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Bright Infrared Emission from Electrically Induced Excitons in Carbon Nanotubes

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Science  18 Nov 2005:
Vol. 310, Issue 5751, pp. 1171-1174
DOI: 10.1126/science.1119177

Abstract

We used the high local electric fields at the junction between the suspended and supported parts of a single carbon nanotube molecule to produce unusually bright infrared emission under unipolar operation. Carriers were accelerated by band-bending at the suspension interface, and they created excitons that radiatively recombined. This excitation mechanism is ∼1000 times more efficient than recombination of independently injected electrons and holes, and it results from weak electron-phonon scattering and strong electron-hole binding caused by one-dimensional confinement. The ensuing high excitation density allows us to observe emission from higher excited states not seen by photoexcitation. The excitation mechanism of these states was analyzed.

The optical properties of single-walled semiconducting carbon nanotubes (CNTs) are currently the focus of intense study (18). CNTs are direct band-gap materials, and their optical spectra have long been attributed to transitions between free-particle bands. Theoretical studies, on the other hand, have pointed out that there should be strong electron-hole (e--h+) interactions in these quasi–one-dimensional (1D) materials, resulting in strongly bound excitons (911). Recent experimental evidence for the formation of CNT excitons is provided by two-photon fluorescence excitation spectroscopy (3) and photoconductivity (8). CNTs offer the possibility of a unified electronic and optoelectronic technology (12). Therefore, it is important to understand electroluminescence (EL) from CNTs. Moreover, the study of EL provides further insights into e--h+ interactions in quasi-1D materials.

Here we discuss an excitation mechanism that leads to a strongly enhanced EL in the infrared (IR) from a partially suspended CNT field-effect transistor (CNTFET) operating under unipolar transport conditions. In light-emitting diodes (LEDs) or ambipolar CNTFETs, the participating carriers (both e- and h+) are injected from the source and drain electrodes separately (2, 13). In our devices, carriers are generated locally when a single type of carrier is accelerated under high local electric field to energies sufficient to create strongly correlated e--h+ pairs (excitons).

This impact excitation process differs greatly in 3D and 1D systems. In bulk 3D semiconductors, the weak Coulomb interaction between e- and h+ creates weakly bound excitons (14) that mostly dissociate under high field and contribute to the electrical current (15). In 1D CNTs, on the other hand, exciton binding energies are predicted to be more than an order of magnitude larger (911), so that the 1D excitons are expected to recombine and contribute little to the current. We find that the intensity of light emission increases exponentially with the drive current in partially suspended CNTFETs [in 3D materials, light emission is usually proportional to the product of the e- and h+ currents (14)] and has a similar dependence on both the gate and drain bias, whereas the current itself increases linearly with bias.

These observations are a manifestation of the strong e--h+ interactions in the quasi-1D CNTs that prevent e--h+ pairs from dissociating and validate the exciton picture. We also find that the current-voltage (I-V) characteristics of the suspended CNTFETs display negative differential conductance (NDC), which, by comparison with the light emission, we find to be correlated with the onset of the generation of excitons by hot carriers (16). This local EL mechanism leads to a 102 to 103 times increase in efficiency over that achieved by supported ambipolar CNTFETs (16). From both the position of the emission spot and the dependence of the IR emission on the drain and gate bias, we conclude that the high local electrical field at the suspension interface is mainly responsible for the enhanced emission efficiency. By removing the underlying substrate and suspending the CNT, nonradiative recombination channels involving the substrate can also be reduced (5). The extraordinary current-carrying capability of a CNT (12) and its ultra-small size lead to an ultra-bright light source. Finally, the ∼100 times higher exciton density (0.14 nm–1) achieved in our devices, compared with that in typical photoluminescence (PL) experiments, allows us to detect emission from the second allowed exciton (E22) state in CNTs. We show that E11 exciton-exciton annihilation is primarily responsible for the E22 emission. In agreement with a very recent study (17), where high exciton densities were achieved in PL using pulsed laser excitation, we did not see direct evidence for a Mott transition, which is expected to take place when excitons start to spatially overlap.

The CNTFETs (∼25 devices) with a partially suspended CNT channel used in this study were fabricated by etching 0.4-to-15-μm-wide trenches in a 200-nm-thick SiO2 film on Si wafers. The trenches extended through the SiO2 film and 2 μm into the Si substrate. CNTs with diameters in the range of 2 to 3 nm were grown on the trenched substrate by chemical vapor deposition (18). Palladium source and drain electrodes were then patterned on CNTs with channel lengths between 4 and 80 μm. The highly doped silicon substrate was used as a back gate. Detailed experimental setup and sample fabrication are discussed in the supporting online materials (18).

A spatial map of the IR emission, collected with a bandpass filter centered around 1.6 μm (in the E11 emission band) from a single CNTFET, was superimposed on an optical image of the device structure (Fig. 1A). Unlike nonsuspended CNTFETs, whose emission from ambipolar injection can be spatially translated along the length of a CNT by changing the gate bias (13), the emission from the partially suspended device is localized at the SiO2 supported/suspended CNT interfaces under a wide range of gate biases. Figure 1B shows the drain current and the emission intensity at 1.6 μm occurring at the suspension interface, as a function of the gate voltage (Vg) at a constant drain bias of Vd = –5 V. We observed no detectable emission when the gate bias was below a threshold gate overdrive |VgVth| of ∼0.5 V, where Vth is the threshold voltage (–2.6 V in this sample) at which the CNTFET is electrically turned on. At |VgVth | > 0.5 V, the emission intensity increases rapidly with increasing current.

Fig. 1.

(A) E11 infrared emission overlaid with an optical image of a partially suspended CNTFET with 200 nm SiO2, Pd source/drain contacts and a Si back gate. The length of the channel is 26 μm, the width of the trench is 5 μm, and the CNT diameter is ∼2 nm. (B) Drain current (solid squares) and emission intensity (solid circles) versus gate bias at 1.6 μm of a partially suspended CNTFET at Vd = –5 V. One unit of emission intensity corresponds to about 240 photons per second per 4π solid angle in all the following figures. The inset shows the emission intensity increases exponentially with drive current. The solid lineis meant as a guide to the eyes. (C) Schematics of impact excitation process. An incoming hot electron is accelerated by the band-bending at the suspended/supported interface to energies larger than the band gap and generates an exciton that decays radiatively. Subsequently, the “cooled” electron picks up more energy from the electrical field and continues this process.

There are three major differences in the IR emission from suspended CNTFETs compared with that from nonsuspended devices: (i) The dominant emission from the suspended CNT occurs under unipolar transport conditions (Vg < –3.1 V for h+ and Vg > –2.1 V for e-), and no appreciable emission is observed at the ambipolar region where the current shows a minimum (Vg = –2.6 V); (ii) The emission intensity increases exponentially with the drive current in the suspended tube (Fig. 1B, inset), whereas in a nonsuspended CNT biased under ambipolar conduction, the emission intensity is proportional to the minority carrier density (19); (iii) The minimum drain bias needed to observe emission is notably smaller in suspended tubes (Vd ∼2.5 V) than that in nonsuspended tubes (Vd ∼15 V) (13). In turn, a CNTFET operated under ambipolar conditions needs to be driven to higher drain/gate fields and currents to generate the same amount of light as the suspended CNT, indicating that EL via ambipolar conduction is a much less efficient process. Indeed, the emission efficiency defined as photons per electron measured on the suspended samples (16) is about 10–3 to 10–4, that is, the partially suspended samples exhibit an increase of 2 to 3 orders of magnitude from that of supported CNTs operated under ambipolar conduction conditions (16). Although the efficiency (photons/electron) of the suspended CNTs is numerically comparable to that of CNTs wrapped in micelles in PL measurements (emitted photons/adsorbed photon) (1), the small optical cross section of CNTs (10–11 to 10–12 cm2 per CNT) (20) reduces the effectiveness of exciton generation by photoexcitation. For a typical injection current of 3 μA, ∼20 electrons per ps are injected in a steady state in a CNT, generating ∼0.02 photons per ps by EL; correspondingly, ∼2 × 1013 cm–2 ps–1 per CNT input photons are required by photoexcitation. The small emitting area coupled with the high current-density–carrying capability in a CNT makes it possible to produce an ultra-bright nano–light emitter. For example, a 3-μA current in a partially suspended CNTFET generates about 107 photons nm–2 s–1.

How is the light generated in the supported/suspended CNT interface? Figure 1C shows a schematic band diagram of a partially suspended CNT with a gate biased to produce unipolar conduction. At the junction between the SiO2-supported part of the CNT and the part suspended over the trench, the decrease in dielectric constant (21) leads to a reduced capacitive coupling to the Si back gate. This process gives rise to a bending of the CNT bands, which, together with the source-drain field, generates a high local electric field Embedded Image and produces hot carriers. Thus, electrons injected into the conduction band are accelerated toward the source by the high field at the interface. If an electron can be accelerated to a sufficiently high energy and does not lose that energy by optical phonon scattering, it can create an exciton that can decay radiatively. The electron that lost energy to the generated exciton could, in turn, pick up energy from the field and continue this process. For an impact excitation process to occur, both energy and momentum need to be conserved. The threshold energy should be at least equal to the lowest exciton energy, and the need to conserve momentum typically increases the threshold energy by a factor of ∼1.5 (22). Exciton-band–mixing effects (10, 11) and interactions with the substrate can, however, relax the momentum conservation law, and the threshold energy can be as low as the exciton energy.

A rough estimate of the threshold electrical field Embedded Image needed for impact excitation is given by 1.5Egph, where Eg is the transition energy [optical band gap ∼0.56 eV for a 1.9-nm-diameter CNT (23)] and λph ≈ 10 to 20 nm is the optical phonon scattering length reported in CNTs (24, 25). Compared with 3D materials (22), the longer optical phonon scattering length implies a lower threshold field for the onset of impact excitation in 1D CNTs, whereas the larger exciton binding energy in 1D CNTs prevents e--h+ pairs from dissociating. These two factors make emission from impact excitation in 1D a more probable process than that in 3D materials. Indeed, Embedded Image for the 1D CNT is estimated to be ∼1.5Egph = 0.3 to 0.6 MV/cm, i.e., it is ∼7 times smaller than that in bulk materials with the same excitation energy (22).

The emission intensity generated by the high interface field Embedded Image should be proportional to the impact excitation rate (22), Embedded Image. The probability for an electron to travel without scattering a distance L is given by exp(L/λph). Therefore, the probability to accelerate an electron to energy Eth is Embedded Image, where e is the electron charge and where field Embedded Image has contributions from both the band-bending and the source-drain fields, Embedded Image and Embedded Image, respectively. Embedded Image can be estimated as ΔEcscr ∼[αsub(VgVth) – αsus(VgVth)]/λscr (26), where ΔEc is the band bending, αsub is the coupling between the gate and the substrate-supported CNT, αsus is the coupling between the gate and the suspended CNT, and λscr is the screening length (27). Embedded Image is the contribution from the source-drain field that accelerates the carriers, and can be written as ∼γVdscr, where γ is the fraction of the source-drain field that contributes to the SiO2 supported/suspended interface junction. The IR emission intensity of the radiatively recombining e--h+ pairs is proportional to the carrier impact excitation rate Embedded Image(1) Embedded Image

We first examine the dependence of emission intensity on the gate bias. Figure 2A shows the drain current of another suspended device and the corresponding IR emission intensity at 1.6 μm (within the E11 emission band) versus gate voltage Vg at drain biases of Vd = 6 and 7 V. IR emission occurs at a gate voltage overdrive of ∼2 V. The IR emission is localized at the supported/suspended interface (Fig. 2A, inset). The emission intensity indeed shows the dependence on the gate field predicted by Eq. 1 and can be fit for both drain biases, as shown by the solid curves in Fig. 2A. From the fitting, a γ of 0.05 is obtained at both drain biases. A band-bending of ∼0.4 eV at the peak of light emission can be estimated from electrostatics (27). Embedded Image in our device is estimated to be 0.01 to 0.2 MV/cm for the fields at the onset and the peak of light emission.

Fig. 2.

(A) Drain current (open circles and triangles) and emission intensity versus Vg at 1.6 μm of another partially suspended CNTFET at Vd = 6 V (open and solid circles) and Vd = 7 V (open and solid triangles). The solid curves are fits to the intensity versus gate bias according to Eq. 1. The inset shows E11 IR emission overlaid with an optical image of the partially suspended CNTFET. The length of the CNTFET channel is 28 μm, the width of the trench is 10 μm, and the CNT diameter is ∼2 nm. (B) Drain current (open circles and triangles) and emission intensity (solid circles and triangles) versus Vd at 1.6 μm of the same device at Vg = 0 V(open and solid circles) and Vg = 1 V (open and solid triangles). The solid curves are fits to the intensity with drain bias according to Eq. 1. (C) E11 exciton generation rate r11 as a function of electric field for the three zig-zag tubes with diameters d = 1.5 (red circles), 2.0 (blue squares), and 2.5 nm (green triangles). We define r11 as the generation rate of electron-hole pairs with energy below the second band, which is averaged over the nonequilibrium distribution (from the Boltzmann equation solution) and normalized per single carrier (18). The solid curves are the best fits to Embedded Image with the following threshold fields: Embedded Image, 0.22, and 0.14 MV/cm, respectively. The inset shows the diameter dependence of the threshold field and a power-law fit Embedded Image MV/cm (d in nm) for the zig-zag tubes with mod (n – m,3) = 1. mod (n – m,3) gives a remainder in the division of n – m by 3, where n and m are the chiral indices of a CNT. Zig-zag tubes with mod (n – m,3) = –1 have 15% smaller Embedded Image.

We now turn to the dependence of light emission on the source-drain field. Figure 2B shows the drain current Id and light emission at 1.6 μm versus drain bias Vd at constant gate biases of Vg = 0 and 1 V of the same device. Unlike CNTs on solid substrates (13), the following is true for suspended devices: (i) Approximately 6 times lower drain bias is sufficient under unipolar conduction to generate light emission, benefiting from the high local field generated by the band-bending at the suspended/supported CNT interface. (ii) The suspended devices show NDC in their IdVd characteristics. The appearance of NDC correlates with the observation of IR emission (Fig. 2B). At its onset, impact excitation is expected to generate nonemitting triplet excitons followed, at higher energy, by light-emitting singlet excitons (28). The observed NDC could be attributed to the momentum loss from impact excitation of excitons. In a gate scan where gate overdrive |VgVth| is a variable (Fig. 1C and Fig. 2A), the momentum loss from the charged carriers that have undergone impact excitation can be compensated by the increase in the carrier density caused by the increasing gate overdrive. Therefore, no further reduction of current is observed. The light-emission intensity shows a dependence on the drain field that is also in accord with Eq. 1 and can be fit for both gate biases as shown by the solid curves in Fig. 2B. By biasing the device at different gate overdrives with |VgVth| ≈ 2 and 1 V for Vg = 0 and 1 V, respectively, we find that indeed a higher drain field is necessary (ΔVd = +1 V) to compensate a lower gate overdrive (Δ|VgVth| ≈ –1 V) in order for impact excitation to take place.

To understand the voltage dependences of the light-emission intensity, we calculated the exciton generation rate as a function of the electric field by solving the Boltzmann equation in the presence of phonon and impact excitation scattering for the charge-carrier distribution function (18). The results of the calculations are shown in Fig. 2C for three CNTs with different diameters along with the best fit to Embedded Image predicted by the simple model. In agreement with experiment, impact excitation does not take place for fields below 0.02 to 0.03 MV/cm. The diameter dependence of the threshold field can be well approximated by a power law Embedded Image (Fig. 2C, inset), as a result of both the inversely proportional dependence between Eg and the CNT diameter d and the proportional dependence between λph and d. We calculate λph here as the ratio of the impact excitation threshold energy to the threshold field and find it in the range of 20 to 40 nm (for d =1.5 to 2.5 nm CNTs), in accord with previous studies (24, 25, 29).

The high local density of excitons produced at the suspended/supported CNT interface allows us to directly observe exciton-exciton interactions. Studies of the dynamics of excitation decay in photoexcited CNTs in micelles have shown a nonexponential, laser power–dependent decay, whose short time component was attributed to Auger quenching involving free carriers (3, 30) or exciton-annihilation processes (31, 32). In addition to the exciton-exciton interaction, direct generation of E22 excitons by hot carriers is possible in EL. By examining the evolution of the EL spectrum as a function of the gate voltage and from the results of our simulations, we conclude that E11 exciton-exciton annihilation is primarily responsible for the production of E22 excitons. Figure 3A shows the spectra of a partially suspended, 1.9-nm-diameter tube at various gate biases and a fixed Vd of –5 V. The strong emission peak at 0.56 eV corresponds very well with the lowest optically active transition of the CNT, E11, observed in PL experiments (23).

Fig. 3.

(A) Infrared emission spectra of a partially suspended CNTFET at various gate biases (–4.6, –4.2, –3.9, –2.9 V) that show E11 emission at ∼0.56 eV and E22 emission at ∼1 eV. (B) Integrated emission intensity of E11 versus that of E22. The solid curve is a fit of the data with E22E111.7. (C) Numbers of E22 excitons, n2, versus those of E11 excitons, n1, (red circles) from the solution of the master equation using decay-rate constants from the literature (18). The red solid curve is the best power-law fit n2 ∝ (n1 – 1)1.9. The blue curve shows the fraction of E22 excitons created by the exciton-exciton annihilation mechanism. The inset shows exciton generation rates of E22 excitons—r22 versus r11 (black circles). (r22 has the same definition as r11 except that the electron-hole pair energy is above the second band.) The solid black curve is the best power-law fit r22 = 0.157r111.5 (r is in ps–1) used in simulations of n2 and n1.

In the EL experiments, however, a weaker peak near 1 eV is also observed. The energy of the transition lies at the expected position of the second optically allowed transition, E22, of the CNT [with E11/E22 ∼1.8, also consistent with that of PL studies (23)]. The nature of the excitation mechanism of this state is revealed by examining the light emission intensity of E22 as a function of the intensity of E11 and the results of our simulations (18). Figure 3B shows that I(E22) ∝ I(E11)1.7. This nonlinear dependence alone cannot distinguish between a direct exciton-generation mechanism and a “bimolecular” exciton-exciton annihilation [E11 + E11E22 (+ phonons)] process. Indeed, the direct impact excitation rate of E22 also has a power-law dependence on E11 generation (Fig. 3C, inset). Further carrier-kinetics calculations using the master equation (18) indicate that the formation of E22 excitons is primarily caused by the annihilation of two E11 excitons. There is a negligible E22 exciton density until the exciton-exciton annihilation process becomes possible (Fig. 3C), which is consistent with the experimental data in Fig. 3A. The fraction of E22 excitons generated by the exciton-exciton annihilation mechanism gradually decreases with increasing field, from 100% to slightly above 80% for the typical fields achieved in our devices. From the master equation (18), we estimate that there are about eight E11 excitons at the intrananotube junction at a field of 0.15 MV/cm. The total exciton density (0.14 nm–1) is therefore about 100 times larger than what has been reported in typical PL experiments (32), making it possible to observe the “bimolecular” process. Such annihilation processes are widely observed in molecular crystals, polymers, and j-molecular aggregates (33), and apparently play a key role in the photo- and electroluminescence of CNTs.

Supporting Online Material

www.sciencemag.org/cgi/content/full/310/5751/1171/DC1

Materials and Methods

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