NANO LETTERS
Gate-Variable Light Absorption and Emission in a Semiconducting Carbon Nanotube
2009 Vol. 9, No. 10 3477-3481
Mathias Steiner, Marcus Freitag, Vasili Perebeinos, Anton Naumov,† Joshua P. Small, Ageeth A. Bol, and Phaedon Avouris* IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598 Received May 27, 2009; Revised Manuscript Received July 15, 2009
ABSTRACT We investigate the gate field dependence of light absorption and emission of an individual, suspended semiconducting carbon nanotube using Raman and photoluminescence spectroscopies. We find a strong reduction in the absorption strength and a red shift of the E33 state of the nanotube with increasing gate field. The photoluminescence from the E11 state is quenched even stronger. We explain these observations in terms of field-doping and its effects on both the radiative and nonradiative decay rates of the excitons. Thus, gate field-induced doping constitutes an effective means of controlling the optical properties of carbon nanotube devices.
Semiconducting single-walled carbon nanotubes (CNTs) hold great promise for applications in nano-optoelectronics.1 Incorporated as active channels of field-effect transistors,2,3 they can emit4 and absorb light5 and sustain high electrical currents even at extreme temperatures.6 Excitons with binding energies of up to several hundred meV dominate the optical spectra of CNT7-11 and the dependence of the absorption and emission properties of CNTs on external electric fields has been the focus of experimental and theoretical investigations.12-18 However, a comprehensive experimental study of the gate field dependence of absorption and emission in a single CNT is lacking. In this letter, we report the gate field dependence of excitons in a suspended CNT that acts as the active channel of a field-effect transistor. Specifically, we combine Raman excitation and photoluminescence (PL) spectroscopy in order to differentiate between optical absorption into the E33-state and the luminescence emission from the E11-state as we tune the gate voltage. In Figure 1a, we show a schematic of the CNT field-effect transistor investigated in our experiments. A spatially isolated CNT was grown by a CVD-method similar to reference19 across a trench (width, 1 µm; depth, 750 nm) in a SiO2layer (thickness, 1 µm) on top of a Si-wafer. Both ends of the CNT were covered by metal contacts close to the edges of the trench. Hence, transversal electric fields could be generated by applying a voltage VG between the source/drain * To whom correspondence should be addressed. E-mail: avouris@ us.ibm.com. † Permanent Address: Applied Physics Program, Rice University, Houston, Texas 77005. 10.1021/nl9016804 CCC: $40.75 Published on Web 07/28/2009
2009 American Chemical Society
electrodes and the Si-gate. Zero voltage is applied between source and drain electrodes, and as a result there is no electrical transport along the CNT. Hence, a current-induced self-heating of the CNT as reported in ref 6 is precluded. From the frequency of the radial breathing mode in the measured Raman spectrum (see Figure 1b), ΩRBM ) 162 cm-1, we determine the CNT diameter using dt ) 227/ΩRBM ) 1.4 nm,20 a relation that has been established for freestanding, pristine single-wall carbon natubes. According to the (Eii-dt) and (Eii-ΩRBM) relations (Kataura-Plots) in references 21 and 22, we resonantly excite the E33-level of a semiconducting nanotube energetically located near 2.2 eV. A fast internal conversion of E33-energy populates the lowestlying E11-state in the CNT that we observe through its strong PL band located in the near-infrared (see Figure 1c, peak energy, 0.68 eV; width, 20 meV). Details regarding experimental setup and methods can be found in.23 Raman excitation spectroscopy has been used to map electronic states in CNTs on the single nanotube level.23-26 In this method, the Raman scattering intensity of a specific phonon mode such as, for example, the radial breathing mode (RBM), is recorded as a function of the laser excitation energy. Because of the electronic resonance enhancement provided by an Eii-state in the CNT, the Raman scattering intensities can vary by several orders of magnitude, depending on the detuning between the excitation laser and the Eiistate.27,28 We can use the Raman excitation method to probe the optical absorption of a specific Eii-state, for example the E33, in a single CNT as a function of the gate voltage. The square root of the integrated intensity of the resonanceRaman excitation spectrum provides a measure of the change
Figure 2. (a,b) Gate voltage (VG) dependence of the resonanceRaman excitation spectrum (RBM, Stokes transition) of the semiconducting carbon nanotube that reveals the E33-exciton. (Inset) The doping level F in the carbon nanotube as a function of VG is estimated based on eq 2. Figure 1. (a) Schematic of the carbon nanotube field-effect transistor and scanning electron microscopy image of the device with the carbon nanotube suspended across a trench in the SiO2substrate and contacted by metallic source (S) and drain (D) electrodes. The Si-layer acts as the (back) gate. (b) Raman spectrum of the carbon nanotube excited at λlaser ) 566.7 nm. From the frequency of the RBM, the diameter of the nanotube is determined to be dt ) 1.4 nm. (c) E11-photoluminescence spectrum (PL; peak energy, 0.68 eV; width, 20 meV) of the carbon nanotube excited at λlaser ) 514.5 nm.
of the oscillator strength f33 associated with the optical transition and, hence, of the optical absorption σ33 of the E33-level σ33 ∝ f33 ∝ |〈Ψ33 |pˆ |GS〉| 2 ∝
(∫
1/2 IStokes(Elaser)dElaser E33 RBM
)
if M33, γ33 ) const
(1)
Here, |GS〉 and |Ψ33〉 denote the excitonic levels involved in the optical transition with energy E33, pˆ is the transition Stokes dipole operator, and IRBM (Elaser) is the laser-energy-dependent resonance-Raman RBM Stokes intensity. Note that the proportionality in eq 1 holds only if the exciton-phononcoupling M33 and the resonance width γ33 of the E33-state are not significantly modified by external electric fields, a reasonable assumption for gate fields of the order of a few volts per micrometer. In Figure 2a,b, we show resonance-Raman excitation spectra that have been measured by tuning the laser energy across the E33-resonance of the CNT and integrating the 3478
RBM Stokes scattering intensities. The G-band Raman intensities reflect the same dependence, despite the much broader resonance window due to the larger phonon energy. Each excitation spectrum corresponds to a specific value of the gate voltage VG. Apparently the total intensity of the resonance-Raman spectrum decreases sharply as |VG| increases. In addition, we observe a pronounced red shift of the spectral peak position of the resonance-Raman excitation spectrum as a function of |VG|. The width γ33 of the E33 does not change as a function of |VG| within the experimental resolution. From the spectra shown in Figure 2a,b, we extract γ33 values around 38 meV that are in excellent agreement with experimental and theoretical values reported recently.6 In Figure 3a we plot the integrated scattering intensities of the resonance-Raman excitation spectra shown in Figure 2 and, therefore, the absorption σ33 as a function of the gate voltage (see eq 1). We observe a symmetric decrease of the integrated Raman intensity and σ33, respectively, for positive and negative gate voltage polarities. At |VG| ) 4 V, σ33 has decreased from its original value by a factor of 3 ≈ 1.7. In Figure 3b, we plot the spectral peak positions of the E33 as a function of |VG|. We obtain a nonlinear gate voltage dependence with a maximum red shift of 20 meV. In principle, strain in the CNT could be responsible for the observed gate voltage dependence of the E33-level.29 However, for gate voltages as high as 4 V, the measured softening of the G-band of ∆Ω G e -0.5 cm-1 is too small to support this interpretation.30,31 Another possible explanaNano Lett., Vol. 9, No. 10, 2009
Figure 3. (a) Integrated resonance-Raman scattering (RRS) intensities and absorption, respectively, of the E33-state and (b) E33 peak energies as a function of the gate voltage. The data has been extracted from the resonance-Raman spectra shown in Figure 2a,b.
tion is a dc Stark-shift. Theoretical estimates based on ref 16 however suggest that the shift would be 1 order of magnitude smaller than that observed in our experiments. Finally, electrostatic doping by the gate field could be responsible for both the decreasing absorption (oscillator strength) and the red shift of the E33-exciton. We determine the doping level F in the CNT as a function of the gate voltage including the quantum capacitance effect by using VG ) (EF/e) + (F/CG).32 Here, EF ) ∆ + (p2VF2kF2/2∆) is the Fermi energy, ∆(≈0.42 eV/dt) is one-half of the single particle band gap energy, VF ) 106 m/s is the Fermi velocity in graphene and kF ) πF/4 is the Fermi wave vector. We estimate the electrostatic gate capacitance CG as CG ) 2πε0ε/ln(4t/dt) ) 0.07 pF/cm
(2)
Here, ε0 is the vacuum dielectric constant, ε ) 1 is the dielectric constant of air, t ) 1000 nm is the thickness of the gate dielectric and dt ) 1.4 nm. In this way, we obtain a maximum charge carrier density of |Fmax| ) 0.16e/nm at |VG| ) 4 V (see inset of Figure 2b). It is expected that the screening of the Coulomb interaction in the CNT would increase with the doping level and would lead to both a renormalization of the band gap and a reduction of the exciton binding energy.1 We assign, therefore, the observed red shift of the E33 transition and the reduction of the absorption (oscillator strength) to the increase of the doping level in the CNT. We want to emphasize that the gate field effect on the Raman scattering intensities in a semiconducting carbon nanotube depends strongly on the detuning between the Nano Lett., Vol. 9, No. 10, 2009
Figure 4. (a) Integrated E11-photoluminescence (PL) intensity plotted as a function of the gate voltage VG. The numbers at the position of the data points (1-11) indicate the sequence of the measurement. The red solid line is a fit based on eq 4. (b) Schematic indicating the filling of the first band (gray area) of the carbon nanotube upon electrostatic doping induced by the gate field (EF, Fermi-energy; ∆1(2), bottom of the first (second) continuum band).
excitation laser and the excitonic resonances. If the excitation laser is tuned away from an excitonic resonance, the modulation of the Raman scattering intensity as a function of the gate field is indeed weak.33 If the laser is tuned on resonance with an excitonic level, however, the measured Raman scattering intensities for both RBM and G-band can vary by more than a factor of 5, as a result of both damping and red shift of the resonance (see Figure 2). Experimental results obtained with electrochemical gating techniques also show that the resonance-Raman scattering intensities of carbon nanotubes decrease as the gate voltage increases.13,34-36 In general, optically excited light emission in CNT is unlikely to occur from high-energy excited states like the E33. This is because of the very efficient, nonradiative relaxation pathways that operate in CNTs, allowing fast nonradiative excited state decay into lower-lying exciton states; see ref 37 and references therein. However, the lowest-lying E11-state offers a luminescence quantum yield of up to a few percent,38-40 enabling PL spectroscopy on the single nanotube level.41,42 In Figure 4a, we plot the integrated E11-PL intensity of the CNT as a function of the gate voltage (for PL spectrum see Figure 1c). As |VG| increases, the integrated PL intensity decreases substantially. By tuning the gate voltage up to |VG| ) 4 V, we observe PL intensity reductions by factors of up to 35. Because of the strong drop of the PL intensity and the associated decrease of the signal-to-noise ratio in the experimental data, we are not able to determine possible shifts of the E11-state as a function of the gate field. 3479
It has been recognized that the PL intensity of CNTs is modified when longitudinal or transversal dc fields are applied.14,17 The gate voltage dependence of the PL intensity shown in Figure 4a could be caused by the following three contributions: (1) the reduction of the optical absorption of the E33-level (see Figure 3a), (2) the shift of the E33-level (see Figure 3b), and (3) the lowering of the E11-PL quantum yield Q ) kr/(kr + knr), where kr,nr are the radiative and nonradiative E11-exciton recombination rates. The contributions (1) and (2) should have a minor influence on our PL experiments since we tuned the laser excitation energy away from the E33-resonance (to Elaser ) 2.4 eV). From the Raman data, we estimate that the gate-induced change of absorption into the E33-level does not exceed a factor of 2 in the present case. Therefore, we will discuss the observed gate voltage dependence of the PL intensity in terms of modifications of the radiative and the nonradiative E11-exciton recombination rates caused by the varying charge carrier densities in the CNT (contribution (3)). Doping has already been identified as causing quenching of the PL intensity in aqueous CNT suspensions and CNT transistors.43 In our analysis of the nonradiative decay contribution, we focus on an Auger-type E11-exciton quenching mechanism that involves the emission of an optical phonon, such that knr ∝ F.37 We associate the reduction of the radiative E11 decay rate kr on the other hand with (a) the loss of the E11 oscillator strength due to exciton screening and (b) the filling of the conduction (valence) band upon electrostatic doping, as indicated schematically in Figure 4b. We assume now that the loss of the E11 oscillator strength due to exciton screening can be captured adequately by a linearF-dependency and discuss in the following, how the band filling affects the exciton oscillator strength. In doped CNTs, unoccupied states in the valence band (or occupied states in the conduction band) cannot contribute to the two-particle exciton wave function Ψ ) ∑k>kFakφckφvk . Here, φck and φvk are the free particle states in the conduction and valence band, respectively. The exciton oscillator strength fexciton is associated with the coefficients ak in the exciton wave function, which can be derived from the BetheSalpeter equation; for examples, see refs 8 and 9. Importantly, fexciton is proportional to the oscillator strength associated with the free particle band-to-band transitions ffree, that is, fexciton ) ηffree. The proportionality coefficient η ) η(ε,F) depends on the strength of the Coulomb interaction9 and on the doping level itself, because doping modifies the kinetic energy of the exciton. In other words, if a band involved in the transition is filled completely, it cannot contribute to the twoparticle superposition described by the Bethe-Salpeter equation and, hence, the associated exciton oscillator strength is zero. We approximate the effect associated with filling of the van-Hove singularity by using the phase space argument, that is, by assuming that the dipole matrix element does not depend on energy δffree ∝
∫
EF
∆
dE(E2-∆2)-1/2 ) ln(EF /∆ + √EF2 /∆2 - 1) (3)
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For moderate doping levels, this leads to δffree ∝ F and at |VG| ) 4 V(|Fmax| ) 0.16 e/nm), we obtain a Fermi-level shift of 11 meV. Filling the first band up to the bottom of the second band (from ∆1 to ∆2 in Figure 4b) requires the charge carrier density F ) 43∆/πpVF ≈ 1.0 e/nm. Even for the highest doping level in our experiments, the first band cannot be filled completely and higher states hence are not affected. We note that the band filling affects both radiative and nonradiative E11-decay contributions. On the basis of the previous discussion, we model the gate dependence of the integrated E11-PL intensity according to IPL ∝
kr kr0(1 - aVG) ) 0 knr knr(1 + bVG)
(4)
0 are the unknown radiative and nonradiative E11 Here, kr,nr recombination rates at |VG| ) 0 and their ratio enters as a fit parameter. From the best fit shown in Figure 4a, we obtain the linear coefficients a ) 0.2 ( 0.04 V-1 and b ) 0.5 ( 0.2 V-1. Note, that the coefficients a, b in the model function eq 4 are not independent and that their sum accounts for the total drop of the integrated PL intensity (factor of 15). As a result, it is not possible to extract the gate-induced changes in kr,nr independently. For example, the initial radiative E11decay rate k0r drops by a factor of 5 or, in other words, δfexciton/ fexciton ) 4/5, at |VG| ) 4 V as a result of both band filling and exciton screening. Under the same conditions, the initial nonradiative E11-decay rate k0nr increases by a factor of 3 due to Auger-type quenching. All in all, the fit then represents a 5 × 3 ) 15-fold reduction of the integrated PL intensity at |VG| ) 4 V (or |Fmax| ) 0.16 e/nm) as compared to the initial PL intensity at |VG| ) 0 V (or |Fmin| ) 0). Finally, we discuss how both the band filling and the exciton screening would contribute to the 5-fold reduction of the radiative E11-decay rate kr0. According to eq 3, the band filling due to |Fmax| ) 0.16 e/nm causes a loss of oscillator strength of the order of δffree/ffree ≈ 0.21at |VG| ) 4 V. The loss of δfexciton due to the screening effect is of the order of δη/η ≈ 0.75. This is consistent with the measured loss of oscillator strength (absorption) of the E33-state (factor of 0.5 at |VG| ) 4 V, see Figure 3a). In our experiments, we found that there are hysteretic effects that limit the reproducibility of the PL quenching induced by the gate field and, hence, the reversibility of the gate control of the PL intensity. As a result, the slopes obtained for successive measurement series (compare, for example, the slope associated with either the data set 1, 2, 3 or data set 6, 7, 8 in Figure 2a) are subject to variations that are beyond the present experimental control. In summary, we found that both absorption and emission of light by excitonic states in a CNT can be quenched if a gate field of arbitrary polarity is applied. The loss of oscillator strength of both E33 and E11 excitons is due to screening by gate-induced charge carriers on the CNT and, in the case of the E11, additionally due to the filling of the free-particle bands. The electrostatic doping decreases the radiative decay rate of the E11 and at the same time increases the nonradiative
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