experimental and numerical ) is shown in Figure 3 . It is seen that both results are wel l correlated since it agree s with finite element solutions . We can point out that the values determined for the elastic properties correspond to typical values reported in the literature for Si3N4 [7, 10,13] and Aluminum [14-15]. Figure 3. Comparison of pressure and maximum deflection curve 4. Conclusions A numerical approach to determine elastic properties of bi-layer (Si3N4/Al) thin films was applied in this study. The analysis was based on bulge test (experimental technique) , classical analytical method and finite element analysis , respectively . The main contribution is focused on the determination of both elastic properties (Young’s modulus and Poisson’s ratio ) for bi-layer films since in a tradition al bulge test analysis only a combination of these parameters can be determined. Results showed that the calculated elastic properties of both films agree with corresponding values reported in the literature. Acknowledgement This research has been supported by the Ministry of Education, Youth and Sports of the Czech Republic under the project m -IPMinfra (CZ.02.1.01/0.0/0.0/16_013/0001823) and Results were obtained during use equipments from the Large Infrastructures for Research, Experimental Develo pment and Innovation - project IPMinfra, LM2015069. The research infrastructure was funded by Ministry of Education, Youth and Sports of the Czech Republic and European Commission (project CZ.1.05/2.1.00/01.0017) and by the Czech Academy of Sciences (proje ct RVO:68081731).