Plastic deformation of indium nanostructures

Abstract

Mechanical properties and morphology of cylindrical indium nanopillars, fabricated by electron beam lithography and electroplating, are characterized in uniaxial compression. Time-dependent deformation and influence of size on nanoscale indium mechanical properties were investigated. The results show two fundamentally different deformation mechanisms which govern plasticity in these indium nanostructures. We observed that the majority of indium nanopillars deform at engineering stresses near the bulk values (Type I), with a small fraction sustaining flow stresses approaching the theoretical limit for indium (Type II). The results also show the strain rate sensitivity and flow stresses in Type I indium nanopillars are similar to bulk indium with no apparent size effects.

Introduction

The functionality, lifetime, and future commercial success of novel nanoelectronic and nanoelectromechanical devices ultimately depend on a thorough fundamental understanding of the mechanical properties and reliability of nanostructures comprising them. To date, a considerable amount of effort has been dedicated to studying the room-temperature small-scale mechanical behavior of single-crystalline metallic nanostructures [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], with homologous temperatures less than 0.5. So far, there have been very few research investigations focusing on low melting temperature nanostructures. The most common technique for assessing small-scale mechanical properties without the presence of strong strain gradients is by uniaxial compressive loading of cylindrical pillars fabricated by focused ion beam (FIB) milling. This approach was first introduced by Uchic et al. [1], [2] for pillars as small as ∼5 μm in diameter, and later extended by Greer et al. [6] and others for pillars with sub-micron diameters. Remarkably, all studies on the compressive strength of single-crystalline metal nanopillars with non-zero initial dislocation densities exhibit size effects which manifest themselves as a pronounced increase in yield strength when external dimensions are reduced to the micron and sub-micron scale [23]. Although these and other studies of size-dependent mechanical properties have spurred a non-trivial amount of computational efforts and theoretical discussions, experimental investigations addressing time-dependent deformation in nanometer scale structures remain limited to very few materials (i.e., molybdenum pillars [19], [22]).

The main objective of this work is to expand the current understanding in small-scale mechanical properties to the deformation mechanisms governing low melting temperature nanostructures. Specifically, we focus our study on indium, which has a melting temperature of ∼156 °C, corresponding to a homologous temperature of approximately 0.7 in ambient conditions. Herein, the important mechanical parameters of this material are investigated, including the stress–strain characteristics, strain-rate effects on flow stress, and the influence of size on mechanical response. A thorough understanding of indium nanostructure deformation generated in the course of this work will further enrich the current small-scale plasticity state-of-the-art, especially in the area of low melting temperature materials. A further motivation for this work is the significant commercial applications of indium and indium-based alloys in the microelectronics industry. They are widely used as an alternative material in advanced lead-free elemental and alloy solders for microelectronic packaging [24], [25], [26]. In addition, novel electroluminescence devices based upon nanostructured indium powders are being developed [27].

Cylindrical indium pillars with sub-micron to nanoscale diameters were chosen for this study because they can be fabricated by the electron beam lithography and electroplating technique [28], [29]. Since the homologous temperature of indium at room temperature is ∼0.7, factors that affect thermally activated processes, such as atomic/vacancy diffusion [30] and dislocation climb [31], [32], are expected to contribute significantly to the time-dependent mechanical deformation mechanism. Indium has a face centered tetragonal (FCT) crystalline structure with a c/a = 1.075 [33], and in bulk is known to be one of the softest metals. Van der Biest and Van der Planken conducted a detailed study to characterize the plastic deformation mechanism of bulk indium single-crystals under tensile stress at 77 K, 195 K, and room temperature [34]. The major observation in their work is that twinning, with the composition plane of (1 0 1), is the prominent deformation mode for nearly all samples. However, the active slip systems depend on the testing conditions. At 77 K, easy glide was observed on (1 1 1) planes, which are the closest packed for this structure. In contrast (0 0 1) and (1 0 1) are the active glide planes in bulk indium deforming at room temperature.

It is important to distinguish the current study from the work of Lucas and Oliver [35], where creep and strain rate sensitivity of bulk indium single-crystals were measured by using nanoindentation with a sharp Berkovich diamond tip. Although nanoindentation is a versatile and powerful technique, it is limited by its ability to only directly measure the hardness of a material. The flow stress of the deformed material may then be estimated indirectly by assuming that measured hardness value for metals is linearly proportional to the yield strength [36], [37]. In addition, the yield stress extracted by this method corresponds only to a characteristic strain value which is defined by the centerline-to-face angle of the indenter tip [36], [38], [39]. These uncertainties and other potential artifacts, such as sink-in, pile-up, and indentation size effects, pose drawbacks to using nanoindentation to obtain stress–strain relationships as a function of strain rates. Finally, the specific nanoindentation experiments conducted by Lucas and Oliver evaluated mechanical properties of indium at the micron scale only, dimensions significantly larger than that of the nanopillars in the current study. In order to accurately characterize the time-dependent mechanical properties of indium at the nanoscale, we conducted uniaxial compression tests on cylindrical indium nanopillars with diameters ranging from 920 nm to 350 nm.

Through these experiments on more than 100 indium nanopillars with different diameters, we observed two fundamentally different deformation mechanisms which govern the plasticity of indium nanostructures. The distinction between the two deformation mechanisms is apparent in the measured flow stress values. We found the majority of indium nanopillars to be relatively weak and plastically deform at engineering stresses near the bulk values of ∼7 MPa (Type I). This bulk value was estimated by using the nanoindentation hardness values reported by Lucas and Oliver [35] under the assumption that hardness is three times of the yield strength [36], [37], [40]. However, a small fraction of the samples were extremely strong and sustained compressive stresses approaching the theoretical limit of ∼435 MPa, or ∼10% of the indium bulk shear modulus, G = 4.35 GPa [41] (Type II). Results also indicate that the stress–strain response of indium nanopillars exhibiting flow stresses near the bulk value is strongly influenced by strain rate, but display no apparent size-dependence. Scanning electron microscopy (SEM) inspections of compressed nanopillars further reveal that the low strength samples display a deformation characteristic, which resembles material extrusion.