Strain mapping in nanowires

Abstract

A method for obtaining detailed two-dimensional strain maps in nanowires and related nanoscale structures has been developed. The approach relies on a combination of lattice imaging by high-resolution transmission electron microscopy and geometric phase analysis of the resulting micrographs using Fourier transform routines. We demonstrate the method for a germanium nanowire grown epitaxially on Si(111) by obtaining the strain components epsilon(xx), epsilon(yy), epsilon(xy), the mean dilatation, and the rotation of the lattice planes. The resulting strain maps are demonstrated to allow detailed evaluation of the strains and loading on nanowires.

Experimental examination of strain field within GP zone in an Al–Zn–Mg–Cu alloy

“…Recently, highresolution transmission electron microscopy (HRTEM) has become a powerful tool for mapping the displacements and the strain fields at the nano-scale level because of the development of quantitative image analysis methods [1,2], and especially, the geometric phase analysis (GPA) technique, whose accuracy has demonstrated that it could be measured to 0.003 nm, is one of such techniques [3,4]. So far, the GPA has successfully been applied to a wide variety of systems, such as quantum dots [5], nanowires [6], Si/Ge heterostructures [7] and low-angle grain boundaries [8]. Furthermore, the GPA technology has also been applied to quantitative measurements of the displacement field of the edge dislocation in metal aluminum and gold [1,9].…”

Strain Mapping at the Atomic Scale in Highly Mismatched Heterointerfaces

“…[7,9] GaN away from the InN quantum dot was chosen as reference material. By combining the phase images, the displacement can be calculated and subsequently the strain field by numerical differentiation using: [6,11] ur À 1 2p…”

Evaluation of strain caused by coherent precipitates in an Al alloy using TEM techniques

“…By using GPA, the variation in the local lattice constant in the HRTEM micrographs is calculated by taking a strain free area as a reference [12]. Despite its limitation of a relatively small field of view, the method has been used successfully to quantify strain fields around dislocations [13], Ge nanowires [14] and more recently on Al-Pb interfaces [15].…”