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Philosophical Magazine Vol. 87, Nos. 14–15, 11–21 May 2007, 2169–2189
Brittle and ductile fracture of semiconductor nanowires
| molecular dynamics simulations
Keonwook Kang and Wei Cai
Department of Mechanical Engineering
Stanford University, Stanford, CA 94305-4040, USA
November 9, 2006
Abstract
Fracture of silicon and germanium nanowires in tension at room
temperature is studied byMolecular Dynamics simulations using sev-
eral inter-atomic potential models. While some potentials predict
brittle fracture initiated by crack nucleation from the surface, most
potentials predict ductile fracture initiated by dislocation nucleation
and slip. A simple parameter based on the ratio between the ideal
tensile strength and the ideal shear strength is found to correlate very
wellwith the observed brittle versus ductile behaviours for all the
potentials used in this study. This parameter is then computed by
ab initio methods, which predict brittle fracture at room tempera-
ture. A brittle-to-ductile transition (BDT) is observed in MD simula-
tions at higher temperature. The BDT mechanism in semiconductor
nanowires is di®erent from that in the bulk, due to the lack of apre-
existing macrocrack that is always assumed in bulk BDT models.
keywords: fracture; brittle-to-ductile transition; semiconductor nanowires; Molecular Dy-
namics simulation; cracks; dislocations; nucleation
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Philosophical Magazine Vol. 87, Nos. 14–15, 11–21 May 2007, 2169–2189
Contents
1 Introduction 3
2 Molecular dynamics simulations 4
2.1 Simulation method . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 4
2.2 Simulation results from SW potential . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Simulation results from other potentials . . . . . . . . . . . . . . . . . . . . 7
2.4 Fundamental questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 E®ect of inter-atomic potential models 9
3.1 Cut-o® radius of inter-atomic potentials . . .. . . . . . . . . . . . . . . . . 9
3.2 Ideal tensile strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Ideal shear strength and ductility parameter . . . . . . . . . . . . . . . . . . 12
4 Beyond empirical potential models 16
5 Brittle-to-ductile transition 17
5.1 Limitations of ductility parameter . . . . . . . . . . . . . . . . . . . . . . . 17
5.2 MDobservations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6 Summary 21
A Alternative ductility indicators 26
B Surface Reconstruction 28
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1 Introduction
Directed growth of semiconductor nanowires (NWs) have attracted signi¯cant interest in
recent years as key enablers of nanotechnology. With their diameter controllable by the size
of the catalyst nanoparticles [1], and withtheir electronic properties tunable by doping [2],
NWs can be used to construct nano-scale electronic devices, such as ¯eld e®ect transistors
(FETs) [3, 4, 5], chemical and biological sensors [6], as well as nano-electrical-mechanical
systems (NEMS) such as actuators [7] and nano-°uidic components [8]. Reliable function-
ing of these novel devices depends critically on the mechanicalstability of the NWs and
their contacts under processing and working conditions. Characterizing and predicting
the mechanical strength of NWs is necessary because signi¯cant stress may build up due
to the thermal or lattice mismatch, even though the primary function of these NWs is
usually not to bear loads.
NWs are attractive systems for studying the fundamental deformation mechanisms
of materials.Establishing a quantitative connection between the physics of defects and
the mechanical properties of materials has been a dream of computational materials sci-
entists for a long time. It remains a signi¯cant challenge because of the large gap in
length scale between the two. The growing ability to fabricate and mechanically test high-
quality micro- and nano-scale specimens presents a...