Evolution of Structure, Composition, and Stress in Nanoporous Gold Thin Films with Grain-Boundary Cracks
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- Sun, Y. & Balk, T.J. Metall and Mat Trans A (2008) 39: 2656. doi:10.1007/s11661-008-9625-z
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Nanoporous gold (np-Au) thin films were fabricated from Au-Ag alloy films sputtered onto substrates. At several stages of dealloying, the evolution of the microstructure and Ag content were analyzed and stress in the np-Au thin films was measured. A nanoporous structure evolved almost immediately throughout the film thickness, and the ligament width coarsened during further dealloying, with a time dependence of t1/8. The initial alloy films, which contained 25 at. pct Au, became stress free after extended dealloying and during thermal cycling up to 200 °C. Preferential dissolution caused cracking at grain boundaries, which accommodated a portion of the volume contraction from dealloying, but the films nonetheless remained attached to their substrates.
Nanoporous gold (np-Au) has received a growing amount of attention recently, due to its potential applications in areas such as sensing, actuation, catalysis, and supercapacitance,[1–4] all of which would benefit from the high surface-to-volume ratio and noble-metal chemistry of np-Au. Nanoporous noble metals are formed by a selective dissolution process called dealloying, during which the less noble atoms (e.g., Ag) are dissolved from a precursor alloy (e.g., Au-Ag), leaving behind a nanoscale, interconnected network of Au ligaments and open pores.[5–7] Although one study of the mechanical properties of np-Au was first published 16 years ago, most research on this material has focused on its synthesis, structure, and mechanism of formation. Several studies have concentrated on the deformation mechanisms and ligament strength of np-Au,[9–15] and this area appears to be gaining research attention. Li et al. analyzed the failure behavior of np-Au beams of various ligament sizes using a three-point bending method, and reported a sample-size-driven ductile-to-brittle transition in np-Au. Biener et al. calculated the hardness and yield strength of np-Au based on nanoindentation measurements and found that the yield strength of np-Au was ∼10 times larger than that predicted by the Gibson–Ashby scaling laws. Volkert et al. reported a high yield strength of 1.5 GPa for 15-nm-diameter np-Au ligaments by uniaxial compression, which approaches the theoretical strength of Au. However, our preliminary work conducted in conjunction with the current study (described in this article) suggests that the strength of bulk np-Au measured by microindentation may be significantly lower than the values reported by Biener et al. and Volkert et al., depending on the initial alloy composition and final microstructure after dealloying. The mechanical behavior of np-Au is not completely understood and requires further investigation.
Thin films of np-Au can be readily produced, with the advantage that the dealloyed structure is uniform through the thickness. Most studies of np-Au thin films[18–20] have used broad, freestanding films. However, these are difficult to handle and fabricate into structures. Producing np-Au thin films supported by a substrate, which is the aim of the current study, may help solve the problems associated with the instability of freestanding np-Au films. Such an approach also lends itself to wafer curvature measurements of np-Au film stress at various processing intervals, as well as to an evaluation of the mechanical behavior of np-Au film as a function of temperature.
In this article, the structure, composition, and mechanical behavior of np-Au thin films during dealloying and thermal cycling are discussed. The 25 at. pct Au precursor alloy yields stress-free but extensively cracked films, which nonetheless exhibit excellent adhesion to the substrate. This system offers an opportunity to systematically study np-Au thin films supported by substrates.
Thin films of a 25 at. pct Au-75 at. pct Ag alloy of various thicknesses were sputtered onto different substrates at room temperature in a high-vacuum chamber (Orion Series, AJA International, Inc., North Scituate, MA) with a base pressure of ∼10−6 Pa. Substrates included glass slides and 180-μm-thick (100)-oriented silicon wafers (CrysTec GmbH, Berlin, Germany) that had been coated with 10 nm of amorphous silicon oxide and 50 nm of amorphous silicon nitride. To improve adhesion of the alloy film to the glass substrates, a 10-nm gold interlayer was deposited before the Au-Ag films were sputtered, which reduced the tendency of the films to flake off the substrates during dealloying. Additionally, for the films on Si substrates, a 10-nm Ta interlayer was sputtered before the pure Au interlayer, to further improve the adhesion of the dealloyed np-Au films to their substrates.
The dealloying of the Au-Ag precursor films was achieved by immersing the samples in concentrated HNO3 (70 pct stock concentration), for times ranging from 10 seconds to 100 minutes. In order to determine the evolution of the composition and surface morphology of the np-Au specimens, additional Au-Ag films were cut into small pieces (∼5 × 5 mm) and dealloyed for 10, 20, and 30 seconds, and 1, 3, 5, 10, 30, 60, and 100 minutes. The morphology of the film surface at various dealloying times was observed with a scanning electron microscope (SEM) (S900, Hitachi, Ltd., Tokyo, Japan). Energy-dispersive X-ray spectroscopy (EDS) (S3200 SEM, Hitachi, Ltd., Tokyo, Japan) was used to determine the film composition at each dealloying stage.
Stress in the np-Au films was measured using a wafer curvature apparatus (FLX-2320-S, Toho Technology Corporation, Nagoya, Japan). The stress evolution of a single sample during dealloying was tracked by measuring the curvature of the film and substrate following each dealloying time interval. A three-dimensional map of film stress was generated from diametric scans performed in rotational increments of 15 deg, which permitted the calculation of an average stress representative of the entire wafer surface. Thermal cycles were monitored with the same wafer curvature system, at a heating and cooling rate of 5 °C/min, while the film stress was periodically measured. The stress-temperature behavior of the Ta/Au interlayer was measured separately, with a different sample, and was subtracted from the overall behavior of the composite film stack (Ta/Au/np-Au), in order to obtain the thermal cycling behavior of the np-Au layer only. Note that all the film stresses were calculated using the initial alloy thickness, since the film thickness was not measured at all stages of dealloying. Given that the film becomes 13 pct thinner during dealloying (as reported in Section IV–A, below), the actual stress of nanoporous films should be slightly (up to 15 pct) higher than the values reported here.
3 Results and observations
Summary of Film Designation and Composition of the Samples in This Study; Total Thickness of Au Ligaments in Film, Calculated from Alloy Thickness and Au Content, is Listed in Final Column; np-Au Films are Designated by Thickness of Initial Alloy Film
Film Layer Sequence
Net Au Thickness in np-Au Layer (nm)
10 nm Au + 130 nm Au-Ag
10 nm Ta + 10 nm Au + 387-nm Au-Ag
10 nm Ta + 10 nm Au + 387-nm Au-Ag
10 nm Ta + 10 nm Au + 387-nm Au-Ag
10 nm Ta + 10 nm Au + 112 nm Au-Ag
3.1 Morphology and Composition
However, the Au interlayer between Ta and Au-Ag was also vital to the integrity of dealloyed films: as-sputtered composite film stacks (identical to samples S9 and S11) were annealed at 450 °C for 20 minutes and then dealloyed, but the resulting np-Au film flaked off the Ta-coated Si substrate. This is most likely due to diffusion of Au atoms from the interlayer into the Au-Ag alloy layer, which effectively removed the Au interlayer. The presence of a continuous Au interlayer provides a better anchor for the np-Au ligaments than does the Ta interlayer alone. Similar work using Cr and Au interlayers to improve the adhesion of np-Au films to Si substrates has also been reported by other researchers. In this study, Ta was chosen as the first interlayer material, because its lack of a ductile-to-brittle transition makes it more suitable for low-temperature thermal cycling experiments.
Spacing and Width of Large (Major) Cracks in Films of Different Thicknesses; Width of Major Cracks Appears to Be Proportional to Crack Spacing
Au-Ag Alloy Film Thickness (nm)
Average Major Crack Spacing (nm)
Average Major Crack Width (nm)
Ratio of Crack Width to Spacing
3.2 Stress Evolution during Dealloying
No compressive stress was measured in either film after dealloying began. Cracking occurs immediately upon dealloying, but the film stress decreases to zero only after extended times. Overall, it appears that dealloying causes stress relaxation, as opposed to the generation of tensile stresses that one could reasonably expect based on volume contraction.
3.3 Thermal Cycling Behavior
During the dealloying of np-Au thin films, several observations were made that not only indicate which compositional and microstructural changes occur, but also reveal the time sequence of their progression. This permits speculation about how these various changes may be connected to one another.
During dealloying, significant volume contraction occurs and should generate tensile stresses in the np-Au films. However, extensive cracking of the film takes place at the grain boundaries and should relieve the film stress. This appears to be the case for almost all of the films studied here, except for the 112-nm film subjected to a liquid nitrogen dip (discussed in Section C, below). Overall, the relaxation processes, including cracking, Ag depletion, and ligament coarsening, dominate the evolution of stress in these films.
4.1 Volume Contraction during Dealloying
First, consider the amount of volume contraction measured in the np-Au films on Si. As shown by the data in Table II and the micrographs in Figures 2 and 3, the ratio of the major crack width to the crack spacing is approximately 9 pct. This can be interpreted as the linear shrinkage (i.e., along one dimension) of the film plane during dealloying. However, as was shown in Figure 4, major cracks have a wedge shape; thus, the average crack width through the film thickness is only half that measured at the surface. The average linear contraction is, therefore, more properly estimated as 4.5 pct. Moreover, since this linear contraction occurs in two dimensions in the plane of the film, this implies a biaxial contraction of ∼9 pct.
To determine the total volume contraction, one must also consider the reduction in thickness caused by dealloying. As was shown in Figure 4, cross-sectional SEM measurements of dealloyed np-Au thin films revealed that the film thickness decreased significantly, e.g., from 382 to 331 nm, for sample S11. This corresponds to a thickness contraction of ∼13 pct in this sample. When this thickness contraction is considered along with the ∼9 pct biaxial contraction in the plane of the film, which was attributed to the grain-boundary cracks discussed earlier, a total volume contraction of 21 pct is calculated (1–0.91 × 0.87). This agrees well with the findings of Parida et al., who observed that the dealloying of bulk Au-Ag alloys resulted in a volume shrinkage of up to 30 pct. In contrast, Dixon et al. measured lower thicknesses for np-Au films than for alloy films, but attributed the possible thickness variations to sputtering conditions rather than to the dealloying process itself. Nonetheless, the films in the present study, which have a lower Au content that appears to lead to film cracking, exhibited a consistent thickness reduction that can be explained by dealloying. The film cracks shown in Figures 1 through 4 appear to partially accommodate the total shrinkage during dealloying, while preserving the lateral overall sample dimensions and allowing the blanket np-Au film to remain attached to the substrate across its width/diameter.
Along with the volume contraction that occurs during dealloying, the relative density of the np-Au changes with respect to the value that would be expected based on the initial alloy composition. The relative density is simply the density of a porous material relative to that of the fully dense bulk material. Because Au and Ag have nearly identical lattice parameters, the volume/thickness percentage of Au in the precursor alloy is taken to be the atomic percentage of Au in the Au-Ag alloy, i.e., 24.3 pct, in the current study. If dealloying simply removed the Ag atoms and did not change the overall film dimensions (or cause cracking), the relative density of the np-Au films would also be 24.3 pct. However, the 21 pct total volume contraction measured here implies that the actual relative density is higher. The corrected value should thus be 0.243/0.79, or 31 pct.
4.2 Time Dependence of Ligament Coarsening
A significant finding of this study is that the Ag loss does not occur simultaneously with the ligament coarsening. Instead, the most rapid rates of Ag depletion appear to precede ligament coarsening, although there is some overlap between the two. As was shown in Figures 5 and 6(a), significant coarsening of np-Au ligaments begins after 1 minute, when over 75 pct of the initial Ag content has been removed. This finding does not appear to be due to a discrepancy between the surface observations from the SEM images and the through-thickness chemical analysis with EDS, since the film surface should either have the same dealloyed composition as the film interior or, perhaps, a slightly lower Ag content. As was shown in Figure 4, the porosity is uniform throughout the film thickness at dealloying times of 1 and 10 minutes, suggesting that the Ag content is also uniform through the thickness. Even if the curves in Figure 5 are indeed affected by a surface-vs-interior discrepancy, the curve representing the Ag content may need to be shifted down or to the left, in order to obtain a lower Ag content at the film surface, for comparison with the SEM measurements of the ligament width. This would still support and, indeed, strengthen the claim that the ligament width increases after the Ag depletion is nearly complete.
In addition to the observation that most of the Ag depletion occurs before ligament coarsening, Figures 5 and 6 indicate that relaxation of the film stress also precedes any significant increase in the ligament width. The rapid, substantial decreases in the Ag content and film stress are concomitant; thus, the initial reorganization of the Au atoms into fine nanoscale ligaments occurs simultaneously with the measured stress reduction. With regard to a mechanism for ligament coarsening, film stress is not expected to play a dominant role. Nonetheless, extended dealloying (beyond 10 minutes) does lead to ligament coarsening and further relaxation until the film is nearly stress free, so film stress may provide a small contribution to ligament coarsening. Alternatively, a nearly stress-free state may facilitate coarsening; a substantial tensile stress, which decreases in accord with the Ag content, could counteract the driving force for ligament coarsening and, thereby, delay the onset of coarsening until stress has dropped to a threshold value that happens to coincide with the nearly complete Ag depletion. Thus, it may be a combination of lowered Ag content and film stress that is a prerequisite for ligament coarsening.
The finding that Ag depletion precedes ligament coarsening may also be due to the fast dealloying time, which, in turn, is due to the low film thickness and correspondingly short distance over which the mass transport of depleted Ag must occur. Nonetheless, this apparent distinction between the Ag loss and the increase in ligament width permits the determination of the time dependence of Au ligament coarsening in np-Au films.
The ligament coarsening discussed here is that which occurs after almost all the Ag has been removed, the so-called “post-etch coarsening.” During dealloying, the coarsening of the ligaments is due to the diffusion of Au atoms and is driven by capillarity, i.e., the reduction in surface energy, as discussed by Erlebacher. Presumably, capillarity is also the driving force in the post-etch coarsening regime, with the surface diffusion of Au creating thicker ligaments.
The time dependence of the ligament coarsening observed in this study cannot be explained on the basis of existing models, although a surface-diffusion model for sintering does come close and should be very relevant to this process. First, in the case of second-phase particle coarsening (within a parent matrix) due to capillary forces, which is driven by a reduction in the total interfacial energy, the radius R exhibits an Ostwald ripening dependence R ∝ t1/3. Since this is clearly different from np-Au ligament coarsening, it is not surprising that it differs from the t1/8 time dependence observed here. Second, if a coarsening model based on surface diffusion is considered, e.g., for two spherical particles that undergo neck growth during sintering, a time dependence w ∝ t1/5 is obtained for the increase in thickness w of the neck region between the two particles. This is closer to the ligament coarsening observed here, but still does not match the t1/8 dependence. One reason for this lack of agreement may be that, in the sintering model, the centers of the two particles are assumed to remain at a constant distance. However, during the coarsening of the np-Au, the average distance between nodes (i.e., the length of the ligaments) increases along with the ligament diameter.
Nonetheless, the sintering model does contain certain important features that apply to the coarsening of np-Au ligaments. In both cases, surface diffusion drives atoms toward the midpoint of each ligament by capillarity. In the sintering model, the rate-limiting flux occurs as one-dimensional surface diffusion along the length of a cylinder of uniform radius, yielding the w ∝ t1/5 dependence. In addition to the geometric differences between ligament coarsening and particle sintering, the presence of the small tensile stress in the np-Au film may play a role. In the current study, coarsening appears to occur in the absence of significant stress, although a slight tensile stress does persist throughout the time interval in Figure 9. A tensile stress would tend to make the ligaments thinner and would, thus, counteract the capillarity-driven coarsening, requiring longer times for a given increase in diameter. Thus, it may be possible, using a new model, to describe the experimental time dependence w ∝ t1/8 found here. This will be examined in more detail in a future study.
4.3 Dealloying-Induced Stress Changes
It was observed that the film stress decreases in accord with the Ag content during the first 10 minutes of dealloying. The correlation between stress and the Ag content, e.g., as shown in Figure 6(a), is very strong and suggests that the two are coupled. A simple interpretation of this correlation is that the depletion of Ag exposes a high concentration of Au atoms on the surface of the eroding alloy, followed by surface diffusion and the agglomeration of Au into stress-free ligaments. Because the Au atoms form a completely new structure (the ligaments), this would presumably relax the pre-existing stress in the Au-Ag alloy, at least partially. Thus, the total film stress would decrease, as long as the Ag is removed during dealloying. As discussed later, however, it appears that the reduction in the stress can be attributed to film cracking.
Within the first minute of dealloying, at least three changes occur: (1) cracks appear in all films (Figures 1(a) and (b), 2(a), and 3(a)), (2) pores form throughout the film thickness (Figure 4(b)), and (3) the film stress and Ag content decrease by more than 75 pct (Figure 6). Dealloying, which necessarily involves the depletion of Ag and the formation of pores, should generate tensile stresses within the evolving nanoporous structure, due to the overall volume contraction. However, the average film stress decreases instead. As discussed here, this may be partly due to the reorganization of the Au atoms. However, it is more likely due to the extensive cracking that occurs at the grain boundaries, at least at the beginning of dealloying, when cracking occurs and the largest decrease in film stress is measured. The cracks are most likely stress free, thereby relieving stress over an area fraction at least as large as the areal crack density (∼9 pct, accounting for the wedge shape of the cracks). This would offset the tension that may develop within the np-Au ligaments in the regions away from cracks and lead to a lower average film stress. Therefore, measurements of stress in dealloyed thin films provide a lower bound for the actual np-Au biaxial stress, and most likely substantially underestimate that actual stress.
As was shown in Figure 6, most of the eventual Ag depletion and stress relaxation occurred in the first minute of dealloying. Within the same time interval, extensive cracking also occurred (Figure 3). In a separate study of crack-free np-Au films, the dissolution of Ag was accompanied by an increase in stress, instead of by the relaxation observed here, implying that the initial formation of nanoporous structure does not reduce film stress. It is, therefore, proposed that the tensile stress expected from the dealloying process was relaxed by cracking, in the films studied here. The amount of stress relaxation due to crack formation can be estimated from equations proposed by Freund and Suresh based on finite-element modeling. According to their model, the curvature change of a cracked film can be estimated by the ratio of the film thickness to the crack spacing. In the case of np-Au films, these ratios are 0.35 and 0.43 for samples S9 and G1, respectively (Table II). A reduction in substrate curvature (or, equivalently, film stress) of 95 to 100 pct is calculated, which agrees well with measurements of stress evolution during dealloying (Figures 6 and 7). Technically, the reduction in the biaxial curvature (film stress) of 95 to 100 pct applies to an array of parallel cracks (not a two-dimensional crack pattern, such as that in a np-Au film), but this calculation can be used as a first-order estimate of the biaxial curvature reduction and indicates that an equivalent one-dimensional crack array would reduce virtually all of the film-stress-induced substrate curvature. The film stress would, therefore, be expected to drop almost to zero, as was measured here.
Nonetheless, since grain-boundary cracking occurs immediately during dealloying, the stress evolution can be used to calculate the minimum stress that must be present in the np-Au ligaments. The highest film stress measured during dealloying was 27 MPa, as shown in Figure 7 for the 112-nm film (sample S12) after 5 minutes. Even for a thicker film (e.g., the 387-nm film in Figure 6(a)), dealloying for 5 minutes is sufficient for reducing the Ag content almost to the steady-state minimum. For the 112-nm film, therefore, it is expected that nearly all the Ag has been depleted by 5 minutes, and that the 27 MPa stress is carried by a relatively pure np-Au film. The Gibson–Ashby scaling law describes the strength of an open-cell porous material as σy = C1σs(ρnp/ρs)n, where σs and ρs are the yield strength and density, respectively, of solid Au, and ρnp is the density of np-Au. The C1 and n are empirical constants, with C1 = 0.3 and n = 3/2. As discussed here, ρnp/ρs is the relative density of the dealloyed np-Au film and is nominally 0.243 (equal to the atomic percentage of the Au in the initial alloy), with a corrected value of 0.31 (accounting for volume contraction). Using the Gibson–Ashby scaling law and the corrected relative density, the minimum equivalent bulk stress that evolved during the dealloying of the 112-nm film is 520 MPa. This stress is significantly lower than the 750 MPa value that would be calculated using the uncorrected relative density. Nonetheless, an equivalent bulk stress of 520 MPa is very high for Au, especially considering that this estimate provides a lower bound to the actual stress that evolves in the crack-free regions of np-Au during dealloying.
Nanoporous gold thin films on glass and on Si substrates were fabricated by dealloying precursor Au-Ag alloy films that had an initial Au content of ∼25 at. pct. The adhesion of the np-Au to both substrate types was significantly enhanced by depositing a Au interlayer before the alloy deposition and, for Si substrates, a Ta interlayer beneath the Au. Pore formation during dealloying was rapid, producing a nanoporous structure throughout the film thickness within 1 minute. Further dealloying caused the structure to coarsen.
Film cracking was prevalent in all the np-Au films produced from the 25 at. pct Au precursor alloy, and is likely due to preferential dealloying at certain grain boundaries. The cracks formed very quickly, many within the first minute of dealloying, and are believed to play an important role in the stress evolution of np-Au during subsequent dealloying and thermal cycling. The cracks should be stress free, thereby lowering the average film stress measured across the entire wafer. Nonetheless, scaling laws predict that an equivalent bulk stress of at least 520 MPa evolves during the dealloying of a 112-nm film. The thermal cycling of thin films did not induce a significant stress in the np-Au, perhaps due to the extensive film cracking that may have accommodated any expansion or contraction of the film.
Both the Ag content and the film stress decreased significantly and rapidly during dealloying, and these changes occurred before the ligament width began to increase appreciably. The dealloying generally caused cracking, followed by subsequent stress increases and then stress relaxation, eventually leading to a stress-free state at extended times. Calculations indicate that film cracking could account for the measured stress relaxation. Finally, ligament width was found to increase with dealloying time, according to w∝t1/8. This differs from existing models for other processes driven by surface diffusion, and may be due to geometric differences or the presence of a small tensile stress in the np-Au films.
The authors thank Ms. Sofie Burger for her assistance with the measurement of the ligament widths and Mr. Larry Rice for his support in using the SEM. The authors also acknowledge the Donors of the American Chemical Society Petroleum Research Fund (Grant No. 43324-G10), for support of this research.