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Taming excitons in II–VI semiconductor nanowires and nanobelts

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2014 J. Phys. D: Appl. Phys. 47 394009

(http://iopscience.iop.org/0022-3727/47/39/394009)

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Journal of Physics D: Applied Physics

J. Phys. D: Appl. Phys. 47 (2014) 394009 (14pp) doi:10.1088/0022-3727/47/39/394009

Taming excitons in II–VI semiconductornanowires and nanobeltsXinlong Xu1,4, Qing Zhang2, Jun Zhang2, Yixuan Zhou1

and Qihua Xiong2,3,4

1 State Key Lab Incubation Base of Photoelectric Technology and Functional Materials, Institute ofPhotonics and Photon-Technology, Northwest University, Xi’an 710069, People’s Republic of China2 Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, NanyangTechnological University, Singapore 637371, Singapore3 NOVITAS, Nanoelectronics Center of Excellence, School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore 639798, Singapore

E-mail: xlxuphy@nwu.edu.cn and Qihua@ntu.edu.sg.

Received 6 April 2014, revised 26 June 2014Accepted for publication 4 July 2014Published 11 September 2014

AbstractExcitons are one of the most important fundamental quasi-particles, and are involved in avariety of processes forming the basis of a wide range of opto-electronic and photonic devicesbased on II–VI semiconductor nanowires and nanobelts, such as light-emitting diodes,photovoltaic cells, photodetectors and nanolasers. A clear understanding of their propertiesand unveiling the potential engineering for excitons is of particular importance for the designand optimization of nanoscale opto-electronic and photonic devices. Herein, we present acomprehensive review on discussing the fundamental behaviours of the excitons inone-dimensional (1D) II–VI semiconductor nanomaterials (nanowires and nanobelts). We willstart with a focus on the unique properties (origin, generation, etc) and dynamics of excitonsand exciton complexes in the II–VI semiconductor nanowires and nanobelts. Then we move tothe recent progress on the excitonic response in 1D nanomaterials and focus on the tailoringand engineering of excitonic properties through rational controlling of the physical parametersand conditions, intrinsically and extrinsically. These include (1) exciton–exciton interaction,which is important for 1D nanomaterial nanolasing; (2) exciton–phonon interaction, which hasinteresting applications for laser cooling; and (3) exciton–plasmon interaction, which is thecornerstone towards the realization of plasmonic lasers. The potential of electric field,morphology and size control for excitonic properties is also discussed. Unveiling andcontrolling excitonic properties in II–VI semiconductor nanowires and nanobelts wouldpromote the development of 1D nanoscience and nanotechnology.

Keywords: nanowires and nanobelts, excitons, photoluminescence

(Some figures may appear in colour only in the online journal)

1. Introduction

Excitons are the quantized elementary ‘excitation waves’(quasi-particles), which involve in many fundamental, andimportant optical processes, such as photosynthesis [1],photovoltaics [2], absorption [3], photoluminescence [4],lasing [5] and so on. An exciton is a bound state of an electron–hole pair formed by the long-range Coulomb interaction [6].

4 Authors to whom any correspondence should be addressed.

This Coulomb attraction provides an energy minimization,which is more stable than the unbound electron and hole.Unlike electrons and holes, excitons are bosons, obeying Bose–Einstein statistics, which provide a platform for Bose–Einsteincondensation [7]. According to the binding energy between theelectron and the hole, there are two kinds of excitons, whichare Frenkel excitons [8] and Wannier–Mott excitons [9]. TheFrenkel excitons are formed by electron–hole tightly bound toeach other within one or two unit cells with a small Bohr radius,

0022-3727/14/394009+14$33.00 1 © 2014 IOP Publishing Ltd Printed in the UK

J. Phys. D: Appl. Phys. 47 (2014) 394009 X Xu et al

which are usually found in organic materials due to lowdielectric constants. However, electrons and holes in Wannierexcitons are weakly bound due to large dielectric constant,which are popular in II–VI semiconductors with a large Bohrradius. In this review paper, we limit our discussions on theWannier type only.

Under the effective mass picture, the exciton spectrumexhibits hydrogen-like spectral lines [10]. For the Wannierexcitons, the energy of excitons can be expressed as [11]

En = Eg +�

2K2

2M− R∗

n2, (1)

where Eg is the electronic bandgap of II–VI semiconductors,K is the wavevector of excitons, M is the effective mass ofexcitons, R∗ is Rydberg constant for excitons andn is the boundstate quantum number. For II–VI semiconductors, Wannierexcitons show small effective masses and small oscillatorstrength. Usually K is equal to zero, however K is not zerofor hot excitons [12].

II–VI semiconductors including ZnO, ZnS, ZnSe, ZnTe,CdS, CdSe CdTe, etc are direct-bandgap semiconductors withrelatively large exciton binding energies. For example, thebinding energies for ZnO (60 meV) [13], ZnS (40 meV) [14]and CdS (29 meV) [15] are higher than the thermal energykBT at room temperature (25 meV), which suggest efficientand stable excitonic response, thus strong light emission atroom temperature.

Excitons are a hot topic in optics and condensed matterphysics, as the exciton formation, dissociation, evolution,dynamics and interaction are important in both fundamentalphysics and device applications. From the fundamentalphysics point of view, excitons are important for the radiativeand nonradiative recombination, energy transfer and theinteractions in the condensed matter physics such as strongcoupling of photon with excitons in the format of polaritons[16]. Excitons in nanomaterials also suggest some intrinsicphysical property changes compared with the counterparts inbulk materials, which demands further investigations. Fromthe application point of view, excitons are the basic activequasi-particles, which manifest themselves in the opticalproperties of II–VI semiconductors for laser, light emissiondisplay, solar cells [17] and so on.

More interesting physical properties bloom fromthe bottom after tailoring and engineering the II–VIsemiconductors into nanoscale. Excitons are attractivebecause of the rising of new excitonic characteristics [6] inthe nanoscale system due to the confinement effect. Firstly,when the dimensions of II–VI semiconductors are pusheddown to the length scale of the exciton Bohr radius, excitonsshow a quantum size effect [18, 19]. Thus, with the decreasein the sizes of nanobelts and nanowires, especially whenthe diameters become comparable to the Bohr radius ofexcitons, the confinement will enhance the efficiency of excitongeneration [6]. Secondly, a larger surface-to-volume ratioemerges in nanostructures, which brings the significant surfacetrapping and scattering effects [20]. The surface effect willinfluence the excitonic properties in nanoscale system, whichis quite different from the bulk materials.

Spatial confinement of excitons in II–VI semiconductornanowires and nanobelts will modify the excitonic propertiesof these materials such as the density of states, the many-bodyinteractions between carriers, trapping by defects, polarizationdependence and so on. These properties can be used aspolarization sensitive photodetectors [21], nanolasers [22], all-optical active switchers [23], photonic circuit elements [24],nanowire photovoltaic cells [25], nanowire waveguide [26] andso on. A clear understanding of these excitonic properties(generation, decay, kinetic, etc) is particularly importantfor improving the performance of these opto-electronic andphotonic devices. Thus a fundamental understanding ofexcitons in nanowires and nanobelts is required for furtherdevelopment of devices based on nanowires and nanobelts.

As a prerequisite, the state-of-the-art synthesis methodshould be able to produce well-dispersed, good morphology,and orientation controllable nanowires and nanobelts fordesirable excitonic functionality [27, 28]. Fortunately, vapourphase and liquid phase syntheses through vapour–liquid–solid,vapour–solid and solution–liquid–solid mechanisms have beenwell developed for this purpose [29]. The vapour phase methodis one of the most simple, accessible and extensive exploredmethods for the growth of nanowires and nanobelts throughcontrolling the nucleation, supersaturation, crystallization inonly one direction [30]. The nanostructures can be grown fromthe vapour phase either by catalytic or self-catalytic vapour–liquid–solid mechanism or by vapour–solid growth mechanism[27]. On the other hand, the solution–liquid–solid methodis developed for highly crystalline II–VI semiconductingnanowires and nanobelts with small diameters and controllablesurface ligation at low temperatures [31]. The solution–liquid–solid growth can afford narrow diameter distributionof nanowires with the diameters of 3–5 nm [32].

In this review paper, we focus on the recent developmentof excitonic properties of nanowires and nanobelts. Thesynthesis and fabrication of a wide range of nanowires andnanoribbons have been extensively reviewed in the previousliterature [27, 29, 31], thus will be skipped in this paper. Wealso find a loose definition of nanowires and nanobelts in theliterature. As a critical definition from the view of electronicdensity of states, one-dimensional (1D) nanostructures shouldhave quantum mechanical effects, which usually be consideredas ‘quantum wires’ and ‘quantum belts’. However, more broaddefinition is usually adopted in the literature. Here we focusour review on the nanowires, which have the diameter on theorder of less than 100 nm and the aspect ratio can achieveseveral hundreds. Accordingly, we define the nanobelts asnanostructures that have a dimensionality constrained to lessthan 100 nm in width and several hundred nanometres inthickness and an unconstrained length. Firstly, we will discussthe unique properties of excitons and exciton complexes inII–VI semiconductor nanowires and nanobelts, which aremainly due to the vacancies, interstitial defects, dislocations,foreign atoms in the 1D materials. Then we will discuss theexciton dynamics, which is radiative and nonradiative throughdifferent decay channels. After that, taming excitons withthe interactions such as exciton–exciton interaction, exciton–phonon interaction and exciton–plasmon interaction will be

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discussed. These bring the applications of excitonic lasing,lasing cooling and plasmonic lasing. Then we will discuss theinfluence from the electric field, morphology and size to theexcitonic properties. These could result in photodetectors andwavelength-tunable devices in applications. Finally we givean outlook of the fundamental physics and device applicationsof 1D II–VI nanomaterials based on the excitonic propertiesin the future.

2. Excitonic properties in II–VI semiconductornanowires and nanobelts

Excitons can take part in a class of optical processessuch as photoluminescence, photoconductivity, scattering andultrafast carrier dynamics. Unlike the two-dimensional (2D)nanomaterials (such as nanofilms), 1D nanomaterials canconcentrate the electronic density of states and make opticaltransition highly efficient [33]. Secondly, Coulomb interactionwould be more efficient in nanowires and nanobelts, withlarge binding energy, which enhances the optical transitionprobability [33]. Unlike zero-dimensional (0D) nanomaterials(such as quantum dots), Auger recombination process issuppressed in the 1D materials [34], which would lead tohighly efficient nanolasers [22]. Stoichiometric defects formedduring synthesis are the majority of defects in nanowires andnanobelts instead of surface states, which seem to be the mostdeleterious defect formation in 0D quantum dots.

2.1. Excitons and exciton complexes

Intrinsic defects such as vacancies, interstitial defects, anti-sites, dislocations, foreign atoms and even the surface danglingbond of the crystal [35] have much influence to the excitonicproperties in nanowires and nanobelts. From the viewpoint ofthe semiconductor band model, the ionic binding configurationof II–VI semiconductors is as follows:

II[(n − 1)d10ns2] + VI[ms2mp4] → II2+[(n − 1)d10ns0]

+VI2−[ms2mp6], (2)

where s, p, d are the orbital labels of electron configuration,n = 5 for Cd, n = 4 for Zn and m = 2, 3, 4, 5 for O, S,Se, Te. Free electrons occupy the lowest empty s-like levelof the cations in the conduction band, while free holes in thevalence band frequently arise from the highest occupied p-likelevel of the anions [35,36]. Due to the large vapour pressuredifference for II and VI group elements at certain temperatures,the vapour synthesis would naturally introduce stoichiometricdefects as schematically shown in figure 1.

Taken CdS as an example, stoichiometric defects such assulfur and cadmium vacancies (Vs , Vcd), and interstitials (CdI

and SI ) and anti-sites (Scd, Cds)will be unintentionally formed.And these also happened in ZnO [37], ZnTe [38], ZnSe [39]and ZnS [40] nanowires and nanobelts, which introduce richluminescent properties in II–VI semiconductor nanowires andnanobelts.

Excitons can be bound to these defects to form excitoncomplexes. For example, when an exciton (X) is bound toa neutral acceptor, A0X complex is formed. Similarly, an

Figure 1. Illustration of II–VI semiconductor with different defects.

Figure 2. Photoluminescence fine structure of CdS nanobelts at10 K with a 325 nm He–Cd laser excitation. The blue curves areGaussian line-shape decompositions with each peak clearly labelled(adapted with permission from [35]).

exciton bound to a neutral donor and an ionized donor, D0X

and D+X are formed respectively. Historically, A0X, D0X

and D+X complexes are often labelled as I1, I2, I3 [36]. Alsoelectron at the donor level and a hole at the acceptor level canbound to form a donor–acceptor pair (DAP).

Figure 2 gives an example of a typical photoluminescencespectrum of CdS nanobelts measured at 10 K with multipleGaussian functions fitted to determine the peak positions andwidth [35]. The peak at 2.543 eV is ascribed to I2, and thepeak at 2.531 eV is attributed to I1. A series of peaks between2.416 and 2.266 eV demonstrate multiple phonon replicas withan energy spacing of approximately one LO phonon (i.e.37 meV) [35] coupled to DAP. Calculated with the Huang–Rhys relation, strong exciton–phonon coupling is suggested inthese CdS nanobelts [35]. Similar photoluminescence spectracan be found heavily in the literature with different II–VIsemiconductor nanobelts and nanowires [37–40].

It is important to note that this fine structure of thephotoluminescence spectrum is usually more evident at lowtemperatures. Due to the lattice change and exciton–phononinteraction under different temperatures, the bandgap Eg(T )

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J. Phys. D: Appl. Phys. 47 (2014) 394009 X Xu et al

of II–VI semiconductor usually blue shifts with a decreasingtemperature (T ), which can be described by a semi-empiricalVarshni formula as [41]

Eg(T ) = Eg(0) − αT 2

T + β, (3)

where α is the temperature coefficient, β is related to theDebye temperature of a crystal, and Eg(0) is the bandgap atthe zero temperature. It should be pointed out that unlike theideal II–VI semiconductors, which is transparent below thebandgap, the absorption below bandgap is more evident in1D materials [35, 42] due to the defects or doping as well asthe lattice vibrations via electron–phonon interactions, whichfollow the Urbach rule. The absorption coefficient consideringthe Urbach tail can be expressed as [43]

α(E) ={

A0(E − Eg)1/2, E � Eg

K0 exp[

σkBT

(E − Eg)], E < Eg,

(4)

where A0 and K0 are constants and σ is a dimensionless fittingparameter.

Due to the confinement-induced optical selection rules aswell as the possible dielectric contrast effects, 1D materialshave intrinsically anisotropic optical response [44]. Forthe ultrathin nanowires, the wave function of excitons canextend spatially over a long range along the wire longitudinalaxis, while perpendicular to the axis, the wave functionis localized inside the nanowires. For large nanowiresand nanobelts, the anisotropic response would be morecomplicated. For example, Li et al presented polarizationand mode structure of photoluminescence from single ZnOnanowires with the diameter >100 nm [45], and they foundthat in the visible regime, the exciton emission is polarizedalong the longitudinal axis of wires, while from 2.9 to 3.22 eV,the Fabry–Perot-guided modes are polarized perpendicular tothe wires due to the strong coupling. Above 3.22 eV, however,there was no evidence of anisotropy. Utilization of theseanisotropic properties, polarization sensitive photodetectorscan be accomplished [21].

2.2. Dynamics of excitons and exciton complexes

After the photoexcitation, the non-thermodynamic excitonsundergo several stages of relaxation before they recombine[46]. They first experience a quick dephasing period(within several femtoseconds) and then go to a hot-excitonperiod. Recombination occurs through a radiative channel,which is the annihilation of an exciton to generate aphoton. Recombination can also occur via nonradiativedecay channels through intermediate stages of interactionssuch as exciton–exciton scattering, exciton–phonon scattering,trap-assisted recombination, Auger mechanism and so on[47]. These processes can be captured by the time-resolved photoluminescence spectroscopy, optical pump–probe spectroscopy or time-resolved second harmonicspectroscopy, etc.

The intrinsic radiative exciton lifetime is mainlydetermined by the exciton scattering within a coherent volume

of a free exciton [33]. The radiative lifetime of excitons in1D materials may become shorter than that in bulk materials[33], which is due to the finite spatial coherence in thelateral direction. As the coherent volume of exciton varieswith temperature, the radiative exciton lifetime is temperaturedependent. Thermalization effect of the intrinsic radiativelifetime may lead to [48]

τrad(T ) = A0

√T , (5)

where A0 is a constant coefficient and material dependent.In particular, to measure the intrinsic radiative lifetimes ofnanowires and nanobelts, the samples free of defects should beevaluated first of all, which is more challenging in this researchstage.

With the presence of defects and many-body interactions,the nonradiative relaxation can be promoted. The temperature-dependent rate of nonradiative process can be described bythe thermal activation energy in the Boltzmann distribution[35, 49]:

1

τnonrad(T )= 1

τnonrad(T )exp(−Ea/kBT ), (6)

where Ea is the activation energy for a nonradiative process.Overall, the lifetime τ(T ) measured by most of the time-resolved spectroscopy can be expressed as follows:

1

τ(T )= 1

τnonrad(T )+

1

τrad(T ), (7)

Figure 3(a) presents temperature-dependent transient photolu-minescence decay from I2 in CdS nanobelts at a low excita-tion power. The decay constants were extracted as a functionof temperature as shown in the inset. This suggests that theincrease in temperature promotes the nonradiative relaxationprocess of I2 emission, leading to a faster time constant τ1 [35].

Auger relaxation is another important nonradiativechannel when the excitation power is high, which is basedon long-range Coulomb interactions and a new Augerrecombination channel opens [50, 51]. This process is alsodimension dependent. For instance, Htoon et al [51] foundthat with the dimension increase from 0D to 1D of CdSe, theAuger recombination experiences a transition from cubic toquadratic decay, which suggests that Auger process in 1Dsystems is effectively suppressed, in contrast to those in 0Dsystems [34]. This will in turn lead to increased optical gainand efficient light amplification, which count for mainly moreefficient lasing in 1D than in 0D.

Generally, the exciton radiative recombination is onthe scale of ∼1 ns in II–VI semiconductor nanowires andnanobelts. However, with the combination of nonradiativerecombination and the decrease of diameters, the exciton decaycould be faster. For example, Vietmeyer et al found that themeasured emission lifetimes are short (<100 ps) in individualCdSe nanowires with diameters of 20 nm [52]. Generallyspeaking, the LO-phonon decay rates are on the scale of∼100 fs to ∼100 ps and the Auger process is also on the samescale as LO phonons. Puthussery et al suggested that intraband

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Figure 3. (a) Temperature-dependent transient photoluminescence decay from I2 in CdS nanobelts at low excitation power of 2 µW.The decay constants were extracted as a function of temperature as shown in the inset. (b) Normalized transient photoluminescencedynamics of the DAP emission at three different wavelengths (adapted with permission from [35]).

carrier cooling rate of CdS nanowires is on the time scales of300–400 fs [53].

Sometimes, one would observe quite long lifetime ofexciton and exciton complexes because of enhanced singlet-triplet exchange interaction in II–VI semiconductor nanowiresand nanobelts [6]. In figure 3(b) we demonstrate three emissiondecays centred at the different wavelengths of the zero-phononDAP photoluminescence spectroscopy, a lifetime on the orderof hundreds of nanoseconds for our CdS nanobelts [35]. Thisis due to the spin-polarized cadmium vacancy electronic states.For the DAP, the energy of the Hopfield-type donor andacceptor pair can be expressed as [35]

EDAP(r) = Eg − (ED + EA) +e2

4πε0εr, (8)

where ED and EA are the activation energies of donor andacceptor, and ε0, ε are the dielectric constant of vacuum andthe relative dielectric constant of CdS, respectively. Thelast term is the Coulomb energy between the donor and theacceptor, separated by a distance r . Figure 3(b) suggeststhat closer (more energetic) DAP undergoes faster radiativerecombination rates, which shows the characteristic of DAPdecay.

3. Taming excitons through interactions

In principle, there are several elementary excitations suchas phonons, excitons and intrinsic or extrinsic plasmonsin II–VI semiconducting nanowires and nanobelts. Theunderstanding of the excitonic properties can be obtainedbehind those interactions. With increasing pump intensity, theexciton density could increase and the fundamental physicsbecomes more complicated yet interesting as excitons orexciton complexes interact with each other as a function ofpopulation. On the other hand, excitations such as intrinsic

phonons, and extrinsic plasmons could also be used to tailor theexcitonic properties of II–VI semiconducting nanowires andnanobelts through either phonon–exciton or plasmon–excitoninteractions. These interactions could bring out some neweffect and new physical phenomena.

3.1. Exciton–exciton interaction and lasing effect

As shown in figure 4, in the low excitation density regime,excitons or exciton complexes are separated far away and theinteraction between them can be ignored. With increasingpump intensity, the exciton and exciton complex populationand thus the possibility of exciton and exciton complexinteraction and scattering increase, leading to the form ofexciton molecular (biexciton) or exciton liquid. In this regime,collisions between excitons or between the excitations becomeimportant [12]. However, with a further increase in the pumpintensity, the screening effect can decrease the electron–holeattraction energy, which significantly decreases the excitonbinding energy. This will result in the splitting of excitonsinto independent or weakly correlated electrons and holes [54],termed electron–hole plasma [55]. Under extreme high pumpintensity, the effects of band-filling and renormalization ofbandgap effects could become prominent [53].

The optical properties of II–VI semiconducting nanowiresand nanobelts are strongly dependent on the carrier population.For example, even though CdSe has the exciton bindingenergy of 15 meV, both excitonic and free-carrier behaviourin CdSe nanowires can occur depending on the pumpintensity [56]. Photoluminescence intensity as a functionof excitation intensity was used to clarify the nature ofcarriers and their recombination mechanisms [39, 52]. Forexample, the free-carrier dynamics is quite different fromexcitonic behaviour, which can be distinguished from thedistinct photoluminescence intensity dependence on the pump

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Figure 4. Illustration of exciton–exciton interaction effect in II–VI semiconducting nanowires and nanobelts from low excitation to highexcitation. Cubes are for the point defects and spheres are for the electrons and holes.

power [53]. Vietmeyer et al [52] observed a nonlinear power-law between the photoluminescence emission intensity andthe pump intensity due to the free-carrier behaviour. Alinear relation between the emission and excitation intensityis expected in the low pump intensity, due to the fact that theemission intensity simply reflects the increasing concentrationof exciton. With the increase in excitation intensity, theelectron–hole plasma exists, and the emission intensity wouldgrow quadratically with pump fluence [52].

The dynamics of exciton can also change due to thehigh density of excitons in the nanowires and nanobelts andsome new competing processes such as Auger recombinationand amplified spontaneous emission (ASE) become evident.Auger process is one of the blockades for efficient ASEat high pump intensity. However, the strongly reducedAuger decay process in 1D results in increased opticalgain lifetime and hence efficient light amplification [51].The ultrafast dynamics in the ASE region is informative tounderstand the fundamentals of nanolasers based on II–VIsemiconducting nanowires and nanobelts. Johnson et al[57] demonstrated that there are two regions for the pumppower dependence of the exciton decay in ZnO nanowiresand nanobelts by time-resolved second-harmonic generationand transient photoluminescence spectroscopy. Under the lowpump intensity, the ∼80 ps decay component is from the freeexciton, while under high pump intensity, it is only ∼10 psdue to the ASE. Recently, we also observed the ASE processin CdS nanobelts on the time scale of 20 ps [35]. Dynamiccompetition between I2 and DAP has been identified, whichsuggests that compensation of acceptor levels in CdS nanobeltsis required for ASE. The strongly reduced Auger decay rateslead to population inversion developed between the donor leveland valence level, resulting in ASE in CdS nanobelts.

A cavity is required for ASE in II–VI semiconductingnanowires and nanobelts to achieve lasing. The cavitycan be either formed from a natural cavity (Fabry–Perot orwhispering gallery modes) by crystal facets themselves, byrandom scattering pathways (random laser) or by embeddingthe nanostructures to the other cavities. We have recentlyobserved random lasing in CdS nanobelts ensembles [4] andCdSe nanowires ensembles [58] achieved by the van der Waalsepitaxy growth method [59].

Figure 5(a) shows the photoluminescence spectra of asingle CdS nanowire as a function of pump intensity [60].The diameter of the nanowire is ∼260 nm and the length is∼12.8 µm. With increasing excitation intensity, we observeda transition from spontaneous emission (0.4 µJ cm−2) throughASE (0.6 µJ cm−2) to full lasing action (2.0 and 2.6 µJ cm−2).Figure 5(b) shows the output power with a multimode lasermode [61] (on log–log scale), which generates a thresholdfluence of ∼0.76 µJ cm−2. Figure 5(c) shows the modespacing of the observed sharp emission lines �λ as inverselyproportional to the nanowire length L. This agrees well withthe theoretical equation for a Fabry–Perot cavity [62].

As bosons, excitons cannot form an inverted populationwhich is needed in a photonic laser. In the early days, Thomaset al [63] proposed possible exciton complex used as lasingin CdS based on the excitons bound to impurities or defects,which introduces the non-bosonic quality. This is consistentwith what we discuss in the excitons and exciton complexesas shown in figure 1. Whether excitons are involved in lasingin II–VI semiconducting nanowires and nanobelts or not, it isstill in debate. Using many-body theory Vesteegh et al [64]suggest that lasing in ZnO nanowires at room temperatureis not of excitonic nature as is often thought, which insteadis electron–hole plasma lasing. This result suggests that apossible mechanism for the lasing could be due to the excitondissociation into free holes and electrons to form electron–hole plasma [55] at high exciton concentration [65], whichforms fermions for inverted population [63]. Agarwal et alfound that exciton–exciton interaction is critical for lasing upto 70 K, while the exciton LO-phonon process dominates athigher temperatures [66].

On the other hand, light (photon) and matter (exciton)interaction is enhanced in nanowires and nanobelts [67],as the mode volume is reduced compared with those inbulk materials. Strong coupling of photons with excitonsin II–VI semiconductor nanowires and nanobelts can leadto the formation of polaritons, which can demonstratethe low-threshold polaritonic lasing and Bose–Einsteincondensation [16, 26]. This coupling can be considerablyenhanced in cavities with good facets [54] in nanostructures.Bose–Einstein condensation can be used for the phase-coherent parametric amplification of waves [68]. Under the

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Figure 5. Nanowire length-dependence lasing modes for CdS nanowires with 400 nm excitation. (a) Emission spectra for 12.8 µm longCdS nanowires with a diameter of 265 nm photoexcited with different pump intensities. (b) The logarithmic plot of the integratedphotoluminescence intensity as a function of pump fluence with a multimode laser mode fitting (green line). (c) Mode spacing �λ underlasing conditions versus nanowire length for 10 independent nanowires (adapted with permission from [60]).

low temperature, the inelastic exciton–exciton interaction [69]could be observed and a low stimulated emission threshold [70]could be used for the polaritonic lasing.

3.2. Exciton–phonon coupling and laser cooling effect

Excitons can be modified by the vibrational motion of lattices(phonons) in the crystal, which could bring the broadeningof the exciton peaks. The lattice vibrational energy ison the scale of thermal energy kBT at room temperature(25 meV) or even higher in terms of optical phonons. II–VI semiconductors present a pronounced polar character sothat the Frohlich interaciton (LO phonon) is predominant.Phonons in polar crystals usually have a large Frohlichcoupling constant, for example CdS 0.53, ZnSe 0.43, whichis larger than the III–V semiconductors, such as GaAs 0.068and InAs 0.052 [71]. Phonon-assisted photoluminescence,Raman spectroscopy, pump–probe spectroscopy [72] presentimportant information of exciton–phonon coupling for theoptical process in II–VI nanowires and nanobelts. Usually,the exciton–phonon coupling strength can be evaluated fromthe intensity ratio of its overtone mode over the fundamentalRaman mode. Raman scattering cross section for the nthphonon process can be estimated as [73–75]

∣∣Rn(ω)∣∣2 = µ4

∣∣∣∣∣∞∑

m=0

〈n|m〉〈m|0〉Eex + n�ωLO − �ω + i

∣∣∣∣∣ , (9)

where µ is the electronic transition dipole moment, ω is theincident photon frequency, m is the intermediate vibrational

level in the excited state, Eex is the electronic transition energy,and is the homogeneous line-width. The Franck–Condonoverlap integral 〈n|m〉 can be written as [76, 77]

〈n|m〉 =(

n!

m!

)1/2

exp

(−1

2�2

)�n−mLn−m

m (�2), (10)

where � is the dimensionless displacement, L is the associatedLagurre polynomial. Huang–Rhys parameter S, which isrelated to the displacement of the excited state minimum fromthat of the ground state [78], is commonly used to characterizethe coupling strength for Frohlich interaciton. Combining (9)and (10), the Huang–Rhys parameter S, thus exciton–phononcoupling strength, can be calculated based on the 2LO to 1LOmode.

We have identified a strong exciton-LO phonon couplingin CdS nanobelts [35, 79], which is almost a factor of fourenhancement compared with the bulk [79]. Recently, wealso reported up to fifth order LO-phonon Raman scatteringin ZnTe nanorods at room temperature [75]. The couplingstrength is increasing with the diameters of nanorods. Usually,the nanobelts are notably different from the nanowires, as astrong enhancement of the multiphonon response, as provedby Lee et al [80]. They observed that the first order LO-phonon energy systematically increases with increasing lateralsize from nanowires to nanobelts in CdS. Hu et al [81]also observed that the coupling strength of exciton–phononincreases with increase in lateral size.

Exciton–phonon interactions have several effects to theproperties of excitons. Firstly exciton–phonon coupling

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Figure 6. (a) Schematic diagram of the cascade model. (b) Raman spectra of a single ZnTe nanobelt at room temperature with the excitationwavelength of 514 nm. (c) Power-dependent time-resolved photoluminescence spectroscopy of single ZnTe nanobelt pumped by a 488 nmpulsed laser with a duration of 150 fs and a repetition rate of 1KHz (adapted with permission from [82]).

could increase the dephasing rate of the excitonic states [83].Secondly, due to the coupling of exciton with phonons, theexciton kinetic energy distribution in a quasi-equilibrium stateis quite different from the equilibrium state correspondingto the crystal temperature [12]. Coupling could highlyenhance exciton recombination via a nonthermalized hot-exciton emission process [82]. From the cascade relaxationpoint of view [84, 85] as shown in figure 6(a) a primary photonwith energy of hω0 could create a hot exciton together withthe emission of one LO phonon. Hot excitons are scatteredin a cascade mode by LO phonons into states separatedby one LO phonon (hωLO). At the last stage, an indirectannihilation of excitons with a photon generation of hωLO–nhωLO occurs. Figure 6(b) shows the Raman spectra of asingle ZnTe nanobelts at room temperature excited at 514 nm.Three peaks located at 110, 120, 145 cm−1 are assigned to ELO,A1 and ELO/ETO modes of the crystalline Te phase. The peakslocated at 205, 410, 615, 820, 1025, 1230, 1435 cm−1 are thecorresponding nth order (n = 1, 2, 3, 4, 5, 6, 7) LO-phononemission peaks, respectively. Only two LO emission lines areobserved below the centre of the photoluminescence emissionpeaks, which suggest a hot-exciton emission. In the hot-exciton emission process, the excess energy of the exciton isdissipated mainly by the emission of LO phonons, leading to arecombination time scale of tens of picoseconds, which is fasterthan the normal exciton [86]. Figure 6(c) shows the powder-dependent time-resolved photoluminescence spectroscopy ofsingle ZnTe nanobelt, which can be fitted by a double-exponential decay for free exciton decay (∼80 ps) and hot-exciton decay (∼18 ps) under the low pump intensity. Underthe high pump intensity, an additional channel (5 ps) due to theASE appears.

Due to the strong exciton–phonon coupling in thenanobelts, II–VI semiconductor nanobelts can lead to coolingof matter by spontaneous anti-Stokes emission, which was firstdemonstrated by our group [79, 87]. When the anti-Stokes is inresonance, under the strong coupling of exciton–phonon, theIanti−stokes/Istokes > 1, suggesting that LO-phonon annihilationrate can be much faster than the generation under a resonantcondition, which will carry the heat away during the radiationof excitons. The lowest achievable cooling temperature isfound to strongly dependent on thickness [87]. A net cooling

of 40 K was demonstrated in a CdS nanobelt with a thickness∼110 nm starting from 290 K pumped by a 514 nm laser. Thisprocess shows high external quantum efficiency and negligiblebackground absorption compared with laser cooling with III–VGaAs-based quantum wells [88]. This suggests the exciton–phonon coupling could be harnessed to achieve laser coolingand open a new way to optical refrigeration based on II–VI 1 Dnanomaterials.

3.3. Exciton–plasmon interaction and plasmonic effect

Plasmons are also quasi-particles, which result from thequantization of collective oscillations of electron gas.Plasmons play an important role in the optical propertiesof metals, such as the surface plasmon polaritons, whichpropagate along a metal–dielectric interface [89], andlocalized surface plasmon, which oscillates locally in metallicnanoparticles [90]. Plasmons also play a pivotal role in currentnanophotonics, such as the super-resolution imaging, sensingbased on resonance, electric–magnetic field enhancement, sub-wavelength confinement and localization, which can be usedin enhanced spectroscopy [91, 92], nonlinear optics [93, 94],imaging, biosensing and circuitry [89].

Excitons and plasmons can interact with each other viadipole–dipole interaction, which is similar to the Forstermechanism [17]. And the excitonic properties such as excitondynamics and photoluminescence emission of nanowires andnanobelts would experience dramatical change extrinsically.Such exciton–plasmon interactions allow design of absorptionand emission properties, control of nanoscale energy-transferprocesses, creation of new excitations by strong coupling, andincrease in optical nonlinearities [95, 96].

The interaction of excitons with plasmons can be identifiedas weak coupling and strong coupling. In the weak couplingprocess, wave functions of excitons and electromagneticmodes of plasmons are considered unperturbed. Theelectromagnetic modes of plasmons afford localized enhancedfield and will change the density of states of excitons and otherexcitonic properties such as radiative and nonradiative rate ofexcitons, which rely on the exciton–plasmon distance [97].Thus under weak coupling of excitons and plasmons, plasmonsusually affect the spontaneous emission by an enhancement

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Figure 7. (a) Schematic diagram of the nanowire laser devices; the CdS nanowires on top of the Au film (60 nm) are separated by ananometre scale SiO2 buffer layer of thickness h nm. The diameter of the CdS nanowire is d nm. The inset (bottom right corner) is the SEMimage of a typical single CdS nanowire on top of a gold film with h = 5 nm and the scale bar is 100 nm. (b) The lasing peaks of four devicesunder the same pump fluence of 8 µJ cm−2 with the change in the distance between CdS and Au film h (adapted with permission from [99]).

or suppression of exciton emission [98]. Recently, Choet al demonstrated the tuning of the recombination processin CdS nanowires by SiO2/Ag shell, which demonstrate a hot-exciton recombination process through the plasmon-enhancedexciton–phonon coupling effect [86]. Govorov et al [98]proved that the enhanced emission is due to the electric fieldamplified by the plasmon resonance, while energy transferfrom semiconductor to metal results in emission suppression.Either the enhancement or suppression also depends stronglyon the geometrical parameters of the hybrid structure as wellas the physical and material properties.

Recently, we demonstrated that due to the exciton–plasmon interaction, the Burstein–Moss effect in CdSnanowires is enhanced, which can be used as wavelength-tunable single nanowire lasers [99].

The Burstein–Moss effect results from the Pauli exclusionprinciple, which is revealed as a bandgap increase because theabsorption edge is pushed to higher energies as a consequenceof state filling in semiconductors [100, 101]. As a result, a blue-shift in the absorption or photoluminescence spectroscopy canbe observed by either optical doping [102] or by chemicaldoping [101]. Figure 7(a) shows a CdS nanowire on top of theAu films separated by a nanometre scale of SiO2 buffer layerwith thickness h nm. When we change the distance betweenCdS nanowire and Au films, which result in the tuning of theexciton–plasmon interaction, we observed a large blue-shift(more than 20 nm) of the lasing wavelength (figure 7(b)) [99].This is due to the enhancement of the Burstein–Moss effectfrom the plasmons for the nanowires.

The strong coupling process of exciton and plasmonis considered when resonant exciton–plasmon interactionsmodify exciton and plasmon wave functions and lead toexchange energy of exciton and plasmon. In this strongcoupling regime, the excitation energy is shared and oscillatesbetween the plasmonic and excitonic systems, which have thecharacteristic of half-exciton and half-plasmon. A typicalanticrossing and splitting of energy levels at the resonancefrequency is observed for the strong coupling systems [95,103]. However, few experiments report the strong coupling

of exciton and plasmon in nanowires and nanobelts. Thedifficulty of achieving strong coupling of exciton and plasmonis due to the decoherence time of plasmons that is on thefemtosecond time scale and often shorter than the time requiredfor Rabi oscillations.

In return, excitons can also compensate the loss ofplasmons and induce the coherence of plasmons, which hasbeen demonstrated as a plasmonic laser [104]. Oulton et al[105] demonstrated a CdS nanowire-based plasmonic laser,generating optical modes a hundred times smaller than thediffraction limit using a hybrid plasmon–exciton system.

4. Taming excitons by field and morphology

4.1. Exciton under electric field

An electric field demonstrates several phenomena in thespectrum such as modulation of absorption coefficient,broadening of exciton absorption line, shift of the absorptionpeak, dissociation of excitons [106]. Investigation of excitonsin the presence of an extrinsic electric field can provide usefulexcitonic information for the nanowires and nanobelts. Whenthe electric field is applied, it will change both the absorptionintensity, which is known as the Franz–Keldysh effect, andshift frequency of the absorption peak, which is known as Starkeffect [107]. For the bulk semiconductors, the absorption tailbelow the bandgap due to the applied electric field without andwith excitonic effect can be expresses as [108–111]:

α(hν)∞

exp

(−

∣∣∣ hν−Egap

�E

∣∣∣3/2)

, without exictonic effect,

exp(−

∣∣∣ hν−Egap

�E

∣∣∣) , with exictonic effect

(11)where �E is given by [112]

�E = 2

3

(e�ξ)2/3

(m∗)1/3 , (12)

where ξ , m∗ and � are the electric field, effective mass andPlank constant, respectively. This can be used to diagnose

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J. Phys. D: Appl. Phys. 47 (2014) 394009 X Xu et al

Figure 8. (a) Gain spectrum of the nanowire and nanobelt devices with the applied source–drain electric field is 2 kV cm−1. The inset is anSEM image of a typical CdS nanobelt FET device. The scale bar is 1 µm. (b) Electric field dependence of the normalized gain with theelectric field from 1 to 4 kV cm−1 of nanowire near the band-edge region. (c) Photoluminescence (solid curves) and gain spectra (symbolcurves) of a 120 nm nanowires (adapted with permission from [107]).

the excitonic properties from the fitting of the absorption tailbelow the bandgap [111]. Although we can use the externalelectric field, the internal electric field induced by the Fermilevel pinning at the surface of nanowires and nanobelts can alsobe used [109]. Another specific characteristics for the Franz–Keldysh effect is that above the bandgap, the absorption showssome quasi-periodic oscillations [106, 113].

The electric field can also ionize the exciton and giverise to exciton dissociation [106, 114, 115], which results inthe exciton peaks in the photoconductivity spectrum. Underthe nano-confinement, a large electric field is required for theexciton ionization due to the exciton binding energy increases.The exciton can remain resolved under a higher field undernano-system than that in bulk [115]. With the decreasein dimension, the Franz–Keldysh effect will also presentnanoscale characteristics, which is defined as the quantum-confined Franz–Keldysh effect [116].

It is difficult to observe the Stark effect in bulk II–VIsemiconductors due to serious peak broadening and smallfrequency shift because of weak Stark effect under an electricfield. However, the increase in density of states and excitonbinding energy dramatically change the magnitude of theStark effect in quantum-confined materials [18]. This isdetermined by the exciton Bohr radius αB and the dimensionof materials R. With R > αB it is weak confinement,and with R < αB there is a strong confinement [18].The quantum-confined Stark effect has also been observedin single CdSe quantum dots by an electric-field-dependentphotoluminescence spectroscopy [117]. However, thereare few reports on the Stark and Franz–Keldysh effects inII–VI semiconductor nanowires and nanobelts. Recently,we observed exciton ionization, Franz–Keldysh and Starkeffects in electric-field-dependent photoconductivity in CdSnanowires and nanobelts [107], as shown in figure 8.

The inset to figure 8(a) is an SEM image of an individualCdS nanobelt device with the channel length of 1 µm. Toexclude the influence from the variation of the excitation

photon flux on the photocurrent, gain (defined as how manyelectrons are collected by the electrodes with each incidentphoton) is a better physical parameter, which follows

G = Iph/e

P/hν, (13)

where Iph is the photocurrent, P is the light power irradiatedon the device and hν is the photon energy. Figure 8(a)shows the spectral response at the band-edge region withdifferent nanowires and nanobelts, which exhibits a noticeabledimensionality and size dependence. A distinct sharp peakaround 2.43 eV, a small peak near 2.48 eV and a broad bumpclose to 2.56 eV are identified. Away from the band edge at thehigher energy side, oscillations are observed for all nanowireand nanobelt devices [107]. These quasi-periodic oscillationsabove the band edge in nanowires and nanobelts are attributedto a Franz–Keldesh effect. The electric field dependence ofphotoconductivity gain spectra near the band edge are shown infigure 8(b). The observed excitonic response of FXB are due tothe corresponding free exciton B due to the splitting of excitonsunder the crystal field and spin–orbit interaction (FXA, FXB,FXC). Figure 8(c) shows both photoluminescence and gainspectra of a 120 nm nanowires. The considerably large energydifference (∼59 meV) between FXA and photoluminescenceis due to large Stark effect in CdS nanowires.

4.2. Excitons controlled by morphology and size

Morphology and size control is an old but very effective methodfor the exciton manipulation. It is very attractive that inquantum dots as R < αB strong confinement is anticipated,as the exciton properties can be tuned by varying the size.When the diameter is on the scale of exciton Bohr radius [32]in nanowires, the quantum confinement will also dominate,which confirming that the geometric dimensionality influencesexcitonic properties.

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As different from the quantum dots, nanowires andnanobelts with large size R > αB can also showthe morphology and size-dependent excitonic properties[118–120]. This has renewed interests on the tailoringexcitonic properties in nanowires and nanobelts by themorphology, size and cavity. The following four effects areparticularly important.

Firstly, self-absorption from the Urbach tail will intro-duce the redshift of exciton emission with long nanowires andnanobelts. In 1D nanomaterials (nanowires and nanobelts),emissions from exciton recombination could experienceemission–absorption–reemission process along the 1D fila-ment. Due to the rich band-tail states (Urbach tail) due todefects or electron–phonon interactions [121], redshifts of ex-citon emission from the ends after a long propagation of ex-citons along nanowires or nanobelts can be observed [121],compared with the emission wavelength at the body of thenanowires or nanobelts. This re-absorption effect has beenused for the lasing mode tailoring in CdS nanowires [60].

Secondly, the Burstein–Moss effect from different carrierconcentrations of nanowire sand nanobelts could bring theblue-shift of exciton emission. Yang et al found that theultraviolet luminescence of a ZnO nanowire with the diametergradually reduced from 700 to 50 nm was different and a blue-shift of approximately 90 meV was observed, which could beattributed to the Burstein–Moss effect under the high carrierconcentration [122].

Thirdly, the cavity effect (Purcell effect) from differentnanowires and nanobelts with different symmetry couldinfluence the density states of excitons and exciton radiativeand nonradiative recombination. Apart from the criticalparameter Bohr radius, another critical parameter is theelectromagnetic mode volume determined by λ = hc/nE (nis the refractive index, and c is the velocity of light), whichwill determine the photon density of state in nanowires andnanobelts [54]. The exciton recombination depends not onlyon the intrinsic properties of II–VI semiconductors, but alsoon the photon density of states, which in turn is related to thesize and morphology of II–VI semiconducting nanowires andnanobelts [119]. The strong light–matter interaction in II–VIsemiconductor nanowires and nanobelts can further enhancethis effect, which in turn can be used to tailor the excitonicproperties of nanowires and nanobelts by material engineering[54]. According to this, Vanmaekelbergh et al demonstratedthat exciton emission from a ZnO nanowire is not dictated bythe electronic band diagram of ZnO but depends on the wiregeometry with a spatially resolved luminescence spectroscopy[123].

Fourthly, the intrinsic surface effect due to the largesurface-to-volume ratio of nanowires and nanobelts can alsohave an influence to the excitonic properties. The breakingof the translational symmetry of the crystal potential at thesemiconductor surface can lead to the formation of the surfacestates within the gap near the surface [124]. This surface effectcould bring the surface depletion electric field and the surfacedepletion is sensitive to carrier concentration and surface states.

Recently, we have investigated the surface depletion-induced quantum confinement in CdS nanobelts beyond the

quantum confinement regime [118]. Figure 9(a) demonstratesthe thickness (L)-dependent photoluminescence spectra at294 K. As the thickness decreases, the emission peak shiftscontinuously and the line shape of the emission peak evolvesgradually from asymmetric with a long tail at the lower energyside to symmetric at a thickness less than 100 nm. The energiesof the FXA emission peaks can be extracted after fitting [118],as shown in figure 9(b). The energy of the FXA emissionpeak is plotted as a function of 1/L2 at various temperaturesin figure 9(b). From room temperature to 77 K, the emissionenergy of FXA scales linearly with 1/L2 when the thickness L

is less than 100 nm, while a deviation occurs for those nanobeltsthicker than 100 nm due to the re-absorption effect. The1/L2 dependence can be explained by the surface depletion-induced quantum confinement [118]. The surface electric fielddecreased in the surface depletion region due to the decreasein carrier concentration in low temperatures.

Surface states can be passivated by introducing the organicmolecules [125], polymer such as PMMA [118] or core/shellstructure [126]. Core/sell structure such as CdS nanowireas the core and SiO2 as the shell can also be used to tunethe photoluminescence emission of the excitons [126] withcontrolled thickness. The morphology and size of nanowiresand nanobelts can also influence the dynamics of excitons. Adeep understanding of this dependence on the recombinationdynamics of nanowires plays an important role for the designof on-demand nanodevices based on nanowires and nanobelts.Temperature-dependent and time-resolved photoluminescencespectroscopy has been used to study the size-dependentexciton recombination dynamics in single CdS nanowires withdiameters from 80 to 315 nm beyond the quantum confinementregime [120]. The surface recombination decreased with theincrease in nanowire diameters due to the decrease in thesurface-to-volume ratio of the nanowires [120]. Lo et al alsosuggested that the time constants of the ultrafast dynamicsof single CdTe nanowires varied due to the differences inthe energetic and/or density of surface trap sites from themorphology [72]. Reparaz et al [127] investigated the spatialdependence of the exciton lifetimes in single ZnO nanowiresand the dependence is explained by considering the cavity-likeproperties of the nanowires in combination with the Purcelleffect. ASE of II–VI nanowires and nanobelts also dependson the quality and morphology of the samples [128], and theASE threshold power density ranging from several to tens ofµJ cm−2.

5. Perspectives

In this review paper, we summarize the unique excitonicproperties (static and dynamics) in II–VI semiconductornanowires and nanobelts. We also present an account on therecent development of excitonic interaction such as exciton–exciton, exciton–phonon and exciton–plasmon interactions, aswell as the morphology and size influence to the excitonicproperties in II–VI semiconductor nanowires and nanobelts.

Excitonic properties in II–VI nanowires and nanobeltsare fertile for efficient opto-electronics and photonic devices.Unveiling and controlling the fundamental physics properties

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J. Phys. D: Appl. Phys. 47 (2014) 394009 X Xu et al

Figure 9. (a) Photoluminescence spectra of CdS nanobelts with various thickness at 294 K. (b) Photon energy of the FXA emission versusthe thickness of nanobelts at various temperatures (adapted with permission from [118]).

of excitons in the nanowires and nanobelts would be thekey to further applications of these nanodevices. However,taming excitons in these nanowires and nanobelts are still onthe way and more exquisite understanding and controlling isstill needed. For example, full morphology controllable andsize tunable synthesis of nanowires and nanobelts in largescale is very important for the purpose of monodispersiveand large scale excitonic devices. Also, the doping and thedefect engineering in 1D nanomaterials are also importantfor the tailoring of exciton and exciton complex properties.More ability to tailor exciton dynamics from the radiativeor nonradiative channels is also important for the ultrafastopto-electronics and photonics based on the 1D nanowiresand nanobelts. The interaction between the elementaryexcitation and excitons in 1D nanowires and nanobelts will alsosupport the fundamental physics understanding of the excitonicproperties in nanoscale.

Exciton in strong coupling with photon would form thepolariton, which afford a good platform for the Bose–Einsteincondensate [129]. Cavity engineering in nanowires andnanobelts are necessary for both fundamental and practicalapplication of cavity quantum electrodynamics in nanowiresand nanobelts.

Even though we have not discussed II–VI heterostructuresbased on nanowires and nanobelts, 1D nano-heterostructurescan also be one of the methods for tailoring the excitonsand exciton complexes. It will form the interface suchas p–n junctions, unipolar–bipolar junctions, which couldhighly influence the unique excitonic properties in II–VIheterostructures.

Acknowledgments

QX would like to acknowledge the strong support from theSingapore National Research Foundation via a fellowship grant(NRF-RF2009-06) and a Competitive Research Programme(NRF-CRP-6-2010-2), Ministry of Education via twoAcRF Tier2 grants (MOE2011-T2-2-051 and MOE2012-T2-2-086) and start-up grant from Nanyang Technological

University (M58110061). He also acknowledges the fruitfulcollaborations and discussions with Professors Tze ChienSum and Handong Sun from NTU. Dr Xu would like toacknowledge the support from the National Natural ScienceFoundation of China (Nos 11374240), Natural ScienceBasic Research Plan in Shaanxi Province of China (Nos2012KJXX-27), Key Laboratory Science Research Plan ofShaanxi Education Department (13JS101), National Key BasicResearch Programme (2014CB339800), Research Fund for theDoctoral Programme of Higher Education (20136101110007).

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