Metallurgical and Materials Transactions A

, Volume 39, Issue 11, pp 2656–2665

Evolution of Structure, Composition, and Stress in Nanoporous Gold Thin Films with Grain-Boundary Cracks

Authors

  • Ye Sun
    • Department of Chemical and Materials EngineeringUniversity of Kentucky
    • Department of Chemical and Materials EngineeringUniversity of Kentucky
Article

DOI: 10.1007/s11661-008-9625-z

Cite this article as:
Sun, Y. & Balk, T.J. Metall and Mat Trans A (2008) 39: 2656. doi:10.1007/s11661-008-9625-z
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Abstract

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.

1 Introduction

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,[14] 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.[57] Although one study of the mechanical properties of np-Au was first published 16 years ago,[8] 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,[915] and this area appears to be gaining research attention. Li et al.[8] 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.[9] 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.[16] Volkert et al.[12] 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[17] 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.[9] and Volkert et al.,[12] 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[1820] 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.[21]

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.

2 Experimental

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.[22] 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

The microstructure and corresponding mechanical properties of nanoporous metals depend on several factors during dealloying, including the composition of the precursor alloy, dealloying potential, electrolyte composition, and temperature.[6] In this article, np-Au made from alloy films by free corrosion, i.e., no electrical potential was applied during dealloying, is discussed. The actual starting alloy composition measured by EDS was 24.3 at. pct Au. The film designations and compositions are shown in Table I, in which film thicknesses have been calculated from sputtering times and measured deposition rates. Note that, as discussed later, the overall thickness of np-Au (ligaments and pores) after dealloying is less than the thickness of the initial alloy film, due to volume contraction.
Table I

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

Designation

Substrate

Film Layer Sequence

Net Au Thickness in np-Au Layer (nm)

G1

Glass

10 nm Au + 130 nm Au-Ag

32

S8

Si

10 nm Ta + 10 nm Au + 387-nm Au-Ag

94

S9

Si

10 nm Ta + 10 nm Au + 387-nm Au-Ag

94

S11

Si

10 nm Ta + 10 nm Au + 387-nm Au-Ag

94

S12

Si

10 nm Ta + 10 nm Au + 112 nm Au-Ag

27

3.1 Morphology and Composition

The SEM micrographs in Figure 1 show a comparison of the surface morphology of np-Au films on glass (with a Au interlayer only) and on Si substrates (with Ta and Au interlayers). A large number of cracks were observed in both samples, even after 1 minute of dealloying. Cracking commonly occurs in np-Au,[12,23] presumably due to the volume shrinkage during dealloying.[20] Although cracking in the sample with both Ta and Au interlayers was still extensive (Figure 1 (b)), only the films on glass (with a Au interlayer only) were observed to delaminate from the substrate (Figure 1(a)). The primary difference between these two samples is the presence of a Ta interlayer. The Au/np-Au interface should be the same in both samples, implying that the interface between the Au interlayer and the underlying material strongly influences film adhesion and delamination. It is thus inferred that the Ta interlayer enhanced the adhesion of the Au interlayer to the Si substrate and was, therefore, critical to the stability of these np-Au films.
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Fig. 1

SEM micrographs showing surface morphology of np-Au films dealloyed for 1 min: (a) 130-nm np-Au on glass with Au interlayer (sample G1), in which delamination has occurred near film cracks; and (b) 387-nm np-Au on Si with Ta and Au interlayers (sample S9), in which the Ta interlayer has prevented delamination of np-Au

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.[24] 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.

Higher-magnification SEM images of the 130-nm np-Au film on glass (with a 10-nm Au interlayer) are shown in Figure 2. These images reveal several features of the morphology of the film, which are also observed in the np-Au films on Si: (1) significant “cracking” occurred and was observed at the earliest stages of dealloying, even after 1 minute; (2) the cracks appeared to extend all the way down to the substrate; (3) the average spacing of large cracks was ∼300 nm; (4) pore and ligament size increased with prolonged dealloying time; and (5) cracks in the film became less prominent at longer dealloying times, as the ligaments coarsened and the porous structure became more uniform in appearance. Note that the cracks did not shrink or disappear; neither did they grow. Instead, the surrounding ligaments and pores increased in size until they were nearly as large as the cracks (Figure 2(c)).
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Fig. 2

Evolution of nanoporous structure in 130-nm np-Au film on glass substrate (G1), after dealloying times of (a) 1, (b) 5, and (c) 10 min. Cracks appear in the film almost immediately, before pores undergo any significant growth. During dealloying, pores and Au ligaments coarsen, but the width of large cracks remains roughly constant

The evolution of morphology in a 387-nm np-Au film on a Si substrate (with Ta and Au interlayers (sample S9)) is illustrated in Figure 3. In contrast to sample G1, a Ta interlayer was added to sample S9 before sputtering the Au interlayer; this resulted in the excellent adhesion of the np-Au to the substrate at all stages of dealloying. However, cracking was still prevalent throughout the film, as is seen in Figures 3(a) through (c) and in the lower-magnification image in Figure 1(b). At longer dealloying times, the np-Au structure became more “open” and the porosity more interconnected. While the ligaments coarsened, the maximum crack width remained fairly constant (compare Figures 3(a) and (c)), as was also seen for np-Au films on glass (Figure 2).
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Fig. 3

SEM images of nanoporous structure in 387-nm np-Au film on Si substrate (S9, with 10-nm Ta and 10-nm Au interlayers) after dealloying times of (a) 1, (b) 10, and (c) 100 min

Figure 4 shows cross-sectional SEM images of a 387-nm np-Au thin film (S11) on a Si substrate, at various stages of dealloying. Figure 4(a) shows the initial alloy film before any dealloying, and reveals that the film is fully dense, with an average grain size of ∼50 nm. Figure 4(b) shows the cross section, viewed edge on, of a sample dealloyed for 1 minute; Figure 4(c) shows a sample dealloyed for 10 minutes and tilted 20 deg, which permits the film surface to be viewed along with the cross section. Figures 4(b) and (c) reveal that the np-Au layer adheres well to the pure Au interlayer (the continuous, bright line indicated by the white arrow in Figure 4(b)). After 1 minute of dealloying, the nanoporous structure has already developed throughout the entire film thickness (Figure 4(b)), in agreement with findings by Erlebacher et al.[5] The major cracks that were seen in Figures 1 through 3 extend through the film thickness and end at the Au interlayer, as is clearly shown in Figure 4(c), in which it is also seen that many of these large cracks have a wedge shape after 10 minutes of dealloying. However, after 1 minute of dealloying, some film cracks appear to be buried within the film thickness, or even to extend from the Au interlayer toward the film surface (Figure 4(b), to the left of the white arrow). It should be noted that the large, wedge-shaped cracks seen in Figure 4(c) are also observed after 1 minute of dealloying at numerous other locations. Figure 4(b) is included here to illustrate that there is a small additional population of cracks located in the film interior or at the bottom of the np-Au film. Finally, the thickness of the np-Au film in sample S11 after dealloying was measured from cross-sectional images such as those in Figure 4. Following dealloying for 1 to 10 minutes, the average thickness, as measured by SEM, was 331 nm. This is significantly less than the 382-nm alloy film thickness measured from Figure 4(a) (compare to the calculated thickness of 387 nm) before dealloying. Although the film structure before dealloying (Figure 4(a)) may not appear as clearly columnar as after dealloying (Figures 4(b) and (c)), cross-sectional focused-ion-beam imaging of similar films reveals columnar grains. All films were sputtered with identical deposition parameters (except the deposition time), but the contrast in the SEM images of the alloy films is simply lower than it is in the images of nanoporous films and, thus, the microstructure in Figure 4(a) is not as obvious.
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Fig. 4

Cross-sectional view of sample S11 (from 387-nm film of Au-Ag alloy) at different dealloying times and tilt angles: (a) as-sputtered film before dealloying; (b) 1 min of dealloying and almost no tilt (viewed edge on); and (c) 10 min of dealloying and 20-deg tilt, allowing the film surface and crack pattern to be seen clearly. After 10 min of dealloying, most cracks extend from film surface to substrate, although after 1 min of dealloying a small number of cracks are seen to start at the film/substrate interface and terminate within the np-Au film

The measurements of the average spacing of large (“major”) cracks in samples G1 and S9, presented in Table II, revealed that the crack spacing is two to three times the alloy film thickness. This is much larger than the ∼50-nm grain size (Figure 4(a)). In an earlier study of np-Au thin films, it was observed that preferential dealloying occurred at grain boundaries, even in films in which the Au content was too high for complete dealloying of the film to occur.[25] Thus, it appears that preferential dealloying may occur only at certain grain boundaries in the film, leaving clusters of attached grains between the large cracks (Figures 2 and 3). In the current study, the width of major cracks was measured, and this width appears to scale with the crack spacing. As indicated in Table II, the ratio of crack width to crack spacing is approximately 9 pct.
Table II

Spacing and Width of Large (Major) Cracks in Films of Different Thicknesses; Width of Major Cracks Appears to Be Proportional to Crack Spacing

Sample

Au-Ag Alloy Film Thickness (nm)

Average Major Crack Spacing (nm)

Average Major Crack Width (nm)

Ratio of Crack Width to Spacing

G1

130

300

28

0.093

S9

387

1100

94

0.085

At several stages of dealloying, the Ag content in the alloy/np-Au film was measured by EDS. The relative amounts of Au and Ag in each analysis were corrected for the presence of the pure Au interlayer, in order to obtain the composition within the np-Au only. Additionally, SEM micrographs from these same samples were analyzed to determine the ligament width. In each case, at least 100 ligaments were measured, in order to obtain a statistically significant measure of their size. The ligaments were measured at their midpoint, as this region typically has the smallest diameter and should, therefore, be important to an understanding of ligament failure. The variation in the Ag content and ligament width of the np-Au as a function of the dealloying time is shown for three 387-nm np-Au samples in Figure 5. Note that the error for the Ag content is ±1 pct, approximately the same size as the data points in Figure 5. For the ligament width, the 95 pct confidence interval, taken as the range of true values, is nearly constant at ±1.2 nm. When the film was dealloyed for 30 minutes, the Ag content decreased from 76 to 4 at. pct. This trend in the evolution of the Ag content with dealloying time is consistent with the results of another study,[24] although the initial alloy composition and timescale for dealloying were different in that study. As opposed to those results, the plot of the Ag content in Figure 5 focuses on the earlier stages of dealloying. Over a total dealloying time of 100 minutes, the ligament width increased by 85 pct, from 8.7 to 16.1 nm. The Ag loss occurs immediately during dealloying, and seems to precede the ligament coarsening (the ligament width remains nearly constant at 8.7 to 8.8 nm in the first minute of dealloying, whereas more than 75 pct of the initial Ag is lost in this time). This decay in the Ag content agrees well with that observed in sample G1 (a 130-nm np-Au sample on glass) reported in a preliminary study.[22]
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Fig. 5

Changes in composition and ligament width during dealloying of three 387-nm np-Au films on Si (S8, S9, and S11). Data from both samples agree well with each other. The Ag content decreases immediately and rapidly, while ligament width increases noticeably after 1 min of dealloying

3.2 Stress Evolution during Dealloying

The evolution of stress in a 387-nm np-Au film on Si (sample S11) was measured by wafer curvature at several stages of dealloying and is shown in Figure 6(a) for times up to 10 minutes. Also plotted here are the data for the Ag content (samples S8 and S11), as determined by EDS, over the same time period. The Ag content data are similar to those in Figure 5 (for samples S8 and S9) and show in greater detail the film composition during the initial stages of dealloying. For film stress, the total error is estimated at 4.6 pct, including the uncertainty in the measurement of the film thickness (2.0 pct), the accuracy of the substrate curvature values (2.0 pct), and the natural scatter of the repeated curvature measurements on the same sample (0.6 pct). From Figure 6(a), it is clear that the dealloying of the np-Au thin film is very rapid, with more than 75 pct of the Ag being removed in the first minute. Moreover, both the Ag content and the film stress decrease in similar fashion during dealloying. After 5 minutes, both have nearly reached their steady-state minima of ∼7 at. pct Ag and ∼8 MPa stress. The rapid relaxation of the film stress is illustrated in more detail in Figure 6(b), which shows the evolution of stress during the initial stages of dealloying (up to 90 seconds) for sample S8. The film stress drops quickly and reaches a plateau of ∼20 MPa within the first minute of dealloying.
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Fig. 6

(a) Evolution of Ag content and stress in two 387-nm np-Au films on Si (S8 and S11) with dealloying time. Both Ag content and film stress decrease in the same manner, rapidly approaching their steady-state minima. (b) Evolution of stress at short dealloying times for a 387-nm np-Au sample (S8). Film stress exhibits a plateau at ∼20 MPa, similar to S11 in (a)

Stress evolution curves during the longer-term dealloying of 112-nm- and 387-nm-thick np-Au films (samples S12 and S9) are shown in Figure 7. These specimens were dipped into liquid nitrogen before dealloying, in an attempt to induce a compressive stress state and to minimize cracking during dealloying. This attempt was unsuccessful, and these samples exhibited the same degree of cracking as all the others (Figure 3). Note that, for sample S9 (the 387-nm film), the samples for characterization were processed with and without a liquid nitrogen dip before dealloying. The SEM images showed no difference in the nanoporous structure of films that underwent liquid nitrogen immersion, so the microstructure for the film referenced in Figure 7 is accurately portrayed by the images in Figure 3. For both films in Figure 7, the liquid nitrogen dip caused the film stress to decrease by 15 to 17 MPa. In the case of the 112-nm film, this was enough to induce a net compressive stress in the Au-Ag alloy. Furthermore, the 112-nm film exhibited an intermediate peak in stress (27 MPa) at 5 minutes of dealloying time, after which the stress decreased monotonically. However, these differences in the film stress behavior did not affect the final stress of the np-Au after complete dealloying. Stress in both np-Au films decreased with dealloying times beyond 10 minutes; after 100 minutes, the tensile stress dropped to near zero (<1 MPa).
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Fig. 7

Stress evolution of np-Au films on Si (S9 and S12) as a function of dealloying time, following immersion in liquid nitrogen before dealloying. Stresses in Au-Ag alloy films dropped by 15 to 17 MPa when they were dipped into liquid nitrogen and decreased with prolonged dealloying time. Note that sample S12 entered compression due to the liquid nitrogen dip, then exhibited an increase and subsequent decrease in film stress 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.[20]

3.3 Thermal Cycling Behavior

The stress-temperature plot for a 387-nm np-Au film on a Si substrate (sample S11), which was dealloyed for 10 minutes and then thermally cycled, first to 100 °C and then to 200 °C, is shown in Figure 8. The initial room-temperature stress in this film was ∼3 MPa, which was 5 MPa lower than the stress measured after 10 minutes of dealloying in Figure 6 (some additional stress relaxation may have occurred before thermal cycling experiments were performed). Overall, the film exhibits no temperature dependence of stress. Although the film stress may appear to increase slightly during heating to both 100 °C and 200 °C, these changes are minimal, with a total variation in stress of <10 MPa. They appear to lie within the error of the wafer curvature system and, therefore, are more useful as an indication of the scatter in stress measurement during thermal cycling. Based on the thermal cycling studies of another np-Au film system,[26] the nanoporous structure is expected to be stable during heating up to 200 °C, with some additional coarsening of ligaments, but without loss of the open porosity.
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Fig. 8

Stress-temperature curves of a 387-nm np-Au film on Si (S11). For the 100 °C thermal cycle, film stress fluctuates around 2 MPa, while the stress varies around zero during the 200 °C cycle. The total fluctuation is less than 10 MPa for both cycles

4 Discussion

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.,[20] 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.[24] 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,[27] 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.”[6] 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.[7] Presumably, capillarity is also the driving force in the post-etch coarsening regime, with the surface diffusion of Au creating thicker ligaments.

Consider the time dependence of the ligament coarsening measured for a 387-nm np-Au film (sample S9). As was shown in Figure 5, the average ligament width (measured at the midpoint) increased monotonically from 1 to 100 minutes of dealloying time. Based on this plot, it appears that the ligament width has nearly reached a steady-state maximum of 16 to 17 nm. These data have been plotted again in Figure 9, where a log-log plot of width vs time shows a clear trend in this coarsening regime. Between 1 and 100 minutes of dealloying time, the ligament width w exhibits a time dependence w ∝ t0.13 ≈ t1/8. The rate of ligament coarsening, therefore, decreases very quickly with time, and ligaments approach a steady-state size within a relatively short time interval. For this reason, and given the rapid penetration of the etchant through the film at the beginning of dealloying, the ligament width is consistent throughout the nanoporous structure.
https://static-content.springer.com/image/art%3A10.1007%2Fs11661-008-9625-z/MediaObjects/11661_2008_9625_Fig9_HTML.gif
Fig. 9

Log-log plot of ligament width wvs dealloying time for samples S9 and S11, using the data from Fig. 5. For dealloying times longer than 1 min, i.e., once the majority of Ag has been depleted and film stress has nearly been relaxed, the ligament width scales with time according to w ∝ t0.13 ≈ t1/8

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.[28] 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.[28] 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.[20] 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,[29] 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.[30] 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[16] describes the strength of an open-cell porous material as σ= 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.

5 Conclusions

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 wt1/8. 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.

Acknowledgments

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.

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© The Minerals, Metals & Materials Society and ASM International 2008