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Low temperature, pressure-assisted sintering of nanoparticulate silver films
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Acta Materialia 56 (2008) 1820–1829 www.elsevier.com/locate/actamat
Low temperature, pressure-assisted sintering of nanoparticulate silver films Andre D. Albert a, Michael F. Becker b, John W. Keto c, Desiderio Kovar d,* a
Materials Science and Engineering Program, Center for Nano and Molecular Science and Technology and Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA b Department of Electrical and Computer Engineering, Center for Nano and Molecular Science and Technology, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA c Department of Physics, Center for Nano and Molecular Science and Technology, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA d Department of Mechanical Engineering, Center for Nano and Molecular Science and Technology, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA Received 17 August 2007; received in revised form 14 December 2007; accepted 16 December 2007 Available online 14 February 2008
Abstract The laser ablation of microparticle aerosol (LAMA) process was used to direct-write nanostructured, patterned films of silver with thicknesses in the range 20–200 lm at room temperature. A critical difference between the LAMA process and conventional processes for depositing patterned, thick films is that the LAMA process does not require surfactants that can interfere with post-deposition sintering. Thus, LAMA-produced films allow the intrinsic sintering of nanoparticulate films to be studied directly. Post-deposition sintering was conducted over a range of temperatures (100–175 °C) and compression loads (25–600 N) and the strength and electrical resistivity of the sintered samples were measured. The samples were characterized using optical microscopy, profilometry, SEM, and XRD and the density of the deposits were determined from the grain size, resistivity and known relationships between these parameters and density. LAMA-produced films were found to sinter to produce high strength, high conductivity films at temperatures 50–100 °C lower than conventional processes that use organic additives. Mechanisms for the low-temperature sintering of the nanostructured films are discussed and compared with established theory for pressure-assisted sintering. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Silver; Nanoparticles; Nanostructure; Film; Conductivity
1. Introduction There has been recent interest in methods for producing patterned metallic films at low processing temperatures to replace solders as device interconnects, as a die attach method, and for seals for temperature-sensitive MEMS devices. For die attaches and seals, pressure is typically applied during the sintering process to reduce the required processing temperatures. For example, Schwarzbauer and
*
Corresponding author. Tel.: +1 512 471 6271; fax: +1 512 471 7681. E-mail address: [email protected] (D. Kovar).
Kunhert used a paste consisting of micron-size Ag particles to join metallized Si substrates to Mo disks for power device applications [1]. After sintering at 40 MPa and approximately 220 °C, these joints had shear strengths of 100 MPa. In another study, it was reported that pressureassisted sintering conducted at 40 MPa at a temperature of 240 °C resulted in Ag joints with a shear strength of 50 MPa and a resistivity of 2.4 lX cm [2], which is less than twice the value of microcrystalline Ag (1.63 lX cm) [3]. It is well known that properties of nanoparticles (NPs) can be significantly different from the properties of the same material in bulk form. For example, Ag NPs have been observed to coarsen at temperatures as low as
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.12.034
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100 °C [4], even though the melting temperature for bulk Ag is 960 °C. Similarly, Cu NPs have been observed to form necks and sinter at room temperature [5]. Thus, the use of NPs to produce patterned films should significantly lower processing temperatures compared to using conventional micron-sized particles. Previous investigations involving Ag patterned lines generally have utilized Ag particles capped with organic coatings required to prevent agglomeration of the particles. Since there is evidence that bare NPs can sinter at temperatures lower than the pyrolysis temperatures for the organic coatings, these organic coatings can interfere with sintering processes [6]. Therefore, processing temperatures could be further reduced through utilization of a manufacturing process that does not require organic coatings to prevent agglomeration of the NPs. The use of pressure during the sintering process is expected to both further depress the sintering temperatures and inhibit grain growth [7] . To achieve these goals, we have used the laser ablation of microparticle aerosol (LAMA) process to produced patterned films. LAMA can utilize a variety of starting materials, including metals [8–10], glasses [11], and semiconductors to produce a NP aerosol at high volumetric rates [12]. NPs produced by the LAMA process are electrically charged by the ablation process and therefore do not require an organic surfactant to prevent agglomeration. By varying processing parameters, the average NP size can be controlled from about 2–40 nm [13]. Following ablation, the resulting NP aerosol is accelerated through a nozzle to high velocities and then deposited onto a translating substrate to directly write patterned, thick films. Because the NPs generated in an inert gas through LAMA are not capped by an organic, the use of the LAMA process allows study of the low-temperature sintering of NPs in the absence of surfactants or other organics. In this paper, the effects of temperature, compressive stress, and deposit thickness on the microstructure, mechanical and electrical properties, and sintering behavior of pure, nanostructured Ag films are discussed. 2. Experimental procedure 2.1. Deposition procedure A schematic of the LAMA process used to write the nanostructured Ag lines onto metallized Si substrates is shown in Fig. 1. A conventional Ag powder with a mean particle size of 2 lm is used as feedstock for the process. The microparticle powder is aerosolized using a fluidized bed with He as the carrier gas. Laminar flow of the aerosol is maintained by surrounding the flow of aerosol by a buffer flow of He with the same linear velocity. A high energy excimer laser (200 mJ) ablates the micron-sized particles in the aerosol. The laser pulse rate (200 Hz) is set so that each microparticle in the aerosol is struck at least once. The laser pulse results in breakdown and shock wave formation at each microparticle [14]. NPs are nucleated in the rarefac-
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Fig. 1. Schematic of the LAMA process [35].
tion behind the shock and are initially charged by photoionization and thermionic emission. This charging prevents agglomeration of the NPs until charge recombination occurs. Following ablation, the resulting NP aerosol flows through a skimmer and a virtual impactor to remove residual microparticles. The ablation cell and virtual impactor are at ambient pressure while the deposition chamber is pumped to 33.3 Pa (250 mtorr). This pressure differential accelerates the NPs through the deposition nozzle at high velocity, impacting the NPs onto the substrate and forming nanostructured deposits. The density of the resulting deposit and the grain size within the deposit depend strongly on the process parameters (gas type, nozzle type, and nanoparticle size) since these determine the impaction velocity/energy of the NPs. Calculations for our operating conditions show that, the impaction velocities range from greater than 1200 m s1 for 2 nm particles to approximately 500 m s1 for 50 nm particles [15]. The corresponding impaction energies range from
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about 0.8 eV per atom for 2 nm particles to approximately 0.1 eV per atom for 50 nm particles. Since the energy to melt Ag is 0.37 eV per atom, assuming that no heat dissipation occurs by conduction, these impaction energies may be sufficient to cause partial or complete melting during impaction. This is consistent with the MD simulations conducted for impaction of smaller 1 nm Ag and Au [16] particles where amphorphitization/melting is predicted upon impaction at energies of 0.25 eV per atom. In contrast, numerical simulations conducted on much larger 5–25 lm diameter particles suggest that complex stress distributions arise during impaction that can lead to adiabatic shear instabilities. As a result, deformation does not occur uniformly and melting is localized to the shear bands [17,18]. These analyses show that both particle size and impaction velocity/energy influence the deformation response of the particles upon impaction. Unfortunately, analytical calculations of the stress state during impaction are extremely difficult due to the complex temperature and stress distributions that arise and numerical analyses have not been conducted for NPs in the size range studied here. Patterned thick film lines were produced using a computer-controlled x–y stage to move the substrate position relative to the deposition nozzle. For these experiments, two patterns were used: a 5 mm per side square pattern and a serpentine pattern with 10 mm long segments separated by shorter 0.5 mm segments. For the samples with a square pattern, the x–y stage was programmed to make 10, 20 or 30 overlapping passes to build up the deposit thickness. All serpentine lines were deposited with 15 overlapping passes. Both the substrate-to-nozzle distance and the nozzle geometry determine the breadth of the deposited lines. For these experiments, the substrate-to-nozzle distance was fixed at 1 mm and a flat-plate nozzle was used. The motor speed was approximately 1.4 mm s1, so a 30 pass, square pattern was produced in approximately 8 min. The substrates used for the square-patterned samples were silicon wafers that were first coated by evaporation with a thin layer of Cr and then overcoated with a thin layer of Au before depositing the NP Ag. The serpentine-patterned samples were deposited directly onto glass substrates. All substrate surfaces were cleaned with ethanol prior to Ag deposition. 2.2. Post-deposition sintering Pressure-assisted sintering of the patterned lines was performed by applying pressure while heating the sample, as shown schematically in Fig. 2. For these experiments, the deposition substrate was set onto the bottom of a heated punch and a second substrate was placed face down on top of the substrate containing the patterned line. A 150 W band heater was attached directly to the collar to heat the samples. A type K thermocouple was threaded through a hole in the collar, a few millimeters away from the substrate to monitor temperature. An auto-tuned, digital controller was used to control the sample temperature.
Fig. 2. Schematic of the set up for pressure-assisted sintering.
A 10 kN load cell was used to monitor load during compression of the samples, giving a resolution of about ±1 N. A blank, glass substrate was utilized as the top substrate for the serpentine samples in order to prevent bonding between the deposit and top substrate. These unbonded samples were used for characterization of the microstructures of the deposits and to measure electrical conductivity. For the square samples, a metallized blank substrate was utilized (as shown in Fig. 2) in order to promote bonding of the Ag deposit to both substrates for subsequent strength testing. For both the serpentine and square samples, a small preload (10 N) was applied to the sample during temperature equilibration (3–15 min). Following equilibration, the samples were compressed at a rate of 0.15 mm min1 to the desired load, a process that took at most 2 min. The load was cycled just above and below the desired load point (±10 N), allowing the displacement-controlled test frame to run in pseudo-load control. Each sample was sintered under load at the desired temperature for 1 h. The compressive loads that were applied to the samples during sintering were varied between 0 and 600 N. To estimate the corresponding applied compressive pressures on the lines during sintering, the area over which the load was applied was measured. To accomplish this, after sintering, the samples were pulled in tension until fracture occurred (see Section 2.4). The fractured lines were then
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observed in plan view using optical microscopy. A flattened region was clearly visible along the length of each line. SEM observations of these flattened regions did not show evidence of tensile deformation from fracture and thus, the size of the flattened regions were assumed to be representative of the minimum size of the compressively deformed regions of the lines. The line length and the average width of the deformed regions were used to calculate the applied compressive pressures which are shown in Table 1. The mean applied pressures ranged from 38 MPa for lines compressed at a load of 20 N up to 460 MPa for lines compressed at 600 N. 2.3. Characterization of the patterned lines The Ag patterned lines were characterized using a number of techniques to determine the influence of sintering temperature and compression pressure on grain size and density of the deposits. The morphologies of the lines were studied using both plan-view and cross-sectional SEM. The cross-sections of the lines were measured using a diamondtipped stylus profilometer with a diameter of 12.5 lm to determine thickness and cross-sectional area of the deposits. X-ray diffraction patterns were obtained for all of the serpentine pattern samples using a h–h diffractometer with a Cu Ka source and a solid-state detector. Each scan was conducted from 30 to 90° (2h), with a step size of 0.04° and a dwell time of 6 s. The breadth of the (1 1 1) diffraction peak was used to determine the grain size of the deposits (see Section 3.4). The electrical resistivity of the serpentine samples was measured using a four-point probe method using the same procedure described in earlier work [19]. For each sample, the resistivities of two segments of each serpentine were measured, with four different measurements from each segment. The eight resulting resistivity measurements were averaged to obtain each sample resistivity. The probe station was calibrated using a known resistor of similar resistance to the sample deposits. Because of the small mass of the deposits, a direct measurement of the density from the sample mass and volume was not possible. Instead, the density was calculated from the grain size, the conductivity, and known relationships between the grain size, conductivity, and porosity using a procedure developed by Qin et al. [20] and explained in
Table 1 Mean compressive pressures and the standard deviation in the pressures as a function of the compressive pressure applied during sintering Applied compressive load (N)
Mean compressive pressure (MPa)
Standard deviation (MPa)
20 50 100 600
38 67 89 460
11 26 35 250
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detail elsewhere [19]. Qin et al. have analyzed the resistivity of nano-silver films between 45% and 99% dense. They found that the resistivity, q, of nano-grained silver can be written as a single term that takes both grain size, G, and fractional density into account q ¼ qB
lB ðl=GÞ T l
ð1Þ
where qB is the bulk conductivity of polycrystalline silver (large grains), lB and l are the electron mean free paths in the bulk and nano-materials respectively, and T* is the electron transmission coefficient at boundaries, a function of material density. This analysis is based on two important observations. First, a previous model of conductivity by Reiss et al. [21] considered electron motion through boundaries that had an electron transmission of T*. Electrons trapped between the boundaries were removed from the conduction process resulting in the T ðl=GÞ dependence of resistivity. Second, positron spectroscopy studies showed that density completely specified the electron scattering at boundaries in polycrystalline nanomaterials, [22] and thus, samples with the same density have the same T*. In their work on polycrystalline silver, Qin et al. [20] measured the linear dependence of ln(T*) vs. 1/D and confirmed the utility of Eq. (1) for nano-silver over a broad range of densities and grain sizes. From Qin’s experimental data, the empirical relationships between T* and density (for 45% < D < 99%) and between electron mean free path and grain size (for G < 45 nm) were determined. We used this information and calculated T* from our data using Eq. (1) and interpolated ln(T*) vs. 1/D in order to infer the density of our samples. Note that this analysis does not include a contribution to the conductivity due to neck growth during early stage sintering. If neck growth occurred it would result in a further increase in the conductivity. Thus, our calculated density values represent an upper bound to the actual density. 2.4. Tension testing of bonded substrates Following pressure-assisted sintering, the square-patterned samples were prepared for tension testing (Fig. 3) using epoxy to bond a 6.4 mm diameter cylindrical post to the deposition substrate and to bond a bracket to the top substrate. Using a ring and an elastic band to connect the bracket to the testing frame allowed the sample to be smoothly loaded and eliminated a moment or shear resulting from misalignment of the sample relative to the load train. Samples were tested at a displacement rate of 50 mm min1 until failure; a typical test required about 10 min. A 250 N load cell was used for tension testing, giving a resolution of ±0.025 N. After tension testing, optical microscopy was performed on each sample to measure the bonded area between the top substrate and the silver deposit. A flat-topped ridge was clearly visible on each line that resulted from pressure-assisted sintering. It was assumed that the bonded
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Fig. 3. Schematic of the tension testing procedure. Fig. 4. (a) SEM cross-section of a representative as-deposited line; (b) plan view SEM of a representative line after tension testing.
area corresponded to the area of this flat-topped region and that subsequent fracture of the silver during tension testing did not result in significant plastic deformation that would lead to errors in this measurement. The failure stress was calculated from failure load and the bonded areas. 3. Results 3.1. Deposit morphologies An SEM cross-section of a representative, as-deposited line is shown in Fig. 4a and a plan-view SEM micrograph of the fracture surface after testing is shown in Fig. 4b. The pseudo-Gaussian profile observed in the as-deposited line (Fig. 4a) is typical. The peak thicknesses of the deposited lines, measured using profilometry, varied from 20 to 200 lm, and depended on the deposition conditions and the number of times the pattern was overwritten (10, 15, 20 or 30 times). The fracture surface after tension testing (Fig. 4b) shows that significant deformation occurred in the Ag line during the compression process, resulting in the flat top along the ridge of the line. Optical microscopy and SEM/EDS also revealed that, for samples that failed at low stresses, both the bottom deposition substrate and the
top substrate had silver bonded to the metallization layers indicating that bonding occurred between the silver deposit and the metallized surfaces and implying that fracture had initiated in the silver line rather than at one of these interfaces. SEM/EDS were used to confirm that the fracture surfaces consisted of a mixture of Ag, Au/Cr, and Si ripped from the blank substrate. Fracture outside of the Ag deposit was more common for samples that failed at higher stresses. 3.2. Strength The tensile strengths of samples tested after pressureassisted sintering are plotted in Fig. 5 as a function of processing temperature. Each datum point is a single measurement and the bold, vertical lines connect samples processed at the same conditions. The other lines group the data by their approximate thickness (30, 60, or 90 lm) and by the compression load applied during processing. From this plot it is apparent that a sintering temperature of 100 °C resulted in bonding of the Ag to the metallization layer but little cohesive strength in the Ag layer itself, even when sintered under large compressive stresses. Despite the scat-
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Fig. 5. Tensile strength for samples following pressure-assisted sintering. The legend indicates the approximate thickness of the deposit and the compressive load applied during bonding.
ter in the data, it is clear that for temperatures of 125 °C or above there is a general trend of increasing cohesive strength of the layer with temperature. It is also clear that there is not a strong influence of compression load applied during sintering on the tensile strength. For example, similar strengths were measured for two samples that were both 60 lm thick and that were sintered at 150 °C but with compressive forces that varied by more than an order of magnitude (50 N vs. 600 N). Comparing samples sintered at the same temperatures, there also does not appear to be a trend that would suggest that line thickness plays an important role in determining cohesive strength.
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strains associated with thermal expansion mismatch between the substrate and films will result in shifting of diffraction peaks rather than peak broadening and therefore were not analyzed. Examination of Williamson–Hall plots for the LAMAproduced specimens revealed no evidence of peak broadening due to internal strain (i.e. the Williamson–Hall plots did not have positive slope), consistent with previous analysis on similar lines [19]. Since the only significant cause of peak broadening in our samples was due to the ultrafine grain size, a standard Scherrer analysis was then applied. The (1 1 1) peaks from the XRD patterns were utilized for the Scherrer analysis since these peaks had about 5 times the intensity of the next most intense peaks, resulting in a better signal-to-noise ratio compared to the other peaks. The grain sizes, determined from XRD, are shown in Fig. 6 as a function of temperature for different compression loads applied during sintering. The average grain size determined from XRD Scherrer analysis for as-deposited serpentine samples was 25 nm. Upon heating to 100 °C the grain size increased to just over 30 nm and further increases in temperature resulted in more grain growth. Heating to 175 °C resulted in a grain size of 40–45 nm. For the range of loads that were applied (0–600 N) there was there was no obvious effect of applied pressure during sintering on grain size. 3.4. Electrical resistivity The resistivity, normalized to the resistivity of bulk microcrystalline silver (1.63 lX cm) [3], is shown in Fig. 7. The error bars represent the standard deviation of the resistivities measured on different regions of the same sample.
3.3. Grain size Because of the large stresses and localized heating that occurs during impaction, it is possible that defects may be introduced into the lines during writing. To determine if this was the case, X-ray diffraction data for as-deposited and sintered samples were analyzed using Williamson–Hall plots [23]. This analysis allows the two major causes of peak broadening in films (grain size effects and internal strain resulting from defects such as dislocations and stacking faults) to be deconvoluted by analyzing the angular dependence of line broadening. The integral line breadth, b, can be separated into two components that have different dependencies. Broadening due to grain size effects is proportional to cos h whereas the line breadth associated with strain is proportional to tan h, where h is the Bragg angle. Thus, a plot of b cos h vs. sin h should yield a straight line with a positive slope. The slope of the line is proportional to the magnitude the internal strain and the intercept is related to the grain size. Note that biaxial
Fig. 6. Grain size vs. sintering temperature. The legend indicates the compression load applied during sintering.
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3.5. Density The influence of processing temperature on average density is shown in Fig. 8. This figure shows that there is a general correlation between sintering temperature and density, with increasing density at higher sintering temperatures. Samples sintered at 100 °C had an average density of around 74% of bulk microcrystalline silver, while samples processed at 150–175 °C reached an average density of slightly greater than 83%. For reference, in previous work, the density for as-deposited samples produced under similar conditions to those used in this study was about 70%. For the range of compression loads that were studied (0– 600 N) there does not appear to be a significant effect of compression load applied during sintering on the density of the deposits. 4. Discussion and analysis Fig. 7. The effect of temperature on the resistivity, normalized to the resistivity of bulk, polycrystalline Ag. The legend indicates the compressive load applied during sintering.
The data do not indicate that there is a significant effect of compressive load on the resistivity of the samples. From Fig. 7 it is apparent that increasing the sintering temperature decreased the resistivity of the samples. Samples processed at 100 °C had resistivities as high as 9.7 times the bulk resistivity of Ag, while samples processed at 150 °C had resistivities as low as 2.7 times the bulk resistivity of silver. For comparison, the resistivity for as-deposited Ag produced by LAMA is nearly 13 times bulk resistivity [19] .
4.1. Strength and resistivity Comparisons of the current work to previous work on pressure-assisted sintering of nanostructured silver are complicated by differences in the processes used to produce the samples. Most of the previous work has utilized screenprinting of silver pastes containing Ag NPs and then subsequent bonding of the substrates by applying either heat or heat and pressure [1,24,25]. Required temperatures for this process are above 225 °C because they require that the organics needed for screen-printing of the paste be removed before sintering can take place. For example, at a processing temperature of 300 °C, Bai et al. achieved a strength of 43 MPa using a nanopowder silver dispersed in a paste [25]. At a processing temperature of 240 °C, Zhang et al. achieved a shear strength of 50 MPa using a commercially available silver paste deposited as a slurry [2]. Despite the large scatter in strengths that we observed, which was likely caused by variations in line thickness along the length of the line (See Fig. 4b), the LAMA-produced samples had maximum strengths similar to the strengths to those reported by Zhang et al. but were sintered at temperatures 50–100 °C lower [2]. While Schwarzbauer and Kuhnert reported higher strengths [1], given their sample geometries, it is likely that geometric strengthening contributed to their measured strengths. Comparing the measurements of resistivity to previous results, similar resistivities are obtained [2,25–27], but similarly to our observed strength measurements, we see that the LAMA process is capable of achieving these resistivities at processing temperatures that are 50–100 °C lower than other thick film manufacturing processes. 4.2. Deformation of the NPs
Fig. 8. Effect of processing temperature on average density of the deposited lines. The legend indicates compressive load applied.
Qin et al. prepared bulk samples from nanopowders by applying pressure at room temperature to a powder compact [28]. Their results show that it is possible to achieve
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densities as high as 99% from Ag nanopowders at room temperature by applying large pressures (up to 1.5 GPa). Although they measured the hardness of their compacts, which is sensitive to density, they did not measure the tensile strength after compression, so the degree of bonding that occurred between the particles during room temperature compression is not known. Based on the hardness values obtained by Qin et al., the yield strength for Ag with a 20 nm grain size should be about 500 MPa. The nominal applied pressure during our sintering experiments ranged from 40 to 460 MPa. However, this pressure is transmitted through particle-to-particle contacts and thus the local stresses at the contact points between particles is significantly higher than the nominal pressure. For example, from Hertzian contact theory, the maximum stress, r0 is given by r0 ¼
3P 2pa2
ð2Þ
where P is the applied load and a is the contact area between the two particles. Thus, the local stresses during pressure-assisted sintering are likely much larger than the yield strength of the Ag, particularly during the early stages of compaction when the contact area between particles is small. We expect that the NPs located near the top of the LAMA-produced lines, where the pressures are highest, undergo severe plastic deformation that results in densification of these portions of the lines. However, neither strength nor resistivity were found to be correlated to sintering load. For example, the resistivity of a sample processed at 600 N was comparable to the resistivity of a sample processed at the same temperature but with no load (Fig. 6). Thus, our results cannot be explained simply by plastic deformation of the NPs. Further, the results of our tensile tests show that, although the density of portions of the line may be increased by plastic deformation, the degree of bonding that occurs between the particles is negligible at temperatures less than 100 °C. This suggests that although plastic deformation may occur in nanograined Ag even at temperatures of 100 °C or less, under typical conditions for pressure-assisted sintering, bonding of the NPs requires higher temperatures. 4.3. Diffusional processes In previous work we have shown that during pressureless sintering of LAMA-produced Ag, significant coarsening occurs but little or no densification takes place when samples are heated at slow-to-moderate heating rates (5– 25 °C min1) to 100–400 °C [19]. It was postulated that coarsening takes place during slow heating due to the dominance of surface diffusion at low temperatures. Thus, faster heating rates would reduce the residence time at low temperatures and aid in densification. This hypothesis was confirmed in nanostructured gold films that were heated at fast rates (1200 °C min1) [29]. Thus, in this study, fast heating rates and pressure-assisted sintering
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were both employed in an attempt to increase the ratio of grain boundary to surface diffusivity, and therefore to increase densification rates. Coble’s model for pressure-enhanced densification has been used to explain the influence of pressure on densification kinetics [30]. In that model, the densification rate, dD/ dt is given by 1 dD 15 Dgb dgb X 2csv ¼ / þ P ð3Þ a D dt 2 r G3 RT where Dgb is the grain boundary diffusivity, dgb is the effective width of the grain boundaries where grain boundary diffusion occurs, X is the atomic volume of Ag = 1.03 105 m3 mol1, G is the grain size, R is the gas constant, T is temperature, Pa is the applied pressure, u is the pressure multiplication factor acting at the particle contacts, csv is the surface/vapor interfacial energy, and r is the pore radius. Since the relative densities of the as-deposited lines are about 70%, the intermediate and final stages of sintering are the relevant stages of sintering in this study; in this regime u 1/r. The pore radius is expected to vary with density. If the grains are assumed to be uniform tetrakaidecahedra, then the porosity, p = 1D, can be related to the size of the pore radius and the grain size by [7] ! p r3 p¼ ð4Þ 2 l3p where lp is the length of a side of the tetrakaidecahedron and is given by G lp ¼ pffiffiffiffiffi 10
ð5Þ
Thus, the pore radius is given by r ¼ 0:24Gð1 DÞ
1=3
ð6Þ
To use Coble’s model to predict densification rates, we must know Dgb, dgb, and csv. Although the grain boundary structures in nanomaterials are similar to those in materials with conventional grain sizes [31], there is evidence that diffusion phenomena are fundamentally different in nanograined materials. Therefore, it is possible that the values of these parameters that are typically obtained using single crystal or polycrystals with grain sizes an order of magnitude or larger than those used in our studies may not be accurate for ultra-fine grained materials [32]. In addition, diffusion data are typically gathered at much higher temperatures than those studied here. Thus, comparison of our results with existing data requires three assumptions: (1) diffusivities are not strongly sensitive to grain size; (2) the diffusivities can be extrapolated to lower temperatures; (3) the grain boundary energy is not strongly sensitive to grain size. These assumptions cannot be justified for quantitative comparisons. However, it is nevertheless useful to assume these to be valid and assess the corresponding trends. With these assumptions, it can be shown that there is not a strong influence of the relative density on the
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predicted densification rate [33]. Surface energy also has only a modest effect on densification rate [34]. Therefore, for the remainder of our comparisons, we will assume a constant relative density of 90% and a constant surface energy of 1.14 J m2. A temperature-independent surface diffusivity of 1 1013 m2 s1 and a grain boundary diffusivity ranging from 1.4 1018 m2 s1 at 100 °C to 8.3 1013 m2 s1 at 400 °C were used for the calculations. The predicted densification rate (log scale) is plotted against pressure in Fig. 9 at a temperature of 100 °C. This plot shows that applied pressure has a much stronger influence on conventional, microcrystalline materials than ultra-fine-grained materials. For example, the predicted densification rate increases by more than two orders of magnitude for a 500 nm grain size upon increasing the pressure from zero to 1.5 GPa. For a material with a 5 nm grain size, however, the predicted densification rate only increases about 10% over the same pressure range. Thus, although pressure is an effective means for enhancing diffusion-assisted densification for materials with conventional grain sizes, pressure is much less effective at enhancing diffusion-assisted densification in nanograined materials. This prediction is consistent with our experimental results that showed little effect of pressure during processing on the properties of the deposits. In Fig. 10, the predicted densification rate (log scale) is plotted against temperature for materials with a range of grain sizes from 5 to 500 nm. For these plots, an applied pressure of 500 MPa was used, which is similar the highest pressures used for our experiments. From Fig. 10, it is apparent that the predicted densification rate is strongly dependent on both temperature and grain size. For exam-
Fig. 9. The effect of pressure on densification rate for Ag with different grain sizes at an initial density of 0.9 and a temperature of 100 °C. Numbers beside lines indicate the grain/particle size.
Fig. 10. The effect of temperature on densification rate for Ag with different grain sizes at an initial density of 0.9 and a pressure of 500 MPa. Numbers beside lines indicate the grain/particle size.
ple, at a temperature of 100 °C, the predicted densification rate is increased by approximately seven orders of magnitude by decreasing the grain size from 500 nm to 5 nm. The predicted densification rate is increased by three orders of magnitude by increasing the temperature from room temperature to 100 °C and increased another two orders of magnitude upon increasing the temperature from 100 °C to 175 °C. From this plot, the predicted densification rate for a LAMA-produced film with a 15 nm grain size ranges from 1 106 s1 at 100 °C to 1 101 s1 at 175 °C. The approximate densification rate measured from our experiments is 4 105 s1, if we assume that densification occurred uniformly during the pressure-assisted sintering process. However, it is possible that complete densification takes place early during the compression process, resulting in a non-uniform densification rate, so this inferred strain rate represents a lower bound. Although a strict quantitative comparison between the experiment and theory is not advisable given the assumptions required both in the model and in the diffusivity data, based on the level of agreement between the predicted and experimental results, diffusion could be responsible for nearly complete densification of the deposits over the range of temperatures and pressures that were investigated for these nanograined materials. However, given that plastic deformation also occurs at these pressures, it is likely that at least some of the densification occurs by rapid plastic deformation. Even in this case, however, grain boundary diffusion is important in that it leads to rounding of the triple junction pores, increased neck growth, and results in the increased bonding between the particles that is likely responsible for the high tensile strengths that we observed.
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5. Conclusions The LAMA process combined with low temperature post-processing can be used to produce high-strength bonds from nanostructured silver. The strengths of our bonded samples exceed 100 MPa at the processing temperature of 175 °C. These strengths are similar to the strengths of bonded nanostructured Ag achieved previously, but at processing temperatures that are 50–100 °C lower. Electrical conductivity measurements on our samples following pressure-assisted sintering show that the processing temperatures required to achieve high conductivities are lower than those achieved by using most other direct-write methods. At post-processing temperatures of 150 and 175 °C, our samples have electrical conductivities approaching 33% of bulk polycrystalline Ag with micron-sized grains. We suggest that the reason for the lower processing temperatures is that, unlike NPs that were studied previously, the LAMA process utilizes bare NPs that are not capped with organics that interfere with sintering. Comparing our experimental results with data for yield strengths of nanocrystalline Ag and existing pressureless and pressure-assisted densification models showed that our results can be explained based a combination of plastic deformation and pressure-assisted sintering. An existing model for pressure-assisted sintering was used to show that pressure does not strongly effect densification for ultra-fine grain samples such as ours. Increasing the sintering temperature, however, has a significant effect on the densification of nanocrystalline materials, as predicted by theory. Comparisons with previous work show the necessity of rapid heating to the processing temperature to limit coarsening and promote densification. Acknowledgments We gratefully acknowledge support from the National Science Foundation through NIRT grant DMI-0304031 and additional financial support from Stellar Micro Devices Inc., Austin, TX. References [1] Schwarzbauer H, Kuhnert R. IEEE Trans Ind Appl 1991;27:93–5. [2] Zhang Z, Lu G-Q. IEEE Trans Electr Pack Manufact 2002;25:279–83. [3] Buch A. Pure metals properties: a scientific-technical handbook. Materials Park, OH: ASM International and Freund Publishing; 1999. [4] Yeadon M, Yang JC, Averback RS, Bullard JW, Olynick DL, Gibson JM. Appl Phys Lett 1997;71:1631–3. [5] Olynick DL, Gibson JM, Averback RS. Mat Sci Eng 1995;A204:54–8.
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[6] Chen Y, Palmer RE, Wilcoxon JP. Langmuir 2006;22:2851. [7] Rahaman MN. Ceramic processing and sintering. New York: Marcel Dekker; 2003. [8] Lee J-M, Becker MF, Brock JR, Keto JW, Walser RM. IEEE Trans Magn 1996;32:4484–6. [9] Nichols WT, O’Brien DT, Malyavanatham G, Becker MF, Keto JW. In: Komarneni S, Vaia RA, Lu GQ, Matsushita J-I, Parker JC, editors. MRS proceedings: nanophase and nanocomposite materials IV, vol. 703. Warrendale, PA: The Materials Research Society; 2002. p. 209–14. [10] Malyavantham G, O’Brien DT, Becker MF, Keto JW, Kovar D. J Nanoparticle Res 2004;6:661–4. [11] Juang C-B, Cai H, Becker MF, Keto JW, Brock JW. Appl Phys Lett 1994;64:40–2. [12] Nichols WT, Keto JW, Henneke DE, Brock JR, Malyavanatham G, Becker MF, Glicksman HD. Appl Phys Lett 2001;78:1128–30. [13] Nichols WT, Malyavanatham G, Beam MP, Henneke DE, Brock JR, Becker MF, Keto JW. In: Komarneni S, Parker JC, Hahn H, editors. MRS proceedings: nanophase and nanocomposite materials III, vol. 581. Warrendale, PA: Materials Research Society; 2000. p. 193–8. [14] Becker MF, Brock JR, Cai H, Henneke DE, Keto JW, Lee J, Nichols WT, Glicksman HD. Nanostruct Mater 1998;10:853–63. [15] Huang C, Nichols WT, O’Brien DT, Becker MF, Keto JW, Kovar D. J Appl Phys 2007;101:064902. [16] Hou Q, Hou M, Bardotti L, Pre´vel B, Me´linon P, Perez A. Phys Rev B 2000;62:2825–34. [17] Assadi H, Gartner F, Stoltenhoff T, Kreye H. Acta Mater 2003;51:4379–94. [18] Borchers C, Gartner F, Stoltenhoff T, Assadi H, Kreye H. J Appl Phys 2003;93:10064–70. [19] Huang C, Becker MF, Keto JW, Kovar D. J Appl Phys 2007;102:054308. [20] Qin XY, Zhang W, Zhang LD, Jiang LD, Liu XJ, Lin D. Phys Rev B 1997;56:10596–604. [21] Reiss G, Vancea J, Hoffmann H. Phys Rev Lett 1986;56:2100–3. [22] Schaefer H-E, Wu¨rschum R, Birringer R, Gleiter H. Phys Rev B 1988;38:9545–54. [23] Williamson GK, Hall WH. Acta Metall 1953;1:22–31. [24] Palm M, Zhang LC, Stein F, Sauthoff G. Intermetallics 2002;10:523–40. [25] Bai JG, Zhang ZZ, Calata JN, Lu G-Q. In: Proceedings of IMEC2005, p. 415–24. [26] Kim D, Moon J. Electrochem Solid State Lett 2005;8:J30–3. [27] Lee H-H, Chou1 K-S, Huang K-C. Nanotechnology 2005;16:2436–41. [28] Qin XY, Wu XJ, Zhang LD. Nanostruct Mater 1995;5:101–10. [29] Seker E, Gaskins JT, Bart-Smith H, Zhu J, Reed ML, Zangari G, Kelly R, Begley MR. Acta Mater 2007;55:4593–602. [30] Coble RL. J Appl Phys 1970;41:4798–807. [31] Siegel RW, Thomas GJ. Ultramicroscopy 1992;40:376–84. [32] Yeadon M, Yang JC, Averback RS, Bullard JW, Gibson JM. Nanostruct Mater 1998;10:731–9. [33] Kovar D, Albert AD, Becker MF, Keto JW. In: Proceedings of the ASME conference on manufacturing science and engineering (MSEC 2007). Atlanta, GA: ASME; 2007. [34] Albert AD. Nanostructured Ag Produced by LAMA. Ph.D. Dissertation, University of Texas at Austin, Austin; 2007. [35] Albert AD, Huang C, Becker MF, Keto JW, Kovar D. In: Proceedings of the international symposium on synergistic effects of materials and processing (ISSEMP 2006), vol. 06–207. Kumamoto: VCH; 2006. p. 1–6.
Acta Materialia 56 (2008) 1820–1829 www.elsevier.com/locate/actamat
Low temperature, pressure-assisted sintering of nanoparticulate silver films Andre D. Albert a, Michael F. Becker b, John W. Keto c, Desiderio Kovar d,* a
Materials Science and Engineering Program, Center for Nano and Molecular Science and Technology and Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA b Department of Electrical and Computer Engineering, Center for Nano and Molecular Science and Technology, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA c Department of Physics, Center for Nano and Molecular Science and Technology, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA d Department of Mechanical Engineering, Center for Nano and Molecular Science and Technology, Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA Received 17 August 2007; received in revised form 14 December 2007; accepted 16 December 2007 Available online 14 February 2008
Abstract The laser ablation of microparticle aerosol (LAMA) process was used to direct-write nanostructured, patterned films of silver with thicknesses in the range 20–200 lm at room temperature. A critical difference between the LAMA process and conventional processes for depositing patterned, thick films is that the LAMA process does not require surfactants that can interfere with post-deposition sintering. Thus, LAMA-produced films allow the intrinsic sintering of nanoparticulate films to be studied directly. Post-deposition sintering was conducted over a range of temperatures (100–175 °C) and compression loads (25–600 N) and the strength and electrical resistivity of the sintered samples were measured. The samples were characterized using optical microscopy, profilometry, SEM, and XRD and the density of the deposits were determined from the grain size, resistivity and known relationships between these parameters and density. LAMA-produced films were found to sinter to produce high strength, high conductivity films at temperatures 50–100 °C lower than conventional processes that use organic additives. Mechanisms for the low-temperature sintering of the nanostructured films are discussed and compared with established theory for pressure-assisted sintering. Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Silver; Nanoparticles; Nanostructure; Film; Conductivity
1. Introduction There has been recent interest in methods for producing patterned metallic films at low processing temperatures to replace solders as device interconnects, as a die attach method, and for seals for temperature-sensitive MEMS devices. For die attaches and seals, pressure is typically applied during the sintering process to reduce the required processing temperatures. For example, Schwarzbauer and
*
Corresponding author. Tel.: +1 512 471 6271; fax: +1 512 471 7681. E-mail address: [email protected] (D. Kovar).
Kunhert used a paste consisting of micron-size Ag particles to join metallized Si substrates to Mo disks for power device applications [1]. After sintering at 40 MPa and approximately 220 °C, these joints had shear strengths of 100 MPa. In another study, it was reported that pressureassisted sintering conducted at 40 MPa at a temperature of 240 °C resulted in Ag joints with a shear strength of 50 MPa and a resistivity of 2.4 lX cm [2], which is less than twice the value of microcrystalline Ag (1.63 lX cm) [3]. It is well known that properties of nanoparticles (NPs) can be significantly different from the properties of the same material in bulk form. For example, Ag NPs have been observed to coarsen at temperatures as low as
1359-6454/$34.00 Ó 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.12.034
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100 °C [4], even though the melting temperature for bulk Ag is 960 °C. Similarly, Cu NPs have been observed to form necks and sinter at room temperature [5]. Thus, the use of NPs to produce patterned films should significantly lower processing temperatures compared to using conventional micron-sized particles. Previous investigations involving Ag patterned lines generally have utilized Ag particles capped with organic coatings required to prevent agglomeration of the particles. Since there is evidence that bare NPs can sinter at temperatures lower than the pyrolysis temperatures for the organic coatings, these organic coatings can interfere with sintering processes [6]. Therefore, processing temperatures could be further reduced through utilization of a manufacturing process that does not require organic coatings to prevent agglomeration of the NPs. The use of pressure during the sintering process is expected to both further depress the sintering temperatures and inhibit grain growth [7] . To achieve these goals, we have used the laser ablation of microparticle aerosol (LAMA) process to produced patterned films. LAMA can utilize a variety of starting materials, including metals [8–10], glasses [11], and semiconductors to produce a NP aerosol at high volumetric rates [12]. NPs produced by the LAMA process are electrically charged by the ablation process and therefore do not require an organic surfactant to prevent agglomeration. By varying processing parameters, the average NP size can be controlled from about 2–40 nm [13]. Following ablation, the resulting NP aerosol is accelerated through a nozzle to high velocities and then deposited onto a translating substrate to directly write patterned, thick films. Because the NPs generated in an inert gas through LAMA are not capped by an organic, the use of the LAMA process allows study of the low-temperature sintering of NPs in the absence of surfactants or other organics. In this paper, the effects of temperature, compressive stress, and deposit thickness on the microstructure, mechanical and electrical properties, and sintering behavior of pure, nanostructured Ag films are discussed. 2. Experimental procedure 2.1. Deposition procedure A schematic of the LAMA process used to write the nanostructured Ag lines onto metallized Si substrates is shown in Fig. 1. A conventional Ag powder with a mean particle size of 2 lm is used as feedstock for the process. The microparticle powder is aerosolized using a fluidized bed with He as the carrier gas. Laminar flow of the aerosol is maintained by surrounding the flow of aerosol by a buffer flow of He with the same linear velocity. A high energy excimer laser (200 mJ) ablates the micron-sized particles in the aerosol. The laser pulse rate (200 Hz) is set so that each microparticle in the aerosol is struck at least once. The laser pulse results in breakdown and shock wave formation at each microparticle [14]. NPs are nucleated in the rarefac-
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Fig. 1. Schematic of the LAMA process [35].
tion behind the shock and are initially charged by photoionization and thermionic emission. This charging prevents agglomeration of the NPs until charge recombination occurs. Following ablation, the resulting NP aerosol flows through a skimmer and a virtual impactor to remove residual microparticles. The ablation cell and virtual impactor are at ambient pressure while the deposition chamber is pumped to 33.3 Pa (250 mtorr). This pressure differential accelerates the NPs through the deposition nozzle at high velocity, impacting the NPs onto the substrate and forming nanostructured deposits. The density of the resulting deposit and the grain size within the deposit depend strongly on the process parameters (gas type, nozzle type, and nanoparticle size) since these determine the impaction velocity/energy of the NPs. Calculations for our operating conditions show that, the impaction velocities range from greater than 1200 m s1 for 2 nm particles to approximately 500 m s1 for 50 nm particles [15]. The corresponding impaction energies range from
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about 0.8 eV per atom for 2 nm particles to approximately 0.1 eV per atom for 50 nm particles. Since the energy to melt Ag is 0.37 eV per atom, assuming that no heat dissipation occurs by conduction, these impaction energies may be sufficient to cause partial or complete melting during impaction. This is consistent with the MD simulations conducted for impaction of smaller 1 nm Ag and Au [16] particles where amphorphitization/melting is predicted upon impaction at energies of 0.25 eV per atom. In contrast, numerical simulations conducted on much larger 5–25 lm diameter particles suggest that complex stress distributions arise during impaction that can lead to adiabatic shear instabilities. As a result, deformation does not occur uniformly and melting is localized to the shear bands [17,18]. These analyses show that both particle size and impaction velocity/energy influence the deformation response of the particles upon impaction. Unfortunately, analytical calculations of the stress state during impaction are extremely difficult due to the complex temperature and stress distributions that arise and numerical analyses have not been conducted for NPs in the size range studied here. Patterned thick film lines were produced using a computer-controlled x–y stage to move the substrate position relative to the deposition nozzle. For these experiments, two patterns were used: a 5 mm per side square pattern and a serpentine pattern with 10 mm long segments separated by shorter 0.5 mm segments. For the samples with a square pattern, the x–y stage was programmed to make 10, 20 or 30 overlapping passes to build up the deposit thickness. All serpentine lines were deposited with 15 overlapping passes. Both the substrate-to-nozzle distance and the nozzle geometry determine the breadth of the deposited lines. For these experiments, the substrate-to-nozzle distance was fixed at 1 mm and a flat-plate nozzle was used. The motor speed was approximately 1.4 mm s1, so a 30 pass, square pattern was produced in approximately 8 min. The substrates used for the square-patterned samples were silicon wafers that were first coated by evaporation with a thin layer of Cr and then overcoated with a thin layer of Au before depositing the NP Ag. The serpentine-patterned samples were deposited directly onto glass substrates. All substrate surfaces were cleaned with ethanol prior to Ag deposition. 2.2. Post-deposition sintering Pressure-assisted sintering of the patterned lines was performed by applying pressure while heating the sample, as shown schematically in Fig. 2. For these experiments, the deposition substrate was set onto the bottom of a heated punch and a second substrate was placed face down on top of the substrate containing the patterned line. A 150 W band heater was attached directly to the collar to heat the samples. A type K thermocouple was threaded through a hole in the collar, a few millimeters away from the substrate to monitor temperature. An auto-tuned, digital controller was used to control the sample temperature.
Fig. 2. Schematic of the set up for pressure-assisted sintering.
A 10 kN load cell was used to monitor load during compression of the samples, giving a resolution of about ±1 N. A blank, glass substrate was utilized as the top substrate for the serpentine samples in order to prevent bonding between the deposit and top substrate. These unbonded samples were used for characterization of the microstructures of the deposits and to measure electrical conductivity. For the square samples, a metallized blank substrate was utilized (as shown in Fig. 2) in order to promote bonding of the Ag deposit to both substrates for subsequent strength testing. For both the serpentine and square samples, a small preload (10 N) was applied to the sample during temperature equilibration (3–15 min). Following equilibration, the samples were compressed at a rate of 0.15 mm min1 to the desired load, a process that took at most 2 min. The load was cycled just above and below the desired load point (±10 N), allowing the displacement-controlled test frame to run in pseudo-load control. Each sample was sintered under load at the desired temperature for 1 h. The compressive loads that were applied to the samples during sintering were varied between 0 and 600 N. To estimate the corresponding applied compressive pressures on the lines during sintering, the area over which the load was applied was measured. To accomplish this, after sintering, the samples were pulled in tension until fracture occurred (see Section 2.4). The fractured lines were then
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observed in plan view using optical microscopy. A flattened region was clearly visible along the length of each line. SEM observations of these flattened regions did not show evidence of tensile deformation from fracture and thus, the size of the flattened regions were assumed to be representative of the minimum size of the compressively deformed regions of the lines. The line length and the average width of the deformed regions were used to calculate the applied compressive pressures which are shown in Table 1. The mean applied pressures ranged from 38 MPa for lines compressed at a load of 20 N up to 460 MPa for lines compressed at 600 N. 2.3. Characterization of the patterned lines The Ag patterned lines were characterized using a number of techniques to determine the influence of sintering temperature and compression pressure on grain size and density of the deposits. The morphologies of the lines were studied using both plan-view and cross-sectional SEM. The cross-sections of the lines were measured using a diamondtipped stylus profilometer with a diameter of 12.5 lm to determine thickness and cross-sectional area of the deposits. X-ray diffraction patterns were obtained for all of the serpentine pattern samples using a h–h diffractometer with a Cu Ka source and a solid-state detector. Each scan was conducted from 30 to 90° (2h), with a step size of 0.04° and a dwell time of 6 s. The breadth of the (1 1 1) diffraction peak was used to determine the grain size of the deposits (see Section 3.4). The electrical resistivity of the serpentine samples was measured using a four-point probe method using the same procedure described in earlier work [19]. For each sample, the resistivities of two segments of each serpentine were measured, with four different measurements from each segment. The eight resulting resistivity measurements were averaged to obtain each sample resistivity. The probe station was calibrated using a known resistor of similar resistance to the sample deposits. Because of the small mass of the deposits, a direct measurement of the density from the sample mass and volume was not possible. Instead, the density was calculated from the grain size, the conductivity, and known relationships between the grain size, conductivity, and porosity using a procedure developed by Qin et al. [20] and explained in
Table 1 Mean compressive pressures and the standard deviation in the pressures as a function of the compressive pressure applied during sintering Applied compressive load (N)
Mean compressive pressure (MPa)
Standard deviation (MPa)
20 50 100 600
38 67 89 460
11 26 35 250
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detail elsewhere [19]. Qin et al. have analyzed the resistivity of nano-silver films between 45% and 99% dense. They found that the resistivity, q, of nano-grained silver can be written as a single term that takes both grain size, G, and fractional density into account q ¼ qB
lB ðl=GÞ T l
ð1Þ
where qB is the bulk conductivity of polycrystalline silver (large grains), lB and l are the electron mean free paths in the bulk and nano-materials respectively, and T* is the electron transmission coefficient at boundaries, a function of material density. This analysis is based on two important observations. First, a previous model of conductivity by Reiss et al. [21] considered electron motion through boundaries that had an electron transmission of T*. Electrons trapped between the boundaries were removed from the conduction process resulting in the T ðl=GÞ dependence of resistivity. Second, positron spectroscopy studies showed that density completely specified the electron scattering at boundaries in polycrystalline nanomaterials, [22] and thus, samples with the same density have the same T*. In their work on polycrystalline silver, Qin et al. [20] measured the linear dependence of ln(T*) vs. 1/D and confirmed the utility of Eq. (1) for nano-silver over a broad range of densities and grain sizes. From Qin’s experimental data, the empirical relationships between T* and density (for 45% < D < 99%) and between electron mean free path and grain size (for G < 45 nm) were determined. We used this information and calculated T* from our data using Eq. (1) and interpolated ln(T*) vs. 1/D in order to infer the density of our samples. Note that this analysis does not include a contribution to the conductivity due to neck growth during early stage sintering. If neck growth occurred it would result in a further increase in the conductivity. Thus, our calculated density values represent an upper bound to the actual density. 2.4. Tension testing of bonded substrates Following pressure-assisted sintering, the square-patterned samples were prepared for tension testing (Fig. 3) using epoxy to bond a 6.4 mm diameter cylindrical post to the deposition substrate and to bond a bracket to the top substrate. Using a ring and an elastic band to connect the bracket to the testing frame allowed the sample to be smoothly loaded and eliminated a moment or shear resulting from misalignment of the sample relative to the load train. Samples were tested at a displacement rate of 50 mm min1 until failure; a typical test required about 10 min. A 250 N load cell was used for tension testing, giving a resolution of ±0.025 N. After tension testing, optical microscopy was performed on each sample to measure the bonded area between the top substrate and the silver deposit. A flat-topped ridge was clearly visible on each line that resulted from pressure-assisted sintering. It was assumed that the bonded
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Fig. 3. Schematic of the tension testing procedure. Fig. 4. (a) SEM cross-section of a representative as-deposited line; (b) plan view SEM of a representative line after tension testing.
area corresponded to the area of this flat-topped region and that subsequent fracture of the silver during tension testing did not result in significant plastic deformation that would lead to errors in this measurement. The failure stress was calculated from failure load and the bonded areas. 3. Results 3.1. Deposit morphologies An SEM cross-section of a representative, as-deposited line is shown in Fig. 4a and a plan-view SEM micrograph of the fracture surface after testing is shown in Fig. 4b. The pseudo-Gaussian profile observed in the as-deposited line (Fig. 4a) is typical. The peak thicknesses of the deposited lines, measured using profilometry, varied from 20 to 200 lm, and depended on the deposition conditions and the number of times the pattern was overwritten (10, 15, 20 or 30 times). The fracture surface after tension testing (Fig. 4b) shows that significant deformation occurred in the Ag line during the compression process, resulting in the flat top along the ridge of the line. Optical microscopy and SEM/EDS also revealed that, for samples that failed at low stresses, both the bottom deposition substrate and the
top substrate had silver bonded to the metallization layers indicating that bonding occurred between the silver deposit and the metallized surfaces and implying that fracture had initiated in the silver line rather than at one of these interfaces. SEM/EDS were used to confirm that the fracture surfaces consisted of a mixture of Ag, Au/Cr, and Si ripped from the blank substrate. Fracture outside of the Ag deposit was more common for samples that failed at higher stresses. 3.2. Strength The tensile strengths of samples tested after pressureassisted sintering are plotted in Fig. 5 as a function of processing temperature. Each datum point is a single measurement and the bold, vertical lines connect samples processed at the same conditions. The other lines group the data by their approximate thickness (30, 60, or 90 lm) and by the compression load applied during processing. From this plot it is apparent that a sintering temperature of 100 °C resulted in bonding of the Ag to the metallization layer but little cohesive strength in the Ag layer itself, even when sintered under large compressive stresses. Despite the scat-
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Fig. 5. Tensile strength for samples following pressure-assisted sintering. The legend indicates the approximate thickness of the deposit and the compressive load applied during bonding.
ter in the data, it is clear that for temperatures of 125 °C or above there is a general trend of increasing cohesive strength of the layer with temperature. It is also clear that there is not a strong influence of compression load applied during sintering on the tensile strength. For example, similar strengths were measured for two samples that were both 60 lm thick and that were sintered at 150 °C but with compressive forces that varied by more than an order of magnitude (50 N vs. 600 N). Comparing samples sintered at the same temperatures, there also does not appear to be a trend that would suggest that line thickness plays an important role in determining cohesive strength.
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strains associated with thermal expansion mismatch between the substrate and films will result in shifting of diffraction peaks rather than peak broadening and therefore were not analyzed. Examination of Williamson–Hall plots for the LAMAproduced specimens revealed no evidence of peak broadening due to internal strain (i.e. the Williamson–Hall plots did not have positive slope), consistent with previous analysis on similar lines [19]. Since the only significant cause of peak broadening in our samples was due to the ultrafine grain size, a standard Scherrer analysis was then applied. The (1 1 1) peaks from the XRD patterns were utilized for the Scherrer analysis since these peaks had about 5 times the intensity of the next most intense peaks, resulting in a better signal-to-noise ratio compared to the other peaks. The grain sizes, determined from XRD, are shown in Fig. 6 as a function of temperature for different compression loads applied during sintering. The average grain size determined from XRD Scherrer analysis for as-deposited serpentine samples was 25 nm. Upon heating to 100 °C the grain size increased to just over 30 nm and further increases in temperature resulted in more grain growth. Heating to 175 °C resulted in a grain size of 40–45 nm. For the range of loads that were applied (0–600 N) there was there was no obvious effect of applied pressure during sintering on grain size. 3.4. Electrical resistivity The resistivity, normalized to the resistivity of bulk microcrystalline silver (1.63 lX cm) [3], is shown in Fig. 7. The error bars represent the standard deviation of the resistivities measured on different regions of the same sample.
3.3. Grain size Because of the large stresses and localized heating that occurs during impaction, it is possible that defects may be introduced into the lines during writing. To determine if this was the case, X-ray diffraction data for as-deposited and sintered samples were analyzed using Williamson–Hall plots [23]. This analysis allows the two major causes of peak broadening in films (grain size effects and internal strain resulting from defects such as dislocations and stacking faults) to be deconvoluted by analyzing the angular dependence of line broadening. The integral line breadth, b, can be separated into two components that have different dependencies. Broadening due to grain size effects is proportional to cos h whereas the line breadth associated with strain is proportional to tan h, where h is the Bragg angle. Thus, a plot of b cos h vs. sin h should yield a straight line with a positive slope. The slope of the line is proportional to the magnitude the internal strain and the intercept is related to the grain size. Note that biaxial
Fig. 6. Grain size vs. sintering temperature. The legend indicates the compression load applied during sintering.
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3.5. Density The influence of processing temperature on average density is shown in Fig. 8. This figure shows that there is a general correlation between sintering temperature and density, with increasing density at higher sintering temperatures. Samples sintered at 100 °C had an average density of around 74% of bulk microcrystalline silver, while samples processed at 150–175 °C reached an average density of slightly greater than 83%. For reference, in previous work, the density for as-deposited samples produced under similar conditions to those used in this study was about 70%. For the range of compression loads that were studied (0– 600 N) there does not appear to be a significant effect of compression load applied during sintering on the density of the deposits. 4. Discussion and analysis Fig. 7. The effect of temperature on the resistivity, normalized to the resistivity of bulk, polycrystalline Ag. The legend indicates the compressive load applied during sintering.
The data do not indicate that there is a significant effect of compressive load on the resistivity of the samples. From Fig. 7 it is apparent that increasing the sintering temperature decreased the resistivity of the samples. Samples processed at 100 °C had resistivities as high as 9.7 times the bulk resistivity of Ag, while samples processed at 150 °C had resistivities as low as 2.7 times the bulk resistivity of silver. For comparison, the resistivity for as-deposited Ag produced by LAMA is nearly 13 times bulk resistivity [19] .
4.1. Strength and resistivity Comparisons of the current work to previous work on pressure-assisted sintering of nanostructured silver are complicated by differences in the processes used to produce the samples. Most of the previous work has utilized screenprinting of silver pastes containing Ag NPs and then subsequent bonding of the substrates by applying either heat or heat and pressure [1,24,25]. Required temperatures for this process are above 225 °C because they require that the organics needed for screen-printing of the paste be removed before sintering can take place. For example, at a processing temperature of 300 °C, Bai et al. achieved a strength of 43 MPa using a nanopowder silver dispersed in a paste [25]. At a processing temperature of 240 °C, Zhang et al. achieved a shear strength of 50 MPa using a commercially available silver paste deposited as a slurry [2]. Despite the large scatter in strengths that we observed, which was likely caused by variations in line thickness along the length of the line (See Fig. 4b), the LAMA-produced samples had maximum strengths similar to the strengths to those reported by Zhang et al. but were sintered at temperatures 50–100 °C lower [2]. While Schwarzbauer and Kuhnert reported higher strengths [1], given their sample geometries, it is likely that geometric strengthening contributed to their measured strengths. Comparing the measurements of resistivity to previous results, similar resistivities are obtained [2,25–27], but similarly to our observed strength measurements, we see that the LAMA process is capable of achieving these resistivities at processing temperatures that are 50–100 °C lower than other thick film manufacturing processes. 4.2. Deformation of the NPs
Fig. 8. Effect of processing temperature on average density of the deposited lines. The legend indicates compressive load applied.
Qin et al. prepared bulk samples from nanopowders by applying pressure at room temperature to a powder compact [28]. Their results show that it is possible to achieve
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densities as high as 99% from Ag nanopowders at room temperature by applying large pressures (up to 1.5 GPa). Although they measured the hardness of their compacts, which is sensitive to density, they did not measure the tensile strength after compression, so the degree of bonding that occurred between the particles during room temperature compression is not known. Based on the hardness values obtained by Qin et al., the yield strength for Ag with a 20 nm grain size should be about 500 MPa. The nominal applied pressure during our sintering experiments ranged from 40 to 460 MPa. However, this pressure is transmitted through particle-to-particle contacts and thus the local stresses at the contact points between particles is significantly higher than the nominal pressure. For example, from Hertzian contact theory, the maximum stress, r0 is given by r0 ¼
3P 2pa2
ð2Þ
where P is the applied load and a is the contact area between the two particles. Thus, the local stresses during pressure-assisted sintering are likely much larger than the yield strength of the Ag, particularly during the early stages of compaction when the contact area between particles is small. We expect that the NPs located near the top of the LAMA-produced lines, where the pressures are highest, undergo severe plastic deformation that results in densification of these portions of the lines. However, neither strength nor resistivity were found to be correlated to sintering load. For example, the resistivity of a sample processed at 600 N was comparable to the resistivity of a sample processed at the same temperature but with no load (Fig. 6). Thus, our results cannot be explained simply by plastic deformation of the NPs. Further, the results of our tensile tests show that, although the density of portions of the line may be increased by plastic deformation, the degree of bonding that occurs between the particles is negligible at temperatures less than 100 °C. This suggests that although plastic deformation may occur in nanograined Ag even at temperatures of 100 °C or less, under typical conditions for pressure-assisted sintering, bonding of the NPs requires higher temperatures. 4.3. Diffusional processes In previous work we have shown that during pressureless sintering of LAMA-produced Ag, significant coarsening occurs but little or no densification takes place when samples are heated at slow-to-moderate heating rates (5– 25 °C min1) to 100–400 °C [19]. It was postulated that coarsening takes place during slow heating due to the dominance of surface diffusion at low temperatures. Thus, faster heating rates would reduce the residence time at low temperatures and aid in densification. This hypothesis was confirmed in nanostructured gold films that were heated at fast rates (1200 °C min1) [29]. Thus, in this study, fast heating rates and pressure-assisted sintering
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were both employed in an attempt to increase the ratio of grain boundary to surface diffusivity, and therefore to increase densification rates. Coble’s model for pressure-enhanced densification has been used to explain the influence of pressure on densification kinetics [30]. In that model, the densification rate, dD/ dt is given by 1 dD 15 Dgb dgb X 2csv ¼ / þ P ð3Þ a D dt 2 r G3 RT where Dgb is the grain boundary diffusivity, dgb is the effective width of the grain boundaries where grain boundary diffusion occurs, X is the atomic volume of Ag = 1.03 105 m3 mol1, G is the grain size, R is the gas constant, T is temperature, Pa is the applied pressure, u is the pressure multiplication factor acting at the particle contacts, csv is the surface/vapor interfacial energy, and r is the pore radius. Since the relative densities of the as-deposited lines are about 70%, the intermediate and final stages of sintering are the relevant stages of sintering in this study; in this regime u 1/r. The pore radius is expected to vary with density. If the grains are assumed to be uniform tetrakaidecahedra, then the porosity, p = 1D, can be related to the size of the pore radius and the grain size by [7] ! p r3 p¼ ð4Þ 2 l3p where lp is the length of a side of the tetrakaidecahedron and is given by G lp ¼ pffiffiffiffiffi 10
ð5Þ
Thus, the pore radius is given by r ¼ 0:24Gð1 DÞ
1=3
ð6Þ
To use Coble’s model to predict densification rates, we must know Dgb, dgb, and csv. Although the grain boundary structures in nanomaterials are similar to those in materials with conventional grain sizes [31], there is evidence that diffusion phenomena are fundamentally different in nanograined materials. Therefore, it is possible that the values of these parameters that are typically obtained using single crystal or polycrystals with grain sizes an order of magnitude or larger than those used in our studies may not be accurate for ultra-fine grained materials [32]. In addition, diffusion data are typically gathered at much higher temperatures than those studied here. Thus, comparison of our results with existing data requires three assumptions: (1) diffusivities are not strongly sensitive to grain size; (2) the diffusivities can be extrapolated to lower temperatures; (3) the grain boundary energy is not strongly sensitive to grain size. These assumptions cannot be justified for quantitative comparisons. However, it is nevertheless useful to assume these to be valid and assess the corresponding trends. With these assumptions, it can be shown that there is not a strong influence of the relative density on the
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predicted densification rate [33]. Surface energy also has only a modest effect on densification rate [34]. Therefore, for the remainder of our comparisons, we will assume a constant relative density of 90% and a constant surface energy of 1.14 J m2. A temperature-independent surface diffusivity of 1 1013 m2 s1 and a grain boundary diffusivity ranging from 1.4 1018 m2 s1 at 100 °C to 8.3 1013 m2 s1 at 400 °C were used for the calculations. The predicted densification rate (log scale) is plotted against pressure in Fig. 9 at a temperature of 100 °C. This plot shows that applied pressure has a much stronger influence on conventional, microcrystalline materials than ultra-fine-grained materials. For example, the predicted densification rate increases by more than two orders of magnitude for a 500 nm grain size upon increasing the pressure from zero to 1.5 GPa. For a material with a 5 nm grain size, however, the predicted densification rate only increases about 10% over the same pressure range. Thus, although pressure is an effective means for enhancing diffusion-assisted densification for materials with conventional grain sizes, pressure is much less effective at enhancing diffusion-assisted densification in nanograined materials. This prediction is consistent with our experimental results that showed little effect of pressure during processing on the properties of the deposits. In Fig. 10, the predicted densification rate (log scale) is plotted against temperature for materials with a range of grain sizes from 5 to 500 nm. For these plots, an applied pressure of 500 MPa was used, which is similar the highest pressures used for our experiments. From Fig. 10, it is apparent that the predicted densification rate is strongly dependent on both temperature and grain size. For exam-
Fig. 9. The effect of pressure on densification rate for Ag with different grain sizes at an initial density of 0.9 and a temperature of 100 °C. Numbers beside lines indicate the grain/particle size.
Fig. 10. The effect of temperature on densification rate for Ag with different grain sizes at an initial density of 0.9 and a pressure of 500 MPa. Numbers beside lines indicate the grain/particle size.
ple, at a temperature of 100 °C, the predicted densification rate is increased by approximately seven orders of magnitude by decreasing the grain size from 500 nm to 5 nm. The predicted densification rate is increased by three orders of magnitude by increasing the temperature from room temperature to 100 °C and increased another two orders of magnitude upon increasing the temperature from 100 °C to 175 °C. From this plot, the predicted densification rate for a LAMA-produced film with a 15 nm grain size ranges from 1 106 s1 at 100 °C to 1 101 s1 at 175 °C. The approximate densification rate measured from our experiments is 4 105 s1, if we assume that densification occurred uniformly during the pressure-assisted sintering process. However, it is possible that complete densification takes place early during the compression process, resulting in a non-uniform densification rate, so this inferred strain rate represents a lower bound. Although a strict quantitative comparison between the experiment and theory is not advisable given the assumptions required both in the model and in the diffusivity data, based on the level of agreement between the predicted and experimental results, diffusion could be responsible for nearly complete densification of the deposits over the range of temperatures and pressures that were investigated for these nanograined materials. However, given that plastic deformation also occurs at these pressures, it is likely that at least some of the densification occurs by rapid plastic deformation. Even in this case, however, grain boundary diffusion is important in that it leads to rounding of the triple junction pores, increased neck growth, and results in the increased bonding between the particles that is likely responsible for the high tensile strengths that we observed.
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5. Conclusions The LAMA process combined with low temperature post-processing can be used to produce high-strength bonds from nanostructured silver. The strengths of our bonded samples exceed 100 MPa at the processing temperature of 175 °C. These strengths are similar to the strengths of bonded nanostructured Ag achieved previously, but at processing temperatures that are 50–100 °C lower. Electrical conductivity measurements on our samples following pressure-assisted sintering show that the processing temperatures required to achieve high conductivities are lower than those achieved by using most other direct-write methods. At post-processing temperatures of 150 and 175 °C, our samples have electrical conductivities approaching 33% of bulk polycrystalline Ag with micron-sized grains. We suggest that the reason for the lower processing temperatures is that, unlike NPs that were studied previously, the LAMA process utilizes bare NPs that are not capped with organics that interfere with sintering. Comparing our experimental results with data for yield strengths of nanocrystalline Ag and existing pressureless and pressure-assisted densification models showed that our results can be explained based a combination of plastic deformation and pressure-assisted sintering. An existing model for pressure-assisted sintering was used to show that pressure does not strongly effect densification for ultra-fine grain samples such as ours. Increasing the sintering temperature, however, has a significant effect on the densification of nanocrystalline materials, as predicted by theory. Comparisons with previous work show the necessity of rapid heating to the processing temperature to limit coarsening and promote densification. Acknowledgments We gratefully acknowledge support from the National Science Foundation through NIRT grant DMI-0304031 and additional financial support from Stellar Micro Devices Inc., Austin, TX. References [1] Schwarzbauer H, Kuhnert R. IEEE Trans Ind Appl 1991;27:93–5. [2] Zhang Z, Lu G-Q. IEEE Trans Electr Pack Manufact 2002;25:279–83. [3] Buch A. Pure metals properties: a scientific-technical handbook. Materials Park, OH: ASM International and Freund Publishing; 1999. [4] Yeadon M, Yang JC, Averback RS, Bullard JW, Olynick DL, Gibson JM. Appl Phys Lett 1997;71:1631–3. [5] Olynick DL, Gibson JM, Averback RS. Mat Sci Eng 1995;A204:54–8.
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[6] Chen Y, Palmer RE, Wilcoxon JP. Langmuir 2006;22:2851. [7] Rahaman MN. Ceramic processing and sintering. New York: Marcel Dekker; 2003. [8] Lee J-M, Becker MF, Brock JR, Keto JW, Walser RM. IEEE Trans Magn 1996;32:4484–6. [9] Nichols WT, O’Brien DT, Malyavanatham G, Becker MF, Keto JW. In: Komarneni S, Vaia RA, Lu GQ, Matsushita J-I, Parker JC, editors. MRS proceedings: nanophase and nanocomposite materials IV, vol. 703. Warrendale, PA: The Materials Research Society; 2002. p. 209–14. [10] Malyavantham G, O’Brien DT, Becker MF, Keto JW, Kovar D. J Nanoparticle Res 2004;6:661–4. [11] Juang C-B, Cai H, Becker MF, Keto JW, Brock JW. Appl Phys Lett 1994;64:40–2. [12] Nichols WT, Keto JW, Henneke DE, Brock JR, Malyavanatham G, Becker MF, Glicksman HD. Appl Phys Lett 2001;78:1128–30. [13] Nichols WT, Malyavanatham G, Beam MP, Henneke DE, Brock JR, Becker MF, Keto JW. In: Komarneni S, Parker JC, Hahn H, editors. MRS proceedings: nanophase and nanocomposite materials III, vol. 581. Warrendale, PA: Materials Research Society; 2000. p. 193–8. [14] Becker MF, Brock JR, Cai H, Henneke DE, Keto JW, Lee J, Nichols WT, Glicksman HD. Nanostruct Mater 1998;10:853–63. [15] Huang C, Nichols WT, O’Brien DT, Becker MF, Keto JW, Kovar D. J Appl Phys 2007;101:064902. [16] Hou Q, Hou M, Bardotti L, Pre´vel B, Me´linon P, Perez A. Phys Rev B 2000;62:2825–34. [17] Assadi H, Gartner F, Stoltenhoff T, Kreye H. Acta Mater 2003;51:4379–94. [18] Borchers C, Gartner F, Stoltenhoff T, Assadi H, Kreye H. J Appl Phys 2003;93:10064–70. [19] Huang C, Becker MF, Keto JW, Kovar D. J Appl Phys 2007;102:054308. [20] Qin XY, Zhang W, Zhang LD, Jiang LD, Liu XJ, Lin D. Phys Rev B 1997;56:10596–604. [21] Reiss G, Vancea J, Hoffmann H. Phys Rev Lett 1986;56:2100–3. [22] Schaefer H-E, Wu¨rschum R, Birringer R, Gleiter H. Phys Rev B 1988;38:9545–54. [23] Williamson GK, Hall WH. Acta Metall 1953;1:22–31. [24] Palm M, Zhang LC, Stein F, Sauthoff G. Intermetallics 2002;10:523–40. [25] Bai JG, Zhang ZZ, Calata JN, Lu G-Q. In: Proceedings of IMEC2005, p. 415–24. [26] Kim D, Moon J. Electrochem Solid State Lett 2005;8:J30–3. [27] Lee H-H, Chou1 K-S, Huang K-C. Nanotechnology 2005;16:2436–41. [28] Qin XY, Wu XJ, Zhang LD. Nanostruct Mater 1995;5:101–10. [29] Seker E, Gaskins JT, Bart-Smith H, Zhu J, Reed ML, Zangari G, Kelly R, Begley MR. Acta Mater 2007;55:4593–602. [30] Coble RL. J Appl Phys 1970;41:4798–807. [31] Siegel RW, Thomas GJ. Ultramicroscopy 1992;40:376–84. [32] Yeadon M, Yang JC, Averback RS, Bullard JW, Gibson JM. Nanostruct Mater 1998;10:731–9. [33] Kovar D, Albert AD, Becker MF, Keto JW. In: Proceedings of the ASME conference on manufacturing science and engineering (MSEC 2007). Atlanta, GA: ASME; 2007. [34] Albert AD. Nanostructured Ag Produced by LAMA. Ph.D. Dissertation, University of Texas at Austin, Austin; 2007. [35] Albert AD, Huang C, Becker MF, Keto JW, Kovar D. In: Proceedings of the international symposium on synergistic effects of materials and processing (ISSEMP 2006), vol. 06–207. Kumamoto: VCH; 2006. p. 1–6.