carbon-nanotube photonics and optoelectronics -...

nature photonics | VOL 2 | JUNE 2008 | www.nature.com/naturephotonics 341

REVIEW ARTICLE

Phaedon avouris*, Marcus Freitag and vasili Perebeinos

IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA*e-mail: [email protected]

Single-walled CNTs possess outstanding electrical and thermal conductivities and enormous tensile strength, which make them an engineer’s dream1–3. Despite the fact that all nanotubes are based on a hexagonal honeycomb carbon lattice, different orientations of this basic structure with respect to the nanotube axis lead to materials with different properties. For example, depending on this orientation, nanotubes can either behave as semiconductors or metals1–3 (Box 1). Semiconductor nanotubes are the subject of extensive studies in nano-electronics as a possible replacement for silicon-based transistors4–6. What is of particular interest for photonics is that semiconducting nanotubes are direct-bandgap materials that can be used to both generate and detect light. In fact, it is possible to create a CNT device that can operate either as a transistor, a light emitter or a light detector simply by changing the applied voltage. Thus, nanotubes offer potential for building a unified electronic and optoelectronic technology based on the same material. Moreover, nanotubes provide a unique model system to study basic optical and optoelectronic phenomena in one dimension.

In the first part of this review we discuss the fundamental optical properties of CNTs, including their radiative and non-radiative decay rates, which determine their optical efficiency, their optical properties under an external electric field, and nonlinear optical phenomena. In the second part, we review the transport properties of CNTs and electroluminescence phenomena in ambipolar and unipolar regimes, and the

Carbon-nanotube photonics and optoelectronicsCarbon nanotubes (CNTs) are nearly ideal one-dimensional (1D) systems, with diameters of only

1–3 nm and lengths that can be on the scale of centimetres. Depending on the arrangement of

the carbon-atom honeycomb structure with respect to their axis, CNTs can be direct bandgap

semiconductors, or metals with nearly ballistic conduction. The excited states of semiconducting

CNTs can be produced by either optical or electrical means and form strongly bound (with dissociation

energies of around 0.5 eV), luminescent, 1D excitons. The single-atomic-layer structure makes the

optical properties of CNTs especially sensitive to their environment and external fields, and this can

be used to tune them. Here we review the nature and properties of CNT excited states, the optical

and electrical mechanisms of their production, their radiative and non-radiative modes of decay, the

role of external electric fields, and their possible technological use as nanometre-scale light sources,

photodetectors and photovoltaic devices.

possibility of using CNTs in LED applications. Finally, we review their photoconductivity and photovoltage properties, which may find applications in nanoscale photodetectors.

oPtical ProPerties oF carbon nanotubes

radiative and non-radiative decaYThe separation of CNT bundles by sonication (the use of ultrasonic energy) followed by coating individual CNTs with surfactants has provided a way of studying their luminescence properties7 and assigning the CNT’s (n, m) indices8 — integers that describe the direction with respect to the planar hexagonal lattice along which the graphite sheet is rolled to form the tube. Early studies of mixtures of surfactant-coated CNTs gave low fluorescence quantum yields, QF, of the order of 10–3−10–4. More recent studies on individual, suspended nanotubes show yields as high as 10% (ref. 9). These yields were measured by exciting CNTs to the state E22 and then observing the fluorescence from the state E11 (see Box 1 for further details of CNT states). Experimental studies have also shown that the environment has a strong influence on QF (ref. 10).

At room temperature, the reported fluorescence lifetimes of unconfined CNTs, τF, are typically in the range of 10 ps to 100 ps (refs 11–15). As 1/τF = 1/τR + 1/τNR, where τR and τNR are the radiative and non-radiative lifetimes, respectively, and QF = τR

–1/(τR–1 + τNR

–1), the latest reported QF values and fluorescence lifetimes can be used to estimate an ‘effective’ radiative lifetime at room temperature of the order of 1–10 ns, in agreement with theoretical predictions16,17.

Photoexcitation produces high-energy E22 excitons that have zero momentum, and relax by means of phonons to lower-energy E11 states for which the momentum is finite. As a result, the measured radiative lifetime represents an averaged

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decay from a distribution of excited E11 states and is a function of temperature, T (refs 16,17). For a single 1D exciton band with parabolic dispersion, the radiative decay rate is proportional to T–1/2 (ref. 18). In the case of CNTs, strong electron–electron interactions remove the degeneracy of the fourfold degenerate electron–hole pair excitations originating from the doubly degenerate valence and conduction single-particle bands. This produces four low-energy exciton states16,17,19. The lowest-energy exciton has zero circumferential angular momentum20 and

consists of a symmetric linear combination of electron–hole pairs originating from bands with the same angular momentum16,17. This exciton cannot couple radiatively to the ground state, because its wavefunction is spatially even. The odd-symmetry exciton with zero circumferential angular momentum has a higher energy owing to electron exchange interactions and, according to the dipole approximation, does couple to the light field. The remaining two excitonic states have finite circumferential angular momenta, because they originate from

The electronic structure of CNTs is usually discussed on the basis of the bandstructure of graphene, which has a linear dispersion, such that the two-dimensional energy, E2D, is given by E2D = ħvF|k|, where k is the two-dimensional wavevector and vF is the Fermi velocity, and of the order of 106 m s–1 (ref. 1). In a nanotube, the wavevector component perpendicular to the axis, k , is quantized, such that the minimum allowed value of k , k min, is equal to 0 or 2/3d depending on the integer indices (n, m) that define the direction along the planar hexagonal lattice along which the graphite sheet is rolled into a CNT (ref. 1). d is the nanotube diameter. Specifically if |(n – m) mod(3)|, where ‘mod’ is ‘division by modulus’, the CNT is metallic, that is Eg = 0. If |(n – m) mod(3)| = 1 or 2, the CNT is semiconducting with a bandgap, Eg = 4ħvF/3d. The larger values of k give rise to the electronic states with higher angular momenta, as shown in Fig. B1a. The single-particle density of states is shown in Fig. B1b.

In the above single-particle model, electronic excitations are interband transitions that produce free electron–hole pairs. However, electron–hole interactions allow formation of bound

electron–hole pairs37. Thus, one or a series of bound states (analogous to the Rydberg series in atoms) — so-called excitons — form below the free particle continuum (Fig. 1c). The exciton binding energies in nanotubes have been predicted20,97,98 and are found to be large90,91, as great as several hundred meVs, and to depend inversely on d (refs 20,99). Moreover, most of the oscillator strength is transferred away from the interband transitions to the excitonic transitions that dominate37, except when the electron–hole interaction is heavily screened20. Both the electrical bandgap, Eeg ≈ Eg + Eee, and the optical gap, Eog ≈ Eg + Eee – Eeh, (where Eee and Eeh are the electron–electron and electron–hole interaction energies, respectively) depend on the single-particle bandgap, Eg. They can be modified depending on the dielectric function, εm, of the environment, as this screens both Eee ≈ 1/εm (refs 100,101) and Eeh ≈ 1/εm

1.4 (ref. 20). Experimental studies102–105 indicate that Eee > Eeh and, therefore, interactions increase the excitation energy, Eog, above its Eg value. Recombination of the electron and hole in response to incident light gives rise to photoluminescence (Fig. B1d).

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Figure B1 spectroscopy of cnt excitons. a, valence (bottom) and conduction (top) bands with different angular momentum for a (19, 0) semiconducting cnt. red: k = ±k min; blue: k = ±2k min; green: k = ±4k min. kψ is the wave vector along the cnt axis. b, single-particle density of states. c, low-lying exciton states of a (19, 0) cnt. dipole-allowed or ‘bright’ transitions are solid lines and forbidden or ‘dark’ transitions are green (k = ±2k min) and navy (k = 0) dashed lines. the parallel (k = 0) or perpendicular (k = ±3k min) polarizations with respect to the cnt axis of a state relating to an allowed transition are indicated by red and blue solid lines, respectively. black ellipses indicate the states relating to the following first allowed transitions: E11 for parallel and E12 for perpendicular polarizations. the state relating to the second allowed transition (E22) and the free-particle continuum (Δ11) are also shown in black. the ellipse labelled ‘rydberg’ indicates rydberg states with k = 0. ke is the electron wave vector and kh is the hole wavevector. Parts a–c reprinted with permission from ref. 31. d, three-dimensional plot of exciton photoluminescence from a mixture of surfactant-coated cnts. courtesy of r.b. Weisman, rice university.

Box 1 Nanotube electronic structure and excited states


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electrons and holes from bands with different angular momenta, and thus they cannot be excited by light. Therefore, the transition from the lowest energy state by optical excitation is forbidden. However this transition is thermally accessible, which leads to a non-monotonic temperature dependence of the radiative decay rate, with a maximum at a certain temperature as predicted in refs 16 and 17 and observed in refs 21 and 22. It should be noted, however, that the lowest-energy, forbidden transition can acquire oscillator strength and thus be ‘brightened’ through defects, distortions or the application of external fields23. The spontaneous radiative decay of CNTs can be further modified by confining the CNT in a half-wavelength microresonator, which modifies the photonic density of states24,25 (the Purcell effect). This was demonstrated for Raman scattering, which has a cross-section that also depends on the photonic-mode density.

Measured QF values indicate the presence of a rather efficient non-radiative decay process. Recent work suggests that only about 10% of the E22 excitons decay to free electrons and holes26. It must therefore be concluded that a non-radiative-decay process controls the E11 exciton lifetime. At high excitation densities, collisional processes such as exciton–exciton annihilation dominate the decay14,27,28. At low excitation densities, the dark exciton state can not fully account for the small fluorescence yield and fast decay because the splitting of the dark and bright energy levels is rather small, about 10 meV (refs 17,21,23), and thermal equilibrium would still leave a significant proportion (about 40%) of the exciton population in the bright state. Another intrinsic energy dissipation channel must therefore control the relaxation of the lowest exciton state. By analogy to molecular systems multiphonon decay to the ground state should be possible. The multiphonon decay rate decreases with the number of phonons needed to absorb the electronic energy. Nanotubes have high-energy C–C stretching modes (referred to as G-modes, with an energy of about 200 meV) which have strong electron–phonon coupling29, and the nanotube bandgap decreases with increasing tube diameter1. Calculations indicate that indeed for nanotubes with a diameter greater than 2 nm the multiphonon emission rate could account for the observed lifetimes30,31. Because free excitons couple less strongly to phonons than localized excitons, the multiphonon decay rate is enhanced on localization30. Indeed, evidence has been presented recently that the emission from surfactant-coated nanotubes involves localized excitons32. Given, however, that short lifetimes are also observed for tubes with small diameters, where more than three phonons are required for multiphonon decay, it must be concluded that yet another efficient, electronic decay channel exists. Namely, phonon-assisted indirect exciton ionization30, which relies on a finite doping of nanotubes and involves exciton decay into an optical phonon and an intraband electron–hole pair.

The width of the exciton absorption is not only dependent on the population decay, but also on dephasing processes, which involve scattering by low-frequency acoustic phonons. Fluorescence linewidth measurements on a single 1-nm-diameter CNT gave an exciton peak with a full-width at half-maximum of 0.29 kBT (ref. 33), where kB is Boltzmann’s constant, which is consistent with the scattering rate between electrons and acoustic phonons34. The characteristics of the optical emission from CNTs in the experiments reported up to now can be understood within classical electromagnetic theory. Very recently, however, it was reported35 that emission from a single CNT at low temperature has a zero-value second-order correlation function, indicating that the emitted photons show strong antibunching. This is clear evidence of a quantum effect, and could have applications for the development of single-photon sources for optical communications and cryptography35. Fibre-optic confinement and the guided

propagation of visible light using arrays of multiwalled CNTs have also been demonstrated36.

electric-Field eFFects on the excited states oF carbon nanotubesWhen CNTs are used in electronics and optoelectronics devices, such as field-effect transistors, light emitters, light detectors or electro-absorption modulators, they experience an external electric field. It is important, therefore, to understand the effect of such fields on the structure and properties of CNT excited states.

The electro–optical response of three-dimensional semiconductors was discussed almost 50 years ago by Franz and Keldysh37. An electric field can modify the absorption spectrum of a CNT in several ways: (1) it can modulate the absorption coefficient; (2) it can increase the spectral weight of the band-to-band absorption; (3) it can shift the absorption peak energies (Stark effect); and (4) it can dissociate the bound exciton. In bulk three-dimensional semiconductors the exciton binding energy is small, whereas in confined structures it is much bigger and the orientation of the field with respect to the confinement direction is important. In 1D systems, such as CNTs and π-bonded polymer chains, the biggest effects are expected to occur when the field is oriented along the axis of the CNT or polymer chain. For CNTs, relatively large changes in the absorption at the first excitonic peak and the first band-to-band absorption are to be expected. In other structures, such as quantum wells, large changes are observed when the field is directed perpendicular to the confinement direction37.

So far, experiments investigating the effect of an electric field on the optical absorption spectra of well-defined, single CNT samples have not been conducted. However, experiments have been performed on ensembles of CNTs with the field directed perpendicular to the CNT axis38,39 and these found oscillatory changes in the absorption coefficient and small Stark redshifts for thin-film CNT transistors when a perpendicular electric field was applied. The intensity of the transition from the E11 state was also found to decrease as a result of carrier accumulation with an accompanying increase of Drude-like absorption in the far infrared.

The influence of an electric field along the CNT axis on the absorption spectra of CNTs was studied theoretically by solving the Bethe–Salpeter equation for excitons in an external

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Figure 1 effect of an external field on cnt excitons. the computed absorption spectra of a (16, 8) nanotube (d = 1.7 nm) in fields of different strengths (black: 0.0 v µm–1; blue: 2.0 v µm–1; red: 6.0 v µm–1; green: 10.0 v µm–1). the first optically active exciton at zero field is at 0.5 ev and the band-to-band absorption is at an energy about 0.2 ev higher. data reprinted with permission from ref. 40.


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d.c. electric field40. An example of results for a (16, 8) CNT are shown in Fig. 1. For zero electric field, there is no absorption in the energy range between the first exciton at 0.5 eV and the onset of the band-to-band absorption at 0.7 eV. In the presence of the electric field, however, an absorption peak develops in the optically forbidden region, that is, below the bandgap at about 0.7 eV. With increasing field strength, spectral weight is transferred from the excitonic peak to the band-to-band absorption. At some critical field, Fc

(6.0 V μm–1 in Fig. 1), the band absorption merges with the first exciton absorption peak. This is in contrast to the behaviour of conventional three-dimensional semiconductors at room temperature, where the band-to-band absorption simply decays exponentially below the bandgap edge. The same authors found quadratic dependences on the external electric field for both the growth in the spectral weight of the band-to-band absorption (proportional to d4F2, where d is the nanotube diameter and F is the field) and of the Stark shift (proportional to d3F2). The Stark shift was as large as 10 meV at 15 V µm–1 in a tube with d = 1.5 nm (ref. 40). The effects are most pronounced in large-diameter tubes with large excitonic radii20, as the field coupling of the bound exciton to the free electron–hole continuum states is proportional to the exciton radius40.

The presence of the electric field can also lead to the ionization (dissociation) of the exciton. This is essential for the observation of CNT photoconductivity on excitation of the low-energy (E11) bound exciton state (higher energy states, for example, the E22 state are autoionizing). This issue was investigated experimentally in ref. 41, where the effect of a perpendicular electric field on both the E11 and E22 absorption transitions along with the displacement photocurrent spectra of CNT films were studied. Although the absorption and photoconductivity spectra of the E22 state appeared identical and were observable even at zero field, photoconductivity from the E11 state was not observed until high enough fields were applied41.

aPPlications oF the nonlinear oPtics oF nanotubes Few fundamental studies of the nonlinear optical properties of well-characterized nanotubes have been made. It has been determined, however, that they possess a high third-order susceptibility (refs 42,43), and a number of applications have appeared. Assemblies of nanotubes in suspension or in polymeric matrices have been used as saturable absorbers for near-infrared light44–46. For example a femtosecond laser beam at an intensity of around 50 MW cm–2, and a wavelength of 1.78 µm, incident on such a nanotube saturable absorber, is attenuated by about 40% (ref. 47). In addition, the fast non-radiative decay of excited CNTs leads to a fast response (within less than 1 ps). Such nanotube assemblies and films have been used as passive mode-lockers for femtosecond lasers48–51. The advantages of CNTs as saturable absorbers are that they offer much simpler and cheaper fabrication than conventional semiconductor saturable absorber mirrors and can be easily integrated into optical-fibre communication systems.

electroluMinescence

uniPolar and aMbiPolar Field-eFFect transistorsA CNT field-effect transistor is a three-terminal switching device in which the current from the source to the drain through the CNT is controlled by an applied voltage at a capacitively coupled gate6. In addition to modulating the carrier density in the CNT, the gate voltage also modulates the injection of carriers at the source and drain Schottky barriers52,53. The polarity of the device depends on the Schottky barrier heights for electrons and holes, and can be engineered to some degree by adjusting the metal work functions. For example, for palladium contacts, the Schottky barriers for holes are small and devices are p-type54, whereas annealed titanium contacts produce ambipolar devices with intermediate Schottky barrier heights for electrons and holes53.

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Figure 2 infrared emission from an ambipolar cnt-Fet. a, schematic of the device. holes (h+) are injected from the source and electrons (e–) from the drain. light is emitted from a recombination spot about 1 μm in length, where electrons and holes overlap. b, characteristic of the gate voltage, Vg, for a constant current as Vg is varied. light emission is only observed in the ambipolar state, depicted in orange. c, three-dimensional rendering of the ambipolar infrared emission as a function of Vg at constant current. the recombination region, where electrons and holes overlap, produces light that is translated along the cnt by changing Vg. the cnt is 50 µm long.


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Ambipolar CNT field-effect transistors53,55–57 (FETs) are not particularly desirable for logic operations, because they lack a well-behaved off state. As a result, ways have been developed to regain a unipolar device characteristic by using a double gate58 or by chemically doping the contact region59. On the other hand, ambipolar transistors enable the injection of electrons and holes from opposite contacts into the CNT, and thus are very useful for electro–optic applications.

electron–hole recoMbination in aMbiPolar nanotubesElectron–hole pairs in semiconductors may recombine by a variety of mechanisms. In most cases, the energy will be released as heat (phonons), but a fraction of the recombination events may involve the emission of a photon. This electroluminescence (EL) process is widely used to produce solid-state light sources such as LEDs. To produce an electroluminescent device that emits a significant amount of light, a large number of electrons and holes must recombine. In an LED, this is achieved at an interface between a hole-doped (p-doped) and an electron-doped (n-doped) material. In ambipolar CNT-FETs, electrons and holes can be simultaneously injected at opposite ends of the CNT channel (Fig. 2a). This enables radiative recombination to take place in the CNT and EL is generated60. Although the emission mechanism is the same as that in LEDs, ambipolar CNT-FETs do not require any chemical doping, a significant simplification of the fabrication process.

Carbon-nanotube EL exhibits a number of interesting properties. The emitted light, as with photoluminescence, is polarized along the tube axis60, and the radiation has a characteristic energy that depends on the diameter and chirality of the excited single-walled CNT (ref. 61). The length of the electroluminescent region is of the order of the recombination length, lrec, which is less than or equal to 1 μm (ref. 62). At a gate voltage halfway between the value of the source and drain voltages, about an equal numbers of electrons and holes are injected. The total current is minimized, but the amount of light generated is maximized60 (see the ambipolar gate-voltage range in Fig. 2b). In short devices (shorter than lrec), the light emission encompasses the entire CNT (ref. 60). In long devices (much longer than lrec), where electron–hole recombination is fast compared with carrier transit times through the channel, light emission originates from a small part of the CNT, where electrons and holes coexist and can annihilate (Fig. 2a). As a result, the emission is localized to where the concentrations of electrons and holes overlap most strongly62. In the regions above and below this recombination spot, transport is unipolar and charge carriers are of opposite sign. Most importantly, because no chemical doping is involved, the electron–hole overlap region and thus the region of light emission can be physically moved along the CNT using the gate electrode (Fig. 2c).

A CNT-EL device is thus a translatable light source62,63.In long CNT-FETs, a simple drift transport model63 accounts

well for the main features of the movement of the light emission.

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For intermediate-length devices numerical calculations for the light emission have been performed64. The EL spectra can be similar to photoluminescence spectra. However, electrical pumping is usually much stronger than optical pumping, excitation densities are much higher, and a broad emission with a low-energy onset at the E11 exciton energy is usually observed61.

hot-carrier induced excitation and uniPolar eMission In addition to photon irradiation and electron–hole recombination, excitation of CNTs can be achieved through energetic — ‘hot’ — carriers flowing through the CNT. This is an impact-scattering mechanism that involves coulombic interactions between electrons. Electron–electron interactions are very strong in 1D materials such as CNTs. Indeed, calculations suggest that impact-excitation processes in CNTs, are much more efficient (about four orders of magnitude stronger) than in conventional bulk semiconductors65. The carriers are accelerated by the applied electric field, gain energy and then lose some of it to phonons, primarily optical phonons. When an energy threshold, Eth, is reached, electronic excitation of the CNT across the bandgap can take place. The value of Eth is determined not only by the E11 energy, but also by the requirement to conserve the circumferential angular momentum of the CNT in the impact-excitation process.

Solving the Boltzmann equation shows that the exciton production probability, P, varies exponentially with F, that is, P ~ exp(–Eth/eFλop), where e is the charge of an electron, Eth ≈ 1.5E11 and λop (about 20–40 nm) is the electron mean free path with respect to optical-phonon scattering65. The hot-carrier-induced impact excitation of CNTs can be used to create an efficient EL source62,66–68. The current is carried by only one type of carrier (either electrons or holes), and inhomogeneities actively generate electron–hole pairs by impact excitation. The emission occurs near defects, trapped charges in the gate insulator, CNT–CNT contacts, the Schottky contacts, or any other inhomogeneities that produce large, local electric fields that can accelerate the carriers to energies above Eth (refs 62,68). For example, for the straight CNT in Fig. 3a, there are at least three stationary spots (indicated by arrows) that do not move with the gate voltage. Each of them appears to the negative voltage side of the ambipolar spot, where the corresponding CNT segment has become n-type. They disappear past the ambipolar spot68. Experiments like these suggest that locally p-doped segments act as n–p–n junctions during electron conduction, owing to pockets of trapped electrons in the SiO2 used as the gate dielectric. Thus, monitoring localized EL provides a tool for detecting defects in CNT devices. Figure 3a also shows stationary emission at the drain past the ambipolar spot. This is due to the high fields at the Schottky contact.

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Figure 3b shows looped nanotubes, where hot carriers tunnel from one end of the CNTs to the other end across the base of the loop and produce light by impact excitation68 . Different loops on the same CNT may or may not show unipolar EL, depending on the microscopic properties of the junction. An analogous variation in contact properties has been observed in photovoltage measurements of looped CNTs that, unlike EL measurements, probe the low-bias behaviour of devices69. The light emission also depends on the charge in the surrounding CNT segments, which can be changed by moving the ambipolar spot across the base of the loop using the gate bias. For example, in Fig. 3b two of the loops become active for hole conduction. Note that the ambipolar infrared spot never moves through the interior of the loop and instead jumps across the CNT–CNT contacts, which suggests strong intertube electron–hole coupling.

Artificial structures can also be fabricated to create the abrupt change in the potential that is required to generate localized light emission by impact excitation66. An example of such a structure is shown in the inset of Fig. 3c. It consists of a back-gated CNT-FET in which a trench has been cut in the gate oxide by etching so that a portion of the CNT channel is suspended. The difference in the coupling to the gate of the oxide-supported and the suspended part of the CNT leads to band-bending at the interface of the two segments. Carriers reaching this interface are accelerated and, through impact excitation, can produce excitons or electron–hole pairs that recombine radiatively (see the schematic in Fig. 3d).

Light intensity, I, from unipolar devices depends exponentially on the applied electric field, I(photon) ∝ exp(–Fth/F), where Fth is the threshold field required for electronic acceleration within the band. Furthermore, impact excitation is not subject to the same selection rules as photoexcitation, so impact-excited spectra can be different from photoexcitation spectra65. Although interband transitions are suppressed in favour of exciton transitions in photoexcitation, impact excitation does produce free electron–hole pairs65. Thus, using internal impact excitation, both exciton and bandgap CNT emission can be observed31 (Fig. 3c). In suspended metallic tubes under high-bias conditions, light emission was also observed as a result of the hot-carrier distribution70.

nanotubes and ledsSingle-walled CNT films are conductive, optically transparent and flexible. These properties have been used to make anodes for organic LEDs (OLEDS, see refs 71,72). The advantage over the traditionally used indium tin oxide films is their cheaper price, flexibility and resilience to corrosion. For example, polymer OLEDs with CNT anodes that have a maximum light output of 3,500 cd m–2 and a current efficiency of 1.6 cd A–1 have been reported72.

Another way to use CNTs in light-emitting devices is in the form of composites with conjugated polymers. Indeed, enhanced EL in such composites has been reported by many authors73–76, and enhanced photovoltaic behaviour was also observed in such composites77–79.

PhotoconductivitY and Photovoltage

A semiconducting CNT can act as a nanoscale photodetector that converts light into a current or voltage80, and several implementations of individual-CNT photodetectors have been demonstrated69,80–85. The principle of operation is that, above-bandgap photons generate excitons in the CNT, which can decay into free electrons and holes. These electrons and holes are either separated by an externally applied bias80, by internal fields at the Schottky barriers81,82,85, at p–n junctions83 or at defects69,84. When an externally applied bias is used, a change in current (photoconductivity) results, whereas in the other cases a photovoltage is also generated. Schottky barriers at the

contacts are beneficial, because they reduce the injection of carriers into the CNT without affecting the flow of photocurrent generated inside the CNT.

Films of carbon nanotubes also produce a photocurrent, but the detection mechanism in film-based photodetectors

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Figure 5 switching action of the schottky barrier region in an ambipolar cnt. reprinted with permission from ref. 85. a, sequence of Voc images of the contact region for the indicated gate voltages. the first panel is a schematic of the device. b, integrated Voc along the cnt showing the band bending as the device switches from hole to electron conduction. c, bandstructure at the threshold voltages for electron (red) and hole (blue) conduction. the schottky barrier heights for electrons and holes (Φel and Φho) and the depletion width at the threshold for electron conduction (Wd) are indicated. Eg is the nanotube bandgap and EF is the Fermi energy. the x axis indicates position and the y axis indicates the energy.


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is thermal in nature, that is, bolometric (ref. 86), unlike that in individual tubes. The non-radiative decay of the excited nanotubes heats the CNT network and the change in temperature strongly affects the film resistivity because of the presence of CNT–CNT junctions. To optimize the response, CNT films are suspended between two electrodes and cooled to the point where the electrical response becomes semiconducting, that is, the resistance decreases for increasing temperature (ref. 86).

By tuning the wavelength of the light incident on an individual CNT and recording the current, a photocurrent spectrum of the CNT can be obtained80,87–89. Not only is photocurrent spectroscopy useful in characterizing the CNT’s chirality, it also provides a valuable insight into the nature of the CNT electronic states. For example, the presence of phonon sidebands in the photocurrent spectra provides strong evidence of the excitonic nature of the transition29,87. The strongest sideband involves the high-frequency G-phonon mode of the CNTs at the Brilloin zone boundary29, which can be optically excited together with a dark state that has an energy above the optically active exciton17.

Higher-energy excitons are embedded in lower-state continua and can decay to free electrons and holes leading to a photocurrent. In contrast, the first exciton (E11) should not easily decay to free particles because of its large exciton binding energy, which is of the order of several hundreds of meV (refs 90,91). A capacitive ‘displacement photocurrent’ measurement has shown that E11 decay can nonetheless create a photocurrent when a perpendicular electric field is applied41,92. Interestingly, the E11 transition also gives a strong photocurrent response in suspended CNT p–i–n diodes88,89. It was suggested that the CNT bandgap could be modified across the edge of the trench, leading to a CNT heterostructure, across which the exciton can decay89.

From the magnitude of the photocurrents from individual CNTs under known incident light intensities and with known CNT cross-sectional areas, an external quantum efficiency of 10–2 electrons per incident photon can be estimated80. Photovoltaic devices are also characterized by the open-circuit photovoltage, VOC, the short-circuit photocurrent, ISC, and the fill factor, FF, which is given by FF = Pmax/(VOCISC), where Pmax is the maximum obtainable power generated at an optimum load resistance. Typical values for individual CNT photovoltage detectors are VOC ≈ 100 mV and ISC ≈ 100 pA for incident power densities of 1 kW cm–2, and FF ≈ 0.4 (refs 81,83,85). Photo-enhancement of switching in three-terminal devices has also been demonstrated93.

By focusing a laser to subdevice dimensions and scanning the light along the CNT, the active CNT regions generating the photovoltage can be identified69,82,84,85 (Fig. 4). This is possible even in mirror-symmetric devices that show no macroscopic photovoltage on full device illumination. For this measurement, ISC, VOC, or the entire I–V curve is recorded as a function of the lateral laser-spot position. Figure 4a shows a simple CNT-FET, where ISC is generated at the two Schottky contacts. No bias is applied between source and drain during this measurement, so the built-in band-bending, which occurs in opposite directions at the two contacts, is responsible for the observed contrast. The direction of band-bending is consistent with the p-type characteristics of palladium-contacted CNTs (ref. 54). A weak photocurrent due to internal photoemission or heating of the electrode can also be generated when the laser spot is incident not on the CNT, but on the source or drain electrode in close proximity to the tube85.

Intentional or unintentional modulations of the potential along the length of the CNT also contribute to a photocurrent. Nanotube p–n diodes have an active region where the potential varies at the p–n interface83, but even potential modulations

associated with defects in the CNT or trapped charges in the gate dielectric can produce a photocurrent69,84. Figure 4b shows the ISC image of the previously discussed CNT with a single introduced defect at the centre of the device. In addition to the signal from the Schottky barriers, there are now two regions, just to the left and to the right of the defect, where a photovoltage is generated. Under the assumption that the photocurrent is proportional to the local potential gradient, the functional form of the band-bending can be extracted by integrating the photocurrent along the length of the CNT (refs 85,94,95), see Fig. 4c. Raman spectroscopy of the defect-sensitive D-band96 can be used as a complementary technique to locate the defects. The D-band Raman map (Fig. 4e) and the integrated photocurrent plot (Fig. 4f) show clearly that the defects in this CNT are associated with potential maxima69.

Photovoltage microscopy also allows imaging of the transition from p- to n-type in ambipolar devices85. As the gate voltage is swept, the photovoltage at a Schottky barrier switches sign (Fig. 5a). The potential in the CNT is extracted for different gate voltages in Fig. 5b, and from these plots important device parameters, such as depletion lengths and p- and n-Schottky barrier heights can be estimated, Fig. 5c (ref. 69).

conclusion

In summary, we have described the unique optical properties of CNTs. Semiconducting CNTs are direct-bandgap materials, with strongly bound 1D excitons, whose transition energies are inversely proportional to the CNT diameter. These energies can be further tuned by placing them in different dielectric environments. Such excitons can be excited by light absorption, electron–hole recombination or internal impact excitation by hot carriers flowing through the CNTs. Their radiative decay leads to fast luminescence characteristics. Ambipolar CNTs can be used to form LED-like three-terminal devices without the need for external doping. Furthermore, the origin of the resulting emission can be translated along the tube at will by the gate field. Even stronger, localized EL can be excited by hot carriers under unipolar conditions. Higher-energy exciton states produce photocurrents and photovoltages that can be used for the spectroscopic identification of CNTs and to determine important device parameters, such as band-bending and Schottky barriers, or to fabricate nanoscale photodetectors. However, this is only the beginning of the study and of the application of nanotube photonics. As the production of pure CNTs advances, we expect to see applications in electrically pumped solid-state nanoscale light sources and lasers, CNT light guides and nonlinear devices. Applications in biology, where CNTs are already used as fluorescent probes, photosensitizers and sensors, are expected to grow. An understanding of 1D optics, exciton localization and exciton–exciton interactions would also greatly benefit from the study of these model systems.

doi:10.1038/nphoton.2008.94

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