3314
J. Phys. Chem. C 2007, 111, 3314-3321
Frequency-Modulated, Single-Molecule Absorption Detected by Scanning Tunneling Microscopy Erin S. Carmichael,†,‡ Joshua B. Ballard,†,# Joseph W. Lyding,†,§ and Martin Gruebele*,†,‡,⊥ Beckman Institute of AdVanced Science and Technology, Department of Chemistry, Department of Electrical and Computer Engineering, Department of Physics, UniVersity of Illinois, Urbana, Illinois 61801 ReceiVed: NoVember 2, 2006; In Final Form: December 5, 2006
We image frequency-modulated single-molecule optical absorption using a scanning tunneling microscope as the detector (SMA-STM). As a first example of the technique, a semiconducting carbon nanotube adsorbed on a silicon surface is studied. Excitation is achieved using laser amplitude as well as frequency modulation, and these two complementary approaches are compared. Detection is achieved via the resulting change in tunneling current through the excited molecule. We distinguish three mechanisms, direct, relaxed, and bolometric, for detecting single-molecule absorption spectra. Kinetic models for these mechanisms as well as for surface heating are presented. The latter effect can be eliminated by frequency modulation, keeping the laser power density on the surface constant.
1. Introduction
2. Single-Molecule Absorption Mechanism
Single-molecule absorption spectroscopy has the advantage of universality over single-molecule fluorescence. Optical absorption occurs even when fluorescence is quenched by fast, nonradiative processes. We recently reported laser absorption by a single carbon nanotube deposited on a passivated silicon surface using scanning tunneling microscopy to detect absorption-induced changes in the tunneling current at the tipmolecule-surface junction.1 Coupling optical excitation with scanning tunneling microscopy is difficult because of the side effects of laser-illuminating a junction and surface.2,3 A combination of two techniques was required to minimize undesirable background signals from heating, lateral tip drift, or tip-surface electronic excitation. Coupling radiation through the back of a transparent substrate minimizes spurious heating and molecule-substrate relaxation processes. Modulating the laser at a frequency higher than the scan rate yields a difference image of the absorption process concurrently with the topography image, eliminating drift problems and greatly increasing sensitivity. In our previous study of single-molecule absorption, we used amplitude modulation of the laser in a total internal reflection geometry to detect tunneling current modulation with a lock-in amplifier and, hence, molecular absorption.1 Although rear illumination reduces the potential for heating-induced signals, amplitude modulation results in modulated tip or substrate heating or excitation not related to molecular absorption. Here, we introduce frequency modulation4 combined with rear illumination as a tool for differentiating the absorption signal unambiguously. We present data on isolated carbon nanotubes5 adsorbed onto a passivated silicon surface, simulations of the excitation and detection process, and general mechanisms for single-molecule absorption spectroscopy on surfaces.
Molecular absorption is usually detected indirectly by attenuation of light transmitted through a sample. For a thin sample, the absorption signal should be proportional to RI, the product of absorption coefficient and incident intensity. In contrast, bolometric experiments detect absorption directly by placing a calorimetric detector in the path of an optically excited molecular beam.6 Single-molecule absorption scanning tunneling microscopy (SMA-STM) relies on mechanisms ranging from direct detection of excited molecular electron density to bolometry to yield a signal linear in the absorption coefficient at sufficiently low laser power. Figure 1 illustrates the geometry and energetics of our experiment. We chose ≈1-nm-diameter carbon nanotubes deposited on a passivated Si(100) surface as convenient test molecules for our technique. These tubes are easy to identify by STM and absorb ≈1250 nm laser light, allowing excitation within the substrate band gap.7 A frequency- or amplitudemodulated laser beam is focused through a wedge in the back of the substrate, allowing total internal reflection at the front surface. The evanescent wave penetrates ∼λ/2 into the vacuum of the surface-molecule-tip junction, reducing tip-laser overlap, but still allowing the nanotube to absorb the polarization component of the wave along the tube axis.8 It has been shown that tip-dependent enhancement of the electric field by f ≈ 5001000 occurs at such junctions.9 Efficient absorption of radiation by the molecule at the junction is detected by a change in tunneling current at the laser modulation frequency. A substrate transparent at the molecular absorption frequency is key to success not only by reducing tip heating, but also by reducing energy relaxation into the surface. As shown in Figure 1, there is no direct electronic mechanism for transfer of the molecular excitation (the E11 electronic transition of the nanotube) to the substrate because the band gap of the silicon exceeds the optical excitation energy. A phonon-assisted process is required for energy dissipation. This situation is very different from excitation on metal surfaces, which readily couple to adsorbates through their zero band gap,10 or from visible laser excitation well above the band gap of a semiconductor
* Corresponding author. E-mail:
[email protected]. † Beckman Institute of Advanced Science and Technology. ‡ Department of Chemistry. § Department of Electrical and Computer Engineering. ⊥ Department of Physics. # Current address: NOAA, Boulder, CO.
10.1021/jp067237n CCC: $37.00 © 2007 American Chemical Society Published on Web 01/18/2007
FM SMA Detected by STM
J. Phys. Chem. C, Vol. 111, No. 8, 2007 3315
Figure 1. Left: Schematic diagram of the tip-molecule-surface junction on logarithmic horizontal and vertical scales. The enhanced optical field is shaded red. Right: Band structure of p-Si (dashed line) and van Hove band structure for a semiconducting carbon nanotube of the type investigated here (solid line); optical transitions are indicated by arrows. By exciting the E11 transition of a sufficiently large diameter carbon nanotube, energy or charge transfer to the larger silicon band gap can be reduced. Inset: I-V curve for the nanotube in Figure 2 and p-doped Si background showing the smaller band gap of the nanotube required to avoid bulk absorption.
substrate,11 or from tunneling observed in the absence of optical excitation when sufficiently large bias voltages are applied to the molecule. Once a single molecule has absorbed a photon, three mechanisms affecting the tunneling current can be distinguished. In the direct mechanism, the intramolecular relaxation rate (kIVR) and molecule-substrate relaxation rate (kms) are small compared to the Rabi frequency. The resulting saturation of the molecular excitation alters the local electronic density of states, permitting direct imaging of the altered electronic density. In the relaxed mechanism, kIVR is large. This case is important for molecules whose fluorescence quantum yield is small. Absorbed energy equilibrates rapidly within the molecule by radiationless transition or by intramolecular vibrational energy redistribution (IVR). The resulting change in local density of states does not reflect the originally excited molecular electron density distribution but still directly monitors the absorption process. In the bolometric mechanism, both kms and kIVR are large. Local heating of the substrate or tip occurs, and mechanical distortions are detected. The latter process has been observed in thin absorbing films.12 One might expect distortions of the molecular image from a bolometric process, making it less desirable as a detection mechanism. Our current experiments will be explained by a combination of the first two mechanisms. Signals unrelated to direct molecular absorption include direct heating-induced modulation of the tip or surface position13 and optical excitation of tip or substrate electrons, followed by nonradiative processes, such as formation of an anionic radical state after injection of a tip electron into the molecule.11,14 The narrow-band frequency-modulation (FM) scheme described here, coupled with rear illumination, is designed to eliminate such processes. The best vertical resolution of an STM is 0.01 nm. To observe an SMA-STM signal, the laser radiation must be capable of driving the molecular absorption transition within 2 orders of magnitude of saturation. Otherwise, the alteration of the local density of states in the excited state is too small for detection because of noise in the tip z-position and in the electronic measurement system. For a transition whose homogeneous
lifetime is limited by a relaxation process with lifetime τr, the saturation intensity is given by6
IS )
2x2hc ≈ 100-400 mW/cm2 f 2πτrλ3
(1)
The numerical value is obtained for a nanotube whose fluorescence lifetime is reduced from 100 ps to τr ) 100 fs by a nonradiative homogeneous (Lorentzian) broadening process (quantum yield φ ) 10-3) at an excitation wavelength of 1250 nm.15-17 The tip-field enhancement f ≈ 500-1000 of the evanescent wave is critical for approaching the saturation intensity with a beam of a few milliwatts focused to a 100-µm spot size. 3. Experimental Data Experiments were conducted with a home-built ultrahighvacuum (UHV) STM (≈10-11 Torr) similar to ones previously reported.18 A 15° polished wedge was machined into the rear face of a p-doped (3 × 1018 cm-3 boron) Si(100) wafer to allow for total internal reflection. Upon introduction to the UHV chamber, the sample was hydrogen-passivated to form a (2 × 1)-H surface reconstruction. STM tips were made from electrochemically etched tungsten. The sample was stamped in situ with HiPco-produced single-walled carbon nanotubes19 via the dry-contact transfer technique.20 The tube we discuss in detail was chosen so that its absorption edge lies in the frequency modulation range of our laser. To achieve frequency modulation with variable amplitude modulation, two diode lasers operating at different frequencies were amplitude-modulated with 1.2 kHz, 180° out-of-phase square waves (see Modeling Section and Figure 5B). The beam profiles were overlapped on a dielectric beamsplitter and focused by a 30-cm-focal-length lens to a 100-µm-diameter spot on the wedge in the back of the substrate. A flip-in mirror and a translatable razor blade were used to obtain exact overlap on the sample. In the experiment discussed below, the wavelengths are 1255 and 1243 nm. The 1255-nm laser is always modulated
3316 J. Phys. Chem. C, Vol. 111, No. 8, 2007
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Figure 3. SMA cross sections (arbitrary units) of the nanotube in Figure 2 at four modulation depths of the 1243-nm laser (0-39, 67, 117, and 161 mW/cm2) relative to the nearby Si background. The 1255nm modulation was a constant 0-150 mW/cm2.
Figure 2. STM and SMA-STM images. The 1255-nm laser is modulated from 0 to 150 mW/cm2 in all images. The sample bias is -2.5 V at a 0.05-nA tunneling current. A: Single topographic scan of a 1.03-nm-diameter semiconducting carbon nanotube under laser illumination; dimer rows and individual dangling bonds are resolved. B: Same image with analysis areas color coded (black grid/box, nanotube cross sections/sampled area; red boxes, near-nanotube background; green boxes, selected far backgrounds with numbers matching inset in Figure 4; white ovals, optically undetectable dangling bonds; yellow ovals, dangling bonds associated with optically detectable defects defects). C: SMA signal of the same region, with 1243-nm square wave modulation from 0 to 39 mW/cm2. The dark signal indicates less absorption at 1243 nm than at 1255 nm. D: SMA signal with 1243-nm square wave modulation from 0 to 181 mW/cm2. The light signal indicates a small excess absorption at 1243 nm, as compared to 1255 nm. Inset A: 1.18-nm tube topography scan. Inset B: 1.18nm tube off-resonant SMA scan; only edge noise is visible in the signal, as discussed in ref 1.
from 0 to 150 mW/cm2. The modulation depth of the 1243-nm laser varies from 0 to 180 mW/cm2 and is 180° out of phase. Overall power density is constant when both lasers are modulated to 150 mW/cm2. The tunneling current was measured by a current-voltage amplifier and used in the usual way to obtain topography and current images. At the same time, the current fluctuations induced by the laser modulation were detected by a lock-in amplifier (LIA). The lock-in reference signal was in-phase with the 1243-nm laser. This results in a dark (out of phase) signal when the tunneling current increases during the 1255-nm portion of the excitation and a bright (in-phase) LIA signal when the tunneling current increases during 1243-nm excitation. Images were taken in constant average current mode (0.05 nA, -2.5 V sample bias), simultaneously saving the topography, feedback current, and lock-in amplifier outputs for each scan. Figure 2A shows a topography image of a carbon nanotube with a diameter of 1.03 nm. The diameter was determined from the height profile at constant tunneling current. On the basis of height profiles calibrated using a semiconducting nanotube of known (m, n) from atomic resolution images,21 and on the basis of errors caused by tip shape effects,22 we expect that our measured diameter can be compared to geometrical diameters within (0.1 nm.23 The tube has a defect near the lower end; however, measured diameters and I-V curves of both segments are identical within measurement uncertainty. Figure 2B shows
the same topography with a number of regions highlighted where SMA-STM images were analyzed. Parts C and D of Figure 2 show SMA-STM images obtained at a constant 0-150 mW/cm2 modulation of the 1255-nm laser. The 1243-nm laser was modulated 0-39 mW/cm2 (3C), or 0-181 mW/cm2 (3D). As shown in parts C and D of Figure 2, the phase of the more strongly modulated laser determines the sign of the SMA-STM signal. In part C, the in-phase laser is modulated to a lower power density, so the SMA-STM signal is negative (dark). In part D, the in-phase laser is modulated to a higher power density, so the SMA-STM signal detected by the lock-in is positive (bright). In both differential absorption images, there is noise superimposed on the signal. The source of random phase noise, especially near the edges of the nanotube, has been analyzed quantitatively in ref 1. The noise is due to vertical tip position fluctuations coupled to the scan direction. Such fluctuations have a broad noise spectrum, part of which falls within the narrow (-6dB/octave) detection bandwidth of the lock-in amplifier. Our single-molecule absorption model, discussed qualitatively in Section 2 and quantitatively in Section 4, makes straightforward predictions for the signal phase and amplitude as a function of laser modulation depth. These are tested in Figures 3 and 4. In one limit, one laser is off, and the other laser is fully modulated from power density 0 to I. This corresponds to pure AM modulation, which yields the largest signal, but also the greatest potential of contamination from modulated laserinduced heating or photocarrier generation. When both lasers are on, two laser power density combinations are of particular interest,
I1243 ) I1255 and
I1243R1243 ) I1255R1255
(2)
Here, R is the molecular absorption coefficient. The first case is perfect FM modulation, in which the surface is exposed to a constant power density when one laser turns off and the other laser turns on (Figure 5B). In the second case, the linear absorption signal cancels because the same change in density of states is induced upon excitation of a homogeneous profile at both wavelengths (an indication of the direct absorption mechanism).
FM SMA Detected by STM
Figure 4. A: Lock-in signals as a function of 1243-nm laser power density (1255-nm laser modulated to 150 mW/cm2). The carbon nanotube signal (black) changes much faster than the background signal (red dashed, taken from red dashed boxes in Figure 2B) between 30 and 160 mW/cm2. Below 30 mW/cm2, both signals turn around perhaps due to a heating contribution in the amplitude modulation limit. The inset compares the tube and several background signals on both sides of the nanotube (dashed boxes in Figure 2B, numbered in same way). The background signal shows little variation as a function of distance from the tube. B: Nanotube-background difference signal. The points where the net lock-in absorption signal cancels (where I1R1 ) I2R2) and where the laser power densities are equal (minimal heating effect) are indicated by vertical dashed lines.
Figure 3 shows SMA-STM signals as the 1243-nm laser power density is scanned. These signals are averaged over cross sections of the nanotube, shown as a black grid in Figure 2B. As discussed above, the signal changes phase from negative to positive with increasing I1243 power density. This phase flip occurs not when differential heating is minimized (I1243 ) I1255 ) 150 mW/cm2), but when I1243 ) 90 mW/cm2. In this case, the net absorption signal is nulled, and the ratio of molecular absorption coefficients can be determined (R1243/R1255 ≈ 1.7 ( 0.1). The situation is summarized in Figure 4B, which was obtained by subtracting the background signal from the signal on the carbon nanotube in Figure 4A. The background signal shows a much smaller variation with laser power density than the nanotube signal, and its electronic offset and laser-dependent heating contribution can be removed by subtraction, yielding a monotonic change in SMA signal with laser power. Modulated heating is completely eliminated when both lasers are equally modulated (150 mW/cm2), at which point we still see a positive absorption signal on the nanotube. To exclude the possibility of a bolometric mechanism, we examined the background signal at various distances from the nanotube (numbered dashed boxes in Figure 2B). We found little difference in the background signals collected at different distances from the tube, as indicated in the inset in Figure 4A. Similar results were obtained for other tubes, even in the AM limit. Finally, we investigated the signal of dangling bonds, larger surface defects (white and yellow circles in Figure 2B), and
J. Phys. Chem. C, Vol. 111, No. 8, 2007 3317 nonresonant nanotubes. The net signal of most dangling bonds in Figure 3C is within the noise level. The noise is explained in terms of the scanning behavior of the tip at sharp edges, as modeled in detail in ref 1; however, a small amount of absorption by dangling bonds cannot be excluded. A few defects show SMA-STM beyond the noise level (yellow circles in Figure 2D). That signal could be due to dopant-enhanced dangling bond absorption or paired dangling bonds with broader absorption spectra.24 Vertical tip position fluctuations also occur at the edges of nanotubes, even when the laser is off, and they should not be mistaken for absorption signals. An example of an off-resonant, nonabsorbing nanotube is shown in the insets of Figure 2. The tube’s 1.18-nm diameter yields a band edge below our excitation wavelengths (1243 nm modulated to 117 mW/cm2 and 1255 nm modulated to 150 mW/cm2 in the insets). The edge noise is still present, but no net signal is detected on the body of the tube relative to the background. Other examples of resonant and off-resonant tube signals and an accurate model calculation for the edge noise are found in ref 1. Modeling. Steady-State, Three-State Model. We modeled the modulated absorption scheme using two kinetic schemes. The first of these is designed to address the basic question of whether we are monitoring the excited state or the relaxed excited state. Consider the simplified three-level kinetic scheme where A and
B are Einstein coefficients, |0> is the electronic ground state, |1> is the first excited state, and |2> is the ensemble of intramolecular relaxed states. kIVR is the nonradiative intramolecular relaxation rate, and kms is the molecule-surface relaxation rate. The state |0> thus stands for the ground state of the molecule with or without surface heating, so the model cannot be used to analyze the bolometric detection mechanism, which we rule out by other means. For simplicity, modulation of the laser power or wavelength is not considered. Steady-state solutions for the three first-order differential equations describing the populations in the above scheme (3) are
B01ILaser/c n1 ) n0 B01ILaser/c + A + kIVR and
n2 kIVR ) n1 kms
(4)
If the molecule-surface relaxation rate is slow compared to the intramolecular relaxation rate (i.e., no localized heating of the surface around the molecule occurs), the relaxed population, n2, builds up. At high laser power, the unrelaxed excited-state population, n1, is nearly the same as the ground state population, and the signal results from a 50:50 average of the ground and excited molecular electronic state densities. For a process with small quantum yield (A , kIVR), B01ILaser e kIV still results in a substantial signal, but the signal contains contributions from the excited, relaxed, and ground state molecular electron densities. If B01ILaser , kms, no significant signal is observed by the direct or relaxed mechanisms.
3318 J. Phys. Chem. C, Vol. 111, No. 8, 2007
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Figure 5. Simulation of background and on-tube STM current signals leading to the observed SMA signal. A: Measured slow part of the tip response under laser illumination. Back illumination reduces the drift. B: AM (50-150 mW/cm2)/FM (∆λ ) 10 nm) laser modulation of the junction. C: Heating-induced expansion near t ) 0 and after equilibration. D: LDOS modulation induced by the laser. E: Tip feedback signal, including SMA and heating component. F: Laser-modulated tunneling current. By equalizing the laser powers in B, heating and tip-surface charge-transfer effects in the tunneling current (small slopes after initial decay) can be canceled out.
The data summarized in Figures 2-4, according to eq 1, was obtained in a laser power regime in which both the excited state and the relaxed excited state can contribute. Indeed, the net SMA-STM signal in Figure 4B is seen to saturate in the limit of pure AM modulation from 0 to 150 mW/cm2. The surface heating contribution at >120 mW/cm2 net power density modulation (below 30 mW of the 1243-nm laser in Figure 4A) has the opposite sign and occurs on the background as well as on the tube. Time-Dependent Tunneling Model. To model the timedependent signals shown in Figure 5, we turn to the tunneling model of Tersoff and Hamann.25 The current at the STM junction can be expressed as
I(z, t) ) I0Frel(t)e -κ[z-z0(t)]
(5)
Here, z is the piezo position set by feedback, z0 is the vertical substrate position set by heating, and Frel is the unitless relative local density of states. I0 is a constant that incorporates tip geometry effects, the tunneling voltage dependence, and a baseline density of states. κ ) [mφ/2p]1/2 is the vacuum tunneling distance as a function of carrier mass, m, and effective work function, φ. In constant current mode, the piezo adjusts z with a feedback bandwidth of ≈3 kHz in response to current changes. In our model, the laser modulates the tunneling current in two ways. Upon laser absorption by the molecule, Frel changes in both the direct and relaxed mechanisms. Alternatively, either the laser directly heats the tip and surface, or the excited molecule transfers heat to the surface (bolometric mechanism), causing the substrate position, z0, to change relative to the tip. Molecule-tip heat transfer at the tunneling distance is improbable compared to molecule-surface transfer.
We model Frel(t) by assuming that there are no coherent effects. The molecule is cycled by the laser several times between the ground and excited states during the 1 ms . A-1 ≈ kIVR laser modulation period. We further assume that the molecule’s optical absorption transition is homogeneously broadened over the full modulation of the laser wavelength. In that case, the excited-state population, w, is approximately given by
w(t) )
I(t) 1 2 Is(t) + I(t)
(6)
In this equation, I(t) is the laser intensity in W/m2, modulated both in magnitude I and center wavelength λ. Is ) c/R(t) is the saturation intensity, where the absorption coefficient R is also modulated according to the laser wavelength. Equation 6 reaches a maximum of 1/2, so the relative density of states contributing to the tunneling current never contains more than a 50% contribution from the excited state. The relative density of states becomes
Frel(t) ) [1 - w(t)]F0 + w(t)Fexc
(7)
where F0 is the relative local density of states of the unexcited tip-adsorbate-surface junction, and Fexc is the relative local density of states of the excited tip-adsorbate-surface junction. According to DFT-LDOS calculations, the relative density of states of carbon nanotubes varies by up to a factor of 2 at defects or upon excitation to unoccupied electronic orbitals.26 When the excitation frequency and intensity are modulated below saturation, eq 6 reduces to w(t) ≈ [R1I1(t) + R2I2(t)]/2c, and the population transfer is simply linearly proportional to the molecular absorption and laser intensity at each wavelength,
FM SMA Detected by STM
J. Phys. Chem. C, Vol. 111, No. 8, 2007 3319 measured responses with τth ≈ 1-100 s (Figure 5A). The equilibration in Figure 5A is not a single exponential, but we model it as such for simplicity. A residual modulation remains due to the fast tip response (Figure 5C), contributing a heating background signal. In terms of laser intensities I1243 and I1255 in pulses of equal duration, the modulation depth in Figure 5C is given by
δz0 )
g|f1243I1243 - f1255I1255| CPFλ2νmod
(8)
where νmod ≈ 1 kHz is the laser modulation frequency, and g is a tip-laser geometry factor on the order of unity. For tungsten, the absorptivity f1243 ≈ f1255. Likewise, bulk silicon absorption is nearly constant over the modulation interval (see Figure 6). We can now use eq 5 to compute current modulation from the STM-detected absorption signal and heating effects, with typical results shown in Figure 5. The STM current can be read with a bandwidth τelec-1 ≈ 20 kHz limited by the amplifier electronics. The actual feedback in z occurs at a much smaller bandwidth, τfb-1 ≈ 3 kHz and
dκz 1 I(κz,t) - Iset ) dt τfb Iset
Figure 6. Comparison of the FM modulation range (red dotted lines) with band contours of carbon nanotubes and absorption of tungsten and p-Si. A: Band contours adapted from a DFT model by shifting.28 On the basis of our diameter and absorption measurements, (9, 5) and (11, 3) tubes are the only candidates for the tube in Figure 2. B: Band contours adapted from a Rayleigh scattering study.29 C: W and p-Si absorption coefficients showing that our choices of excitation wavelengths and small modulation depth minimize bulk substrate and tip contributions to the signal.
as given in eq 2. In addition, F depends linearly on w. Thus, the FM-modulated SMA-STM experiment genuinely measures the absorption coefficient difference between the two wavelengths, as do transmission and bolometric experiments. The second ingredient needed in eq 5 is the motion of z0(t) induced by thermal effects. The tip itself responds instantaneously on the time scale on which the laser power switches during AM/FM modulation (Figure 5B), so tip motion is stepwise linear with an instantaneous slope dependent on the applied laser power, I(t) (Figure 5C). We showed this by modeling the tip as a 3-D 45° cone subject to an infrared pulse (using F ) 19.3 g/cm3, CP ) 132 J/mol/K, ) 4.5 × 10-6/K, f ) 10% absorption by Tungsten, 50 mW/cm2 average laser power, evanescent wave penetration 600 nm), resulting in a ≈0.6 nm/s average expansion rate, in good agreement with Figure 5A. z0 eventually equilibrates due to reradiation, transfer of heat into components expanding orthogonally to the z-axis, and heat conduction on the substrate. These phenomena have slow
(9)
To detect a signal, two modulation frequency regimes can be distinguished. If νmod is much lower than τ-1 fb , the STM feedback will move z to keep the tunneling current constant at the setpoint Iset with high fidelity. The signal should be detected by reading the z feedback signal to the piezo. If νmod is much higher than τfb-1, the feedback will not move the tip in response to the modulated tunneling current, and the modulation of the tunneling current should be detected. We operated in an intermediate regime and detected current. Figure 5 illustrates a calculation in which τfb-1 ) νmod. In FM modulation, eq 8 can be made to vanish at f1I1 ) f2I2 or I1 ≈ I2. This assumes, of course, that the absorption profiles, fi, of the tip (typically tungsten) and surface as a function of wavelength are much smoother than the absorption profile, Ri, of the molecular sample (Figure 6C), and that there are no contributions due to lateral displacements. 4. Discussion and Conclusions At the point where the FM signal is nulled, the ratio of laser power densities is 150:90 ( 6, so R1243 ) R1255 × 1.7 ( 0.1. The absorption coefficient of the nanotube rises significantly with increasing photon energy, so the lasers are probing the low-energy side of the absorption edge. This is illustrated in Figure 6A, which compares the FM modulation range with absorption profiles of two different chirality tubes. In the literature, computational work at various levels of electron correlation27 and experimental work have indicated line shapes ranging from sharp onsets to exciton-broadened edges. In Figure 6A, we compare with E00-E11 transition van Hove profiles,28 and in Figure 6B, for broader profiles obtained by Rayleigh scattering,29 to account for this range. SMA-STM provides simultaneous imaging and spectral information that can be used as an analytical tool for identifying molecules. We can use the imaging-absorption spectroscopy combination to assign the nanotube in Figure 2 to one of two chiralities. The band edge energy of nanotubes generally varies inversely with diameter, but fluctuates depending on the exact (m, n) values5 describing the structure of the nanotube. On the basis of ref 23, our measured diameter of 1.03 ( 0.1 nm and
3320 J. Phys. Chem. C, Vol. 111, No. 8, 2007 ratio of absorption coefficients 1.7 ( 0.1 leaves only two structural candidates for the nanotube: (m, n) ) (9, 5) or (11, 3). In this case, the slightly wider nanotube happens to have the slightly higher absorption maximum. Although a unique assignment cannot be made with only two absorption coefficients, it seems reasonable to assume that by making use of a widely tunable excitation laser, accurate absorption contours can be obtained that allow a unique assignment when combined with a topographic diameter. The observed slope of ∆R/(R j ∆λ) ) 0.043 ( 0.004 nm-1 indicates an onset of absorption more gradual than predicted by single-electron models, such as in Figure 6A (van Hove profiles). A more gradual onset is predicted to arise from excitonic broadening of the absorption band, for which evidence has been seen in bulk measurements.16,30 In addition, thermal broadening on the order of ∼100 meV (∼3.5 kT) would be expected in our room temperature measurements. Figure 6B illustrates this with Rayleigh scattering profiles from ref 29, shifted to match the (9, 5) and (11, 3) center frequencies. For one-photon transitions, laser absorption is expected to produce an excited state of s symmetry.30 This is compatible with the uniform absorption signal monitored by SMA-STM (Figure 2) and reported previously by AM modulation.1 However, the nonradiative relaxation time of the E11 state is very fast,15 so the uniform signal is equally compatible with rapid relaxation, distributing the energy among vibronic degrees of freedom of the nanotube. According to the estimate in eq 1 and on the basis of the simplified three-state model, both direct and relaxed mechanisms can contribute to the signal over the 75-165 mW/cm2 combined average power density coupled into the STM junction in the experiments described here. A molecule with localized changes in absorption will have to be studied to separate the two mechanisms clearly. Relaxation would cause a laser-intensity-dependent tunneling image as saturation is approached. This effect could be used to study electronic or vibrational dynamics of molecules upon absorption. Although AM-modulated single-molecule absorption spectroscopy produces the largest signal, FM modulation over a narrow wavelength range has the advantage that several undesirable mechanisms can be suppressed or subtracted out because they are nearly wavelength-independent. The existence of a net signal at equal laser power densities immediately rules out surface or tip heating. The absorption coefficients of silicon and tungsten vary much more slowly with wavelength than that of a nanotube (Figure 6), so modulated heating as illustrated in Figure 5C is eliminated by complementary modulation of two laser colors within 12 nm of one another. Only when AM modulation dominates (an upturn in signal below I1243 ) 30 mW/cm2 in Figure 4) is there a significant contribution from heating with the same trend on the substrate as on the molecule. Tip and substrate carrier excitation followed by charge transfer (e.g., ref 14) are also nearly wavelength-independent over a 12-nm interval near 1250 nm. The Si absorption coefficient in Figure 6C goes through a minimum, and the tungsten absorption coefficient is nearly constant. Carrier excitation thus provides a constant background, even if the laser power is not set for exact cancellation. This background can simply be subtracted out after measuring it on a molecule-free part of the substrate (Figure 4). Finally, we can exclude the bolometric mechanism. No distortion of the surface near the molecule comparable to the signal on the molecule was detected (Figure 4A, inset). The tip and molecule are not in close enough contact to allow efficient heat transfer, as compared to relaxation of excess energy into
Carmichael et al. the substrate, which is in direct van der Waals contact with the molecule. At the same time, heat conduction within a covalently bonded surface is expected to be much more effective than energy transfer from the molecule to the surface. Thus, one should not expect a large signal from local distortion of the surface, and indeed, none is observed. This situation is different from that previously reported for a monolayer of absorbers, in which many molecules transfer a much larger amount of heat into the surface.12 Laser FM/AM modulation combined with detection by an STM tip can be used to measure single-molecule absorption coefficients. The molecular absorption signal can be differentiated from background signals due to heating or tip-substrate carrier excitation. We propose three mechanisms: direct, relaxed, and bolometric. In future applications, relative contributions of these mechanisms could reveal dynamics, and tunable laser spectroscopy will provide analytical capability for singlemolecule absorption measurements. Acknowledgment. This work was supported by grants from the National Science Foundation (CHE 9986670 to MG and CHE 0103447 to MG and JL), and Grant 45421-AC5 from the American Chemical Society Petroleum Research Fund to M.G. J.B. was supported by a Beckman Fellowship, and M.G., by a Lycan Professorship during the period this work was carried out. Some of the equipment used in this work was funded by the Beckman Institute for Advanced Science and Technology at UIUC. E.S.C. and J.B.B. contributed equally to this work. References and Notes (1) Ballard, J.; Carmichael, E.; Lyding, J.; Gruebele, M. Nano Lett. 2006, 6, 45. (2) Gerstner, V.; Knoll, A.; Pfeiffer, W.; Thon, A.; Gerber, G. J. Appl. Phys. 2000, 88, 4851. (3) Grafstro¨m, S. J. Appl. Phys. 2002, 91, 1717. (4) Grafstrom, S.; Schuller, P.; Kowalski, J. J. Appl. Phys. 1998, 83, 3453. (5) Avouris, P.; Appenzeiler, J.; Martel, R.; Wind, S. J. Proc. IEEE 2003, 91, 1772. (6) Demtro¨der, W. Laser Spectoscopy, 2nd ed.; Springer: Berlin, 1996. (7) Bachilo, S. M.; Strano, M. S.; Kittrell, C.; Hauge, R. H.; Smalley, R. E.; Weisman, R. B. Science 2002, 298, 2361. (8) Li, Z. M.; Tang, Z. K.; Liu, H. J.; Wang, N.; Chan, C. T.; Saito, R.; Okada, S.; Li, G. D.; Chen, J. S.; Nagasawa, N.; Tsuda, S. Phys. ReV. Lett. 2001, 87, 127401. (9) Bragas, A. V.; Landi, S. M.; Martinez, O. E. Appl. Phys. Lett. 1998, 72, 2075. (10) Ho, W. J. Phys. Chem. 1996, 100, 13050. (11) Takeuchi, O.; Yoshida, S.; Shigekawa, H. Appl. Phys. Lett. 2004, 84, 3645. (12) Smith, D. A.; Owens, R. W. Appl. Phys. Lett. 2000, 76, 3825. (13) Lyubinetsky, I.; Dohnalek, Z.; Ukraintsev, V. A.; Yates, J. T. J. Appl. Phys. 1997, 82, 4115. (14) Wu, S. W.; Ogawa, N.; Ho, W. Science 2006, 312, 1362. (15) Huang, L.; Krauss, T. Proc. 17th Ann. Meet. IEEE 2004, 1, 449. (16) O’Connell, M. J.; Bachilo, S. M.; Huffman, C. B.; Moore, V. C.; Strano, M. S.; Haroz, E. H.; Rialon, K. L.; Boul, P. J.; Noon, W. H.; Kittrell, C.; Ma, J. P.; Hauge, R. H.; Weisman, R. B.; Smalley, R. E. Science 2002, 297, 593. (17) Hartschuh, A.; Pedrosa, H. N.; Novotny, L.; Krauss, T. D. Science 2003, 301, 1354. (18) Lyding, J. W.; Shen, T.-C.; Hubacek, J. S.; Tucker, J. R.; Abeln, G. C. Appl. Phys. Lett. 1994, 64, 2010. (19) Nikolaev, P.; Bronikowski, M. J.; Bradley, R. K.; Rohmund, F.; Colbert, D. T.; Smith, K. A.; Smalley, R. E. Chem. Phys. Lett. 1999, 313, 91. (20) Albrecht, P. M.; Lyding, J. W. Appl. Phys. Lett. 2003, 83, 5029. (21) Lyding, J. Personal communication. (22) Tapastzto´, L.; Mark, H. I.; Koo´s, A. A.; Lambin, P.; Biro´, L. P. J. Phys. Condens. Matter 2006, 18, 5793. (23) Weisman, R. B.; Bachilo, S. M. Nano Lett. 2003, 3, 1235. (24) Hitosugi, T.; Hashizume, T.; Heike, S.; Kajiyama, H.; Wada, Y.; Watanabe, S.; Hasegawa, T.; Kitazawa, K. Appl. Surf. Sci. 1998, 130, 340.
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