The effect of grain and pore sizes on the mechanical behavior of thin Al films deposited under different conditions

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ScienceDirect Acta Materialia 87 (2015) 321–331 www.elsevier.com/locate/actamat

The effect of grain and pore sizes on the mechanical behavior of thin Al films deposited under different conditions ⇑ E. Ben-David,a, M. Landa,b M. Janovska´,b H. Seiner,b O. Gutman,a T. Tepper-Faranc and D. Shiloa a

Department of Mechanical Engineering, Technion-Israel Institute of Technology, 32000 Haifa, Israel Institute of Thermomechanics, Academy of Sciences of Czech Republic, Dolejsˇkova 5, 18200 Prague, Czech Republic c Microsystems Department, R&D and Technology Center, MANOR A.D.T Div., Rafael Advanced Defense Systems, Israel b

Received 10 November 2014; revised 28 December 2014; accepted 29 December 2014

Abstract—This paper presents a comprehensive study of the relationships between deposition conditions, microstructure and mechanical behavior in thin aluminum films commonly used in micro and nano-devices. A particular focus is placed on the effect of porosity, which is present in all thin films deposited by evaporation or sputtering techniques. The influences of the deposition temperature on the grain size, pore size and crystallographic texture were characterized by X-ray diffraction and scanning electron microscopy. The mechanical behavior of the films was investigated using four different methods. Each method is suitable for characterizing different properties and for testing the material at different length scales. Nanoindentation was used to study hardness at the level of individual grains; resonant ultrasound spectroscopy was used to measure the elastic moduli and porosity; and bulge and tensile tests were used to study released films under biaxial and uniaxial tensions. Our results demonstrate that even low porosities may have tremendous effects on the mechanical properties and that different methods allow the capture of different aspects of these effects. Therefore, a combination of several methods is required to obtain a comprehensive understanding of the mechanical behavior of a film. It is also shown that porosity with different pore size leads to very different effects on the mechanical behavior. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Thin films; Mechanical properties; Tensile tests; Bulge tests; Porosity

1. Introduction Thin metallic films are commonly employed in Micro/ Nano Electro Mechanical Systems (MEMS/NEMS) [1] and are frequently subjected to various mechanical constraints, which may result in plasticity, wear, creep or fatigue [2,3]. Thus, the design of more reliable and sophisticated thin-film-based devices relies on the ability to characterize and adjust the mechanical properties of thin films. A characteristic trait of thin films is that specimen dimensions become comparable with the characteristic length scales that govern the mechanical behavior. Therefore, specimens at the micrometer and submicrometer scales often exhibit a mechanical behavior that may be different from the mechanical behavior of bulk specimens; this phenomenon is often referred to as the “size effect”. Another important characteristic trait of thin films is that their mechanical properties are strongly dependent on the microstructure, which, in turn, is determined by deposition conditions and further by fabrication processes [4,5]. For example, Espinosa et al. [6] reported significant brittleness and hardness in Au films with thicknesses below 0.5 lm; however, this was not been observed by Emery and

⇑ Corresponding author; e-mail: [email protected]

Povirk [7], who studied Au films in the same range of thicknesses and used the same deposition method, but with different substrates and fabrication processes. In pure elemental metallic films, as are commonly used in MEMS and NEMS applications, there are two microstructural characteristics that strongly affect the mechanical properties, i.e. the grain size and porosity. Grain size has a well-known effect on the yield stress and ductility through the Hall–Petch effect [8]. The effect of porosity has been extensively studied in materials produced from powders (e.g. ceramic materials produced by sintering) [9,10] and glasses [11,12]. However, this effect has rarely been studied and is often overlooked in cases of thin metallic films. Previous studies have focused on the porosity [13] and pore size [14] in thin metallic films, but have not considered the influence of porosity on the mechanical properties of the films. In fact, pores are formed in almost all deposition techniques of thin metallic films, and in particular in evaporation and sputtering, which involve phase transformations from vapor to solid [15]. These pores can be extremely small (down to approximately 1 nm) and high in density (approximately 1  1017 cm3) [15–17], which makes them difficult to observe using conventional microscopy. It is generally argued that porosity results in a decrease in both strength and ductility, and is therefore considered to be

http://dx.doi.org/10.1016/j.actamat.2014.12.041 1359-6462/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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undesirable. More specifically, the porosity can affect the mechanical behavior of metallic materials in two different ways. First, pores induce local stress concentrations, which may lead to the initiation of cracks [18,19]. Second, an inhomogeneous distribution of pores results in the development of paths with high pore content, which are high-probability regions for flow localization and fracture [20,21]. It is expected that the first effect will be more prominent in cases of large pores separated by long distances, while the second effect will be more prominent in cases of small pores separated by short distances. Thus, both the overall porosity and the pore size play important roles. In addition to these two effects, elemental gases located within the pores, such as oxygen and hydrogen, may induce local corrosion, which would affect the mechanical properties [22]. Grain size, pore size and overall porosity are strongly influenced by the deposition rate and temperature. Fast deposition rates and low temperatures (i.e. small diffusion lengths) result in small grains and high porosities, whereas slow deposition rates and high temperatures result in larger grains and lower porosities. Due to geometrical considerations, it is expected that the pore size will be comparable to the grain size. Thus, a deposition at a high temperature may result in a lower porosity but larger pore sizes, which may not necessarily be advantageous. The deposition temperature also has a strong influence on the film’s residual stress [23]. Another factor that influences the porosity is the crystallographic orientation of the deposited film [24]. In face-centered cubic (fcc) metals, the most densely packed planes are the (1 1 1) planes, followed by the (1 0 0) planes and then the (1 1 0) planes. Therefore, for a given atom flux, grains oriented with the (1 1 1) face parallel to the surface grow more slowly than grains oriented along the (1 0 0) or (1 1 0) faces. A film with a strongly preferred (1 1 1) orientation is expected to have a lower porosity than a film with a strongly preferred (1 0 0) or (1 1 0) orientation. However, films without preferred orientations are expected to have grains which grow at different rates, which may increase the porosity. There are numerous experimental methods for studying the mechanical behavior and properties of thin films. These methods can be classified and considered according to several different variables. One variable is the size of the probed volume; another, more important variable is the number of grains within the probed volume. Modulus mapping [25] allows the mapping of elastic properties at nanoscale resolutions, but only in a very thin region close to the surface. In nanoindentation [26], the probed volume is usually between tens and hundreds of nanometers in each direction, lengths which span a single or a few grains. When testing films with low porosities, this probed volume may contain just one pore or even no pores. All other techniques typically probe a large number of grains; local effects are thus minimized and the measurement can be considered a representative average of the material. Another variable, which is important for the analysis of mechanical measurements, is the uniformity of the stress and strain fields. In tensile tests of dog-bone-shaped samples, the stresses and strains are approximately uniform and uniaxial. Thus, stress–strain curves can be plotted, and the mechanical behavior over entire elastic and plastic regimes can be directly observed. In other methods, such as nanoindentation, microbeam bending [27] and bulge testing [28,29], the stress and strain fields are multiaxial and

non-uniform. As a result, the overall measured behavior represents integrations over regions which experience different stresses and respond in different (elastic or plastic) manners. In the purely elastic regime, these measurements can be analyzed by assuming a linear Hooke’s law. However, as soon as the region yields and exhibits plasticity, the analysis becomes very complicated, especially in cases where the material response in the plastic regime is unknown. When considering the effect of porosity, different loading conditions (e.g. uniaxial vs. multiaxial) result in different pore stress concentration factors and different effects. Another important variable is the appropriateness of the mechanical testing method for measuring specific properties. For example, nanoindentation is based on semi-phenomenological analysis rules [26], which provide rough evaluations of the Young’s modulus and hardness. Tensile tests are suitable for measuring properties related to plasticity (e.g. the yield and ultimate stress values and the strain at failure) but have inherent difficulties in measuring the Young’s modulus [30]. In particular, in test methods where the strain is determined by measuring the overall sample elongation, even a small compliance in the sample grippers or a minor slip of the sample with respect to the grippers may result in a significant underestimation of the Young’s modulus. Methods based on resonant ultrasound spectroscopy (RUS) [31–33] and surface acoustic waves [34] are specifically designed for measuring the elastic properties of thin films. In these methods, the strain amplitude is on the order of 106 (for a comparison, the strain amplitude in nanoindentation is approximately 101) and the measurement is not affected by rigid body motions. As a result, only elastic strains are measured. The methods provide better accuracy than other mechanical testing methods. The above discussion indicates that there is no one mechanical testing method which is advantageous over all other methods. Instead, a combination of several methods must be applied to study different mechanical properties under different length scales. This statement is especially relevant when considering a comprehensive study of the effect of porosity. In this paper, we present a comprehensive study of the influence of deposition conditions on the microstructure and mechanical properties of thin aluminum films. In Section 3, we characterize the grain size, pore size and crystallographic texture of films that have been deposited under different temperatures. In Section 4, we characterize the mechanical behavior of the films using four different methods, which characterize different properties at different length scales. Specifically, nanoindentation is used to study the hardness at the level of individual grains, RUS is used to measure the elastic moduli and estimating the amount of porosity, bulge tests are used to study released films under biaxial tension and tensile tests are used to study released films under uniaxial tension. As will be shown, porosity has various effects on the mechanical behavior and different methods are required for capturing different aspects of these effects. 2. Materials and methods This study used thin aluminum film samples, which were e-beam evaporated from 99.999% pure aluminum pellets onto 4” silicon (1 0 0) substrates. The silicon substrates consisted of previously deposited external layers of 400 nm

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low-stress low-pressure chemical vapor deposited silicon nitride. Prior to deposition, the silicon substrates were cleaned using SC1 solution (a mixture of NH4OH, H2O2 and deionized water, with a volume ratio of 1:1:7). The base pressure prior to deposition was at most 4  106 torr. In all samples the deposition rate was intentionally maintained ˚ s1), to achieve films with a relatively at a low value (2–3 A small amount of porosity. The substrates were loaded onto a planetarium to achieve good layer uniformity across the wafers. Two main deposition conditions were investigated: (i) not heating the sample stage and (ii) heating the sample stage to 200 °C during the deposition, then allowing the wafer to cool down slowly (over approximately 12 h) in a vacuum. In the case of deposition without heating, the wafer temperature was expected to be lower than 40 °C; we defined this condition as room temperature (RT) deposition. Note that 200 °C is related to a 0.5 homologous temperature for aluminum. At this temperature, rapid diffusion and grain growth are observed. We characterized the microstructures of the samples that were deposited under two other conditions (see Section 3). A deposition at 150 °C resulted in a microstructure similar to that of a deposition at 200 °C, but with slightly smaller grain and pore sizes. A deposition at RT, followed by heating the wafer to 200 °C for 80 min in situ inside the deposition chamber, resulted in a microstructure similar to that of the samples deposited at RT but without the subsequent heat treatment. This behavior was probably a result of the presence of a small amount of oxygen atoms, which likely settled in grain boundaries and prevented grain growth [35]. We performed such mechanical characterizations only on samples that were deposited at RT and 200 °C because the other deposition conditions did not result in significantly different microstructures (we discuss this issue in Section 3 in light of the experimental results). After the lithographic patterning and the wet etching of the resultant layers, the film thicknesses were measured. The thickness was measured at five points across each wafer, using a Dektak mechanical profiler. The average aluminum layer thickness was found to be 1.22 ± 0.03 lm for all substrates. The internal stress of each film when attached to the substrate was evaluated based on the Stoney method [36]. The radius of curvature of the entire wafer was measured by a mechanical profiler. The elastic properties of the 250 lm thick Si substrate were taken from Ref. [37]. The effect of the 0.4 lm thick silicon nitride layer was neglected due to its small thickness compared to the silicon substrate. The evaluated internal stress was 34 MPa (compression) in the RT-deposited films and 90 MPa (tension) in the 200 °C-deposited films. It has been shown that internal stress calculations based on the Stoney’s equation may provide an error of up to a few tens of percentages of the real value [38,39]. This level of accuracy was deemed adequate for our investigation because the measured values of the internal stress were considered to be small and were not expected to have an effect on the evolution of the microstructures or the measured mechanical properties. Emphasis was then placed on the bulge and tensile tests for the released films, starting from approximately zero stress and strain. Phase contents and textures (i.e. preferred crystallographic orientations) were characterized by a Rikagu SmartLab X-ray diffractometer. The main purpose of this test was to examine the influence of the deposition temperature

323

on the texture. As mentioned earlier, the film crystalline orientation significantly influenced the rate of pore closure during deposition and therefore influenced the amount of porosity in the film. In-plane grain and pore sizes (along directions parallel to the surface) were evaluated based on scanning electron microscopy (SEM) images. SEM images were taken with an FEI Quanta 200 microscope under an accelerating voltage of 30 kV in secondary electrons mode. Four different mechanical characterization methods (nanoindentation, resonant ultrasound spectroscopy, bulge and tensile tests) were employed. Each of these methods is suitable for characterizing different properties and for testing the material at different length scales. Nanoindentation (with a Hysitron triboindenter) was used to determine the local hardness (H). Measurements were conducted by penetrating the film with a Berkovich tip indenter up to depths of 100–120 nm, i.e. slightly less than 10% of the film’s thickness, to avoid any influences from the substrate [40]. At these penetration depths, the indent lateral size was approximately 300 nm. Before each indentation test, a topography scan was applied to map the local surface area and observe the local grain arrangement. For samples deposited at 200 °C, the average grain size was much larger than the indent lateral size. Therefore, the indents were performed in the center of individual grains. Samples deposited at RT had an average grain size slightly smaller than the indent lateral size. Therefore, each indentation test covered a few grains, and was more affected by grain boundaries and the local porosity. In all measurements, a trapezoidal load function was applied in which the load was linearly increased to its maximal value over 10 s, then held constant for 10 s and finally linearly decreased over 10 s. The drift rate was less than 0.1 nm s1. For each film, 10 measurements were performed in different areas of the film. The experimental determination of porosity is a complicated task, especially for thin films with low porosity, where methods such as porosimetry and mass measurements cannot be applied. In this study, we evaluated the amount of porosity based on accurate measurements of the Young’s modulus. For this purpose, we used the RUS method, in which the Young’s modulus was determined based on the measurement of the resonant spectra of free elastic vibrations. The RUS samples were 3  4 mm2 rectangles cut from two types of wafers. The fully non-contacted experimental modification of RUS was employed, with the ultrasonic vibrations of the sample both generated and detected by lasers [41,42]. The elastic properties of both the RT and 200 °C-deposited films were determined by the RUS method. First, the resonant spectrum of the substrate with a deposited film was measured. Subsequently, the aluminum film was removed by wet etching, using a Transene type A aluminum etchant (composed of nitric, acetic and phosphorous acids), and the resonant spectrum of the substrate alone without the film was measured. Our previous experience with this etchant proved that it is capable of completely removing the aluminum film without causing any observable (by SEM) damage to the silicon nitride film. The elastic constants of the deposited film were determined from the resonant frequency shifts corresponding to the presence of the film. Approximately 20 resonant frequencies between 400 kHz and 2 MHz were involved in the calculation. The shifts of the resonant frequencies were dependent on the elastic modulus and the density of the

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layer. This relation was dependent on the modal shapes of the involved vibrational modes. As shown by Ru˚zek et al. [32] for a layer of thickness that is much smaller than the thickness of the substrate, the shifts were approximately linearly dependent on both the Young’s modulus and the density. If the layer consisted of an isotropic material (i.e. characterized by two independent elastic constants – the Young’s modulus E and the bulk modulus K) – this linear dependence would be written as where A, B and C are constants specific to the individual modes. If, however, the substrate was a thin plate, all modes from the lowest part of the resonant spectrum would purely be bending modes (these modes are the easiest to generate and detect with the RUS laser setting). This would result in two fundamental consequences: the resulting shifts would be completely independent of the bulk modulus K, i.e. A  B, and the constants A and C would be nearly identical for all modes. As a result, the Young’s modulus E and the density q were not independently determined from the RUS measurements. The relation between E and q was obtained with a high accuracy. If the thickness of the layer was non-negligible (as for the case of a 1.22 lm thick layer on a 250 lm substrate, as examined in this study), then relation (1) would be approximately valid. However, even in this case, it would be impossible to determine the values of E and q individually, though the relation E = E(q) was accurately predicted. Thus, the results from RUS for all examined samples were obtained in the form of the relation E = E(q). For further analysis of this result, E and q were assumed to depend on the porosity p. As a function of porosity, the density is expressed by

agreement between the pore shapes considered in the models and the actual pore shapes, and is hard to estimate. The overall (macroscale) mechanical behavior of released films was measured by both bulge and tensile tests. The bulge test is a known method for the measurement of mechanical properties of thin films. It benefits from several advantages, such as the measurement of a free-standing film, a relatively simple fabrication process and a relatively simple experimental setup. Bulge test samples were produced by fabricating microdevices consisting of four free-standing aluminum membranes having circular shapes with diameters of 750, 1000, 1300 and 1700 lm, as shown in Fig. 1(a). The microdevices were fabricated from silicon wafers with two types of aluminum film, as mentioned earlier. The membranes were released by a deep reactive ion etching of the silicon under the thin films and a reactive ion etching of the silicon nitride layer under the membranes. The membrane microdevices were attached by epoxy glue to an aluminum vessel (Fig. 1(b)) that was gradually evacuated, in discrete intervals, to a gauge pressure of 0.85 bars. While the vacuum was being applied, the corresponding membrane deflection correlated with the applied gauge pressure. The deflection and curvature of the membranes were measured simultaneously for all four membranes using a Veeco Wyko NT9300 optical profiler system with an accuracy of 0.5 lm (Fig. 1(c)). In previous studies [44,45], the bulge tests of circular membranes were analyzed by considering the membranes as sections of a spherical thin-walled pressure vessel. The tangential and circumferential stretching strains and stresses were equal and uniform. Based on the geometry and the free body diagram, the tangential stress r and strain e can be expressed as

q ¼ q0 ð1  pÞ

r¼

Df ¼ ðAE þ BK  CqÞ=f

ð1Þ

ð2Þ 3

where q0 = 2700 kg m is the density of non-porous aluminum. The dependence of E on p was more complicated than relation (2) and was dependent on geometrical parameters, such as the pore shape. A common expression for this dependence is given by [43]  n p E ¼ E0 1  ð3Þ pc where the values of n and pc depend on the shapes of the pores. Usually, pc < 1, which reflects the fact that above the critical value of p = pc there is a continuity of the pores and hence E = 0. Ref. [43] provides evaluations of n and pc for three models, each of which represents a different type of porous microstructure. Among these, two models are relevant for porosity which is formed during film deposition (the other model is relevant only for sintering processes): the model using spherical pores with n = 1.65 and pc = 0.818 and the one using ellipsoidal pores with n = 2.25 and pc = 0.798. Utilizing these theoretical models, the RUS results were analyzed in the following way: by combining the relation of Eq. (2) with the experimental data, an experimental relation E = E(p) was obtained. Consequently, by finding the intersection points of the experimental curves E = E(p) with the model predictions given by Eq. (3), the corresponding values of E were found for each pore morphology type model. The accuracy of this procedure depends on the level of

PR 2t

ð4Þ

and Rh  a ð5Þ a where P is the gauge pressure, R is the bulge radius of the curvature, t is the film thickness, a is the bore radius and h is the tangential angle formed by the bulged membrane. In most cases, the bulging height (h) is measured rather than R and h, which can be calculated based by the following geometrical relations: e¼

R¼

a2 þ h2 2h

and h ¼ 2arctan

ð6Þ   h a

ð7Þ

The substitution of Eqs. (6) and (7) into Eqs. (4) and (5), together with the small strain approximation, i.e. ha  1, provides r¼

Pa2 4th

ð8Þ

2 h2 3 a2

ð9Þ

and e¼

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325

Fig. 1. (a) A silicon microdevice with an array of aluminum deposited membranes (view from the bottom of the device). (b) The microdevice attached with epoxy glue to the top surface of the vessel. (c) A measurement of membrane deflection by optical profiler.

However, the basic assumptions on which this solution was based were not valid. In fact, the tangential and circumferential stretching strains (and stresses) were neither equal nor uniform [46,47]. In particular, the tangential strains remained nearly constant, but the circumferential strains were forced to zero at the boundaries of the membrane and rapidly increased toward the center of the membrane. Tsakalakos [46] developed a numerical solution that did not assume a membrane shape. This solution was found to be in excellent agreement with finite element calculations. According to the Tsakalakos solution, the stresses were at a maximum at the center of the membrane and gradually decreased toward the perimeter. Surprisingly, Tsakalakos found that the tangential and circumferential stretching strains and stresses were equal at the center of the membrane, and approximately follow Eqs. (8) and (9). The Tsakalakos solution was not suitable for analyzing bulge tests for two reasons. First, the solution assumed a linear elastic behavior without any plasticity. Second, the solution assumed that initially, when P = 0, the membrane was fully flat. This condition was rarely met due to the presence of mismatch strains between the film and the substrate. After the substrate under the film had been etched, the film membrane returned to a zero strain by changing its shape. Because the perimeter of the membrane remained fixed due to the surrounding substrate, the membrane deflected and formed an initial bulging h0. Because the mismatch strains were comparable to the strains applied in the test, h0 is comparable to h, so cannot be ignored. Eqs. (8) and (9) can be corrected to account for the plasticity and initial bulging. Eq. (8) remained unchanged, whereas Eq. (9) was changed to 2 h2  h20 ð10Þ 3 a2 to account for the initial bulging. Thus, Eqs. (8) and (10) can be used to analyze bulge tests, provided that these stress and strain values are good approximations only for the center of the membrane. Far from the center, both the tangential and circumferential stresses decreased, and therefore the yield was expected to first occur at the center of the membrane. Under a zero gauge pressure, the deflected shape of the membrane was not well predicted, and did not follow the shape predicted by the Tsakalakos solution or by the solution that assumed a spherical shape. To overcome this problem, the initial bulging h0 was measured under a small gauge pressure at which it was assumed that Eqs. (8) and (10) were already followed. The value of the minimally required gauge pressure that assures these conditions was unknown and resulted in measurement uncertainties. e¼

Uniaxial tensile tests were conducted using a self-made experimental setup, which was introduced in detail in our previous studies [30,48,49]. Samples for these tests had a dog-bone shape, with a length of 98 lm and a width of 23.7 lm for the RT specimen and a length of 126 lm and a width of 23.6 lm for the 200 °C specimen. The samples were produced as a part of a microdevice (Fig. 2), which includes S-shaped springs to protect the sample and an encoder grating for measuring the direct displacement of the sample.

3. Microstructure characterization SEM images taken from all four sample types were used to characterize the grain and pore sizes. Clear differences were observed between samples deposited at RT (Fig. 3(a)) and at 200 °C (Fig. 3(c)). The analyses of the SEM images showed that the average grain size of the RT-deposited films was 0.18 ± 0.02 lm, while that of the 200 °C-deposited films was 0.7 ± 0.2 lm, which is nearly fourfold larger. The samples deposited at 200 °C exhibited relatively large pore sizes, with similar values to the average grain size. Pores were not readily observed in the samples deposited at RT, but it has previously been shown [15] that samples with small grains also exhibit small pores that are undetectable by SEM. Samples deposited at 150 °C (Fig. 3(b)) exhibited microstructures similar to those of samples deposited at 200 °C, with slightly smaller average grain (0.6 ± 0.2 lm) and pore sizes. Samples deposited at RT and subsequently annealed in situ at 200 °C for 80 min (Fig. 3(d)) exhibited a microstructure similar to that of samples deposited at RT without annealing. The absence of grains or pore growth was likely due to the presence of oxygen, which is known to settle in grain boundaries and prevent their migration [35]. This study focused on the differences between samples deposited at RT and at 200 °C, which showed maximum variances in their microstructures. As observed in Fig. 3, the other deposition conditions did not result in significantly different microstructures. X-ray diffraction (XRD) profiles taken from both the RT- and 200 °C-deposited films are presented in Fig. 4. The measured data were compared with the Joint Committee on Powder Diffraction Standards (JCPDS) cards and are presented in Table 1. JCPDS data were taken from a powder which has uniform distribution of crystallographic orientations. Therefore, comparison of the relative intensities measured in our samples with respect to the JCPDS data provides information about the preferred crystallographic orientations. It was observed that the ratio between

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Fig. 2. A top view of the microdevice (dimensions 13.8  8.5 mm2): (1) the thin film, (2) encoder grating, (3) S-shaped silicon springs, and holes for the (4) static and (5) moving grippers, respectively.

Fig. 3. SEM images of (a) RT-deposited aluminum film, (b) 150 °C-deposited aluminum film (pores are indicated by arrows), (c) 200 °C-deposited aluminum film (pores are indicated by arrows) and (d) RT-deposited aluminum film that was annealed at 200 °C for 80 min.

the intensities of the (2 0 0) and (2 2 0) reflections was approximately 2:1 in both samples and in the JCPDS data. The ratio between the intensities of the (1 1 1) and (2 0 0) reflections was 2.1 in the JCPDS data, 2.7 in the sample deposited at RT and 1.5 in the sample deposited at 200 °C. Thus, the (1 1 1) orientation was slightly favored in samples deposited at RT and was slightly disfavored in samples deposited at 200 °C. In both samples, the preferred orientation was minor; therefore, the bulk value of E0 can be assumed from the analysis of the RUS measurements (see Eq. (3)). As mentioned in the introduction, films with a (1 1 1)-preferred orientation were expected to have lower level of porosity than films with other crystallographic orientations. However, a higher temperature was also expected to reduce the porosity. Thus, it is not possible to ascertain which deposition condition resulted in the greater porosity from the XRD data alone.

4. Mechanical characterization The average values of the measured hardness for each type of film deposition are presented in Table 2. As mentioned earlier, the nanoindentation tests probed individual grains of the 200 °C-deposited samples and a few grains of the RT-deposited samples. Thus, it was expected that the probed volumes did not contain pores. As shown, the hardness of the RT-deposited films was greater than that of the 200 °C-deposited films, by about 60%. This indicates that, at the nanoscale level and due to a minor porosity effect, the 200 °C-deposited samples yielded at a lower stress and were more ductile than the RT-deposited samples. Such a behavior was expected and can be explained due to the Hall–Petch effect on the grain size. RUS measurements were performed on two samples from each deposition temperature. This method provided

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327

Fig. 4. XRD patterns of the aluminum films. RT-deposited film is presented in blue; 200 °C-deposited film is presented as red dashes. Taken from JCPDS cards, relevant information, including the crystalline orientation, the predicted angle and the predicted relative intensity, is presented above each peak. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1. Comparison of XRD relative intensities results for aluminum thin films deposited at RT and 200 °C. 2h (degrees)

hkl

JCPDS intensity

Intensity at RT

Intensity at 200 °C

38.47 44.74 65.13 78.23 82.44

111 200 220 311 222

100 47 22 24 7

100 37.1 17.7 15.3 7.3

100 65.1 37.2 21.3 8.5

Table 2. Averaged nanoindentation results for 10 measurements in different locations over both types of film. Film deposition temperature

H average value (GPa)

RT 200 °C

1.28 ± 0.18 0.79 ± 0.14

a measurement of E = E(p), as discussed in Section 2. Based on the values of q0 = 2700 kg m3 and E0 = 70.6 GPa [50], we calculated the model predictions of E = E(p) using Eq. (3). The aforementioned value for E0 was measured in non-textured, non-porous bulk aluminum. As discussed in Section 3, our samples exhibited a small amount of the preferred orientation. Therefore, the use of this value of E0 was reasonable. Fig. 5 shows the intersections of the theoretical and experimental E(p) curves. For each given material, these intersections provide estimates of the porosity and Young’s modulus of the given pore geometry. The experimental E = E(p) dependencies were nearly linear, indicating the validity of the linearized relation of Eq. (1). This method for the evaluation of p depends on the level of agreement between the pore shapes considered in the models and the actual pore shapes, which are hard to evaluate. Nevertheless, several important conclusions were obtained based on Fig. 5. First, there was a clear difference between the RT- and 200 °C-deposited samples. Second, although pores were not detected in the SEM images of the RT-deposited samples, evidence of porosity was shown in these samples (5%, assuming ellipsoidal pores, or 14.9%, assuming spherical pores) at amounts that were likely lar-

Fig. 5. Experimental E(p) curves (solid lines) obtained by the RUS method and their intersections with theoretical E(p) dependencies for various pore shapes (dashed lines). The open symbols denote the intersection points (the corresponding values are listed in the upper right corner). The shaded areas denote the scatter intervals for experimental E(p) curves for samples taken from different locations on the wafer; the solid lines are the averaged values.

ger than those of the 200 °C-deposited samples. Third, for the 200 °C-deposited samples, the evaluated E values are in the narrow range of 64–66 GPa. For the RT samples, assuming ellipsoidal porosity, the Young’s modulus was as low as 50 GPa. Fourth, while the RUS samples taken from different locations on the wafer of 200 °C-deposited samples gave similar E(p) curves, there was significant heterogeneity observed for the RT-deposited samples. Our thin films were deposited by an evaporation technique that is known to provide for relatively high porosities. Other deposition techniques, such as radio frequency sputtering, are considered to provide lower porosities [51]. Measurements of the Young’s modulus in thin released films, based on methods like the tensile and bulge tests, often provide values at approximately half the bulk property [52,53]. Our results indicate that these measurements have significant errors due to the assumed and unrealistic porosity values of approximately 25%. Fig. 6 presents the typical stress vs. strain curves measured by the bulge test. Because a vacuum was applied, the maximum gauge pressure achieved was 0.85 bars. This gauge pressure was not sufficient to tear the membranes. However, plastic strain was evident. In small diameter membranes, the highest pressure resulted in a stress of approximately 60 MPa, at which level yield was not observed. Nevertheless, low residual plastic strains were observed after unloading the membranes. Although the stresses and strains were not uniform across the membrane, Fig. 6 shows that the biaxial stress values are equal and maximal at the center of the membrane. The Von Mises stress was also at a maximum at the center, and was equal to the value of the biaxial stress values presented in Fig. 6. Thus, it can be concluded that, for both types of film, the yield stresses were above 60 MPa.

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Fig. 7. Tensile test results for both types of film. Fig. 6. Bulge test results for 750 lm diameter (filled markers) and 1700 lm diameter (empty markers) membranes, for both aluminum film deposition temperatures.

In large diameter membranes, higher stress values of up to 100 MPa were obtained and clear yields were observed. In addition, residual plastic strains were observed after the membranes had been unloaded. Thus, in both samples, the yield stresses were approximately the same, and were between 60 and 100 MPa. This result was observed in all tests performed on films using the four different membrane diameters. However, the RT-deposited films exhibited significantly higher plastic strains than the 200 °C-deposited films. This was observed in all four membrane diameters and indicated that the RT-deposited films had less strain hardening than the 200 °C-deposited films. In bulge tests, the higher ductility of the RT-deposited films than the 200 °C-deposited films was unexpected. The former films have much smaller grain sizes, and hence, according to the Hall–Petch effect [8], they should be less ductile. Indeed, in nanoindentation tests, the RT-deposited films were less ductile, but these tests were hardly affected by the porosity due to the small volume probed. Thus, the enhanced ductility of the RT-deposited films in our bulge tests was probably due to an effect of the porosity. The bulge test is not an accurate method for measuring the Young’s modulus and was not used for this purpose due to the presence of non-uniform stresses and because the analysis was based on approximated expressions (for a detailed discussion see e.g. Ref. [47]). In addition, as mentioned in Section 2, there was some uncertainty in the evaluations of the initial bulging h0 and the final bulging hf after unloading the membrane. The values of h0 and hf were estimated by measurements taken under a pressure which was small, but large enough to bulge the membrane into a shape predicted by the models. Taking into account the aforementioned drawbacks, we can still evaluate the biaxial modulus E/(1  t) , where t is Poisson’s ratio. This evaluation is based on the slopes of the unloading curves and assuming that the plastic strain remained constant during unloading while the elastic strain changed. The unloading curves consist of only two points, i.e. the last point of the loading segment and the point at which hf was measured. The values of the Young’s modulus obtained by this evaluation, for a value of t = 0.34 [54], were in the range of 20–50 GPa. A comparison of these values with the more accurate measurements obtained by the RUS method (50.6–65.4 GPa) shows that the bulge tests provided an underestimation of the Young’s modulus. The tensile tests of dog-bone-shaped samples provided uniaxial and uniform stress and strain states, which

significantly simplified the analysis of the experimental results for the bulge test. Fig. 7 presents the stress–strain curves taken from both types of film. As discussed in the introduction, the tensile tests often provide significant underestimations of the Young’s modulus [52,53,55–57]. In our experimental system, we previously showed [49] that the slope of the stress–strain curve was smaller than the actual Young’s modulus due to the compliance of a mechanical part that connected the static pin gripper with the force sensor. We also showed that. when taking very rapid tests, in which the elastic loading times were less than 0.1 ms, bulk mechanical parts of the setup did not have time to comply, and the measured Young’s modulus (71 GPa) was in excellent agreement with the known value for bulk samples [50]. The slopes of the stress–strain curves presented in Fig. 7 provide values of 15.5 GPa for the RTdeposited films and 10.5 GPa for the 200 °C-deposited films. These results are much lower than the Young’s modulus values measured by the RUS method, demonstrating the inadequacy of the tensile testing setup for measuring the Young’s modulus. Note that the difficulty associated with accurately measuring the Young’s modulus was due to an overestimation of the strain. This had a significant role in the elastic regime, where the strains were smaller than 0.1%. This problem had a minor or minimal effect on evaluating the characteristic stress values (e.g. yield or ultimate stress) and the total strain at failure, which were the main reasons for using the tensile tests in our study. The stress–strain curve of the RT-deposited sample exhibited a yield stress of approximately 120 MPa, which was slightly larger than the value estimated based on the bulge tests (approximately 80 MPa). This difference may be associated with the significant difference between the strain rates applied in these tests. The strain rate applied in the tensile test was 1.2  103 s1, whereas the average strain rate applied in the bulge test was approximately 2.6  106 s1. The tensile test of the RT-deposited sample also provided the highest stress (160 MPa) and the total strain at failure (approximately 2.5%), which could not be evaluated based on the bulge test. The sample deposited at 200 °C unexpectedly exhibited different behaviors to the sample deposited at RT. The sample yielded and failed at a stress of approximately 30 MPa and exhibited very low plasticity (i.e. less than 0.4% total strain at failure). The small amount of plasticity exhibited by the 200 °C-deposited sample agreed with the bulge test results, where the film also exhibited lower plastic strains than the RT-deposited film. However, the 200 °C-deposited film survived a stress of 100 MPa in the bulge test but failed

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Table 3. Summary of results for both film deposition temperatures, from all demonstrated methods. Type

Property

RT results

200 °C results

Method

Size of region probed

Microstructure

Grain size Pore size Crystallographic orientation

0.18 ± 0.02 lm N/A Favor (1 1 1)

0.7 ± 0.2 lm 0.7 ± 0.2 lm Disfavor (1 1 1)

SEM

102 lm2

XRD

106 lm2

Hardness Local yield stress Porosity Young’s modulus Uniaxial yield stress Uniaxial UTS Strain at the UTS Biaxial yield stress Biaxial UTS Strain at the UTS

1.28 ± 0.18 GPa 458 ± 64 MPa 5%14.9% 50.6–61 GPa 120 MPa 160 MPa 2.1% 80 MPa 100 MPa >0.8%

0.79 ± 0.14 GPa 282 ± 50 MPa 2.7%4.8% 63.9–65.4 GPa 30 MPa 40 MPa 0.3% 80 MPa 100 MPa 0.38%

Nanoindenter

101 lm2

RUS

1.2  107 lm2

Tensile test

2.9  103 lm2

Bulge test

2.3  106 lm2

Mechanical properties

at a stress of 30 MPa in the tensile test. These observations indicate that the effect of porosity was different on the 200 °C-deposited films than on the RT-deposited films. Additionally, different porosity effects on the 200 °C-deposited film were observed in the bulge and tensile tests (i.e. under biaxial and uniaxial stress conditions).

5. Discussion and conclusions In this study, we have introduced a comprehensive characterization of thin aluminum films deposited under different conditions. The characterization includes both a microstructure study using XRD and SEM, and a mechanical characterization study performed using four different methods: nanoindentation, RUS, and bulge and tensile tests of free-standing thin films. We show that, different methods were required to achieve a comprehensive characterization of a wide range of properties and behaviors of thin films. We also suggested a method for evaluating the porosity of thin films based on accurate Young’s modulus measurements. The results of this analysis indicate that previous reports of low Young’s modulus values in thin films may be misleading and derived from overestimations of the measured strains. The results from all the methods used are summarized in Table 3. Our nanoindentation tests were not significantly affected by porosity. These measurements showed that the RTdeposited samples were much harder than the 200 °Cdeposited samples. This effect is in accordance with the Hall–Petch effect and takes into account the significant difference between the grain sizes of the different films. A number of works [58,59] have provided an approximated relation H = Cry between the hardness H and the yield stress ry, where C is a constant between 2.7 and 3. Using a representative value of C = 2.8, our nanoindentation tests provided local yield stress values of 458 MPa for the RTdeposited samples and 282 MPa for the 200 °C-deposited samples, as shown in Table 3. These values are much larger (by at least threefold) than those obtained from the bulge and tensile tests. Thus, we showed that the overall (largescale) yield stress was different from the local (nanoscale) value due to the effect of porosity. Additionally, there was no clear relation between the local mechanical behavior as measured by nanoindentation and the global mechanical behavior of the thin film as measured by the bulge or tensile tests.

Porosity had different effects on the mechanical behaviors of the RT- and 200 °C-deposited films: the RT-deposited samples exhibited higher ductility and lower brittleness than the 200 °C-deposited samples (e.g. see the values for the ultimate tensile strength (UTS) and the strain at the UTS in Table 3). This behavior was opposed to the trend observed for the grain size and was attributed to the effect of porosity. We assumed that in the RT-deposited samples, which have small pores separated by short distances, the porosity increased the ductility (i.e. reduced the strain hardening) by forming easy paths for plastic deformation. In the 200 °C-deposited samples, which have larger pores separated by longer distances, the main effect of the pores was the generation of local stress concentrations. Thus, in these samples, the porosity increased the brittleness. This accounted for the different behavior of the 200 °C-deposited samples in the bulge and tensile tests. The stress concentration factor (K) formed by the pores was larger under uniaxial tension than under biaxial stretching. For example, in the simple geometry of a circular hole in an infinite plate, K = 3 under uniaxial tension and K = 2 under biaxial tension. In addition, in the tensile test, an ensemble of pores near the edges of the dog-boned sample may have induced a crack. This option did not exist in bulge tests where the samples had no edges. In summary, this study demonstrated that the relationships between deposition condition, microstructure and mechanical behavior may be very complicated due to the effect of grain size, porosity and pore size. Moreover, it shows that, due to the porosity, different mechanical test methods for different length scales and loading conditions provided different results. Thus, a combination of several mechanical test methods was essential to obtain a comprehensive understanding of the mechanical behavior of a film. Our results indicated that porosity may have different effects on the mechanical behavior, depending on the pore size. The knowledge and insight obtained in this study could provide a roadmap for choosing deposition conditions that provide the best mechanical properties in an application. Acknowledgements The work of H.S., M.J. and M.L. was financially supported by the bilateral Czech–Israeli project M100761203 of the Academy of Sciences of the Czech Republic.

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