Deformation mechanisms in free-standing nanoscale thin films: A quantitative in situ transmission electron microscope study

M. A. Haque* and M. T. A. Saif†‡

*Department of Mechanical and Nuclear Engineering, Pennsylvania State University, 317A Leonhard Building, University Park, PA 16802; and †Department of Mechanical and Industrial Engineering, University of Illinois at Urbana–Champaign, 140 MEB, 1206 West Green Street, Urbana, IL 61801

Edited by Jan D. Achenbach, Northwestern University, Evanston, IL, and approved March 1, 2004 (received for review January 5, 2004) We have added force and displacement measurement capabilities the TEM has so far been a major analytical instrument in in the transmission electron microscope (TEM) for in situ quanti- materials research (29), nonuniformity in specimen cross-section tative tensile experimentation on nanoscale specimens. Employing and space restrictions for the accommodation of force and the technique, we measured the stress–strain response of several displacement sensors have limited its application to qualitative nanoscale free-standing aluminum and gold films subjected to in situ straining without simultaneous measurement of stress– several loading and unloading cycles. We observed low elastic strain response (30–32). Our experimental setup consists of a modulus, nonlinear elasticity, lack of work hardening, and macro- free-standing tensile sample with uniform width and thickness, scopically brittle nature in these metals when their average grain cofabricated with a microtensile stage with force and displace- size is 50 nm or less. Direct in situ TEM observation of the absence ment sensors. They are made by microelectromechanical systems of dislocations in these films even at high stresses points to a (MEMS) fabrication technology based on lithography. Cofabri- grain-boundary-based mechanism as a dominant contributing fac- cation and the specific flexure design of the stage ensure tor in nanoscale metal deformation. When grain size is larger, the alignment between the loading and the specimen directions, and same metals regain their macroscopic behavior. Addition of quan- minimize the setup size.

titative capability makes the TEM a versatile tool for new funda- Fig. 1 shows the microtensile test stage with a 100-nm-thick ENGINEERING mental investigations on materials and structures at the nano- aluminum specimen bonded to a force sensor beam at one end, scale. and to a set of supporting beams at the other end. The beams are made of single-crystal silicon (27). Quasistatic displacements are anomechanical behavior of materials has gained consider- imposed on one end of the stage and are then transmitted to the Nable attention because of the ever-shrinking dimensions of force sensor beam through the free-standing specimen. The thin-film materials in microelectronics, data storage, and micro- displacement sensors (in the form of two marker gaps, F and D) electromechanical sensors͞actuators, and also the advancements read the specimen elongation. The force on the specimen is given in bulk nanostructured materials. Mechanical properties of by the spring constant and the displacement (marker F) of the materials are influenced by their length-scales. For example, force sensor beam. The spring constant is calibrated with a yield stress of polycrystalline metals increases with a decrease in nanoindenter after the tensile experiment is completed. The grain size [Hall–Petch behavior (1, 2)], and strain-gradient- supporting flexural beam assembly prevents misalignment of the dependent strengthening (3–6) occurs when the specimen size is specimen. A finite element analysis of the stage shows that it reduced to the micrometer scale. Dislocations have been attrib- suppresses any misalignment error in loading by six orders of uted to cause both of these behaviors as long as the grain size or magnitude (27). The clearance (XXЈ) between the fixed and the thickness is Ͼ100 nm. At smaller length-scales, strain- moving parts allows spring-loading of the stage on a TEM gradient-dependent strengthening disappears (7) and reverse straining stage and prevents any prestress on the specimen. Hall–Petch behavior is observed (8–13). Another less under- stood size effect observed at nanoscale is the reduction of Results and Discussions Ϫ Young’s modulus, which has been attributed to specimen density All of the films tested in this paper are dc sputtered [1 ϫ 10 6 (13) and grain boundary compliance (14, 15). Models that torr (1 torr ϭ 133 Pa) base pressure, 2.7 mtorr Argon pressure, attempt to explain the nanoscale size effect are of two basic 300 W, room temperature], 99.99% pure, and deposited on bare types: (i) models describing nanocrystalline materials as two- silicon substrate. The films are subjected to compressive residual phase composites with grain interiors and boundaries, where the stress. Hence, the free-standing specimen buckles (Fig. 1) and mechanical properties are averaged by simple ‘‘rule of mixtures’’ relieves most of the stress. Because the critical buckling load is (16, 17); and (ii) models considering dislocation motion (10, 18, small, the compressive stress in the specimen after buckling is 19), grain boundary sliding (20, 21), and diffusion (12, 22) as negligible compared to the tensile stress applied during testing. competing deformation mechanisms. Although the literature The microinstrument is first used to apply tensile stress on has compelling evidence of these size-effects, the underlying 100-nm-thick free-standing aluminum films in situ in a Philips deformation mechanisms are not yet well understood (23). CM200 TEM at 160 kV. The average grain size of the films was 50 nm. The experiments were performed quasistatically, and Experimental Methods microstructures were visually monitored continually with digital Direct experimental observations of the deformation mecha- image acquisition. TEM images were recorded as single frames nisms mentioned above while the materials behavior is measured after each increment of strain of the sample. No video camera quantitatively is difficult at the nanoscale even with the recent was used for recording. Fig. 2 shows the stress–strain diagram for novel existing approaches (24–28). We overcome the difficulty by developing microinstrumentation that combines quantitative tensile testing of thin films with the qualitative capabilities of the This paper was submitted directly (Track II) to the PNAS office. transmission electron microscope (TEM) so that one can simul- Abbreviation: TEM, transmission electron microscope (microscopy). taneously measure the stress–strain states in solids and observe ‡To whom correspondence should be addressed. E-mail: [email protected]. the deformation mechanisms during materials testing. Although © 2004 by The National Academy of Sciences of the USA

www.pnas.org͞cgi͞doi͞10.1073͞pnas.0400066101 PNAS ͉ April 27, 2004 ͉ vol. 101 ͉ no. 17 ͉ 6335–6340 Downloaded by guest on October 1, 2021 Fig. 1. (a) Scanning electron micrograph of the microstage showing the freestanding aluminum thin-film specimen being attached to the force sensor beam at one end and to supporting beams at the other. Markers D and F, read displacements at both ends of the specimen. The left end of the microstage is pulled by a piezo actuator of a TEM straining stage. Deflection of the sensor beam (read by marker F), multiplied by its spring constant, gives the force on the specimen. The difference between the two markers’ (D and F) gaps gives the elongation of the specimen. The gap XXЈ prevents accidental straining of the sample during mounting of the microstage on to the TEM straining stage. The TEM straining stage has to move and deform the microstage to close the gap XXЈ before loading the sample. (b) Microtensile test stage on a TEM straining stage. (c) Zoomed view of the specimen and the two displacement sensors D and F. There is no substrate under the specimen so that the TEM beam can go through the sample for microstructural inspection.

three specimens tested in TEM and one in scanning electron loading direction. Elastic modulus for the four samples is found microscope to highlight the consistency of the experimental to be 68 GPa, which is close to the bulk value of 70 GPa. The films results. Also shown are TEM images of a sample at different had ͗111͘ texture. levels of stress and strain, and during failure. The top right TEM The TEM images show neither any dislocation activity within the image shows the film after failure with a crack normal to the grains nor any generation even at high stress. However, one cannot

Fig. 2. Quantitative, in situ TEM test results for 100-nm-thick freestanding aluminum films. Three TEM test results are shown along with a scanning electron microscope test result to demonstrate experimental consistency. (Insets) Microstructures corresponding to the different stress–strain states for experiment 1 (triangle data markers). The rightmost Insets show crack growth through the grains and between the grains. The top right Inset shows the film after fracture.

6336 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0400066101 Haque and Saif Downloaded by guest on October 1, 2021 ENGINEERING

Fig. 3. (a) Low elastic modulus and nonlinear elastic response with small plastic deformation in small-grained but thick gold film. (b) As the grain size of gold is increased while the film thickness is decreased, bulk gold behavior is approached (elastic modulus of bulk gold with ͗111͘ texture is 80–87 GPa, depending on isostrain and isostress condition). (c) Low elastic modulus and nonlinear elastic response in small-grained Al. (d) Reduced permanent strain hardening in 65-nm-grain-sized aluminum (150-nm-thick film), but macroscopic strain hardening in 212-nm-grained-sized (480-nm-thick film) samples. Resolutions in stress measurements are as follows: 2.4 MPa for 350-nm-thick Au, 5 MPa for 50-nm-thick Al, 9 MPa for 150-nm-thick Al and 200-nm-thick Au, and 8 MPa for 485-nm-thick Al. Resolution in strain measurement for all of the tests is 0.05%.

rule out the possibility that dislocations might have moved from one sputter deposit thin metal films with such control on grain size grain boundary to another through small grains at high speeds and and thickness, we deposit gold films with small thickness (200 were not captured in the recorded frames. Gradual, and not sudden, nm) and large (75 nm) grains, and with large thickness (350 nm) change of contrast was observed in some grains (grain A, Fig. 2) and small (15 nm) grains. Both the films had ͗111͘ texture. We over many strain increments, perhaps induced by grain rotation and tested these films under uniaxial loading with the microinstru- or global tilting of the film (30, 31). The specimens behaved as ment. We find that the Young’s modulus of the small-grained (15 macroscopically brittle and failed at Ϸ680 MPa with a crack nm) film is 52 GPa, whereas the modulus for the larger (75 nm)- initiating from the edge and advancing both through the grain grained sample is 73 GPa, closer to the modulus F: (80 GPa boundaries and grain interiors. No dislocation activities were ob- under isostrain condition, 87 GPa under isostress condition) of served ahead of the crack tip (TEM image in Fig. 2). It is worth bulk polycrystalline gold with ͗111͘ texture. The small-grained noting that ex situ TEM studies of 200-nm-thick aluminum films sample with larger thickness shows nonlinear elasticity upon un- reveal significant dislocation activities within grains of dimension loading with small permanent deformation (Fig. 3a), whereas the 150 nm and higher, whereas no such activity was observed in films larger-grained sample with smaller thickness showed macroscopic with thickness of 100 nm and lower and with average grain size of plasticity (Fig. 3b). These observations suggest that grain size is the 50 nm and lower. No void or intergranular crack was observed in critical dimension (8) that determines the mechanical behavior of any of the films except during failure. Earlier in situ straining metals, at least when the grains are much smaller (2–3 times) than experiments (32) in TEM on 10-nm-grained gold films also show the film thickness, unless the thickness is so small that both the lack of dislocation activity and negligible change in grain size, surface energy and its strain dependence play a major role in although grain rotation was observed, and deformation was attrib- determining the overall stress–strain response (34). uted to the grain boundary sliding and rotation. Note that in the To explore the size effect in aluminum, we measure the study described in ref. 32, applied stress on the specimen was not stress–strain response of several aluminum specimens with thick- measured, and local strain was estimated from TEM images. In the nesses 50, 150, and 480 nm, with the corresponding average grain work described in ref. 33, specimens of nanocrystalline n-Ni from sizes of 22, 65, and 212 nm, respectively (Fig. 3 c and d). All of the tip of a microhardness indent were studied under TEM and no the specimens had ͗111͘ texture. We find that the elastic modulus dislocations were found. Here the average grain size was 28 nm. of the smallest-grained (22 nm) sample is 63 GPa, whereas it is To reveal the relative importance of grain size and thickness 70 GPa, the bulk value, for the larger-grained samples. Note that on the mechanical behavior of thin metal films, ideally, one 50-nm-grained Al (Fig. 2) has an elastic modulus of 68 GPa. needs to test such films with fixed thickness but with varying Thus, elastic modulus of gold decreases much more with grain average grain size, and with fixed average grain size but with size than it does for aluminum. The results for aluminum and varying thickness. Although it is difficult, if not impossible, to gold films suggest that at small grain size (50 nm or smaller for

Haque and Saif PNAS ͉ April 27, 2004 ͉ vol. 101 ͉ no. 17 ͉ 6337 Downloaded by guest on October 1, 2021 Fig. 4. (a) Interatomic force between two aluminum atoms from Morse potential (47). Two pairs of atoms representing grain boundary are shown. The atoms of one pair are farther apart from equilibrium distance by d, a measure of distortion from the crystalline arrangement. These atoms attract each by a force Fa. The atoms of the other pair are closer to one another than the equilibrium distance such that they repel each other by a force Fr ϭ Fa. The atomic pair system is analogous to a three-spring system brought together to equilibrium by two free plates. Here, the short springs are in tension and the longer spring isin compression. (b) The combined spring constant of the two atomic pair system compared to a system where the atoms of both the pairs are at an equilibrium distance, r0, apart is shown as a function of d. Their ratio is a measure of the elastic modulus of the grain boundary compared to grain interior, Egb͞Eg.(c) The net force needed to increase the gap between the atoms of both the pairs by a distance x is shown. The system behaves as a softening nonlinear spring.

Al) (i) elastic modulus decreases with decreasing grain size. (ii) prepared from gold bicrystals and found that the lattice spacing Upon unloading, the metals behave nearly as nonlinear elastic, on either side of the interfacial plane is dilated by 45%, and the i.e., they almost follow the loading stress–strain path, with a small dilation is totally localized in a slab of three atomic planes permanent deformation. Note that this nonlinear elastic re- occupying Ϸ0.3 nm. A similar conclusion was drawn from a sponse occurs at much smaller strains than that expected from theoretical study on grain boundary (44). Siegel and Thomas single-crystal whiskers [nonlinearity starts at Ϸ3% strain (35)]. (40) studied grain boundary structure of cluster consolidated (iii) Upon reloading, metals show negligible strain hardening, nanophase Pd by using a HRTEM. They found that the lattice i.e., the increase of ‘‘yield stress’’ (stress at the onset of nonlin- fringes end abruptly near the grain boundary, and any disorder earity) is negligible compared to the corresponding increase for of atoms in the grain boundary, if present, is limited to within 0.4 macroscopic metals. As grain size is increased [even when nm, again consistent with ref. 44. The authors concluded that the thickness is decreased (Fig. 3b)], metals regain macroscopic grain boundaries of the nanophase metal are not different from elastic modulus, plastic behavior with large permanent defor- large-grained boundaries, i.e., the boundaries are not influenced mation, and strain hardening. by the close proximity of other boundaries. However, HRTEM It is suggested (36–38) that nanocrystalline materials exhibit studies on electrodeposited nanocrystalline Ni–1 wt % P (45), anelastic relaxation behavior at low temperatures, which may and electrodeposited palladium and titanium films (46) found result in the lower values of the Young’s modulus (Enanocrystal ϭ evidence of amorphous region at some boundaries and at triple ␴͞(␧elastic ϩ ␧anelastic) Ͻ Ebulk ϭ ␴͞␧elastic). To explore anelasticity junctions of nanograins. Although there are some controversies as a possible mechanism for reduced modulus of nanograined on the structure of grain boundaries in the literature, the samples, we carried out uniaxial tension experiments on alumi- following are generally accepted: grain boundaries, irrespective num films with average grain size of 60 nm at varying temper- of the grain size, host various defects such as dislocations, partial atures (up to 160°C) and strain rates. We find that the elastic dislocations, steps, disordered regions [may appear at a regular modulus is consistent with that found in scanning electron spacing along the interface (41)], lattice dilatations, and distor- microscopy and TEM, and that there is negligible dependence of tions. Such defects allow for accommodation of the misfit modulus on temperature and strain rate as long as the temper- between the two meeting grains (41). The width of the grain ature is Ͻ80°C and strains are small. Thus, anelasticity does not boundary region and its structure depends on various factors appear to be a dominant mechanism for reducing elastic mod- such as the orientations of the adjoining grains and the process- ulus at room temperatures. ing history of the metal. The atoms within the grain boundary We believe that a single mechanism can explain both reduced regions have higher energies than those within the grains, but the Young’s modulus and nonlinear elasticity of small nanograined boundary atoms collectively maintain force equilibrium. Thus, sputter deposited metals at room temperatures as follows: grain some atom pairs have interatomic spacing larger than equilib- boundary region is elastically softer than grain interior, and it rium spacing. These atoms attract one another, resulting in a becomes increasingly softer with increasing tensile strain. tensile region. Some other pairs have spacing smaller than the At small grain size, grain boundary regions occupy a signifi- equilibrium spacing. These atoms repel each other giving rise to cant part of the bulk (39–42). The structure of the grain a compressive region. Such tension–compression ensures overall boundary region is not yet fully understood. Direct experimental equilibrium. To illustrate, consider the two pairs of aluminum observation of grain boundary by using a high-resolution TEM atoms in Fig. 4a. The spacing for one pair is r0 ϩ d, where r0 is (HRTEM) are available for limited cases in the literature. the equilibrium distance between aluminum atoms and d Ͼ 0is Krakow et al. (43) studied 33៮1 ͚ϭ19͞[110] tilt boundary the measure of deviation from the granular lattice spacing. These

6338 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0400066101 Haque and Saif Downloaded by guest on October 1, 2021 atoms are subjected to attractive force, Fa, which can be com- be reduced permanent strain hardening than that expected for puted from the interatomic potential of aluminum (47). The large-grained metals. Here, the dislocation density is low, and spacing between the atoms of the second pair is r0 Ϫ dr, where dislocation forests, which cause permanent strain hardening in dr ϭ dr(d) is such that the repulsive force between the atoms Fr bulk metal samples, may not yet exist. However, for larger grains, ϭ Fa, and the arrangement is in equilibrium. The arrangement higher dislocation density (Fig. 3d) results in the typical quali- is analogous to a three spring system with two short and one long tative behavior of bulk aluminum such as strain hardening as spring, put together at self equilibrium between two plates. The observed in a 480-nm-thick aluminum sample with a 212-nm shorter springs are in tension and the longer one is in compres- average grain size. There is thus a transition of the deformation sion, but the spring-plate system is in equilibrium. The stiffness mechanism: at small grain size, dislocation slip ceases to operate or the spring constant of the two atomic pair system of the grain and deformation is contributed by grain boundary mechanisms, boundary can be compared to that of their granular counterpart whereas as grain size increases, dislocation dynamics overwhelms ͞ ϭ Ј ϩ ϩ Ј Ϫ with interatomic spacing of r0 as Egb Eg (f (r0 d) f (r0 the grain boundary mechanisms. At the transition size, where ͞ Ј dc)) 2f (r0), where f(r) is the interatomic force for aluminum (47) there are not enough grain boundaries to assist in deformation and the prime denotes derivative with respect to interatomic but the grain size is small enough so that dislocation dynamics is distance. The ratio is thus a measure of the modulus, Egb,ofthe energetically unfavorable, metal may show highest strength (42). grain boundary region with respect to its granular counterpart, For aluminum, this critical grain size seems to be Ϸ50 nm from Ͼ Eg (Fig. 4b), and is found to be less than unity for any d 0 for our experimental observations, close to 20–30 nm predicted by aluminum. Thus, grain boundary region at self equilibrium must theory (42). It is interesting to note that aluminum exhibits be more compliant than its granular counterpart, because the strain-gradient-induced strengthening when grain size is Ͼ50 nm ϩ loss of stiffness due to the pair with atomic spacing r0 d is not but ceases to show the gradient effect below 50 nm. The fully compensated by the increase of stiffness due to the pair with characteristic length scale, l, that quantifies the strain gradient Ϫ spacing r0 dc. It is thus not surprising that amorphous materials strengthening increases from zero and takes a steady value of Ϸ4 have consistently lower elastic modulus than their crystalline ␮m as the grain size increases from 50 nm to Ϸ100 nm (7). counterpart. The actual modulus of the grain boundary will Strain-gradient strengthening has been attributed to geometri- depend on the number of atoms under attraction and repulsion cally necessary dislocations (6, 48). As grains become smaller and their distribution, which depends on the processing of the than the critical size when dislocations cannot exist within the Ͼ film. It is likely that there are more atoms with r r0 than there grains, strain-gradient-induced strengthening disappears, and it Ͻ ENGINEERING are with r r0, because the attractive force due to many atoms is not surprising that l vanishes. can be equilibrated by only a few in compression because of the Ͻ We note that Shen et al. (15) used nanoindentation technique steeper interatomic force distance relation in the r r0 region. to measure elastic modulus of polycrystalline Fe, Ni, Cu, and The net effect is the higher compliance of the grain boundary Cu-Ni alloys prepared by mechanical milling. The range of grain than that predicted by the two pair system. Note that the two size was 17–27 nm for Cu, Ni, and Cu-Ni alloys, and 7–80 nm for atomic pair system is different from the three spring analogue if Fe. Elastic modulus of Cu, Ni, and Cu-Ni alloys was found to be the springs are linear, in which case the combined spring similar to their bulk polycrystalline counterpart. Modulus de- constant of the system is the sum of the three individual creased with grain size for Fe, although the decrease was only constants, i.e., the system spring constant does not change Ϸ5% when the grain size was 7 nm. These results may, at first because of residual stress in the linear springs. look, appear contradictory to the experimental findings and the If the two atomic pair system is now strained under tension arguments presented in this paper for Al and Au. Here, we (along x, Fig. 4a), the interatomic spacing increases for both attributed to grain boundaries (when no flaws or voids could be the pairs and the right atoms of the pairs ride along the detected by TEM) of nanocrystalline aluminum and gold for the force–distance curve, both with decreasing slopes, although reduction of their elastic modulus and their nonlinear elastic the slope decreases faster for the atoms initially under attrac- response. However, the structure of the grain boundary region, tion. Consequently, the system behaves as a softening nonlin- ear spring that, upon unloading, returns along the loading and hence its influence on mechanical properties, depends on path. Thus, with increasing tensile strain, the compliance of the the processing of the metal. Thus, it is not surprising that grain boundary increases, the boundary shares an increasingly mechanical behavior of nanocrystalline metals show varying larger part of the total strain compared to its granular coun- degrees of sensitivity to grain size depending on the metal and terpart, and the metal shows increasing softening. Grain its processing conditions. boundary may accommodate the large strain by various pro- As exemplified in this study, addition of quantitative capa- cesses such as rotation (32), widening, and shearing. Upon bility complements the qualitative prowess of the TEM. Po- unloading, both the grain boundary region and the grains tential application of similar quantitative testing in TEM follow the loading path, and the metal behaves as nonlinear includes characterization of ceramics, semiconductors, poly- elastic. Thus, for metals with nanograins where grain bound- mers, biomaterials, nanotubes, nanorods, and wires, and other aries are abundant but dislocations are rare (32, 33, 41, 42) novel nanostructures and composites for their stress- even at high stresses as evidenced in our in situ TEM studies, dependent mechanical and electronic properties and stress- deformation mechanism is primarily contributed by the bound- assisted evolution of microstructures. The significance of the aries. At small strains, they contribute to reduced elastic developed technique is even more profound because it opens modulus of the metal. With increasing strain, they behave as up new possibilities for all science and engineering disciplines softening springs and the metal behaves as a nonlinear elastic where TEM is used. material. The metal is macroscopically brittle with high frac- ture stress and low ductility. The small plastic permanent The devices were fabricated in the MicroMiniature Systems Lab of the deformation is probably contributed by ‘‘secondary’’ irrevers- Mechanical and Industrial Engineering Department at the University of ible mechanisms such as dislocation slip in a few larger grains Illinois at Urbana–Champaign and tested in the Imaging Technology Group Lab of the Beckman Institute at the University of Illinois at in the polycrystalline metal, and by grain boundary sliding. Urbana–Champaign. We thank Professors William Nix (Stanford Uni- When the average grain size is increased, many grains begin versity) and John Hutchinson (Harvard University) for their valuable to accommodate dislocations that allow higher ductility and comments on the work and on the manuscript. This work was supported plastic deformation, but as observed in the 65-nm-grain-sized by National Science Foundation Career Award ECS 97-34368 (to aluminum sample in Fig. 3d (film thickness 150 nm), there may M.T.A.S.).

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