Effective Use of Focused Ion Beam (FIB) in Investigating Fundamental Mechanical Properties of Metals at the Sub-Micron Scale
I would like to share some of our more recent findings on nano-pillar compression, namely the role of the surface treatment in plastic deformation at the nano-scale. Recent advances in the 2-beam focused ion beams technology (FIB) have enabled researchers to not only perform high-precision nanolithography and micro-machining, but also to apply these novel fabrication techniques to investigating a broad range of materials' properties at the sub-micron and nano-scales. In our work, the FIB is utilized in manufacturing of sub-micron cylinders, or nano-pillars, as well as of TEM cross-sections to directly investigate plasticity of metals at these small length scales. Single crystal nano-pillars, ranging in diameter between 300 nm and 870 nm, were fabricated in the FIB from epitaxial gold films on MgO substrates and subsequently compressed using a Nanoindenter fitted with a custom-fabricated diamond flat punch. We show convincingly that flow stresses strongly depend on the sample size, as some of our smaller specimens were found to plastically deform in uniaxial compression at stresses as high as 600 MPa, a value ~25 times higher than for bulk gold. We believe that these high strengths are hardened by dislocation starvation. In this mechanism, once the sample is small enough, the mobile dislocations have a higher probability of annihilating at a nearby free surface than of multiplying and being pinned by other dislocations. Contrary to this, if the dislocations are trapped inside the specimen by a coating, the strengthening mechanism is expected to be different. Here we present for the first time the comparison of plastic deformation of passivated and unpassivated single crystal specimens at the sub-micron scale. The role of free surfaces is investigated by comparing stress results of both as-FIB'd, annealed, and alumina-passivated pillars. Preliminary results show that ALD-coated pillars exhibit much higher flow stresses at equivalent sizes and strains compared with the uncoated samples. We also found that while FIB damage during pillar fabrication might account for a small portion of the strength increase, it is not the major contributor.
In the last decade or so, the Focused Ion Beam has become one of the most widely used tools for sample fabrication, testing, and imaging,,. This multidisciplinary tool is applicable to a broad range of projects like fabrication and testing of MEMS, sensors, micro-actuators, microfluidic devices, etc. With some care, FIB can be utilized in fabrication of intricate 3-D structures by both etching of the starting material and by deposition of metals from gas phase. One of the key contributions of FIB's availability for mechanical experiments is that it bridges the experimental length scale with the computational results, where sample sizes are generally specified in a number of atoms. One of the areas where the community has benefited greatly from using the FIB is mechanics. Until recently, mechanical deformation has largely been carried out in thin films due to their relative ease of deposition and their industrial relevance. The development of the Focused Ion Beam (FIB) as a user-accessible fabrication tool has enabled constraining the specimens not only vertically but also in the in-plane directions. For example, an increasing number of research groups are studying size effects in plasticity by investigating fundamental mechanical deformation in micron- and sub-micron-sized pillars,,,. Although a unified theory explaining plasticity below a certain length scale remains a matter of great research and controversy, the results of most computational and experimental studies indicate an inevitable strength increase associated with the reduction in sample size, or a so-called size effect.
UNIAXIAL COMPRESSION EXPERIMENTS
In this work, we focus our attention on size effects arising in uniaxial deformation of gold nano-pillars with and without passivation on MgO substrates. The FIB is instrumental in nearly every step of these experiments, starting with pillar fabrication, micro-machining of the flat-punch indenter tip, and ending with machining TEM samples for dislocation activity investigation. The compression is conducted in the DCM module of the MTS Nanoindenter, where a uniform top load is applied to the single crystalline sample of sub-micron dimensions, whose initial dislocation density is on the order of 1012/m2. This particular type of deformation is chosen because the material is not expected to strengthen through one of the known mechanisms like strain gradient plasticity, dislocation confinement, grain size hardening, or initial lack of dislocations. The uniaxial compression procedure and methodology for stress-strain calculations, as well as the FIB fabrication technique are described in detail elsewhere. An example of gold pillar on MgO substrate is shown in Figure 1.
The experiments presented here are unique in their attempt to assess the effects of surfaces on the pillar strength. While passivation of thin films is done routinely via sputtering or evaporation, uniform coating of complex geometries is much more challenging. The availability of Atomic Layer Deposition (ALD) for high-aspect ratio features is complementary to the FIB fabrication technique as it allows for studying the effects of passivation on the features of interest Key aspect of ALD is its utilization of sequential precursor gas pulses to deposit a film one layer at a time. The first precursor gas is introduced into the process chamber to produce a monolayer of gas on the substrate surface. The second precursor gas is then introduced into the chamber to react with the first gas on the surface of the substrate and to produce exactly a monolayer of film. Since each pair of gas pulses produces exactly one monolayer of film, the thickness can be precisely controlled.
The results of our uniaxial compression experiments indicate a strong size effect: the flow stresses for gold pillars are much higher than the typical strength of bulk gold, estimated at 20 MPa at 2% strain. Moreover, the flow stresses for single-crystalline <001>-oriented pillars increase from ~50 MPa to 600 MPa as the diameter is reduced from 870 nm to 300 nm. Figure 2(a) shows the typical stress-strain curves for several uncoated nano-pillars, whose diameters varied from 300 nm to 870 nm.(see attached Figure 2)Figure 2. Stress-strain curves generated from compression of sub-micron-sized gold nanopillars on MgO substrates. (a) All pillars were tested immediately after fabrication while the 500-nm diameter pillar was annealed prior to deformation. (b) Comparison of uncoated pillars (black) which exhibit virtually no strain-hardening at >10% strains vs. two alumina-coated pillars (colored) which show pronounced linear hardening.An unusual feature of these curves is the near-saturation of the flow stress past ~ 10% strain, as it remains nearly constant upon further compression. This is consistent with the apparent lack of the Stage II strain-hardening region associated with the multiple dislocation cross-slip processes as their density increases. Contrary to this, the stress-strain behavior agrees more with the Stage I-type deformation, or the "easy glide" section of a low-symmetry oriented single crystal deformation curve. Moreover, the discrete slip events associated with the dislocation nucleation and glide are present in nearly every curve, with a larger number of slips in smaller-sized pillars. As reported earlier, the proposed hardening mechanism here is "hardening by dislocation starvation" where the mobile dislocations escape the crystal at an available free surface. On the contrary, the alumina-coated pillars behave differently, as they exhibit conventional strain-hardening, with a higher hardening exponent for the smaller specimen size, as also shown by colored curves in Figure 2(b). Here, the curves for the uncoated pillars (black) are compared with those of the passivated pillars (colored). Not only do the coated pillars achieve higher strengths than their free-surface counterparts of equivalent sizes, but they also demonstrate a fundamentally different strengthening mechanism. Here, the dislocations are trapped inside the pillar by the outer layer, and hardening occurs through dislocation pile-ups within the pillar. In order to estimate the role of the surface on the strength of the specimen, the results of three 500-nm diameter pillars with different surface treatments were compared. Figure 3 shows the stress-strain data for these specimens where the top-most curve corresponds to the pillar with alumina coating, and the open-circles and filled-circles curves represent the "as-FIB'd" and "post-FIB annealed" pillars, respectively. (see attached)Figure 3. Stress vs. strain for 500-nm-diameter pillars. Stresses achieved by both "as-is" and annealed FIB pillars are similar to each other while the coated pillar is ~1.5x stronger.This graph clearly demonstrates that a passivated 500-nm pillar continues strengthening throughout the compression, achieving its maximum stress of ~900 MPa at 20% strain. The coated pillar attains ~1.5X higher stresses at 10% strain than the uncoated pillars and experiences a significant amount of linear strain-hardening, with the slope of ~4 GPa, which is absent in the uncoated pillars. Unlike the passivated sample, the stresses of the annealed and unannealed pillars achieve similar levels between 350 MPa and 500 MPa and remain nearly constant upon further compression. This suggests that the dislocation nucleation stresses required to generate new dislocations from the surface steps in the uncoated pillars are lower than those required to move dislocations through the dislocation forest.
While our simple phenomenological model cannot adequately describe the dislocation behaviour, it shows that the strength increase observed in these nano-pillars is not due to the presence of the FIB damage layer as the resistance stress represents a rather small fraction of the observed axial stresses.
Computational efforts like Dislocation Dynamics (DD) simulations are needed to gain more insight into the pillar strengthening phenomena. It is encouraging that the results reported here agree well with the recent work of Nicola, et al., where the researchers also found that in sufficiently thin films, the strength increased with the inverse of the film thickness, with a significantly higher slope for the passivated films. The results of discrete dislocation plasticity calculations reported in that work are in remarkably good agreement with the experimental data.
A quantitative comparison of strength vs. sample size has been carried out for passivated and unpassivated single crystal gold pillars on MgO substrates. The samples used in this work, or nano-pillars, were fabricated by the use of Focused Ion Beam (FIB) and ranged in diameter between 300 nm and 870 nm. The unpassivated pillars demonstrated a significant rise in flow stress at 10% strain, from 150 MPa up to 600 MPa for the smallest pillar. The common feature among all unpassivated curves was the apparent lack of stain-hardening and flow stress saturation at a high value past 10% strain. Contrary to this, the alumina-passivated pillars exhibited a fundamentally different strengthening behavior, as a typical curve had a significant amount of linear strain-hardening. The strengths attained by the coated pillars were some 1.5 times higher than those of the unpassivated samples of equivalent size. This suggests that in the uncoated pillars "dislocation starvation" might be the primary hardening mechanism responsible for the observed size effect, while that in the passivated pillars is most likely explained by trapping of the mobile dislocations inside the specimen, requiring ever higher stresses to overcome the formed dislocation pile-ups.
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 The methodology for stress calculation from the Nanoindenter-generated data is presented in detail elsewhere 
 Here, we assumed the resistance stress of 0 and calculated the required axial stress to encourage dislocation glide. As expected, very little force would be required to activate slip.
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