|Home | About | Journals | Submit | Contact Us | Français|
Nanowires offer a unique approach for the bottom up assembly of electronic and photonic devices with the potential of integrating photonics with existing technologies. The anisotropic geometry and mesoscopic length scales of nanowires also make them very interesting systems to study a variety of size-dependent phenomenon where finite size effects become important. We will discuss the intriguing size-dependent properties of nanowire systems with diameters in the 5 – 300 nm range, where finite size and interfacial phenomena become more important than quantum mechanical effects. The ability to synthesize and manipulate nanostructures by chemical methods allows tremendous versatility in creating new systems with well controlled geometries, dimensions and functionality, which can then be used for understanding novel processes in finite-sized systems and devices.
Nanowires, quasi one-dimensional structures which exhibit high anisotropy between their nanometer-scale diameters and micrometer-scale lengths, have received significant attention in the last decade for their resultant unique physical and chemical properties as well as for their promise for applications in a variety of devices and systems . Synthesized as early as the 1960s by Wagner and Ellis , these novel nanostructures have since been actively researched to study their potential as active device components such as field-effect transistors , logic devices , microprocessors and complete programmable circuits , sensors [6-10], nanogenerators [11, 12], light-emitting diodes [13, 14], electrically-driven lasers , solar cells , and lithium-ion battery anodes  amongst many notable examples. Benefits gained from high-surface-to-volume ratios, as well as electrical or optical confinement in the radial direction, are accessible due to the long lengths of the nanowires, which allow electrical connections and interconnection to be made via conventional lithographic techniques. In the cases where benefits gained from radial confinement are unaffected by nanowire length, nascent techniques have potential for scaling single-nanowire devices to multi-nanowire systems: microfluidic assembly [18, 19], electric field [20, 21], dielectrophoresis [22-24], mechanical transfer [25-27], optical tweezers [28-31], for instance, have potential for aiding in precise placement within smaller-scale systems, while techniques such as Langmuir-Blodgett [32-34], branched nanowire growth [35-37], or 3-D assembly [38, 39] could eventually mature sufficiently for large-scale deterministic system assembly.
While nanowire synthesis cannot currently produce large-scale integrated systems as complex as those possible via top-down fabrication methods, however, the bottom-up methods utilized in nanowire synthesis allows for creating unique material systems to study their intriguing properties. Because novelty in nanowire material properties largely arises from size-related aspects such as surface-to-volume ratio, anisotropy, and radial confinement, an explicit understanding of property size-dependence is critical to maximizing the potential of their morphology. Unfortunately, diminutive dimensions and a complete control over the nanowire dimensions during their synthesis can make systematic characterization as a function of size challenging, and thorough size-dependent studies of nanowire material properties are sparse as a result. While electrical , magnetic , thermal , and mechanical  properties of nanowires, among others, have all been evaluated in the literature to some degree, we will focus on the systematic size-dependent studies of chemical reactions, structural phase-change, and optical properties in this topical review. Studies into these disparate, yet representative properties can provide insight into global size-dependent trends, and recognition of recurrent themes could ultimately aid in understanding other phenomena. It is for these reasons that the size-dependence of these properties in nanowires will be the focus of this article, with examples drawn from our group’s research over the last five years.
The unique properties of nanostructured materials enable their transformation into complex and occasionally kinetically-controlled morphologies, which cannot be obtained during their growth. Solution-phase cation-exchange reactions can transform sub-10 nm nanocrystals and nanorods into varying compositions and superlattice structures; however, due to their small size, ion-exchange reaction rates are extremely fast, which limits control over the transformed products and possibilities for obtaining new morphologies. On the other hand, ion-exchange phenomena in bulk materials are quite slow, occur at very high temperatures, and also damage the material due to the large stress that builds up during the course of the reaction. We will discuss recent efforts in transforming nanowires with length scales that bridge the gap between nanocrystals and bulk materials into kinetically controlled products using ion-exchange reactions in the gas phase. These studies also shed new insights into how diffusion, domain growth, and percolation occur at the nanoscale, leading to novel transformations.
With regards to structural phase-change properties, we will discuss recent efforts in studying reversible crystalline to amorphous phase transitions in chalcogenide nanowires, which are becoming important materials for phase change memory (PCM) devices. Of the different memory device concepts being currently explored, PCM devices based on Ge-Sb-Te alloys are very promising for scalable device size, high-speed operation with non-volatile data storage. However, the top-down nature of thin film device fabrication and etching-induced material damage leads to scalability problems at sub-100 nm size. Therefore, there is great interest in developing new materials and processing techniques to overcome this barrier. Self-assembled nanowires are particularly promising in this context owing to their sub-lithographic size that is free of etch-induced damage. Reversible phase transitions in single-crystalline nanowire devices scaled down to 20 nm sizes have been observed with dramatic reduction in power consumption. These studies demonstrate that phase-change nanowires hold great promise as building blocks for miniaturized memory devices and as model systems for in-depth understanding of size-dependent phase transitions in confined geometries in self-assembled, defect-free nanostructures.
Finally, we will review recent studies detailing the propagation of light in subwavelength nanowire optical cavities, where the diameter of nanowires is smaller than the waveguided light. Due to strong photonic confinement, intriguing size-dependent dispersion properties of various waveguided modes are observed. In addition to altered dispersions, tight optical confinement leads to very strong and size-dependent light-matter coupling in nanowires, leading to formation of exciton-polaritons. The effect of size-dependent mode-dispersion and polariton formation on subwavelength photonics will be discussed.
Ion-exchange is a useful technique for chemically transforming one material to another, partially or completely, in order to modify its structural, chemical and physical properties. In bulk materials, ion-exchange is mainly circumscribed to the surface due to the high activation energy required for diffusion of atoms, thus making the transformation extremely sluggish . However, nanostructures, owing to their high surface to volume ratios, effectively reduce the kinetic barrier for diffusion . This enables their fast and complete chemical transformation while undergoing ion-exchange. Researchers have displayed controllability of ion-exchange both in terms of the extent of composition and volume transformation. Moreover, nanostructures have shown not just compositional but morphological transformation as well, which makes ion-exchange at the nanoscale an exciting method of making novel multi-component materials with highly complex structures, morphologies and composition modulation. In this section, we will look at some of the notable work in the field of ion-exchange in nanostructures that promises to deliver the next generation of engineered nanomaterials and focus on our group’s recent work in the area of controlled gas-phase transformation of semiconductor nanowires. This review mainly focuses on some of the ground breaking work in the field of ion exchange, however for a more comprehensive perspective, please refer to .
For ionic compounds, it is well known that anions form the rigid framework of the crystal lattice whereas the cations are relatively mobile . Therefore it is kinetically more challenging to perform anion exchange, which often involves complete transformation of the crystal framework as opposed to cation exchange which is a much simpler diffusion process. In fact, anion exchange often leads to more drastic morphological changes than its cationic counterpart. Hence, the latter has been studied more widely due to the ease with which it can be accomplished.
Some of the early work in the field of cation exchange in nanostructures was reported by Alivisatos et al. on the rapid (t << 1 s) and reversible transformation of CdS nanocrystals into Ag2Se in solution phase under ambient conditions in a very short period . The extremely fast transformation was attributed to the lowering of the kinetic barrier for diffusion in nanostructures. They also studied the size dependent morphological transformation in anisotropic non-equilibrium nanostructures such as rods. It was found that if the initial diameter of the nanostructure is smaller than the reaction zone width, then the entire structure becomes unstable during transformation and can equilibrate in form of a lower surface energy morphology such as a sphere, but if not, the initial morphology remains stable and the reaction zone continues progressing from the surface towards the core. The same group demonstrated superlattice formation in nanorods as a result of partial cation exchange . The starting material was chosen as CdS nanorods which on reaction with a limited source of Ag+ ions resulted in the formation of alternating segments of CdS and Ag2S. Formation of such a superlattice was explained by limited cation exchange in the CdS nanorods that led to small islands of Ag2S on the surface. These islands found it energetically favourable to merge into segments through Ostwald ripening since it would reduce the surface area between CdS and Ag2S domains. This process continued until the point that these segments spanned the entire diameter of the rod and joining of these segments would be kinetically unfavourable. Regular spacing of the stripe pattern was explained by elastic repulsion between Ag2S segments due to the strain in CdS region in-between. This elastic strain was generated so that Ag2S lattice can match the basal lattice constant of CdS. This phenomenon has been further studied with some theoretical explanation for the formation of these superlattices . Another important work by the same group showed how the anionic framework is conserved in ionic nanocrystals when they undergo cation exchange . This was proven by performing cation exchange on CdS nanorods embedded with a CdSe nanocrystal (CdSe/CdS) to obtain a PbSe/PbS product via a Cu2Se/Cu2S structure. During this two-step exchange process, the size and the position of the selenide nanocrystal within the nanorod was preserved. Alivisatos and co-workers also looked at synthesis of nanocrystal heterostructures as a result of selective cation exchange on different facets of the parent nanocrystal . Experimental and theoretical models of cation exchange by Cu on different crystallographic facets of CdS nanorods were studied. They observed and justified, based on interfacial energy arguments, how Cu2S segments were formed on the ends of the CdS nanorods. These results were also compared with some of their previous work .
Jeong and co-workers transformed Ag2Te nanowires into CdTe (also ZnTe and PbTe) nanowires and then into PtTe2 nanotubes through cation exchange in solution phase . In this work, they showed how solubility products (Ksp) of ionic solids can be used to predict if transformation is thermodynamically favourable or not. Ideally, an ionic solid with a relatively high Ksp value will undergo cation exchange to form another ionic solid with relatively low Ksp. The solubility product itself can be adjusted as a function of temperature, presence of common ions and also the size of the ionic solid. The change in morphology was explained by the volume transformation that takes place during cation exchange: if the volume change in the material is large, then it can lead to stress accumulation, which relieves itself leading to morphological changes. For example, severe axial stress in a nanowire can cause it to fracture into smaller nanorods and radial stress can cause migration of material from or towards the surface. Formation of PtTe2 nanotubes was also explained by a large volume change on cation exchange in CdTe nanowires which causes stress accumulation that forces Te to be driven out from the core, leading to a hollow 1-D nanostructure. Jeong and co-workers also synthesized uniform CdSe nanowires from Ag2Se nanowires in the solution phase such that both the morphology as well as the single crystallinity of the parent phase was preserved [52, 53]. Ma and colleagues synthesized trigonal Se nanowires from amorphous Se nanoparticles and transformed them into Ag2Se and CdSe nanowires through cation exchange .
Even though energetically and structurally challenging, several successful attempts have been reported to obtain anion exchange in nanostructures. Könenkamp and co-workers converted columnar ZnO films into ZnS coated ZnO nanocolumns (aspect ratio ~10) in the vapor phase by reaction with H2S at 400°C . The core of the column was etched away by H2SO4 leaving behind ZnS nanotubes. Könenkamp et al. further extended their work by substituting zinc with copper in the solution phase to yield Cu2S nanotubular structures . Similar work was done to create PbS-PbSe  and CdS-CdSe  core-shell nanostructures in the solution phase. Metal hydroxides have been used by numerous researchers to obtain metal chalcogenides by employing an anion exchange reaction. Kim et al.  used Cd(OH)2 nanowire bundles as a starting template to synthesize CdSe nanotubes in the solution phase, and the resulting tubular morphology was a result of the Kirkendall effect due to faster outward diffusion of Cd in comparison with inward diffusion of Se . Another novel work is the spatial confinement of anion exchange reaction in a single walled carbon nanotube (SWCNT);  metal halide/SWCNT core-shell system was synthesized via impregnation of SWCNTs with low melting cadmium iodide. Subsequently, anion exchange was carried out by sulfidation in molten sulphur to obtain CdS/SWCNT core-shell structure. This experiment was extended to other systems to yield similar MX/SWCNT core-shell morphologies (M = Cd, Zn, Pb; X = S, Se, Te).
Most of the ion-exchange work has focused on transformations in the solution phase of nanocrystals in the sub-10 nm size scale, where the transformations occur very rapidly. It would be interesting to extend ion-exchange work for larger systems (10-100 nm) and in the gas phase to make it more compatible with a wide range of nanomaterials grown using gas phase techniques. Park and co-workers have attempted cation exchange on nanowires by chemical vapor transport; in their earlier work, they converted CdS nanobelts into ZnS nanobelts by Zn vapor (evaporated Zn metal) transport at 800° C . They also showed that the reverse reaction cannot be achieved completely even at higher temperatures pointing out the thermodynamic stability of one phase over the other. In another similar work, they transformed ZnTe nanowires into CdTe nanowires through an intermediate ZnCdTe-CdTe core-shell nanowire structure . The extent of transformation was controlled by the reaction time which dictated how deeply the CdTe growth front would penetrate inside the wire.
The first successful attempt at a precisely controlled composition and morphology in nanostructures via cation exchange in the gas phase was reported by Agarwal and co-workers . Starting from CdS nanowires, they were able to obtain compositionally tunable CdxZn(1-x)S nanowires, Zntube-CdxZn(1-x)S superlattices, ZnS nanotubes, ZnS nanowires and pure Zn nanowires as a function of increasing Zn precursor (dimethyl Zn, DMZn) inside an atomic layer deposition (ALD) furnace (Figure 1). They also observed size dependent variation in transformation in nanowires performed at under different reaction temperatures. It was observed that at elevated temperatures (220°C), thin nanowires (< 25 nm) completely transformed into ZnS nanowires, slightly thicker ones (30–90 nm) formed CdxZn(1-x)S nanowires (‘x’ decreases as a function of decreasing nanowire diameter) and the thickest ones only displayed cation exchange 25-30 nm from the surface whereas the core remained intact. Nanowires which were less than 10 nm in size could undergo complete transformation even at temperatures as low as 50°C. They measured the decrease of the activation energies of the exchange reactions with decreasing nanowire diameters, which is a sum of diffusion and exchange reaction energies. This provided a concrete proof of how cation exchange is a much faster phenomenon in nanostructures as compared to bulk mainly due to the dramatic decrease in diffusion activation energies.
To study the morphological transformations obtained upon increasing amount of Zn precursor, the Agarwal group chose nanowires of a tight distribution range (~50-60 nm) and carried out reactions at 350°C. The results and proposed mechanisms were as follows. As shown in Figure 2, on introducing a small amount of DMZn, CdxZn(1-x)S nanowires were formed as a result of partial cation exchange with the morphology intact due to very little strain in the system. On increasing the DMZn, Zntube-CdxZn(1-x)S superlattices were formed as a result of segregation between Zn rich and CdxZn(1-x)S segments. The mechanism was thought to be similar to the one observed in Alivisatos’ work , the only difference being that cadmium and sulphur escaped from the zinc rich regions because of the radial stress generated during the transformation. On further increasing DMZn concentration and subsequent annealing, ZnS nanotubes were formed. This result was explained by a complete radial stress from ZnS shell formation, which pushes unbound Cd and S towards the core-shell interface where they are trapped. Upon annealing, these materials eventually escaped, leaving behind a ZnS nanotube. Upon a further increase in DMZn concentration, complete cation exchange occurred and ZnS nanowires were formed. Higher concentrations caused severe diffusion and system instability, resulting in formation of pure polycrystalline zinc nanowires by rapid outward diffusion of cadmium and sulphur.
Accomplishments in the field of nanostructure ion-exchange have provided us with novel materials exhibiting very promising electrical, thermal and optical properties. The study of the underlying science of ion exchange promises to open new frontiers in the field of nanomaterial synthesis. Cation exchange is now a well-studied field and even though anion exchange hasn’t been probed into as much as it deserves, it will be interesting to see how the chemical and structural evolution occurs at the nanoscale when the structural pillars (anions) in an ionic solid are replaced. The underlying science is still being probed carefully and promises to open new frontiers in the field of nanomaterial synthesis.
Phase-change memory based on chalcogenide (Ge-Sb-Te alloys) materials is a relatively new class of electronic memory, and it is increasingly drawing a substantive amount of attention due to its potential for overcoming the drawbacks of conventional electronic memories. Dynamic random access memory (DRAM), widely employed in modern computers, exhibits fast memory switching, scalability and reliable performance, but is limited by data volatility. Flash memory, on the other hand, while being scalable has a cost advantage and exhibiting data non-volatility, suffers from slow switching speeds and limited write/read cycle capability [65, 66]. Therefore, there is a growing need to find material systems that can be utilized as the next generation memory devices with the combined capabilities of scalability, fast switching speeds, data non-volatility, and long-time cyclability, and recent demonstrations in academic and industrial laboratories have shown that phase-change memory could be a viable candidate to replace conventional technologies. However, many challenges remain before they can be successfully commercialized, including demonstrations of continued scalability, and understanding their electronic [67-71], mechanical [72, 73], and thermal [74-76] properties along with the operating mechanisms at the atomic scale as well as issues related to data drift (discussed below).
The memory switching in chalcogenide materials is based on the change of electrical resistivity of the materials owing to their intrinsic structural change. Reversible transitions between crystalline and amorphous phases represents two distinct low (crystalline)/high (amorphous) resistive states, and each state is assigned a binary value for data storage purposes [77-82]. This structural change is realized through the Joule heating of phase-change materials, where the amount of heating and the subsequent cooling rates determines the resultant structures [77, 78]: it has been widely assumed that sufficient Joule heating and rapid cooling causes the structure to be quenched into an amorphous phase, while heating above the crystallization temperature followed by slow cooling switch it back to a crystalline phase. However, recent work has started to question this rather simplistic description of phase change in these materials both for amorphization [83-85] and recrystallization [86-88] where the effect of the applied electric field is otherwise ignored. In practical electronic devices, the phase change is realized by applying electrical pulses: high amplitude with short duration times introduce for crystalline-to-amorphous change, while long pulses with small amplitude are used to switch back to the crystalline phase. The underlying physical mechanism for the rapid and reversible phase-change is attributed to the unique electronic band structures of chalcogenide materials [89-93]. Weak covalent bonding, owing to the lone-paired electrons of chalcogens, leads to low transition temperatures, suitable for facile phase-change introduced by minimum input energy.
Phase-change materials suitable for memory applications are mostly selected from IV-V-VI compound materials, in particular, along the pseudo-binary line in the phase-diagram of GeTe-Sb2Te3 [94, 95]. Each stoichiometric compound along this line possesses different material properties and therefore presents different electrical switching characteristics [78, 96]. Despite the high potential of phase-change memories for future storage media, many technical/practical issues, such as higher switching current (thereby, higher power consumption) caused with increasing memory density, remain to be resolved for reliable device operation. More fundamentally, the scaling limit of phase change memories needs to be answered. This issue is not only about investigating the minimum size limit of memory devices without limiting their performance, but also about understanding the size-dependent change of physical/structural properties (for example, bistability of amorphous/crystalline phases) of phase change materials themselves. These questions have led to the development of various zero-or-one dimensional nanomaterials which are applied to phase-change memory devices either as active memory materials [97, 98] or interconnects  for lowered Joule heating. Amongst them, recently developed one-dimensional chalcogenide phase-change nanowires synthesized by bottom-up approaches have drawn extensive research interest in terms of both fundamental science and practical engineering perspectives [100-106]. This new class of phase-change materials displays reliable memory switching performance at the length scale that conventional top-down based fabrication methods cannot approach easily and without damaging or altering the surface properties of the device. Moreover, they also present ideal model systems to study a variety of intrinsic size-dependent material properties due to their defect-free single-crystalline structures and tunable sizes, which are difficult to realize in thin film polycrystalline phase-change materials.
Here, we review various size-dependent phenomena in bottom-up synthesized phase-change nanowires. Owing to the facile control of nanowire thickness, systematically studies of the change of various physical and electrical properties of phase-change nanowires will be reviewed. Following this, we will discuss the ultimate size limit toward extremely high memory density.
Phase-change nanowires of various compositions, such as GeTe[100-102], Sb2Te3 GeSb, Ge2S22Te5 (GST) [105, 106], and InSe have been synthesized by the vapor-liquid-solid (VLS) process. The thickness (diameter) of the nanowires is tunable by controlling the size of metal catalysts  that seed the nanowire growth, and uniform chemical composition can be obtained throughout the entire nanowire using precursors of different compositions. The as-grown nanowires are single crystalline, as characterized by various electron microscopy techniques and x-ray diffraction (XRD). Figure 3  illustrates, as an example, the structural and chemical characterization of GeTe nanowires, which shows they are single-crystalline and with uniform composition down to few tens of nanometer length scales.
The memory switching properties of phase-change nanowires are characterized by measuring the current (I) vs. voltage (V) characteristics especially in the amorphous phase and the details of the device state is further obtained by the programming curve, i.e., change of the device resistance (R) as a function of the applied pulse amplitude. Figure 4 demonstrates typical memory switching characteristics of Ge2Sb2Te5 nanowires. In Figure 4a, the as-synthesized nanowire shows low-resistive ohmic behavior (red circles) owing to its original crystalline phase. After the application of a writing current (100 ns duration, 0.6 mA amplitude) for amorphization, the nanowire undergoes memory switching, signified by the drastic change in the I-V curve (blue squares). At low applied bias (<1.1 V), the I-V curve exhibits a highly resistive RESET state (amorphous phase) which transits to a low-resistive SET state at a threshold voltage of 1.1 V, eventually recovering the original I-V characteristics (crystalline phase). Figure 4b shows the variation of the resistance of the nanowire device upon the application of electrical pulses with varying amplitudes. The initial low resistance (SET; red circles) sharply increases by over two orders of magnitude after applying a current pulse (>0.43 mA, duration; 100 ns) leading to device amorphization. This high-resistive amorphous phase (RESET; blue squares) fully recovers to the SET state after a current pulse with smaller amplitude (0.25 mA), yet longer duration (300 ns), for crystallization.
One of the main advantages with phase-change nanowires is that size-dependent property changes can be systematically studied owing to their largely defect-free structures and uniform chemical compositions. This size-dependent fundamental study of the materials properties of phase change chalcogenides is critical for the development of highly miniaturized memory devices. Figure 5 shows size-dependent switching characteristics of Ge2Sb2Te5 nanowires of different diameters. The resistance (R) vs. writing current (I) curve representing crystalline-to-amorphous switching (Figure 5a) shows a systematic shift to lower writing currents with decreasing thickness. A dramatic reduction of writing currents down to 0.16 mA (Figure 5b, red circles) is observed for a 30 nm-thick nanowire in comparison to 1.3 mA for a 200 nm-thick nanowire. The corresponding power for the crystalline-to-amorphous transition also scales down with decreasing nanowire thickness (Figure 5b, blue circles).
Size-dependent memory switching can be quantitatively understood based on the one-dimensional heat transport model, which describes the Joule heating effect in phase-change nanowires. In a phase-change material of cylindrical geometry with radius r and length L, the heat transport equation is expressed by , where J is current density (J = I / πr2), and k and ρ are the thermal conductivity and the electrical resistivity, respectively [109, 110]. The writing current is given by , where ΔT is the temperature change from room temperature to transition temperatures. This equation indicates that given intrinsic material properties, the nanowire morphology is the main factor in determining the writing current, and thus, power efficiency. The writing currents for both GeTe and Ge2Sb2Te5 nanowires are observed to linearly scale with the cross sectional areas of nanowires given the same spacing L between electrodes . Such linear scaling of writing currents was also experimentally observed in thin film phase-change memory devices where the contact area is defined as the area of the bottom electrode in contact with the active phase-change material layer [112, 113]. In addition, the writing currents for these one-dimensional phase-change nanowires are approximately 30% less in comparison to conventional thin film memory devices based with similar contact areas. This advantage is attributed to current localization and effective heat confinement in the one-dimensional geometry  where Joule heating and subsequent crystal nucleation/growth are radially confined, while two-dimensional thin films suffer from significant heat dissipation [112-114]. The geometrical advantage of confined structures for lower power consumption has been experimentally and theoretically verified in the lateral, bridge-type thin film phase-change memory devices with various cross-sectional areas fabricated by top-down lithographic techniques [112-114]. Figure 6 compares the linear scaling behavior of RESET currents in one-dimensional nanowires and two-dimensional thin film memory devices, both made of Ge2Sb2Te5. Furthermore, locally reducing the cross-sectional area of one-dimensional nanowires by sculpting a “notch” can also be effective for confining Joule heating in specific regions, which can be inspected for visualizing structural change during the course of phase-change by in situ TEM characterization [115, 116] in order to provide detailed and unprecedented insights into the phase change mechanisms.
Another important figure of merit for phase-change memory devices is data non-volatility (data retention time), which is related to the recrystallization time-scale of the amorphous phase. Since the crystalline phase is thermodynamically more favorable, the kinetics of the spontaneous recrystallization of the amorphous phase limits data non-volatility, and thus determines data retention time. To explicitly quantify data retention properties as a function of device size, which is also very important for device scaling analysis, temperature-dependent time-evolution of resistance was measured using amorphized nanowire phase change memory devices. Figure 7a shows the time-dependent resistance change of a 60 nm thick amorphized Ge2Sb2Te5 nanowire measured at various temperatures. An Arrhenius-like linear plot of recrystallization time (t) vs. 1/kBT (Figure 7b) indicates the thermally-activated nature of spontaneous recrystallization, where kB is the Boltzmann constant and T is temperature. The recrystallization activation energy (Ea) of 2.12 eV was obtained from the slope, and a data retention time of ~20 years at 80 °C was extrapolated from the data. The size-dependent temporal resistance change of amorphized nanowires under isothermal conditions also reveals that recrystallization for thinner nanowires is faster in comparison to thicker ones (Figure 7c). The Arrhenius plots for nanowires of different diameters clearly show strong size-dependent behavior in data retention times: thinner nanowires exhibit reduced data retention times (Figure 7d) and correspondingly smaller activation energies (Figure 7e).
The observed size-dependent recrystallization kinetics in nanowire memory devices can be quantitatively understood based on a modified heterogeneous nucleation model [117, 118]. The model predicts faster recrystallization for thinner nanowires with enhanced surface-to-volume ratio, since a surface provides more heterogeneous sites for nucleation when compared with bulk material. The analysis was confirmed by cross-sectional TEM characterizations of partially recrystallized phase-change nanowires, which show evidence of surface-initiated heterogeneous crystallization . The decrease of activation energy with decreasing nanowire thickness further indicates size-dependent changes in phase transition temperatures in phase-change nanowires. Suppression of the phase transition temperature (crystallization, in this case) with decreasing thickness of nanowires has been theoretically predicted by the phonon softening model; the enhanced phonon softening due to the increased density of atoms with broken bonds exposed on the heterogeneous sites (surfaces) facilitate phase-change at reduced temperatures [119-121]. Quantitative agreement was found between the phonon softening model and the experimentally obtained activation energies for nanowire devices . The lower transition temperatures in phase-change nanowires were also directly evidenced by several other research groups who melted and sublimed phase-change nanowires by heating them inside a TEM [122, 123]. Significantly lower melting temperatures (~40-60% lower than bulk material) were observed in GeTe nanowires, further supporting size-dependent, reduced writing currents observed with electrical characterization of nanowire devices.
This size-dependent change is in contrast to the observations on chalcogenide thin films [124-126] or nanocrystals  in embedded geometries which show an increase of phase transition temperatures with decreasing sizes. Recent studies suggest stress as a main factor to cause this discrepancy: embedded phase-change materials are under compressive stress from cladding materials which increase the activation energy barrier for phase-change kinetics by diminishing the process of covalent bond rupturing in atomic transition . This situation is not applicable to our nanowires which have exposed surfaces and are thus free of compressive stress, resulting in intrinsic heterogeneous nucleation and growth kinetics. More detailed studies are needed for further clarification.
Reduction of transition temperatures has also been observed in a variety of other zero-dimensional metallic [129, 130], organic [131, 132], and semiconducting [133, 134]nanocrystals with enhanced surface to volume ratio, showing these observations not confined to the nanowire morphology and further generalizing the size-dependent suppression of physical properties which occurs at reduced dimensions.
In addition to electrical switching and recrystallization characteristics, other physical properties critically related to data storage reliability may also vary with nanowire thickness. The electrical and mechanical properties of chalcogenide materials are affected by the time-dependent relaxation process in their amorphous state, sometimes called “drift”, which is detrimental for data storage reliability and further affects the electrical switching parameters in phase change memories [135-148]. The fundamental understanding of the origin of drift of the electrical properties of the amorphous phase in PCM is being actively researched and has been explained by a variety of effects including stress relaxation [135, 136], relaxation processes which anneal the electronic defects [135, 137], and the formation of valence alternation pairs (VAP) [90, 149, 150], all of which can increase the mobility gap causing an increase in material’s resistivity and threshold voltage. Within the electronic relaxation model, it has been proposed that the annealing of traps occurs due to atomic motions resulting in an increase in the inter-trap distance. The stress relaxation model is based on the internal hydrostatic pressure that is built in the embedded amorphous phase due to the large difference between the densities of the crystalline and amorphous phase (5-7%). The slow relaxation of internal stress, consistent with the stress relaxation data  is due to atomic motions within the embedded amorphous dome which increases the Fermi level from the valence band edge causing time-dependent increase in resistance and threshold voltage.
One way to distinguish between these proposed mechanisms is to design experiments on un-embedded nanoscale systems in which the stress upon amorphization can relax efficiently from the surface, which can also be engineered by changing the surface-to-volume ratio or by embedding the nanodevice without altering the material’s electronic properties. If the stress relaxation mechanism dominates over the drift dynamics, then any change in the system’s ability for efficient stress relaxation should significantly influence its drift characteristics. In this regard, phase change nanowires are useful as their sizes can be controlled down to 10 nm to tune the surface-to-volume ratio, and unlike thin films, nanowire devices can be configured with their surfaces exposed or completely embedded. It has been shown that nanowire devices have extremely small values of drift coefficients in comparison to thin films . By systematically varying the stress relaxation parameters such as the surface-to-volume ratio of the nanowires and comparing un-embedded and embedded devices, it was demonstrated that the release of built-in stress upon amorphization is primarily responsible for drift in PCM. The temporal drift of resistance values were characterized with Ge2S22Te5 nanowires of different thickness and thinner nanowires were found to exhibit less drift than thicker nanowires, as represented by the smaller drift coefficient, α, shown in Figure 8 . Moreover, in comparison with thin film memory devices where phase materials are buried in capping oxide layers, phase-change nanowires with surfaces exposed to air typically show significantly less drift of amorphous state resistance threshold voltages  in comparison to the same nanowire device embedded under a dielectric film (Figure 9). These results point to size-dependent stress relaxation mechanism being predominantly responsible for drift in phase-change devices: nanowires with free surfaces (no capping layers) easily and rapidly release the built-in stress caused by the phase-change in comparison with the embedded phase-change devices that can “trap” high built-in stress due to the capping layers, which relax slowly due to atomic motions leading to a power law type increase in device parameters. The thickness-dependent drift of the amorphous resistance in nanowires is also consistent with the easy stress relaxation in thinner nanowires with larger surface-to-volume ratios .
The aforementioned studies on size-dependent electrical switching in nanowires suggest the geometrical importance of phase-change materials for continued size scaling towards obtaining high density memory devices with low power consumption[153-157]. Further development of novel nanomaterials in unconventional geometries offers opportunities to investigate the ultimate size limit of the electrically-driven phase change at the nanometer scale. These nanomaterials can be used as either active phase-change memory elements or used as electrodes to form extremely small contact areas on phase-change materials. One example belonging to the former case is chalcogenide phase-change nanotubes synthesized by the vapor phase transport method (Figure 10a). Owing to the greatly reduced cross-sectional areas (tube wall thickness down to ~20 nm), these hollow nanostructured chalcogenide materials require an order of magnitude smaller writing current in comparison to the nanowires with solid cross-sectional areas of comparable outer diameters, as shown in Figure 10b . The latter case for extremely small contact areas between phase-change materials and electrodes was realized using carbon nanotubes as electrodes . A thin (~10 nm) Ge2Sb2Te5 film deposited on carbon nanotubes with nanometer-scale gaps (~20nm) shows excellent reversible switching characteristics with writing currents on the order of few microamperes, a reduction by two orders of magnitude in comparison to any state of the art phase change thin film devices, including phase-change nanowires .
The size-dependent phenomena discussed in this section are explained by the geometric effect on Joule-heating-based transport, as well as intrinsic material property changes owing to the enhanced surface-to-volume ratios at reduced dimensions. This intriguing behavior inherent to single-crystalline nanostructured materials presents great opportunities for the development of novel phase-change memories beyond the limitations of conventional memory technologies and for understanding the fundamental nanoscale properties of these intriguing materials.
In regards to optical properties, self-assembled, single-crystalline nanowires occupy an important niche among nanostructure morphologies. Due to a high refractive index mismatch with their surroundings, semiconductor nanowires with diameters in the subwavelength regime can strongly confine optical waves in the radial direction while guiding light in the axial direction [160, 161], a unique combination which makes them ideally suited for the development of many nanophotonic systems including modulators , switches, probes , and sensors . Achieving the full potential of nanowire systems, however, requires a fundamental understanding of how properties vary as a function of size, and the size dependence of a variety of optical phenomena in nanowires needs to be systematically investigated. While photoluminescence , optically-pumped lasing [167, 168], electrically-pumped lasing , waveguiding , and photoconductivity , for example, have been extensively documented in individual nanowires, explicit studies of these phenomena and their underlying size-dependent have only recently reached sufficient volume [172-177] for critical meta-analysis.
In addition to the need for controlled synthesis of consistently high-quality, single-crystalline nanostructures of narrow size distribution, certain optical studies of individual nanowires such as optical waveguiding properties, have an additional barrier in that their diameters are typically smaller than the wavelengths of light utilized in far-field optical analysis. The resulting diffraction limitations in this one dimension certainly do not preclude the study of their waveguiding properties. However, a comprehensive, quantitative analysis of light-matter interaction within any condensed matter system requires knowledge of the energy-wavevector dispersion relation, and this measurement is made difficult by the nanowire geometry. Direct measurements of the energy-wavevector dispersion relation are commonly performed by angle-resolved transmission or emission experiments in microcavities [178, 179] and time-resolved transmission experiments can measure its derivative, i.e., the group velocity . For nanowires these measurements are hindered by the scrambling effect of the subwavelength apertures at the wire ends due to diffraction, the short transmission times involved  and the difficulty of in-coupling of probe light with a large energy and wavevector distribution .
Here, we discuss recent investigations into the effect of size on the optical waveguiding properties of nanowires, which are used to obtain a comprehensive knowledge of light-matter interaction in nanoscale structures. Beginning with a review of early investigations into these properties, we will progress into a sequence of studies which progressively led to the quantitative understanding of light-matter interaction in semiconductor nanowires.
The energy-wavevector waveguide dispersion in dielectric nanowire waveguides describing the various propagating confined optical modes is predicted to be strongly size-dependent at the nanoscale ; however, theory does contain a nanowire diameter cutoff for a given dielectric contrast below which no waveguide modes can propagate along the growth axis. Certain size-dependent effects relevant to optical properties, including quantum confinement of electron-hole pairs (excitons)  and enhanced non-radiative surface recombination with respect to bulk structures , can still manifest in crystals of very small diameters, however they are not unique to nanowires. Instead we focus on an intermediate diameter regime of ~100-300 nm where waveguided modes are highly confined in two dimensions (radial confinement), yet still propagate along the long nanowire axis, a configuration indeed unique to the nanowire morphology.
When in this size regime, strong light confinement in the radial direction strongly influences optical properties. Strong coupling of this light field results in the formation of composite quasiparticles with both electronic and photonic character known as exciton-polaritons [185, 186] and it is through this polaritonic coupling mechanism as well as effects such as giant exciton oscillator strength and superradiance effects [187, 188], that crystal sizes comparable to the optical wavelengths can result in material dispersion that is significantly different from that of macroscopic crystals . Associated exciting physical phenomena such as slow light , low threshold polariton lasing  and Bose-Einstein condensation [192, 193] all motivate such studies.
The first demonstration of increased exciton-photon coupling with respect to bulk materials in individual nanowire cavities was reported by van Vugt et al.  using ZnO, a II-VI semiconductor which already exhibits large exciton oscillator strength, and therefore favors strong light-matter interaction, in macroscopic samples . The rate at which energy oscillates back and forth between excitonic and photonic states, known as the Rabi frequency, determined from spatially resolved photoluminescence spectra was found to be significantly enhanced with respect to bulk ZnO crystals. Periodic modulations in photoluminescence spectra beneath transverse exciton resonances, determined elsewhere to correspond with longitudinal Fabry-Pérot resonances with wavevectors parallel to the wire’s long axis (k=k) [196, 197], were plotted at integer multiples of π/L (where L is the nanowire length) in k-space. The resulting experimental material dispersion relation was also found to be substantially modified from bulk material.
From this point, improvements to the theoretical model of dispersion within nanowire cavities gradually allowed for more quantitative analysis. The first study to take into account nanowire geometry and finite size when calculating waveguide dispersion relations  was also the first to explicitly study size dependence. As shown in Figure 11, treating CdS nanowires as air-clad dielectric cylinders when calculating waveguide dispersion allows for successful modeling of successively higher-energy waveguide mode cutoffs with respect to decreasing nanowire diameter. In switching to a dielectric cylinder waveguide dispersion model for this study, however, the material dispersion was simplified by using a phenomenological Sellmeier-type equation in which the coefficients are obtained by numerical fitting to dielectric dispersion obtained from measurements on macroscopic crystals . Significant deviations at energies close to the bandgap prevent such a model from accurately describing waveguide dispersion near exciton resonances, and again keeps direct comparisons to bulk materials partly qualitative. Van Vugt et al.  shortly thereafter corrected this deficiency by directly incorporating electronic resonance effects via polaritonic contributions to the dielectric function, thus combining both waveguide and material dispersion relations to form an accurate theoretical model of dispersion in individual dielectric nanowires.
Accurate determination of excitonic resonance energy levels is crucial in correctly applying the complete nanowire dispersion model. However, literature values can vary, and direct measurement of highly absorbing exciton resonances in individual photoluminescence spectra is difficult. As shown by Piccione et al. , this limitation can be circumvented using propagation loss spectroscopy (Figure 12), a differential measurement technique which utilizes spatially- and spectrally-resolved photoluminescence excitation maps to determine the rate of decay of individual wavelengths as they travel along nanowire waveguides. A typical propagation loss spectrum for a CdS nanowire at low temperatures (77 K), shown in Figure 13, provides precise transverse exciton resonance energies. The spectrum allows for accurate dispersion modeling as well as a quantitative measurement of waveguide loss, highlighting the fact that even in spectral energy ranges typically thought of as “transparent” or having low absorption in bulk CdS, get modified significantly for nanowires on a substrate due to their size, possibly due to enhanced light-matter interaction (discussed later).
Waveguide dispersion modelling, an understanding of propagation loss as a function of wavelength, and improved crystal quality due to surface passivation  combined led to the most complete investigation into the size-dependence of optical properties of dielectric nanowires to date . Figure 14a, c, and e show photoluminescence spectra collected from the end facets of three different surface-passivated CdS nanowires, while b, d, and f show Fabry-Pérot maxima plotted along fitted numerical calculations for the fundamental waveguide mode. Rabi splitting, extracted from each dispersion, was then utilized to determine the exciton-photon coupling parameter, g, as a function of the effective mode volume (Figure 15a). In order to extract the relevant oscillator strengths in their system, van Vugt et al. utilized the expression relating coupling strength with modal volume obtained for cavity-polaritons in microcavities, but with mode volume replaced by effective volume to account for the averaging effect of excitons not confined to positions at antinodes of the electric field :
with e the elementary charge, ε0 the permittivity of vacuum, εr the relative permittivity of 8 for CdS, m0 the electron mass, n(V) the number of oscillators, f(V) their oscillator strength and Veff(V) the mode volume. After obtaining a linear relationship between (n * f) and V and noting both n and V scale linearly with volume while g remains constant, van Vugt et al. obtained a constant effective oscillator strength per unit volume, and hence constant coupling strength, matching known literature values for CdS in the bulk regime. Below mode volumes of Veff=0.5 μm3, however, measured enhancements in g could only be explained through enhancement of f per oscillator via formation of a coherent dipole spanning multiple lattice sites. Due to increased coupling strength the group refractive index also increases dramatically, further highlighting the strong size dependence of material properties in the nanowires. Group index as a function of energy in bulk CdS was numerically calculated and plotted alongside experimental results in Figure 15c, conclusively demonstrating slowed light in the nanostructures.
With an inherent volume-, and not strictly diameter-dependence, light-matter coupling differentiates itself from the aforementioned cation-exchange and phase-change mechanisms in that nanowire length is an important parameter when ruminating upon scaling concerns. Segmenting longer nanowires into smaller lengths via focused ion beam milling  does have potential to allow for construction of moderately-sized systems of multiple photonic elements, though losses at the cut interfaces remain a legitimate concern. Regardless of the ultimate path to implementation, however, these results again highlight the importance of studying size-dependence, and suggest that with better understanding, desired properties may be tuned in the future.
Surface plasmon polaritons (SPPs), quasiparticles consisting of surface plasmons coupled to incident light guided along metal-dielectric interfaces, provide a significant reduction in effective wavelength and therefore allow for an increase in both spatial confinement and local field intensity beyond what is achievable in purely dielectric structures [204-208]. Leveraging these properties, pure metallic nanowires on semiconductor substrates have been utilized for applications as diverse as waveguiding , transmission of single plasmon waves , modulators , and sensors . In general, nanowires which sustain surface plasmon excitations (plasmonic nanowires) have been engineered to function in many of the same roles as their photonic counterparts, and have the ability to do so at dimensions beyond than the diffraction limit: unlike dielectric waveguides, the fundamental mode does not exhibit the cut-off behaviour displayed in Figure 11 .
In analyzing the optical properties of plasmonic nanowires, Fabry-Pérot modes have been utilized in a manner similar to that used for photonic nanowires [214-217] and in some instances have even been used to construct experimental surface plasmon dispersion relations , again analogous to the methods discussed in the previous section. Similar to photonic nanowires, however, explicit size-dependent studies of plasmonic nanowire optical properties are sparse in the literature. Among studies of note, length-dependence measurements [218, 219] have been conducted to estimate plasmon propagation lengths in silver nanowires on various dielectric substrates, giving lengths around ten microns. Though this result is not promising for applications requiring long propagation lengths, the system can be altered through the use of semiconductor nanowires and other gain materials to significantly enhance signal transmission range. For this, and other unique applications, we now turn to recent investigations into dielectric nanowire/metal heterostructures.
Among the earliest systems incorporating dielectric nanowires and surface plasmon polaritons was that proposed by Oulton et al., who designed a hybrid structure consisting of a semiconductor nanowire on a metallic substrate for the purpose of extending the propagation length of surface plasmon polaritons tenfold while maintaining strong mode confinement . The same group later investigated CdS nanowires on silver substrates , and reported both a reduction in the nanowire diameter necessary for the onset of lasing with respect to purely photonic lasers, as well as an optimization of emission rate (Purcell enhancement) by tuning both nanowire diameter and plasmonic mode confinement. Cho et al.  extended this concept to what can be described as truly plasmonic nanowires, coating surface-passivated CdS conformally with a layer of silver to produce core-shell structures and reporting on the size-dependence of the whispering-gallery mode nanocavity plasmons formed about the circumference of the core-shell interface. As shown in Figure 16, changing the nanowire diameter again allows for tuning of radiative enhancement, enabled through the use of standing whispering-gallery significantly altering radiative decay rates of excitons. Such results pave the way for a new class of deep-subwavelength optoelectronic devices which utilize the geometry, and again show that with understanding, tuning of desired properties is possible.
The size-dependence of optical properties of nanowires has only begun to be explored, but progress thus far has shown that photoconductivity, dispersion, group velocity, radiative rate, oscillator strength, and waveguiding properties are all affected by nanowire dimensions. Techniques developed over the past decade have reached a point where quantitative analysis is now possible, and direct comparison with bulk materials have consistently shown nanowires superior in many regards.
Using chemical reactivity, structural phase-change, and optical properties as examples, we have shown that physical phenomena in nanowires can exhibit vastly different characteristics than in bulk material counterparts. In addition to discussing qualitative differences, we have highlighted multiple instances of quantified size-dependent properties in the literature, and shown that size and morphology can exert a strong influence on how a material behaves. Surface-to-volume ratio in particular was found to be largely responsible for recrystallization kinetics and drift of amorphous-phase electrical resistance in structural phase-change nanowires, while the absolute size of nanowires in the radial direction was found to affect both cation exchange reaction activation energies and optical dispersion relations. Longer dimensions along the nanowire long axes facilitate physical access to these novel phenomena, placing nanowires at a unique junction between one-dimensional nanocrystals and bulk materials.
Though the properties discussed here are by no means exhaustive, it is hoped to provide a broader insight into the underlying causes of altered properties in the nanowire morphology in the 5-200 nm length scale. Such explorations are vital to the maturing of technologies based on self-assembled nanostructures. With greater understanding of these phenomena comes the ability to tune these properties, and ultimately will allow for the creation of nanostructures tailor fit to individual applications.
This work was supported by the NSF-CAREER award (ECS-0644737), NSF (DMR-0706381 and DMR-1002164), and Penn-MRSEC (DMR05-20020 and DMR11-20901). Materials Structures and Devices Center at MIT, NSF-U.S. Army Research Office under Grant No. W911NF-09-1-0477 and W911NF-11-1-0024, and the National Institutes of Health through the NIH Director’cs New Innovator Award Program, 1-DP2-7251-01.