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High strength, epitaxial nanotwinned Ag films
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Acta Materialia 59 (2011) 93–101 www.elsevier.com/locate/actamat
High strength, epitaxial nanotwinned Ag films D. Bufford a, H. Wang b, X. Zhang a,⇑ a
Department of Mechanical Engineering, Materials Science and Engineering Program, Texas A&M University, College Station, TX 77843-3123, USA Department of Electrical Engineering, Materials Science and Engineering Program, Texas A&M University, College Station, TX 77843-3128, USA
b
Received 29 July 2010; received in revised form 3 September 2010; accepted 5 September 2010
Abstract Epitaxial silver films with (1 1 1) and (1 1 0) orientations were deposited by magnetron sputtering onto silicon (1 1 1) and (1 1 0) substrates, respectively. High density growth twins with an average spacing of a few nanometers are observed in the (1 1 1) oriented films, with twin boundaries oriented normal to the growth direction. Twins are observed in the (1 1 0) oriented films with a much lower twin density, and the twin boundaries are oriented 60° from the growth direction. The epitaxial nanotwinned Ag (1 1 1) and (1 1 0) films have respective indentation hardness values of 2 and 1 GPa. The influences of deposition parameters, stacking fault energy, and orientation of {1 1 1} planes on the formation of nanotwins are discussed. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Epitaxial growth; Nanoindentation; Nano-scale twins; Sputtering; Transmission electron microscopy (TEM)
1. Introduction Nanotwinned (nt) structures have been reported in facecentered-cubic (fcc) metals, and these highly twinned structures lead to unique electrical [1–3], thermal [4–6] and mechanical properties [1,4,5,7–12]. In comparison to high angle grain boundaries in nanocrystalline metals, coherent R3 {1 1 1} twin boundaries in nt metals have much lower energy, and hence nanotwins are much more stable at higher temperatures. The average twin spacing in sputtered nt Cu only increases from 4 to 16 nm after annealing at 0.8 Tm (Tm is the melting temperature), while grain size increases by an order of magnitude [4]. Meanwhile the electron scattering coefficient of coherent twin boundaries (CTBs) is measured to be an order of magnitude lower than that of high angle grain boundaries [1]. The most extensively studied aspects of nt metals are their mechanical properties. Nanotwins induce a substantial increase in mechanical strength. Experimental observations and molecular dynamics (MD) simulations [7,13–20] have shown that ⇑ Corresponding author. Tel.: +1 979 845 2143.
E-mail address: [email protected] (X. Zhang).
twin boundaries act as strong barriers to the transmission of dislocations, leading to increased mechanical strength. A recent study has shown that a negative Hall–Petch relation, occasionally observed in nanocrystalline metals, may also exist in electrodeposited nt Cu [11]. A similar phenomenon has been observed in large scale MD simulations [21]. Besides high strength, certain nt metals also possess significant ductility as revealed by large strain in tension and under rolling [9–12]. High densities of trapped dislocations are observed at twin boundaries after deformation [22], and the density of mobile dislocations appears greater in nt metals with smaller twin spacing. Our recent studies have shown that twin boundaries can be mobile under stress; detwinning phenomena in sputtered nt Cu have been examined in situ inside a transmission electron microscope, and detwinning mechanisms were further revealed by MD simulations [23,24]. The detwinning mechanisms can explain the annihilation of very fine twins (1–2 nm twin spacing) in rolled polycrystalline nt Cu [25], and may also account for the “softening” (negative Hall–Petch relation) observed in electrodeposited nt Cu. The formation of twin boundaries and stacking faults during growth of sputtered nt metal is a less well
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.09.011
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understood subject. Our thermodynamic model has predicted that twin formation depends strongly on the deposition rate and twin boundary energy (or stacking fault energy, as it tends to correlate with twin boundary energy) [8,26]. Another intriguing phenomenon is the orientation of growth twins. In sputter-deposited polycrystalline Cu and 330 stainless steel films, twin boundaries are oriented predominantly perpendicular to the growth direction [7,9], whereas twin boundaries are often randomly oriented in thick films fabricated by pulsed electrodeposition [3]. In comparison to nt Cu, twins in Ag have received little attention. Silver has the lowest twin boundary energy among all elemental fcc metals, and hence it might form even higher densities of twins than Cu during sputtering. Although some cross-sectional transmission electron microscopy (TEM) work has previously been performed on epitaxial Ag films, the goal of the study was to examine the Ag–Si interface [27]. Hence, the formation of growth twins in Ag films and their effects on mechanical strength have not yet been studied. Also it is of interest to compare twin-induced hardening in nt Ag films with compiled mechanical property data from various types of Ag structures, including single crystals [28], bulk nanocrystals [29], and polycrystalline Ag films with fewer twins [30,31]. Furthermore, Ag has the highest room-temperature electrical conductivity and thermal conductivity among all elemental metals, but it is very soft, and hence its use in microelectronics applications is limited. These attributes make Ag an attractive model system for the study of twin boundary formation and twin-induced strengthening mechanisms, and these studies could have direct effects on the application of Ag in the electronics industry. In this paper, we demonstrate that high density nanotwins can be formed in epitaxial Ag films on both Si (1 1 1) and Si (1 1 0) substrates, and we examine the possible formation mechanisms of nanotwins. By controlling the Ag epitaxial orientation, it is possible to control the orientation and density of growth twins, and consequently affect the film strength significantly.
experiments, performed by a Fischerscope HM2000XYp indenter with a Vickers indenter tip. 3. Results The normal h–2h XRD scans for the Ag films grown on Si (1 1 1) and (1 1 0) substrates are plotted in Fig. 1. The absence of all other Ag peaks in the XRD spectrum of the Ag film on Si (1 1 1) suggests the formation of an epitaxial Ag film along the (1 1 1) orientation. The XRD spectrum for the Ag film on Si (1 1 0) shows a primary Ag (2 2 0) peak with very weak (1 1 1) Ag peaks, which suggests that the film is highly textured in the Ag (2 2 0) orientation. Plane-view TEM micrographs of the Ag (1 1 1) films (Fig. 2a) show numerous nearly hexagonal domains. The boundaries between domains appear less well-defined than those for a typical polycrystalline grain structure. The SAD pattern (Fig. 2a, inset), collected with a large aperture to include numerous domains, shows a structure characteristic of a single crystal viewed along the Ag [1 1 1] zone axis. Cross-section TEM specimens of the Ag (1 1 1) films were examined along orthogonal Ag ½0 1 1 and ½2 1 1 zone axes to reveal the microstructure and epitaxial relationships between the film and the substrate. When viewed from the ½0 1 1 zone axis (Fig. 2b), both the columnar domain structure and twin boundaries are easily discerned. The twin boundaries appear every few nanometers oriented normal to the growth direction, and are so closely spaced that it is impractical to differentiate between the matrix and twins. The SAD pattern (Fig. 2b, inset) shows clear evidence of (1 1 1) twins, as well as a single-crystal-like pattern with distinguished diffraction dots. When examined from the orthogonal ½2 1 1 zone axis (Fig. 2c), columnar domain boundaries are still visible. However, the twin boundaries are invisible, as this direction does not look edge-on at the twin boundaries. When examining the twin boundary by HRTEM along the ½0 1 1 zone axis, the zigzag structure of adjacent twin variants is apparent (Fig. 2d).
2. Experimental Ag films, 2 lm in thickness, were deposited by magnetron sputtering onto HF etched single crystal silicon (1 1 1) and (1 1 0) substrates. The deposition chamber was evacuated to a base pressure of approximately 8.0 108 Torr, and Argon pressure during deposition was 2 mTorr. Xray diffraction (Bruker-AXS D8 Bragg–Brentano X-ray Diffractometer, Cu Ka radiation) was used to analyze the texture in the deposited films. Cross-section and plane-view specimens for TEM studies were prepared by mechanical grinding and polishing followed by low energy ion milling. These specimens were analyzed by a JEOL 2010 transmission electron microscope with 200 kV accelerating voltage. High resolution TEM (HRTEM) imaging was performed with a JEOL 3000F microscope operated at 300 kV. Film hardness was determined by instrumented nanoindentation
Fig. 1. XRD spectra of sputtered films. The absence of other peaks in the XRD spectrum for the Ag (1 1 1) film on the Si (1 1 1) substrate suggests the formation of an epitaxial film. A highly textured Ag (1 1 0) film forms on the Si (1 1 0) substrate with orders of magnitude lower Ag (1 1 1) diffraction peak.
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Fig. 2. (a) Plane-view TEM micrograph from the Ag (1 1 1) film on the Si (1 1 1) substrate showing numerous nearly hexagonal domains with an average size of 120 nm. The inset SAD pattern clearly shows single crystal-like diffraction along the Ag [1 1 1] zone axis. (b) Cross-section view from the ½0 1 1 zone axis reveals high density growth twins with twin boundaries normal to the growth direction. (c) Cross-section view examined from the ½2 1 1 zone axis shows no sign of twins. (d) HRTEM micrograph and the inset FFT show the formation of coherent R3 {1 1 1} twin boundaries.
The inset fast Fourier transform (FFT) in the micrograph confirms the presence of R3 {1 1 1} coherent twin boundaries. The film deposited on the Si (1 1 0) substrate, when examined from the [1 1 1] zone axis, shows a different microstructure from the Ag (1 1 1) film. It shows a much lower density of twin boundaries, and the twins are oriented 60° from the growth direction (Fig. 3). The average twin spacing in the Ag (1 1 1) film is 9 nm, as shown in Fig. 4a, whereas the average columnar domain size (not shown here) is 120 nm. The average twin spacing in the Ag (1 1 0) films is 42 nm as shown in Fig. 4b. Plane-view TEM examination of the Ag (1 1 0) film reveals only large domains with many thickness contours and few grain boundaries, indicating that the average domain size is on the order of a few microns. The cross-section SAD patterns in Fig. 5a–d show the in-plane epitaxial orientation relation between the Ag films and Si substrates. For the Ag (1 1 1) film on the Si (1 1 1)
substrate, it is evident that Ag h1 1 2i//Si h1 1 2i and Ag h1 1 0i//Si h1 1 0i, while for the Ag (1 1 0) film on the Si (1 1 0) substrate, the orientation relationships are Ag h1 1 2i//Si h112i and Ag h1 1 1i//Si h1 1 1i. The substrate–film orientation relationships are summarized schematically in Fig. 6a and b. Zone axes of identical indices are parallel to each other within the film plane, and also along the growth direction. In epitaxial Ag (1 1 1) films there are two twin variants: Ag (1 1 1)//Si(1 1 1) with Ag ½0 1 1//Si½0 1 1, and Ag (1 1 1)//Si(1 1 1) with Ag ½0 1 1// Si½0 1 1 [32–33]. These variants correspond to a 180° rotation about the [1 1 1] axis. A hardness vs. indentation depth profile was compiled for indentation depths of 100–300 nm. Maximum indentation depth was limited to 15% of the total film thickness to avoid substrate effects, and at least nine indents were performed at each indentation depth to determine the average hardness and standard deviations. A plateau of hardness vs. indentation depth is achieved, as shown in Fig. 7. At
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4. Discussion 4.1. Epitaxial growth via domain matching epitaxy
Fig. 3. Cross-section view TEM micrographs collected from the [1 1 1] zone axis of the Ag (1 1 0) film on the Si (1 1 0) substrate reveal an interesting structure. Twin boundaries appear tilted 60° from the growth direction when examined along this orientation. The single crystal-like epitaxial character of the film is evident in the SAD pattern (inset).
Fig. 4. Twin spacing histograms. The average twin spacing in the (a) Ag (1 1 1) film is below 10 nm, and in the (b) Ag (1 1 0) film it is 42 nm.
an indentation depth of 300 nm the Ag (1 1 1) and Ag (1 1 0) films show respective indentation hardness values of 2 ± 0.04 and 1 ± 0.04 GPa.
A 2-lm thick Ag film was calculated to absorb over 95% of the X-ray beam as it passes through to the substrate and then reflects back out of the film. Thus the single crystal Si (1 1 1) and (2 2 0) substrate peaks are weak in comparison to the corresponding peaks in Ag. The XRD spectrum for the Ag (1 1 0) film shows that a small fraction of (1 1 1) and (1 0 0) oriented domains are present within the film, but the majority of the film has (1 1 0) orientation. The single-crystal-like SAD patterns from the plane-view Ag (1 1 1) TEM micrographs confirm the abundance of (1 1 1) crystallographic planes as seen in the XRD spectrum. Furthermore, the SAD patterns indicate that the domains align coherently in-plane. The cross-section and plane-view SAD patterns together indicate that both films retain the single-crystal-like epitaxial structure from the interface and throughout the whole film thickness. Although the XRD spectrum for the Ag (1 1 0) film indicates that some misoriented domains are present, the volume fraction of these domains is presumably small, as the XRD peaks are several orders of magnitude weaker in comparison to the Ag (2 2 0) peak. No differently oriented domains were found in SAD patterns collected from different parts of the TEM specimens, indicating that the whole film is epitaxial. The epitaxial quality of the Ag (1 1 0) film is slightly lower than that of the Ag (1 1 1) film, but the domain size is greater in the former case. Ag preferentially grows in close-packed (1 1 1) planes to minimize surface energy, and it has been previously reported that it is easier to achieve Ag (1 1 1)//Si (1 1 1) epitaxial growth than it is to achieve the Ag (1 1 0)//Si (1 1 0) relationship [34]. The film quality observed in this study is consistent with the previous observations. The large mismatch between the Ag and Si lattices is evident in the SAD patterns (Fig. 5a–d). Ag and Si have a large lattice parameter mismatch (aAg = 4.09 and ˚ ), with a mismatch strain, em, of 33%, calcuaSi = 5.43 A lated by using [35]: as af ð1Þ em ¼ af where as and af are the lattice parameter of substrate and film. Based on such a large mismatch strain, one-to-one epitaxial growth appears impossible. However, epitaxial growth of Ag on various low-index Si substrates has been achieved using various PVD techniques, and characterized by numerous analytical techniques [27,34,36–40]. Epitaxial growth is achieved through domain matching epitaxy with a 3Si-to-4Ag domain match. Taking n and m as the number of respective substrate and film planes involved in the matching, the mismatch strain with domain matching epitaxy, edme, is only –0.43%, estimated by using nas maf ð2Þ edme ¼ maf
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Fig. 5. SAD patterns collected at the Ag–Si interface reveal the orientation relation between the substrates and films. The patterns from the ½2 1 1 zone axis in (a) Ag (1 1 1) and (c) Ag (1 1 0) films, (b) the orthogonal ½0 1 1 zone axis in Ag (1 1 1), and (d) the orthogonal [1 1 1] zone axis in the Ag (1 1 0) films, reveal that identical indices in the film and substrate are parallel to each other.
Fig. 6. Film–substrate orientation relation schematics for (a) Ag (1 1 1)/Si (1 1 1) and (b) Ag (1 1 0)/Si (1 1 0). The films were examined by TEM along the in-plane zone axes illustrated here.
which is an adapted form of the equation used by Narayan and Larson [41] to estimate strain in domain matching epitaxy. The domain matching mechanism operates for both the Ag (1 1 1)//Si (1 1 1) and Ag (1 1 0)//Si (1 1 0) oriented films [27,34]. 4.2. The formation of high density growth twins Cross-section TEM micrographs reveal a high density of twin boundaries oriented perpendicularly to the growth direction in the Ag (1 1 1) films. Similarly structured nanotwins have been observed in other fcc metal films,
Fig. 7. Indentation hardness is plotted as a function of indentation depth. The Ag (1 1 1) films show significantly greater indentation hardness than the Ag (1 1 0) films. The error decreases with increasing depth, and hardness typically reaches a plateau by 200 nm.
notably Cu and stainless steels [4,7,9]. The inclined twins observed in the Ag (1 1 0) film form an unusual structure, and it is likely that the formation mechanism during growth is somewhat different for these twin boundaries. While twins are observed regularly in micrographs of Ag films and bulk materials, the twins observed in this study differ significantly in the high frequency that they appear,
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and in their coherent orientation throughout the films. In the literature most microscopy studies performed on Ag films focus on epitaxial growth, and hence steps were taken to minimize defect nucleation, such as using substrate heating and equilibrium deposition techniques like thermal evaporation or molecular beam epitaxy. Suppressing the formation of growth defects will also reduce the rate of twin formation. Twin density in such Ag films is typically much lower [32,33], with the twin variant only accounting for a volume fraction well below the 50% seen in the nt Ag (1 1 1) films in this study. Numerous factors lead to the formation of nanotwins in sputtered Ag films. First, Ag has a low stacking fault energy (SFE) of 17 mJ m2 [42], which allows the formation of wider stable stacking faults than in metals with higher SFE. Thus a twin boundary can remain stable with longer length in Ag than in other metals. Second, it has been shown from a thermodynamic model that twin boundary energy affects the formation of twin boundaries during film deposition by determining the difference in critical nucleation radius between defect-free and twinned nuclei [8]. From the aforementioned model, the critical nucleation radii for perfect and twinned nuclei, rperfect and rtwin , are described by the following expressions: rperfect ¼ rtwin ¼
kT X
kT X
ln
ln
c h pffiffiffiffiffiffiffiffiffii
ð3Þ
J 2pmkT PS
c h pffiffiffiffiffiffiffiffiffii J 2pmkT PS
cht
ð4Þ
where c is the surface energy, k is the Boltzmann constant, T is the substrate temperature, X is the atomic volume, J is the deposition flux, m is the atomic mass of the film species, Ps is the vapor pressure above the target, ct is the twin boundary energy, and h is the height of the nucleus (taken in this case to be the {1 1 1} interplanar spacing). It is evident from the equation that a low twin boundary energy will facilitate the formation of nanotwins by reducing the critical radius for twin nuclei. Third, higher deposition rates facilitate the nucleation of twins as derived from the same thermodynamic model by further reducing the critical nucleation radius for twin formation to a value comparable to the critical radius for defect-free nucleation [8]. Fig. 8 shows the relative difference between perfect and twin nuclei radius,
rtwin rperfect rperfect
Fig. 8. Plot of the relative difference between perfect and twin nuclei radius,
rtwin rperfect rperfect
, as a function of deposition rate. Curves computed for
materials with high (Al), moderate (Cu), and low twin boundary energy (Ag) show that the difference between the critical nucleation radius drops significantly with increasing deposition rate, and that Ag has a particularly small difference.
This thermodynamic model appears to account well for the formation of {1 1 1} high density growth twins in the Ag (1 1 1) films since the nucleation probability of twinned and perfect nuclei are close to equal. However, at the same deposition rate, the average spacing in Ag (1 1 0) films is drastically greater, 42 nm, with a broad distribution (Fig. 4b). The creation of any {1 1 1} coherent twin boundary requires the introduction of a Shockley partial dislocation with a Burgers vector of 1/6 h1 1 2i, in the closepacked {1 1 1} plane. In the Ag (1 1 1) films only in-plane coordinated movement of one atomic layer (via introduction of a Shockley partial) during growth is needed to form a twin boundary. For the thermodynamic model, the thickness of twinned nuclei is assumed to be the interplanar spacing of one {1 1 1} atomic plane, so the model is in agreement with the twin formation mechanism. However in Ag (1 1 0) films, as shown schematically in Fig. 9, the {1 1 1} plane is inclined to the h1 1 0i growth direction.
, vs. deposition rate for three mono-
lithic metals, Ag, Cu and Al, with low to high twin boundary energy. For Ag films at a deposition rate of 0.2 nm s1, the relative radius difference is only 5%, which is considered sufficient for forming significant numbers of twin boundaries. The deposition rate used in this ˚ s1, and corresponds experiment for both films is 29 A to a critical nucleation radius difference of only 2.5%. The formation of dense twin boundaries in Cu has been ob˚ s1 [2,4] whereas served at deposition rates of 20–40 A growth twins are rarely observed in Al films.
Fig. 9. Schematic of the twin formation mechanism for the Ag (1 1 0) film. During growth the creation of a twin boundary on the inclined {1 1 1} plane by the introduction of a Shockley partial dislocation, 1/6 h1 1 2i, requires out-of-plane displacement of 2–3 atomic layers partially in the growth direction. In contrast, for the Ag (1 1 1) film, the nucleation of a twin boundary is created by displacing atoms by 1/6 h1 1 2i in-plane within one atomic plane normal to the growth direction, i.e. the movement of fewer atomic layers.
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Hence the introduction of a Shockley partial in the (1 1 1) plane will require the coordinated out-of-plane movement (partially along the growth direction) of at least 2–3 {1 1 0} atomic planes. Hence, the probability for the nucleation of (1 1 1) twins is significantly reduced. Such analysis is qualitative in nature, but it indicates that the orientation of the close packed planes relative to the growth direction is another major parameter that can significantly affect the formation of growth twins. It should be noted that in contrast to evaporation techniques, magnetron sputtering is a non-equilibrium process where adatoms have greater kinetic energy which allows them to diffuse across the substrate surface to preferentially fill voids and make a denser film surface. The relatively low Ar pressure used during the deposition also enhances this tendency towards fully dense (1 1 1) and (1 1 0) planes [43]. The Ag (1 1 1) epitaxial nt structure is quite unique as the defect density (i.e. (1 1 1) twin boundaries) is high, but the defects are coherently oriented throughout the film thickness. At low magnification the boundaries between adjacent columnar domains in the Ag (1 1 1) films appear to be abrupt (Fig. 2a–c). However, when examined more closely it is seen that the boundary is less clearly defined, and a significant number of twins do not actually terminate at the domain boundary. The extension of twin variants across the domain boundary is highlighted in Fig. 10. The two images compare the same area in bright field and dark field mode, and the black and white areas indicate two different twin variants. Many black and white twin variants extend
Fig. 10. Continuity of twin domains. Cross-sectional TEM micrograph of twin boundaries in Ag (1 1 1) films examined along the Ag ½0 1 1 zone axis in centered bright field (BF) and dark field (DF) mode. (a) In BF mode, the columnar domain boundaries (marked by the white triangles) appear as distinct barriers between the domains. (b) In DF mode the twin variants often extend through several apparent columnar domain boundaries.
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across two or more vertical domain boundaries. Variants that terminate at the boundary show R3 {1 1 2} incoherent twin boundaries (ITBs), instead of the distinct high or lowangle grain boundaries seen in polycrystalline nt films. There is also evidence of the ITBs in the SAD pattern in the form of two extra spots between the zero-order and (1 1 1) spots (Fig. 2b, inset). Similar ITBs have also been observed in Au and epitaxial nt Cu films [44,45]. 4.3. The influence of twin boundaries on indentation hardness There are some difficulties in comparing hardness values from different nanostructured Ag materials due to differences in measurement techniques. Bulk nanocrystalline specimens are typically analyzed by macro- and microhardness Vickers measurements [46–48], and it is difficult to directly compare nanoindentation experiments to such measurements. Hence we will only compare our nanoindentation results to other nanoindentation studies. Indentation hardness results from this study and the literature (including bulk nanocrystalline, single crystals and other Ag films) are compared in a compiled Hall–Petch type plot in Fig. 11 [28–31,49,50]. The horizontal axis in this plot is the size of the dominant microstructural feature that influences the transmission of dislocations, and hence the hardness. In most cases it is the grain size, but for the films in this study it is the average twin spacing. The slope is fitted for the values gathered from the literature. The indentation hardness from the Ag (1 1 1) film is lower than that predicted by the Hall–Petch slope for larger grains, but the film is ultimately harder than most other films reported in the literature. It has been shown [51] that in the region when dislocation pile-up governs the hardening behavior
Fig. 11. Hardness vs. feature size. Nanoindentation hardness data from different Ag materials is compiled from different sources for comparison in a Hall–Petch type of plot. The results from bulk, bulk nanocrystalline, and other Ag films follow a linear relation as indicated by the dashed line. The Ag (1 1 1) films in this study deviate from the slope, and are among the highest reported indentation hardness results. The hardness of the twinned Ag (1 1 0) films deviates from the general trend, and the details are discussed in text.
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of metal multilayers the critical resolved shear stress to pass a dislocation through the interface is expressed by 1=2 Gbs sHP ¼ s0 þ ð5Þ ð1 mÞph0 where s0 is the resolved shear stress needed to cause a dislocation to glide on the slip plane, G is the shear modulus, b is the Burger’s vector magnitude, s is the “barrier strength” of the layer boundary, v is Poisson’s ratio, and h0 is the distance between obstacles. Based on Eq. (5), s is related to the slope of the Hall–Petch plot via 2 k HP pð1 mÞ s ¼ ð6Þ Gb where kHP is the slope of a Hall–Petch plot showing resolved shear stress as a function of d0.5. To apply this relation, we assume that horizontal twin boundaries act similarly to layer interfaces as barriers to dislocation transmission. If we estimate by the Tabor relation [52,53] H 2:7r, where r is flow stress, and r 3s using a Taylor factor of 3, then kHP can be estimated by dividing the slope in Fig. 11 by 8.1. We then apply Eq. (6) with G = 30 GPa, b = 0.289 nm, and v = 0.37, to find s 0:532 GPa. Hence, the peak hardness estimated using similar factors is 4.3 GPa. The Ag (1 1 1) films in this study achieve nearly 50% of this estimated peak hardness. Twin boundaries have been shown to increase the strength in other fcc metals by acting as barriers to the transmission of dislocations [5,7,54,55]. However, the Ag (1 1 0) indentation hardness falls far short of the value predicted by the Hall–Petch slope in Fig. 11 for an average twin spacing of 42 nm. During loading along the direction normal to the twin boundaries in the Ag (1 1 1) films, there is very little shear stress resolved onto the lateral (horizontal) {1 1 1} plane, and hence dislocations on this {1 1 1} plane cannot migrate. Instead dislocations on the other (non-horizontal) set of {1 1 1} planes will be activated, but as they propagate they quickly encounter strong resistance from a horizontal twin boundary. In this case the hardness is dominated by dislocation activities confined between closely spaced twin boundaries. MD simulations have shown that a resolved shear stress of 1.7–3 GPa is required to transmit a dislocation across a coherent twin boundary in Ni [7,13,14]. In contrast, during normal loading of the Ag (1 1 0) films with inclined twin boundaries, much greater applied stress can be resolved onto the inclined {1 1 1} planes. This will have two consequences, both of which may lead to the observed low hardness of Ag (1 1 0) films. First, perfect dislocations may glide relatively easily on the {1 1 1} planes, and since the glide direction is parallel to the twin boundary, these dislocations may encounter less resistance from coherent {1 1 1} twin boundaries. Second, the resolved shear stress can activate the movement of Shockley partial dislocations, and lead to the migration of twin boundaries. The migration of twin boundaries has been observed by in situ nanoinden-
tation studies in sputtered nt Cu, and in parallel by MD simulations [24]. MD simulations have shown that a relatively low shear stress, 0.3 GPa, is required for the migration of ITBs in 2 nm thick twins in Cu [24]. Further work is under way to investigate the low strength observed in the nt Ag (1 1 0) films. Finally the indentation hardness values seen in the current nt Ag (1 1 1) films are greater than those seen for most other Ag films [30,31]. Twin densities are not available for any of these other films. It is probable that the ˚ s1) and e-beam evaporation lower deposition rate (5 A technique used by Cao et al. [31] resulted in a lower twin density than in this study. The Ag films deposited by Panin et al. [30] were annealed after deposition, which caused an increase in grain size and likely increased twin spacing. 5. Conclusions Epitaxial nanotwinned Ag (1 1 1) and Ag (1 1 0) films were grown successfully on Si (1 1 1) and Si (1 1 0) substrates by magnetron sputtering. The microstructures of these two types of films differ in the density and orientation of twin boundaries. Both films show greatly enhanced hardness in comparison to bulk Ag. Besides the deposition rate and stacking fault energy, we have rationalized that the orientation of close-packed {1 1 1} planes relative to the film growth direction can play a significant role in varying twin density. The strengthening effect can be attributed to high densities of growth twins that resist the transmission of single dislocations, and the different orientation and density of twin boundaries in the Ag (1 1 1) and (1 1 0) films lead to quite different indentation hardness values. High density twins can significantly improve the mechanical strength of the Ag films, which might make Ag more attractive for various industrial applications such as in microelectronics. Acknowledgements We acknowledge financial support by NSF-DMR metallic materials and nanostructures program, under Grant no. 0644835, and access to the Center for Integrated Nanotechnologies at Los Alamos National Laboratory through user program. Access to the microscopes at the Microscopy and Imaging Center at Texas A&M University is also acknowledged. References [1] Anderoglu O, Misra A, Ronning F, Wang H, Zhang X. J Appl Phys; 2009. p. 106. [2] Anderoglu O, Misra A, Wang H, Ronning F, Hundley MF, Zhang X. Appl Phys Lett; 2008. p. 93. [3] Chen XH, Lu L, Lu K. J Appl Phys; 2007. p. 102. [4] Anderoglu O, Misra A, Wang H, Zhang X. J Appl Phys; 2008. p. 103. [5] Zhang X, Misra A, Wang H, Swadener JG, Lima AL, Hundley MF, Hoagland RG. Appl Phys Lett; 2005. p. 87. [6] Xu L, Xu D, Tu KN, Cai Y, Wang N, Dixit P, Pang JHL, Miao JM. J Appl Phys; 2008. p. 104.
D. Bufford et al. / Acta Materialia 59 (2011) 93–101 [7] Zhang X, Misra A, Wang H, Nastasi M, Embury JD, Mitchell TE, et al. Appl Phys Lett 2004;84:1096. [8] Zhang X, Misra A, Wang H, Shen TD, Nastasi M, Mitchell TE, et al. Acta Mater 2004;52:995. [9] Zhang X, Wang H, Chen XH, Lu L, Lu K, Hoagland RG, Misra A. Appl Phys Lett; 2006 p. 88. [10] Lu K, Lu L, Suresh S. Science 2009;324:349. [11] Lu L, Chen X, Huang X, Lu K. Science 2009;323:607. [12] Lu L, Shen YF, Chen XH, Qian LH, Lu K. Science 2004;304:422. [13] Zhang X, Misra A, Wang H, Lima AL, Hundley MF, Hoagland RG. J Appl Phys 2005;97:5. [14] Zhang X, Anderoglu O, Hoagland RG, Misra A. JOM 2008;60:75. [15] Wang J, Huang HC. Appl Phys Lett; 2006. p. 88. [16] Zhu T, Li J, Samanta A, Kim HG, Suresh S. P Natl Acad Sci USA 2007;104:3031. [17] Jin ZH, Gumbsch P, Albe K, Ma E, Lu K, Gleiter H, et al. Acta Mater 2008;56:1126. [18] Jin ZH, Gumbsch P, Ma E, Albe K, Lu K, Hahn H, et al. Scripta Mater 2006;54:1163. [19] Afanasyev KA, Sansoz F. Nano Lett 2007;7:2056. [20] Zepeda-Ruiz LA, Sadigh B, Biener J, Hodge AM, Hamza AV. Appl Phys Lett; 2007. p. 91. [21] Li X, Wei Y, Lu L, Lu K, Gao H. Nature 2010;464:877. [22] Lu L, Zhu T, Shen YF, Dao M, Lu K, Suresh S. Acta Mater 2009;57:5165. [23] Li BQ, Sui ML, Li B, Ma E, Mao SX. Phys Rev Lett; 2009. p. 102. [24] Wang J, Li N, Anderoglu O, Zhang X, Misra A, Huang JY, et al. Acta Mater 2010;58:2262. [25] Anderoglu O, Misra A, Wang J, Hoagland RG, Hirth JP, Zhang X. Int J Plasticity 2010;26:875. [26] Han K, Hirth JP, Embury JD. Acta Mater 2001;49:1537. [27] Legoues FK, Liehr M, Renier M, Krakow W. Philos Mag B 1988;57:179. [28] Pharr GM, Oliver WC. J Mater Res 1989;4:94. [29] Fu YQ, Shearwood C, Xu B, Yu LG, Khor KA. Nanotechnology 2010;21:115707. [30] Panin AV, Shugurov AR, Oskomov KV. Phys Solid State 2005;47:2055.
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[31] Cao YF, Allameh S, Nankivil D, Sethiaraj S, Otiti T, Soboyejo W. Mater Sci Eng A-Struct 2006;427:232. [32] Park KH, Jin HS, Luo L, Gibson WM, Wang GC, Lu TM. Epitaxy of semiconductor layered structures: symposium; 1988. p. 271. [33] Park KH, Smith GA, Rajan K, Wang GC. Metall Trans A 1990;21:2323. [34] Nason TC, You L, Lu TM. J Appl Phys 1992;72:466. [35] Freund LB, Suresh S. Thin film materials: stress, defect formation, and surface evolution. Cambridge, England; New York: Cambridge University Press; 2009. [36] Hata A, Akimoto K, Horii S, Emoto T, Ichimiya A, Tajiri H, et al. Surf Rev Lett 2003;10:431. [37] Mckinley A, Williams RH, Parke AW. J Phys C Solid State 1979;12:2447. [38] Pronin II, Faradzhev NS, Gomoyunova MV. Tech Phys Lett 1997;23:142. [39] Masten A, Wissmann P. Thin Solid Films 1999;343:187. [40] Ichimiya A, Iwashige H, Lijadi M. Thin Solid Films 1996;282:36. [41] Narayan J, Larson BC. J Appl Phys 2003;93:278. [42] Hirth JP, Lothe J. Theory of dislocations. New York: McGraw-Hill; 1967. [43] Marechal N, Quesnel E. Thin Solid Films 1994;241:34. [44] Rittner JD, Seidman DN, Merkle KL. Phys Rev B 1996;53:R4241. [45] Wang J, Anderoglu O, Hirth JP, Misra A, Zhang X. Appl Phys Lett; 2009. p. 95. [46] Qin XY, Wu XJ, Zhang LD. Nanostruct Mater 1995;5:101. [47] Kizuka T, Ichinose H, Ishida Y. J Mater Sci 1997;32:1501. [48] Kobelev NP, Soiver YM, Andrievskii RA, Gunter B. Fiz Tverd Tela 1994;36:216. [49] Christopher D, Smith R, Richter A. Nanotechnology 2001;12:372. [50] Zhao MH, Slaughter WS, Li M, Mao SX. Acta Mater 2003;51: 4461. [51] Anderson PM, Foecke T, Hazzledine PM. MRS Bull 1999;24:27. [52] Tabor D. The hardness of metals: Oxford University Press; 2000. [53] Mata M, Anglada M, Alcala J. J Mater Res 2002;17:964. [54] Christian JW, Mahajan S. Prog Mater Sci 1995;39:1. [55] Babyak WJ, Rhines FN. Trans Am Inst Min Metall Eng 1960;218:21.
Acta Materialia 59 (2011) 93–101 www.elsevier.com/locate/actamat
High strength, epitaxial nanotwinned Ag films D. Bufford a, H. Wang b, X. Zhang a,⇑ a
Department of Mechanical Engineering, Materials Science and Engineering Program, Texas A&M University, College Station, TX 77843-3123, USA Department of Electrical Engineering, Materials Science and Engineering Program, Texas A&M University, College Station, TX 77843-3128, USA
b
Received 29 July 2010; received in revised form 3 September 2010; accepted 5 September 2010
Abstract Epitaxial silver films with (1 1 1) and (1 1 0) orientations were deposited by magnetron sputtering onto silicon (1 1 1) and (1 1 0) substrates, respectively. High density growth twins with an average spacing of a few nanometers are observed in the (1 1 1) oriented films, with twin boundaries oriented normal to the growth direction. Twins are observed in the (1 1 0) oriented films with a much lower twin density, and the twin boundaries are oriented 60° from the growth direction. The epitaxial nanotwinned Ag (1 1 1) and (1 1 0) films have respective indentation hardness values of 2 and 1 GPa. The influences of deposition parameters, stacking fault energy, and orientation of {1 1 1} planes on the formation of nanotwins are discussed. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Epitaxial growth; Nanoindentation; Nano-scale twins; Sputtering; Transmission electron microscopy (TEM)
1. Introduction Nanotwinned (nt) structures have been reported in facecentered-cubic (fcc) metals, and these highly twinned structures lead to unique electrical [1–3], thermal [4–6] and mechanical properties [1,4,5,7–12]. In comparison to high angle grain boundaries in nanocrystalline metals, coherent R3 {1 1 1} twin boundaries in nt metals have much lower energy, and hence nanotwins are much more stable at higher temperatures. The average twin spacing in sputtered nt Cu only increases from 4 to 16 nm after annealing at 0.8 Tm (Tm is the melting temperature), while grain size increases by an order of magnitude [4]. Meanwhile the electron scattering coefficient of coherent twin boundaries (CTBs) is measured to be an order of magnitude lower than that of high angle grain boundaries [1]. The most extensively studied aspects of nt metals are their mechanical properties. Nanotwins induce a substantial increase in mechanical strength. Experimental observations and molecular dynamics (MD) simulations [7,13–20] have shown that ⇑ Corresponding author. Tel.: +1 979 845 2143.
E-mail address: [email protected] (X. Zhang).
twin boundaries act as strong barriers to the transmission of dislocations, leading to increased mechanical strength. A recent study has shown that a negative Hall–Petch relation, occasionally observed in nanocrystalline metals, may also exist in electrodeposited nt Cu [11]. A similar phenomenon has been observed in large scale MD simulations [21]. Besides high strength, certain nt metals also possess significant ductility as revealed by large strain in tension and under rolling [9–12]. High densities of trapped dislocations are observed at twin boundaries after deformation [22], and the density of mobile dislocations appears greater in nt metals with smaller twin spacing. Our recent studies have shown that twin boundaries can be mobile under stress; detwinning phenomena in sputtered nt Cu have been examined in situ inside a transmission electron microscope, and detwinning mechanisms were further revealed by MD simulations [23,24]. The detwinning mechanisms can explain the annihilation of very fine twins (1–2 nm twin spacing) in rolled polycrystalline nt Cu [25], and may also account for the “softening” (negative Hall–Petch relation) observed in electrodeposited nt Cu. The formation of twin boundaries and stacking faults during growth of sputtered nt metal is a less well
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.09.011
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understood subject. Our thermodynamic model has predicted that twin formation depends strongly on the deposition rate and twin boundary energy (or stacking fault energy, as it tends to correlate with twin boundary energy) [8,26]. Another intriguing phenomenon is the orientation of growth twins. In sputter-deposited polycrystalline Cu and 330 stainless steel films, twin boundaries are oriented predominantly perpendicular to the growth direction [7,9], whereas twin boundaries are often randomly oriented in thick films fabricated by pulsed electrodeposition [3]. In comparison to nt Cu, twins in Ag have received little attention. Silver has the lowest twin boundary energy among all elemental fcc metals, and hence it might form even higher densities of twins than Cu during sputtering. Although some cross-sectional transmission electron microscopy (TEM) work has previously been performed on epitaxial Ag films, the goal of the study was to examine the Ag–Si interface [27]. Hence, the formation of growth twins in Ag films and their effects on mechanical strength have not yet been studied. Also it is of interest to compare twin-induced hardening in nt Ag films with compiled mechanical property data from various types of Ag structures, including single crystals [28], bulk nanocrystals [29], and polycrystalline Ag films with fewer twins [30,31]. Furthermore, Ag has the highest room-temperature electrical conductivity and thermal conductivity among all elemental metals, but it is very soft, and hence its use in microelectronics applications is limited. These attributes make Ag an attractive model system for the study of twin boundary formation and twin-induced strengthening mechanisms, and these studies could have direct effects on the application of Ag in the electronics industry. In this paper, we demonstrate that high density nanotwins can be formed in epitaxial Ag films on both Si (1 1 1) and Si (1 1 0) substrates, and we examine the possible formation mechanisms of nanotwins. By controlling the Ag epitaxial orientation, it is possible to control the orientation and density of growth twins, and consequently affect the film strength significantly.
experiments, performed by a Fischerscope HM2000XYp indenter with a Vickers indenter tip. 3. Results The normal h–2h XRD scans for the Ag films grown on Si (1 1 1) and (1 1 0) substrates are plotted in Fig. 1. The absence of all other Ag peaks in the XRD spectrum of the Ag film on Si (1 1 1) suggests the formation of an epitaxial Ag film along the (1 1 1) orientation. The XRD spectrum for the Ag film on Si (1 1 0) shows a primary Ag (2 2 0) peak with very weak (1 1 1) Ag peaks, which suggests that the film is highly textured in the Ag (2 2 0) orientation. Plane-view TEM micrographs of the Ag (1 1 1) films (Fig. 2a) show numerous nearly hexagonal domains. The boundaries between domains appear less well-defined than those for a typical polycrystalline grain structure. The SAD pattern (Fig. 2a, inset), collected with a large aperture to include numerous domains, shows a structure characteristic of a single crystal viewed along the Ag [1 1 1] zone axis. Cross-section TEM specimens of the Ag (1 1 1) films were examined along orthogonal Ag ½0 1 1 and ½2 1 1 zone axes to reveal the microstructure and epitaxial relationships between the film and the substrate. When viewed from the ½0 1 1 zone axis (Fig. 2b), both the columnar domain structure and twin boundaries are easily discerned. The twin boundaries appear every few nanometers oriented normal to the growth direction, and are so closely spaced that it is impractical to differentiate between the matrix and twins. The SAD pattern (Fig. 2b, inset) shows clear evidence of (1 1 1) twins, as well as a single-crystal-like pattern with distinguished diffraction dots. When examined from the orthogonal ½2 1 1 zone axis (Fig. 2c), columnar domain boundaries are still visible. However, the twin boundaries are invisible, as this direction does not look edge-on at the twin boundaries. When examining the twin boundary by HRTEM along the ½0 1 1 zone axis, the zigzag structure of adjacent twin variants is apparent (Fig. 2d).
2. Experimental Ag films, 2 lm in thickness, were deposited by magnetron sputtering onto HF etched single crystal silicon (1 1 1) and (1 1 0) substrates. The deposition chamber was evacuated to a base pressure of approximately 8.0 108 Torr, and Argon pressure during deposition was 2 mTorr. Xray diffraction (Bruker-AXS D8 Bragg–Brentano X-ray Diffractometer, Cu Ka radiation) was used to analyze the texture in the deposited films. Cross-section and plane-view specimens for TEM studies were prepared by mechanical grinding and polishing followed by low energy ion milling. These specimens were analyzed by a JEOL 2010 transmission electron microscope with 200 kV accelerating voltage. High resolution TEM (HRTEM) imaging was performed with a JEOL 3000F microscope operated at 300 kV. Film hardness was determined by instrumented nanoindentation
Fig. 1. XRD spectra of sputtered films. The absence of other peaks in the XRD spectrum for the Ag (1 1 1) film on the Si (1 1 1) substrate suggests the formation of an epitaxial film. A highly textured Ag (1 1 0) film forms on the Si (1 1 0) substrate with orders of magnitude lower Ag (1 1 1) diffraction peak.
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Fig. 2. (a) Plane-view TEM micrograph from the Ag (1 1 1) film on the Si (1 1 1) substrate showing numerous nearly hexagonal domains with an average size of 120 nm. The inset SAD pattern clearly shows single crystal-like diffraction along the Ag [1 1 1] zone axis. (b) Cross-section view from the ½0 1 1 zone axis reveals high density growth twins with twin boundaries normal to the growth direction. (c) Cross-section view examined from the ½2 1 1 zone axis shows no sign of twins. (d) HRTEM micrograph and the inset FFT show the formation of coherent R3 {1 1 1} twin boundaries.
The inset fast Fourier transform (FFT) in the micrograph confirms the presence of R3 {1 1 1} coherent twin boundaries. The film deposited on the Si (1 1 0) substrate, when examined from the [1 1 1] zone axis, shows a different microstructure from the Ag (1 1 1) film. It shows a much lower density of twin boundaries, and the twins are oriented 60° from the growth direction (Fig. 3). The average twin spacing in the Ag (1 1 1) film is 9 nm, as shown in Fig. 4a, whereas the average columnar domain size (not shown here) is 120 nm. The average twin spacing in the Ag (1 1 0) films is 42 nm as shown in Fig. 4b. Plane-view TEM examination of the Ag (1 1 0) film reveals only large domains with many thickness contours and few grain boundaries, indicating that the average domain size is on the order of a few microns. The cross-section SAD patterns in Fig. 5a–d show the in-plane epitaxial orientation relation between the Ag films and Si substrates. For the Ag (1 1 1) film on the Si (1 1 1)
substrate, it is evident that Ag h1 1 2i//Si h1 1 2i and Ag h1 1 0i//Si h1 1 0i, while for the Ag (1 1 0) film on the Si (1 1 0) substrate, the orientation relationships are Ag h1 1 2i//Si h112i and Ag h1 1 1i//Si h1 1 1i. The substrate–film orientation relationships are summarized schematically in Fig. 6a and b. Zone axes of identical indices are parallel to each other within the film plane, and also along the growth direction. In epitaxial Ag (1 1 1) films there are two twin variants: Ag (1 1 1)//Si(1 1 1) with Ag ½0 1 1//Si½0 1 1, and Ag (1 1 1)//Si(1 1 1) with Ag ½0 1 1// Si½0 1 1 [32–33]. These variants correspond to a 180° rotation about the [1 1 1] axis. A hardness vs. indentation depth profile was compiled for indentation depths of 100–300 nm. Maximum indentation depth was limited to 15% of the total film thickness to avoid substrate effects, and at least nine indents were performed at each indentation depth to determine the average hardness and standard deviations. A plateau of hardness vs. indentation depth is achieved, as shown in Fig. 7. At
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4. Discussion 4.1. Epitaxial growth via domain matching epitaxy
Fig. 3. Cross-section view TEM micrographs collected from the [1 1 1] zone axis of the Ag (1 1 0) film on the Si (1 1 0) substrate reveal an interesting structure. Twin boundaries appear tilted 60° from the growth direction when examined along this orientation. The single crystal-like epitaxial character of the film is evident in the SAD pattern (inset).
Fig. 4. Twin spacing histograms. The average twin spacing in the (a) Ag (1 1 1) film is below 10 nm, and in the (b) Ag (1 1 0) film it is 42 nm.
an indentation depth of 300 nm the Ag (1 1 1) and Ag (1 1 0) films show respective indentation hardness values of 2 ± 0.04 and 1 ± 0.04 GPa.
A 2-lm thick Ag film was calculated to absorb over 95% of the X-ray beam as it passes through to the substrate and then reflects back out of the film. Thus the single crystal Si (1 1 1) and (2 2 0) substrate peaks are weak in comparison to the corresponding peaks in Ag. The XRD spectrum for the Ag (1 1 0) film shows that a small fraction of (1 1 1) and (1 0 0) oriented domains are present within the film, but the majority of the film has (1 1 0) orientation. The single-crystal-like SAD patterns from the plane-view Ag (1 1 1) TEM micrographs confirm the abundance of (1 1 1) crystallographic planes as seen in the XRD spectrum. Furthermore, the SAD patterns indicate that the domains align coherently in-plane. The cross-section and plane-view SAD patterns together indicate that both films retain the single-crystal-like epitaxial structure from the interface and throughout the whole film thickness. Although the XRD spectrum for the Ag (1 1 0) film indicates that some misoriented domains are present, the volume fraction of these domains is presumably small, as the XRD peaks are several orders of magnitude weaker in comparison to the Ag (2 2 0) peak. No differently oriented domains were found in SAD patterns collected from different parts of the TEM specimens, indicating that the whole film is epitaxial. The epitaxial quality of the Ag (1 1 0) film is slightly lower than that of the Ag (1 1 1) film, but the domain size is greater in the former case. Ag preferentially grows in close-packed (1 1 1) planes to minimize surface energy, and it has been previously reported that it is easier to achieve Ag (1 1 1)//Si (1 1 1) epitaxial growth than it is to achieve the Ag (1 1 0)//Si (1 1 0) relationship [34]. The film quality observed in this study is consistent with the previous observations. The large mismatch between the Ag and Si lattices is evident in the SAD patterns (Fig. 5a–d). Ag and Si have a large lattice parameter mismatch (aAg = 4.09 and ˚ ), with a mismatch strain, em, of 33%, calcuaSi = 5.43 A lated by using [35]: as af ð1Þ em ¼ af where as and af are the lattice parameter of substrate and film. Based on such a large mismatch strain, one-to-one epitaxial growth appears impossible. However, epitaxial growth of Ag on various low-index Si substrates has been achieved using various PVD techniques, and characterized by numerous analytical techniques [27,34,36–40]. Epitaxial growth is achieved through domain matching epitaxy with a 3Si-to-4Ag domain match. Taking n and m as the number of respective substrate and film planes involved in the matching, the mismatch strain with domain matching epitaxy, edme, is only –0.43%, estimated by using nas maf ð2Þ edme ¼ maf
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Fig. 5. SAD patterns collected at the Ag–Si interface reveal the orientation relation between the substrates and films. The patterns from the ½2 1 1 zone axis in (a) Ag (1 1 1) and (c) Ag (1 1 0) films, (b) the orthogonal ½0 1 1 zone axis in Ag (1 1 1), and (d) the orthogonal [1 1 1] zone axis in the Ag (1 1 0) films, reveal that identical indices in the film and substrate are parallel to each other.
Fig. 6. Film–substrate orientation relation schematics for (a) Ag (1 1 1)/Si (1 1 1) and (b) Ag (1 1 0)/Si (1 1 0). The films were examined by TEM along the in-plane zone axes illustrated here.
which is an adapted form of the equation used by Narayan and Larson [41] to estimate strain in domain matching epitaxy. The domain matching mechanism operates for both the Ag (1 1 1)//Si (1 1 1) and Ag (1 1 0)//Si (1 1 0) oriented films [27,34]. 4.2. The formation of high density growth twins Cross-section TEM micrographs reveal a high density of twin boundaries oriented perpendicularly to the growth direction in the Ag (1 1 1) films. Similarly structured nanotwins have been observed in other fcc metal films,
Fig. 7. Indentation hardness is plotted as a function of indentation depth. The Ag (1 1 1) films show significantly greater indentation hardness than the Ag (1 1 0) films. The error decreases with increasing depth, and hardness typically reaches a plateau by 200 nm.
notably Cu and stainless steels [4,7,9]. The inclined twins observed in the Ag (1 1 0) film form an unusual structure, and it is likely that the formation mechanism during growth is somewhat different for these twin boundaries. While twins are observed regularly in micrographs of Ag films and bulk materials, the twins observed in this study differ significantly in the high frequency that they appear,
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and in their coherent orientation throughout the films. In the literature most microscopy studies performed on Ag films focus on epitaxial growth, and hence steps were taken to minimize defect nucleation, such as using substrate heating and equilibrium deposition techniques like thermal evaporation or molecular beam epitaxy. Suppressing the formation of growth defects will also reduce the rate of twin formation. Twin density in such Ag films is typically much lower [32,33], with the twin variant only accounting for a volume fraction well below the 50% seen in the nt Ag (1 1 1) films in this study. Numerous factors lead to the formation of nanotwins in sputtered Ag films. First, Ag has a low stacking fault energy (SFE) of 17 mJ m2 [42], which allows the formation of wider stable stacking faults than in metals with higher SFE. Thus a twin boundary can remain stable with longer length in Ag than in other metals. Second, it has been shown from a thermodynamic model that twin boundary energy affects the formation of twin boundaries during film deposition by determining the difference in critical nucleation radius between defect-free and twinned nuclei [8]. From the aforementioned model, the critical nucleation radii for perfect and twinned nuclei, rperfect and rtwin , are described by the following expressions: rperfect ¼ rtwin ¼
kT X
kT X
ln
ln
c h pffiffiffiffiffiffiffiffiffii
ð3Þ
J 2pmkT PS
c h pffiffiffiffiffiffiffiffiffii J 2pmkT PS
cht
ð4Þ
where c is the surface energy, k is the Boltzmann constant, T is the substrate temperature, X is the atomic volume, J is the deposition flux, m is the atomic mass of the film species, Ps is the vapor pressure above the target, ct is the twin boundary energy, and h is the height of the nucleus (taken in this case to be the {1 1 1} interplanar spacing). It is evident from the equation that a low twin boundary energy will facilitate the formation of nanotwins by reducing the critical radius for twin nuclei. Third, higher deposition rates facilitate the nucleation of twins as derived from the same thermodynamic model by further reducing the critical nucleation radius for twin formation to a value comparable to the critical radius for defect-free nucleation [8]. Fig. 8 shows the relative difference between perfect and twin nuclei radius,
rtwin rperfect rperfect
Fig. 8. Plot of the relative difference between perfect and twin nuclei radius,
rtwin rperfect rperfect
, as a function of deposition rate. Curves computed for
materials with high (Al), moderate (Cu), and low twin boundary energy (Ag) show that the difference between the critical nucleation radius drops significantly with increasing deposition rate, and that Ag has a particularly small difference.
This thermodynamic model appears to account well for the formation of {1 1 1} high density growth twins in the Ag (1 1 1) films since the nucleation probability of twinned and perfect nuclei are close to equal. However, at the same deposition rate, the average spacing in Ag (1 1 0) films is drastically greater, 42 nm, with a broad distribution (Fig. 4b). The creation of any {1 1 1} coherent twin boundary requires the introduction of a Shockley partial dislocation with a Burgers vector of 1/6 h1 1 2i, in the closepacked {1 1 1} plane. In the Ag (1 1 1) films only in-plane coordinated movement of one atomic layer (via introduction of a Shockley partial) during growth is needed to form a twin boundary. For the thermodynamic model, the thickness of twinned nuclei is assumed to be the interplanar spacing of one {1 1 1} atomic plane, so the model is in agreement with the twin formation mechanism. However in Ag (1 1 0) films, as shown schematically in Fig. 9, the {1 1 1} plane is inclined to the h1 1 0i growth direction.
, vs. deposition rate for three mono-
lithic metals, Ag, Cu and Al, with low to high twin boundary energy. For Ag films at a deposition rate of 0.2 nm s1, the relative radius difference is only 5%, which is considered sufficient for forming significant numbers of twin boundaries. The deposition rate used in this ˚ s1, and corresponds experiment for both films is 29 A to a critical nucleation radius difference of only 2.5%. The formation of dense twin boundaries in Cu has been ob˚ s1 [2,4] whereas served at deposition rates of 20–40 A growth twins are rarely observed in Al films.
Fig. 9. Schematic of the twin formation mechanism for the Ag (1 1 0) film. During growth the creation of a twin boundary on the inclined {1 1 1} plane by the introduction of a Shockley partial dislocation, 1/6 h1 1 2i, requires out-of-plane displacement of 2–3 atomic layers partially in the growth direction. In contrast, for the Ag (1 1 1) film, the nucleation of a twin boundary is created by displacing atoms by 1/6 h1 1 2i in-plane within one atomic plane normal to the growth direction, i.e. the movement of fewer atomic layers.
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Hence the introduction of a Shockley partial in the (1 1 1) plane will require the coordinated out-of-plane movement (partially along the growth direction) of at least 2–3 {1 1 0} atomic planes. Hence, the probability for the nucleation of (1 1 1) twins is significantly reduced. Such analysis is qualitative in nature, but it indicates that the orientation of the close packed planes relative to the growth direction is another major parameter that can significantly affect the formation of growth twins. It should be noted that in contrast to evaporation techniques, magnetron sputtering is a non-equilibrium process where adatoms have greater kinetic energy which allows them to diffuse across the substrate surface to preferentially fill voids and make a denser film surface. The relatively low Ar pressure used during the deposition also enhances this tendency towards fully dense (1 1 1) and (1 1 0) planes [43]. The Ag (1 1 1) epitaxial nt structure is quite unique as the defect density (i.e. (1 1 1) twin boundaries) is high, but the defects are coherently oriented throughout the film thickness. At low magnification the boundaries between adjacent columnar domains in the Ag (1 1 1) films appear to be abrupt (Fig. 2a–c). However, when examined more closely it is seen that the boundary is less clearly defined, and a significant number of twins do not actually terminate at the domain boundary. The extension of twin variants across the domain boundary is highlighted in Fig. 10. The two images compare the same area in bright field and dark field mode, and the black and white areas indicate two different twin variants. Many black and white twin variants extend
Fig. 10. Continuity of twin domains. Cross-sectional TEM micrograph of twin boundaries in Ag (1 1 1) films examined along the Ag ½0 1 1 zone axis in centered bright field (BF) and dark field (DF) mode. (a) In BF mode, the columnar domain boundaries (marked by the white triangles) appear as distinct barriers between the domains. (b) In DF mode the twin variants often extend through several apparent columnar domain boundaries.
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across two or more vertical domain boundaries. Variants that terminate at the boundary show R3 {1 1 2} incoherent twin boundaries (ITBs), instead of the distinct high or lowangle grain boundaries seen in polycrystalline nt films. There is also evidence of the ITBs in the SAD pattern in the form of two extra spots between the zero-order and (1 1 1) spots (Fig. 2b, inset). Similar ITBs have also been observed in Au and epitaxial nt Cu films [44,45]. 4.3. The influence of twin boundaries on indentation hardness There are some difficulties in comparing hardness values from different nanostructured Ag materials due to differences in measurement techniques. Bulk nanocrystalline specimens are typically analyzed by macro- and microhardness Vickers measurements [46–48], and it is difficult to directly compare nanoindentation experiments to such measurements. Hence we will only compare our nanoindentation results to other nanoindentation studies. Indentation hardness results from this study and the literature (including bulk nanocrystalline, single crystals and other Ag films) are compared in a compiled Hall–Petch type plot in Fig. 11 [28–31,49,50]. The horizontal axis in this plot is the size of the dominant microstructural feature that influences the transmission of dislocations, and hence the hardness. In most cases it is the grain size, but for the films in this study it is the average twin spacing. The slope is fitted for the values gathered from the literature. The indentation hardness from the Ag (1 1 1) film is lower than that predicted by the Hall–Petch slope for larger grains, but the film is ultimately harder than most other films reported in the literature. It has been shown [51] that in the region when dislocation pile-up governs the hardening behavior
Fig. 11. Hardness vs. feature size. Nanoindentation hardness data from different Ag materials is compiled from different sources for comparison in a Hall–Petch type of plot. The results from bulk, bulk nanocrystalline, and other Ag films follow a linear relation as indicated by the dashed line. The Ag (1 1 1) films in this study deviate from the slope, and are among the highest reported indentation hardness results. The hardness of the twinned Ag (1 1 0) films deviates from the general trend, and the details are discussed in text.
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of metal multilayers the critical resolved shear stress to pass a dislocation through the interface is expressed by 1=2 Gbs sHP ¼ s0 þ ð5Þ ð1 mÞph0 where s0 is the resolved shear stress needed to cause a dislocation to glide on the slip plane, G is the shear modulus, b is the Burger’s vector magnitude, s is the “barrier strength” of the layer boundary, v is Poisson’s ratio, and h0 is the distance between obstacles. Based on Eq. (5), s is related to the slope of the Hall–Petch plot via 2 k HP pð1 mÞ s ¼ ð6Þ Gb where kHP is the slope of a Hall–Petch plot showing resolved shear stress as a function of d0.5. To apply this relation, we assume that horizontal twin boundaries act similarly to layer interfaces as barriers to dislocation transmission. If we estimate by the Tabor relation [52,53] H 2:7r, where r is flow stress, and r 3s using a Taylor factor of 3, then kHP can be estimated by dividing the slope in Fig. 11 by 8.1. We then apply Eq. (6) with G = 30 GPa, b = 0.289 nm, and v = 0.37, to find s 0:532 GPa. Hence, the peak hardness estimated using similar factors is 4.3 GPa. The Ag (1 1 1) films in this study achieve nearly 50% of this estimated peak hardness. Twin boundaries have been shown to increase the strength in other fcc metals by acting as barriers to the transmission of dislocations [5,7,54,55]. However, the Ag (1 1 0) indentation hardness falls far short of the value predicted by the Hall–Petch slope in Fig. 11 for an average twin spacing of 42 nm. During loading along the direction normal to the twin boundaries in the Ag (1 1 1) films, there is very little shear stress resolved onto the lateral (horizontal) {1 1 1} plane, and hence dislocations on this {1 1 1} plane cannot migrate. Instead dislocations on the other (non-horizontal) set of {1 1 1} planes will be activated, but as they propagate they quickly encounter strong resistance from a horizontal twin boundary. In this case the hardness is dominated by dislocation activities confined between closely spaced twin boundaries. MD simulations have shown that a resolved shear stress of 1.7–3 GPa is required to transmit a dislocation across a coherent twin boundary in Ni [7,13,14]. In contrast, during normal loading of the Ag (1 1 0) films with inclined twin boundaries, much greater applied stress can be resolved onto the inclined {1 1 1} planes. This will have two consequences, both of which may lead to the observed low hardness of Ag (1 1 0) films. First, perfect dislocations may glide relatively easily on the {1 1 1} planes, and since the glide direction is parallel to the twin boundary, these dislocations may encounter less resistance from coherent {1 1 1} twin boundaries. Second, the resolved shear stress can activate the movement of Shockley partial dislocations, and lead to the migration of twin boundaries. The migration of twin boundaries has been observed by in situ nanoinden-
tation studies in sputtered nt Cu, and in parallel by MD simulations [24]. MD simulations have shown that a relatively low shear stress, 0.3 GPa, is required for the migration of ITBs in 2 nm thick twins in Cu [24]. Further work is under way to investigate the low strength observed in the nt Ag (1 1 0) films. Finally the indentation hardness values seen in the current nt Ag (1 1 1) films are greater than those seen for most other Ag films [30,31]. Twin densities are not available for any of these other films. It is probable that the ˚ s1) and e-beam evaporation lower deposition rate (5 A technique used by Cao et al. [31] resulted in a lower twin density than in this study. The Ag films deposited by Panin et al. [30] were annealed after deposition, which caused an increase in grain size and likely increased twin spacing. 5. Conclusions Epitaxial nanotwinned Ag (1 1 1) and Ag (1 1 0) films were grown successfully on Si (1 1 1) and Si (1 1 0) substrates by magnetron sputtering. The microstructures of these two types of films differ in the density and orientation of twin boundaries. Both films show greatly enhanced hardness in comparison to bulk Ag. Besides the deposition rate and stacking fault energy, we have rationalized that the orientation of close-packed {1 1 1} planes relative to the film growth direction can play a significant role in varying twin density. The strengthening effect can be attributed to high densities of growth twins that resist the transmission of single dislocations, and the different orientation and density of twin boundaries in the Ag (1 1 1) and (1 1 0) films lead to quite different indentation hardness values. High density twins can significantly improve the mechanical strength of the Ag films, which might make Ag more attractive for various industrial applications such as in microelectronics. Acknowledgements We acknowledge financial support by NSF-DMR metallic materials and nanostructures program, under Grant no. 0644835, and access to the Center for Integrated Nanotechnologies at Los Alamos National Laboratory through user program. Access to the microscopes at the Microscopy and Imaging Center at Texas A&M University is also acknowledged. References [1] Anderoglu O, Misra A, Ronning F, Wang H, Zhang X. J Appl Phys; 2009. p. 106. [2] Anderoglu O, Misra A, Wang H, Ronning F, Hundley MF, Zhang X. Appl Phys Lett; 2008. p. 93. [3] Chen XH, Lu L, Lu K. J Appl Phys; 2007. p. 102. [4] Anderoglu O, Misra A, Wang H, Zhang X. J Appl Phys; 2008. p. 103. [5] Zhang X, Misra A, Wang H, Swadener JG, Lima AL, Hundley MF, Hoagland RG. Appl Phys Lett; 2005. p. 87. [6] Xu L, Xu D, Tu KN, Cai Y, Wang N, Dixit P, Pang JHL, Miao JM. J Appl Phys; 2008. p. 104.
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