Determination of Mechanical Properties of Copper at the Micron Scale

Abstract

The ongoing trend in miniaturization of micro-electro-mechanical systems (MEMS), medical devices (e.g. STENTs), and microelectronic devices leads to structural elements with one or more dimensions in the range of a few tens of nanometres to a few hundred microns. This requires novel techniques to determine the mechanical properties of materials at this small length scale.The most frequently used method is the nanoindentation technique. [1±4] It is usually straightforward to apply to a wide range of materials, is essentially non-destructive, and material properties like hardness and reduced elastic modulus can be deduced from such experiments. With some additional efforts attributes like yield strength, creep behaviour and fracture toughness can be determined. However, several problems arise when performing indentation experiments. The shape of the indenter tip is usually not exactly known, but it strongly influences the actual contact area and therefore the calculated values of hardness and stiffness at very shallow indentation depths. Furthermore, one has to deal with a complex stress and strain field beneath the indenter tip, which makes it difficult to directly compare indentation data to material properties obtained from tension, compression or bending tests, which all possess a well defined stress and strain distribution.To overcome the problems of indentation tests, efforts were undertaken to adapt conventional material test methods to micron-sized samples. Fleck et al. [5] performed torsion tests on copper wires and reported increasing torsional resistance when the wire diameter was reduced from 170 to 12 lm. Stölken and Evans [6] performed bending tests on nickel foils and observed increasing bending strength as the foil thickness decreased from 50 to 12.5 lm. This increase in yield strength and flow stress was attributed to an increasing strain gradient with decreasing specimen size. [5,7] Weiss et al. [8] performed tension experiments on free standing thin Cu foils and wires and reported a strong influence of the sample thickness on the fracture strain, with thinner samples exhibiting reduced plasticity.In recent times, compression tests on micron-sized samples prepared with the focused ion beam (FIB) technique have been reported in the literature. [9±12] For a variety of materials a strong size effect in flow stress was found, if the diameter of the so-called ªmicro-pillarsº was reduced from 10 to 0.2 lm. This size effect obtained by micro-compression tests can not be explained by strain gradient plasticity approaches. To elucidate the influence of a strain gradient on the deformation behaviour at the micrometer scale, micron-sized compression (no strain gradient present) and bending (strain gradient present) tests were performed. The results are compared and discussed in this paper. Furthermore, quantitative Auger electron spectroscopy (AES) was performed on the damaged zone at the surface of FIB designed miniaturized samples. The results obtained will be used in the interpretation of the mechanical...

Microstructure versus Size: Mechanical Properties of Electroplated Single Crystalline Cu Nanopillars

“…Comparing our results to those reported for FIBfabricated Cu samples, two key differences are apparent: our pillars attain lower flow stresses and negligible hardening relative to data in [15,17,26]. The authors of [17] demonstrate that both hardening and very high flow stresses attained by their pillars are due in part to the very stiff lateral support of their indenter system [15][16][17].…”

“…The most prevalent method to fabricate pillars is by focused ion beam (FIB) [1][2][3][4][5][6][7][8][9]14,[16][17][18][19][20][21][22][25][26][27]. Remarkably, at these length scales, face-centered cubic (fcc) metallic nanopillars exhibit a strong size-dependent strengthening: as the pillar diameter becomes smaller, its flow stress increases as a power law: / d Àn where d is the pillar diameter and n lies between 0.5 and 0.7 [1- 7,11,23,26]. Few alternate fabrication techniques, which do not rely on FIB, have also been used to produce nano-and micronsized samples.…”

Ultrahigh Strength Single Crystalline Nanowhiskers Grown by Physical Vapor Deposition

“…It is clear that large-scale plasticity is not sustainable in these whiskers, as supported by the lack of plastic flow in 2,33,36,37 the stress strain curves, as well as postmortem TEM characterization showing an absence of stored dislocations in fractured whiskers. These results are quite different from the results obtained from a series of small-scale experiments on face-centered cubic (fcc) single crystals of arguably lower crystal quality, which demonstrate smaller strengths with less scatter, and a clear size effect ("smaller is stronger").…”

Fabrication, structure and mechanical properties of indium nanopillars

“…A technique is yet to be developed to analyze these hollow features. This type of "pop-in" displacement at small depths has been reported in gold, copper, molybdenum, molybdenum-alloy, and niobium pillar compression tests [4,6,7,[9][10][11]14,27]. It is often described as the incipient onset of plasticity where dislocations are nucleated within the pillars, allowing them to deform plastically.…”

“…The majority of research conducted in this area has focused on metals with cubic structures, i.e. nickel [1][2][3], gold [4][5][6], copper [7], molybdenum [8][9][10] and niobium [11]. The results of all these studies show that the uniaxial compressive yield strength of crystalline cubic metals increases with reduced sample sizes [12].…”