The role of deposited layers in the nonlinear constitutive behavior of Si nanowires

Abstract

The experimentally measured elastic moduli and yield strengths of nanowires and nanofilaments vary widely in the literature and are often beyond the theoretical limits of the particular material. In this work, Si nanowires with very low defect densities were loaded in uniaxial tension to establish the origins of their apparently nonlinear constitutive behavior. The diameters of the nanowires ranged from 230 to 460 nm and the growth directions were primarily [112] with the exception of a [111] oriented nanowire. The resulting fracture strengths of the nanowires ranged from 3.88 to 10.1 GPa. The nonlinear constitutive behavior was accompanied by fracture surfaces with features that were not commonly observed in Si. A nonlinear continuum elasticity model and electron microscopy established that reports of unusual deformation behavior and fracture surface morphologies are a direct byproduct of the electron and ion beam deposited adhesives (Pt-based in this work) used to affix specimens in place for testing.

On the origins of anomalous elastic moduli and failure strains of GaP nanowires

“…The two main structural beams of the comb drive, located at the top and bottom of the comb drive, behave as Euler-Bernoulli beams (i.e., the force on the beams scales linearly with displacement). Similar analyses have been used on the MEMS testing structures designed by Espinosa [24], as well as previous work by the authors [16,17]. Since the displacement in the comb drive throughout the experiment was too small to be measured optically, the displacement was estimated from equation (4) as…”

“…PDP measurements were performed via tensile experiments that combined a micromachined load frame, piezoelectric actuator, and high resolution force transducer. The micromachined load frames, identical to those used in previous work [16,17], consisted of a thermal actuator, specimen gap, and comb drive (figure 2(A)). However, in the present study the micromachined load frame was used as a specimen holder.…”

“…Nanowires were mounted on the specimen gap of the micromachined load frames in an FEI Quanta 200 3D focused ion beam (FIB) in a similar method to previous work [16,17]. Prior to placing the nanowire, the load frame of interest was located and Pt adhesive pads covering the majority of the specimen gap (∼250 μm 2 ) were deposited with an ion beam current of 1.0 nA.…”

“…where E is the Young's modulus, r is the radius of the nanowire determined from TEM diameter measurements, and L 0 is the length of the nanowire between the Pt adhesive grips measured in SEM images taken after nanowire placement. The ideal nonlinear elastic constitutive behavior, the theoretical strength, and the Young's modulus of GaP was determined using an anisotropic, nonlinear continuum elasticity model [20][21][22] that we used in our previous experiments on single crystal silicon nanowires [17]. The model was implemented in Wolfram Mathematica v7 (Wolfram Inc., Champaign, IL USA), and uses the experimentally measured second and third order elastic constants of GaP [23] in a finite strain framework and is detailed in appendix.…”

“…where L is the length of the Pt adhesive pad, d is the diameter of the nanowire, d 2 is an estimate of the width of the load bearing area of the Pt adhesive pad, and G T Ave ( ) was the ratio of the shear modulus to thickness of the Pt adhesive pad, estimated from the results of similar work on Si nanowires [17]. Since the stiffness of the thermal actuator - 10 000 N m 1 ( ) was significantly greater than that of the nanowire (35-364 N m −1 ) and Pt adhesive (130-890 N m −1 ), we chose to estimate the stiffness of the equivalent spring in equation (1) using only the nanowire and Pt adhesive contributions.…”