Editing Nanowire (section)

== Physics ==

=== Conductivity ===
[[Image:Wire15micron.jpg|thumb|An [[Scanning electron microscope|SEM]] image of a 15 micrometer nickel wire]]

Several physical reasons predict that the conductivity of a nanowire will be much less than that of the corresponding bulk material. First, there is scattering from the wire boundaries, whose effect will be very significant whenever the wire width is below the free electron mean free path of the bulk material. In copper, for example, the mean free path is 40&nbsp;nm. Copper nanowires less than 40&nbsp;nm wide will shorten the mean free path to the wire width. Silver nanowires have very different electrical and thermal conductivity from bulk silver.<ref>{{Cite journal|last1=Cheng|first1=Zhe|last2=Liu|first2=Longju|last3=Xu|first3=Shen|last4=Lu|first4=Meng|last5=Wang|first5=Xinwei|date=2015-06-02|title=Temperature Dependence of Electrical and Thermal Conduction in Single Silver Nanowire|url= |journal=Scientific Reports|language=en|volume=5|issue=1|pages=10718|doi=10.1038/srep10718|pmid=26035288|pmc=4451791|arxiv=1411.7659|bibcode=2015NatSR...510718C|issn=2045-2322}}</ref>

Nanowires also show other peculiar electrical properties due to their size. Unlike single wall carbon nanotubes, whose motion of electrons can fall under the regime of [[ballistic transport]] (meaning the electrons can travel freely from one electrode to the other), nanowire conductivity is strongly influenced by edge effects. The edge effects come from atoms that lay at the nanowire surface and are not fully bonded to neighboring atoms like the atoms within the bulk of the nanowire. The unbonded atoms are often a source of defects within the nanowire, and may cause the nanowire to conduct electricity more poorly than the bulk material. As a nanowire shrinks in size, the surface atoms become more numerous compared to the atoms within the nanowire, and edge effects become more important.{{citation needed|date=December 2023}}

The conductance in a nanowire is described as the sum of the transport by separate ''channels'', each having a different electronic wavefunction normal to the wire. The thinner the wire is, the smaller the number of channels available to the transport of electrons. As a result, wires that are only one or a few atoms wide exhibit quantization of the conductance: i.e. the conductance can assume only discrete values that are multiples of the [[conductance quantum]] {{nowrap|1=''G''<sub>0</sub> = 2''e''<sup>2</sup>/''h''}} (where ''e'' is the [[elementary charge]] and ''h'' is the [[Planck constant]]) (see also ''[[Quantum Hall effect]]''). This quantization has been observed by measuring the conductance of a nanowire suspended between two electrodes while pulling it progressively longer: as its diameter reduces, its conductivity decreases in a stepwise fashion and the plateaus correspond approximately to multiples of ''G''<sub>0</sub>.<ref name="Yanson 1998">{{cite journal | last1=Yanson | first1=A. I. | last2=Bollinger | first2=G. Rubio | last3=van den Brom | first3=H. E. | last4=Agraït | first4=N. | last5=van Ruitenbeek | first5=J. M. | title=Formation and manipulation of a metallic wire of single gold atoms | journal=Nature | volume=395 | issue=6704 | date=1998 | issn=0028-0836 | doi=10.1038/27405 | pages=783–785| arxiv=cond-mat/9811093 | bibcode=1998Natur.395..783Y }}</ref><ref name="Rodrigues 2000">{{cite journal | last1=Rodrigues | first1=Varlei | last2=Fuhrer | first2=Tobias | last3=Ugarte | first3=Daniel | title=Signature of Atomic Structure in the Quantum Conductance of Gold Nanowires | journal=Phys. Rev. Lett. | volume=85 | issue=19 | date=2000-11-06 | issn=0031-9007 | doi=10.1103/PhysRevLett.85.4124 | pages=4124–4127| pmid=11056640 | bibcode=2000PhRvL..85.4124R }}</ref>

The quantization of conductivity is more pronounced in semiconductors like Si or GaAs than in metals, because of their lower electron density and lower effective mass. It can be observed in 25&nbsp;nm wide silicon fins, and results in increased [[threshold voltage]].  In practical terms, this means that a [[MOSFET]] with such nanoscale silicon fins, when used in digital applications, will need a higher gate (control) voltage to switch the transistor on.<ref>{{cite journal|doi=10.1103/PhysRevB.68.075311 |journal=Physical Review B|volume=68|issue=7|page=075311|year=2003|title=Quantum interference in a one-dimensional silicon nanowire|last1=Tilke|first1=A. T.|last2=Simmel|first2=F. C.|last3=Lorenz|first3=H.|last4=Blick|first4=R. H.|last5=Kotthaus|first5=J. P.|bibcode=2003PhRvB..68g5311T}}</ref>

=== Welding ===
Nanowires can be welding together: a [[sacrificial metal]] nanowire is placed adjacent to the ends of the pieces to be joined (using the manipulators of a [[scanning electron microscope]]); then an electric current is applied, which fuses the wire ends. The technique fuses wires as small as 10&nbsp;nm.<ref>{{cite journal|author=Halford, Bethany |title=Wee Welding with Nanosolder|journal=Chemical & Engineering News|volume=86|issue=51 |year=2008|pages=35}}</ref>

For nanowires with diameters less than 10&nbsp;nm, existing welding techniques, which require precise control of the heating mechanism and which may introduce the possibility of damage, will not be practical. Single-crystalline ultrathin gold nanowires with diameters ≈&nbsp;3–10&nbsp;nm can be "cold-welded" together within seconds by mechanical contact alone, and under remarkably low applied pressures (unlike macro- and micro-scale [[cold welding]] process).<ref>{{cite journal|doi=10.1038/nnano.2010.4|pmid=20154688|title=Cold welding of ultrathin gold nanowires|journal=Nature Nanotechnology|volume=5|issue=3|pages=218–24|year=2010|last1=Lu|first1=Yang|last2=Huang|first2=Jian Yu|last3=Wang|first3=Chao|last4=Sun|first4=Shouheng|last5=Lou|first5=Jun|bibcode=2010NatNa...5..218L}}</ref> High-resolution [[transmission electron microscopy]] and [[in situ]] measurements reveal that the welds are nearly perfect, with the same crystal orientation, strength and electrical conductivity as the rest of the nanowire. The high quality of the welds is attributed to the nanoscale sample dimensions, oriented-attachment mechanisms and mechanically assisted fast [[surface diffusion]]. Nanowire welds were also demonstrated between gold and silver, and silver nanowires (with diameters ≈&nbsp;5–15&nbsp;nm) at near room temperature, indicating that this technique may be generally applicable for ultrathin metallic nanowires. Combined with other nano- and microfabrication technologies,<ref>{{cite journal|doi=10.1126/science.1090899 |pmid=14631034 |title=Nanowire Crossbar Arrays as Address Decoders for Integrated Nanosystems |journal=Science |volume=302 |issue=5649 |pages=1377–9 |year=2003 |last1=Zhong |first1=Z. |last2=Wang |first2=D |last3=Cui |first3=Y |last4=Bockrath |first4=M. W. |last5=Lieber |first5=C. M. |s2cid=35084433 |bibcode=2003Sci...302.1377Z |url=https://authors.library.caltech.edu/51862/7/zhong.SOM.pdf }}</ref><ref>{{cite journal|doi=10.1126/science.1162193 |pmid=18703709 |title=Polymer Pen Lithography |journal=Science |volume=321 |issue=5896 |pages=1658–60 |year=2008 |last1=Huo |first1=F. |last2=Zheng |first2=Z. |last3=Zheng |first3=G. |last4=Giam |first4=L. R. |last5=Zhang |first5=H. |last6=Mirkin |first6=C. A. |s2cid=354452 |bibcode=2008Sci...321.1658H |url=https://dr.ntu.edu.sg/bitstream/10220/8553/1/48.%20Polymer%20Pen%20Lithography.pdf |pmc=8247121 |hdl=10356/94822 }}</ref> [[cold welding]] is anticipated to have potential applications in the future [[Top-down and bottom-up design#Nanotechnology|bottom-up]] assembly of metallic one-dimensional nanostructures.

=== Mechanical properties ===
[[File:Si NanoWire Failure.gif|thumb|Simulation of a nanowire [[Fracture|fracturing]]]]
The study of nanowire mechanics has boomed since the advent of the [[Atomic force microscopy|atomic force microscope]] (AFM), and associated technologies which have enabled direct study of the response of the nanowire to an applied load.<ref name=":0">{{Cite journal|last1=Wang|first1=Shiliang|last2=Shan|first2=Zhiwei|last3=Huang|first3=Han|date=2017-01-03|title=The Mechanical Properties of Nanowires|journal=Advanced Science|volume=4|issue=4|pages=1600332|doi=10.1002/advs.201600332 |pmc=5396167|pmid=28435775}}</ref> Specifically, a nanowire can be clamped from one end, and the free end displaced by an AFM tip. In this cantilever geometry, the height of the AFM is precisely known, and the force applied is precisely known. This allows for construction of a force vs. displacement curve, which can be converted to a [[Stress–strain curve|stress vs. strain]] curve if the nanowire dimensions are known. From the stress-strain curve, the elastic constant known as the [[Young's modulus|Young's Modulus]] can be derived, as well as the [[toughness]], and degree of [[strain-hardening]].

==== Young's modulus ====
[[File:Stress Strain Ductile Material.pdf|thumb|upright=1.2|Stress-strain curve provides all the relevant mechanical properties including; tensile modulus, yield strength, ultimate tensile strength, and fracture strength]]

The elastic component of the stress-strain curve described by the Young's Modulus, has been reported for nanowires, however the modulus depends very strongly on the microstructure. Thus a complete description of the modulus dependence on diameter is lacking. Analytically, [[continuum mechanics]] has been applied to estimate the dependence of modulus on diameter: <math>E=E_{0}[1+4(E_{0}/E_{s}-1)(r_{s}/D-r_{s}^{2}/D^{2})]</math> in tension, where <math>E_{0}
</math> is the bulk modulus, <math>r_{s}</math> is the thickness of a shell layer in which the modulus is surface dependent and varies from the bulk, <math>E{s}</math> is the surface modulus, and <math>D</math> is the diameter.<ref name=":0" /> This equation implies that the modulus increases as the diameter decreases. However, various computational methods such as molecular dynamics have predicted that modulus should decrease as diameter decreases.

Experimentally, gold nanowires have been shown to have a Young's modulus which is effectively diameter independent.<ref name=":1">{{Cite journal|last1=Wu|first1=Bin|last2=Heidelberg|first2=Andreas|last3=Boland|first3=John J.|s2cid=34828518|date=2005-06-05|title=Mechanical properties of ultrahigh-strength gold nanowires|journal=Nature Materials|volume=4|issue=7|pages=525–529|doi=10.1038/nmat1403|pmid=15937490|issn=1476-1122|bibcode=2005NatMa...4..525W}}</ref> Similarly, [[Nanoindentation|nano-indentation]] was applied to study the modulus of silver nanowires, and again the modulus was found to be 88 GPa, very similar to the modulus of bulk Silver (85 GPa)<ref>{{Cite journal|last1=Li|first1=Xiaodong|last2=Gao|first2=Hongsheng|last3=Murphy|first3=Catherine J.|last4=Caswell|first4=K. K.|date=Nov 2003|title=Nanoindentation of Silver Nanowires|journal=Nano Letters|volume=3|issue=11|pages=1495–1498|doi=10.1021/nl034525b|issn=1530-6984|bibcode=2003NanoL...3.1495L}}</ref> These works demonstrated that the analytically determined modulus dependence seems to be suppressed in nanowire samples where the crystalline structure highly resembles that of the bulk system.

In contrast, Si solid nanowires have been studied, and shown to have a decreasing modulus with diameter<ref>{{Cite journal|last1=Wang|first1=Zhong Lin|last2=Dai|first2=Zu Rong|last3=Gao|first3=Ruiping|last4=Gole|first4=James L.|s2cid=53588258|date=2002-03-27|title=Measuring the Young's modulus of solid nanowires byin situTEM|journal=Journal of Electron Microscopy|volume=51|issue=suppl 1|pages=S79–S85|doi=10.1093/jmicro/51.Supplement.S79|issn=0022-0744}}</ref> The authors of that work report a Si modulus which is half that of the bulk value, and they suggest that the density of point defects, and or loss of chemical stoichiometry may account for this difference.

==== Yield strength ====

The plastic component of the stress strain curve (or more accurately the onset of plasticity) is described by the [[Yield (engineering)|yield strength]]. The strength of a material is increased by decreasing the number of defects in the solid, which occurs naturally in [[nanomaterials]] where the volume of the solid is reduced. As a nanowire is shrunk to a single line of atoms, the strength should theoretically increase all the way to the molecular tensile strength.<ref name=":0" /> Gold nanowires have been described as 'ultrahigh strength' due to the extreme increase in yield strength, approaching the theoretical value of ''E''/10.<ref name=":1" /> This huge increase in yield is determined to be due to the lack of [[dislocation]]s in the solid. Without dislocation motion, a 'dislocation-starvation' mechanism is in operation. The material can accordingly experience huge stresses before dislocation motion is possible, and then begins to strain-harden. For these reasons, nanowires (historically described as 'whiskers') have been used extensively in composites for increasing the overall strength of a material.<ref name=":0" /> Moreover, nanowires continue to be actively studied, with research aiming to translate enhanced mechanical properties to novel devices in the fields of [[Microelectromechanical systems|MEMS]] or [[Nanoelectromechanical systems|NEMS]].