NANO LETTERS
Measurement of Electronic Transport through 1G0 Gold Contacts under Laser Irradiation
2009 Vol. 9, No. 4 1615-1620
Naomi Ittah,† Gilad Noy,† Ilan Yutsis, and Yoram Selzer* School of Chemistry, Tel AViV UniVersity, Tel AViV 69978, Israel Received December 24, 2008; Revised Manuscript Received February 21, 2009
ABSTRACT Metal quantum point contacts (MQPCs) with dimensions comparable to the de Broglie wavelength of conducting electrons reveal ballistic transport of electrons and quantized conductance in units of G0 ) 2e2/h. We measure the transport properties of 1G0 Au contacts under laser irradiation. The observed enhancement of conductance appears to be wavelength-dependent, while thermal effects on conductance are determined to be negligible. For wavelengths that are not absorbed by Au, the results are consistent with a photoassisted transport mechanism in which conductance depends both on the electronic structure of the leads and on the interaction of the transporting electrons with oscillating electric fields originating from excitation of local plasmons. For wavelengths absorbed by Au, photoinduced mechanism is suggested to be the dominant transport mechanism. The results demonstrate optical control of ballistic transport in MQPCs and are also important for future interpretation of light effects on the conductance of single-molecule junctions.
Near field optical microscopy manipulates light to subwavelength confinement, leading under careful conditions the ability to probe individual molecules or clusters.1 In one specific approach, the necessary confinement is established within the gap of laser-irradiated bow-tie shaped metal junctions.2-7 Because of the frequency invariance of Maxwell’s equations, the bow-tie junction is essentially an optical analogue of electromagnetic antennas widely employed in the radiowave and microwave regimes. The antenna (metal bow-tie) converts the energy associated with free propagating radiation (laser) into localized energy (near-field) centered on a receiver, in this case an individual cluster or molecule placed in the gap of the metal structure, exciting local spectroscopic response such as fluorescence, Raman scattering, and absorption. The enhanced local field can also be utilized to control and steer electrical conductance through the objects placed in the gap. Numerous theoretical studies suggest a broad range of novel effects of confined oscillating electromagnetic fields on the dc conductance of nanoscale junctions,8-29 such as photoassisted transport (PAT),9-11,14,17,22,25-29 photoinduced transport (PIT),24 electron pumping and ratcheting,13,15,16,18-21,23 and coherent destruction of tunneling (CDT).12,17 One very interesting experimental system to study some of these effects is by applying laser irradiation onto metal quantum point contacts (MQPCs), where a constriction of * To whom correspondence should be addressed. † These authors have equally contributed to this work. 10.1021/nl803888q CCC: $40.75 Published on Web 03/24/2009
2009 American Chemical Society
one or few atoms in cross section is connecting between the two metal sides of a bowtie structure. Electronic transport through such contacts is attributed to a small number of independent electronic modes, so-called “conduction channels”, characterized by their transmission coefficients: τ1, τ2,..., τN, which depend both on the chemical properties of the atoms forming the contact and on their geometrical arrangement.30 The conductance of the contacts is given by the Landauer formula: G ) G0∑iN) 1τi, where G0 ) 2e2/h is the conductance quantum. The role of the conduction channels in PAT through 1G0 MQPCs has recently been theoretically discussed.11 An initial experimental attempt to verify these predictions has been presented, using Au contacts formed by a mechanically controlled break junction (MCBJ).31 However, the conductance of most contacts in this study had a magnitude of several G0, and so quantitative comparison to theory regarding the behavior of 1G0 contacts under irradiation is still lacking. Such a comparison is a necessary step en route to conductance measurements of single molecule junctions under intensive irradiation. Here we explore the behavior of 1G0 Au contacts under laser irradiation using our newly presented method to fabricate MQPCs.32 The contacts formed by this method are not suspended as in MCBJs but instead are fully anchored onto Si/SiO2 substrates. As a result they are mechanically highly stable even at room temperature, and under irradiation, as will be described below, their heat dissipation characteristics are far more efficient than those of suspended MCBJs, resulting in only residual heating.
Figure 1. Formation of a 1G0 contact. Conductance is shown in a logarithmic scale in units of G0 as a function of time. Increasing tunneling current (initially at ∼10-6G0) prevails until a “jump-tocontact” to 1G0 process occurs. The formed MQPC is shown to be highly stable at 1G0 for minutes.
Contacts were fabricated by two lithography/evaporation/ lift-off procedures, with some modification to our previous method. In the first step, a Cr/Au (3/50 nm) lead is patterned. In the second step a Cr/Au lead (3/30 nm) is formed by shadow evaporation, following a previously suggested procedure,33 leaving a ∼25-30 nm gap between the two Au leads. Fabrication ends with a final step to form contact pads to the leads. All steps are followed by thorough cleaning by solvent rinsing and plasma etching to avoid any contamination of the junctions. The resulting junctions have a typical width of ∼2 µm. In our previous method,32 the two Au leads overlapped making the interface between the two leads a flux divergence plane of diffusion, so that under electromigartion conditions, a gap could be formed right at the interface between the two leads. Since electromigration was applied without any feedback control, the formed gap was usually tens of nanometers in size. Using the shadow evaporation process described above eliminates the need for electromigration, since it already results in two Au electrodes with a relatively controlled gap size. Similarly to our previous routine, 1G0 contacts are subsequently established by applying a high enough voltage to direct diffusion of Au adatoms toward zones of high field in close vicinity to protrusions extending out of the leads. There, as the density of migrating atoms increases, the probability of nucleation and cluster growth also increases, until growing metal mounds close the gaps. Until a certain contact is formed, conductance between the leads takes place by tunneling, and in general appears to increase as the gap becomes smaller. However, the increase is not monotonic, and fluctuations are observed in this regime, arguably due to creation/annihilation of contacts until a stable enough structure is formed32 (see Figure 1). Importantly, Au contacts fabricated by the above procedure appear to be stable under ambient conditions for hours. They also appear to be highly stable under laser irradiation as described below. Laser irradiation upon chosen junctions is made possible by an optical system that is based on a modified BX Olympus microscope, equipped with long distance objectives from 1616
Figure 2. On the left, conductance response of a certain junction to modulated irradiation using three different lasers, 532 nm (green), 658 nm (red), and 781 nm (black), modulated between 0 and 7 mW. Qualitative wavelength-dependent enhancement of conductance is revealed. On the right, conductance histograms calculated from the response to the modulated irradiation. The relative conductance enhancement is calculated from the position of the two Gaussians.
Mitutoyo, which facilitates the ability to work with micromanipulated probes under the microscope. Three lasers (Blue sky Research, CA) with wavelengths of 532 nm (2.33 eV), 658 nm (1.88 eV), 781 nm (1.58 eV) are coupled into the microscope via single mode optical fibers through a homebuilt cube, residing on top of the microscope, which allows switching between the lasers by means of a rotating mirror. The maximum used power of the lasers was ∼20 mW, corresponding to maximum intensity of ∼0.5 MW cm-2 on the contacts (through a ×50 objective). In order to maximize junctions’ stability, the intensity of the lasers was electronically modulated at a frequency of 10 Hz. The resulting dc currents, measured at 30 mV, were found to rapidly follow the modulation. All measurements were performed under ambient conditions at room temperature. Junctions were placed under the microscope with their long axis parallel to the lasers’ polarization, as at this orientation the effect of irradiation appears to be most pronounced. This behavior is general for all wavelengths used, and is in par with previous studies of local filed enhancement by plasmons.2-7 Figure 2 demonstrates how each junction was measured and the method of data analysis. The left column in this figure depicts the response of a certain junction to sequences of modulated irradiation at three wavelengths. In this case, the power of all lasers was modulated between 0 and 7 mW. In Nano Lett., Vol. 9, No. 4, 2009
Figure 3. Change of conductance as a function of laser intensity. All nine curves (three in each wavelength) were measured using one 1G0 contact. The reproducibility of the light effect and the stability of the contact are evident, ruling out heating effects which are assumed to lead to chaotic and nonreversible structural changes.
all sequences, the initial conductance is 1G0, which then increases upon irradiation. It is qualitatively clear from these sequences that conductance enhancement increases with decreasing wavelength. To quantitatively account for the enhancement, the right column in Figure 2 shows conductance histograms based on the modulated sequences. Irradiation appears to shift the Gaussian describing the distribution of conductance values around 1G0 (“light-off” conductance) to a new and a higher mean value (“light-on” conductance). The relative wavelengthdependent change, G/G0, is shown above each pair of Gaussians. Before quantitatively discussing these results it is essential to rule out the possibility that they are due to structural changes caused by local heating. Such an effect is known from scanning tunneling microscopy (STM) experiments under irradiation.34 Local heating of Au is mainly expected under the 532 nm laser due to interband transitions of d-band electrons into the conduction band35 resulting in reflectivity of 0.64. With reflectivity values of 0.97 and 0.95 for Au at 781 and 658 nm, respectively, heating is expected to be less pronounced. We rule out thermal effects based on several observations: First, we have measured the effective steady state temperature under the various lasers using microfabricated thin film Au/ Ni thermocouples with similar structure to the contacts. Such a procedure has been used by us previously,36 and a method to calibrate the thermocouples self-consistently has been developed by us as well.37 Under the maximum irradiation power used here (20 mW) with the 532 nm laser, the temperature of the junctions appears to increase by as much as ∼2 K. Within agreement with the reflectivity values, the temperature increase with the other two wavelengths is even smaller. We have also determined a temperature increase of ∼20 K under the beam from the anti-Stokes/Stokes ratio of the Raman signal of biphenyl molecules adsorbed on the junctions.36 Since the Raman signal was measured without intensity modulation, we expect to see a higher effective temperature. We have also measured the relative change in the conductance of 17 1G0 contacts upon raising the temperature from 300 to 340 K. The average change in conductance was found to be ∼1.5%, less than all the lightinduced effects reported and discussed below. Third, Figure 3 plots curves depicting conductance changes upon irradiation as a function of laser power for three wavelengths. All Nano Lett., Vol. 9, No. 4, 2009
Figure 4. (A) Schematic presentation of a PAT process. The laser light induces an oscillating potential with frequency ω across a length-scale of a mean free path at the contact between the two metal leads. Ballistic transporting electrons either absorb or emit photons. (B) The change of conductance upon interaction with light depends on the transmission profile at the point contact. Examples for two wavelengths are shown 532 nm (green arrows) and 781 nm (red arrows). The same transmission curve is also used for calculations of the photoinduced transport process.
measurements were made on the same junction and each curve was measured three times. Each point in these curves was calculated following the procedure described in Figure 2. The stability of the junction under irradiation is apparently very high, and structural changes due to possible heating are found to be negligible. Arguably, the junctions in the present study are less sensitive to heating, in contrast to STM and MCBJ experiments, due to more efficient heat dissipation properties of the junctions, which are fully anchored to substrates and are not suspended. We rule out thermal excitation of electrons as a possible source to the observed changes in conductance by considering the theoretical curve in Figure 4b, which describes the transmission values through 1G0 Au contacts as a function of energy. Since the transmission is 1 within an energy range of (1 eV around the Fermi energy, thermal excitation of electrons above 1 eV is needed in order to see a change in conductance, which corresponds to an unreasonable temperature of 12 000 K. We therefore conclude that the observed response of the contacts to irradiation is a true light-induced effect. The nature of this effect is discussed below 1617
We first examine PAT as the governing transport mechanism11 (see Figure 4a). Under laser irradiation, a timevarying potential across the contact is established, defined as Vω cos ωt, which induces inelastic events in which transporting electrons exchange photons of energy pω with the oscillating field. According to the Tien-Gordon theory for this process,9 the zero-bias dc conductance is described by the expression Gdc(ω) ) G0
∑
[J ( R2 )] τ(E + npω) 2
n
n
f
(1)
where Ef is the Fermi energy, n is the sideband index, J2n(R/ 2) is the square of the nth order Bessel function evaluated at R ) eVω/pω, giving the probability that transporting electrons absorb (n > 0) or emit (n < 0) n photons of energy pω and τ(Ef + npω) is the transmission probability at an energy level npω above or below the Fermi level. Vω is the effective amplitude of the light-induced ac bias determined by the light intensity enhanced by local plasmons. This enhancement depends on the environment, structure of the junction, the polarization of light and the frequency itself.1-7 On the basis of eq 1, G/G0 is wavelength-dependent since both R and the transmission θ(Ef + npω) depend on the wavelength. Accurate determination of these parameters is needed for quantitative comparison with theory. However, while the values of τ can be calculated11 (see Figure 4b), the magnitude of R for each junction and for each wavelength is unknown, and its precise determination is not straightforward. Nevertheless PAT mechanism can be revealed by plotting the change of conductance of a certain junction as a function of laser power. Such a plot appears in Figure 5 for two different junctions (open and dark circles) at two different wavelengths. We argue that the apparent nonlinearity for the 658 and 781nm lasers is a direct result of the Bessel function in eq 1, and due to the high reflectivity (∼1) of Au at these wavelengths (see below). To prove this, the curves describing the behavior at these wavelengths (continuous lines in Figure 5) were calculated in the following way: Using eq 1, an R value can be iteratively found to give the correct conductance enhancement at a certain laser power, say 10 mW. By the definition of R ()eVω/pω) a direct correlation between P10mW and Vω is thus established: P10mW ) cVω2, where c is a proportionality constant. For every other laser power in the plot, Vω can immediately be calculated using the same value of c. The calculated Vω can be translated into R, which is then inserted into eq 1 to calculate the corresponding G/G0 value. After establishing the R value for one intensity point, the entire curve is subsequently established by simple proportionality relations. A good fit is observed supporting PAT as a governing mechanism. Another support is in the observed leveling of the conductance enhancement that is also a direct result of the Bessel functions. With a root of first order Bessel functions at R ) 2.4, under high enough laser power the conductance 1618
Figure 5. A comparison between the conductance-enhancement as a function of laser power for two contacts (marked by dark and open circles) under irradiation with two wavelengths. A nonlinear behavior is observed, which is a remnant of the Bessel function in eq 1, describing a photoassisted transport. The procedure of curve fitting is explained in the text. The enhancement by the 658 nm laser appears to be higher with a larger variation (for a similar distribution of R) than the corresponding attributes at 781 nm.
through point contacts should nullify.17 Such a high field cannot be reached with our current experimental setup; however, work toward this goal is under progress. Figure 5 shows the variation in R between junctions, and also that for a similar range of the latter parameter, the range of conductance enhancement is larger for the 658nm wavelength due to the higher transmission value at the corresponding energy (see Figure 4). We plot in Figure 6 the average measured values of G/G0 and their corresponding variation as a function of photon energy, based on 20 junctions each measured and analyzed in the same method discussed above. The experimental results are overlaying theoretical curves based on eq 1 using transmission values taken from reference 11 (also Figure 4). The distribution of the results for the 781 nm (1.58 eV) and 658 nm (1.88 eV) lasers are within the theoretical range of conductance enhancement. The fact that the best agreement is obtained at low photon energies is at least consistent with the expectation that the model works best in that case since absorption in the electrodes is less important then. It is also particularly striking that the onset energy (∼1.5 eV) of the conductance enhancement seems to be quite close to the predicted one. The larger variation in conductance at 658 nm relatively to the variation at 781 nm is evident. Importantly, the Nano Lett., Vol. 9, No. 4, 2009
IPIT )
2e h
∫ dEτ(E)[f*(E) - f (E)] L
(2)
R
where the transmission values, τ(E), can again be taken from reference 11. It can readily be shown (under zero bias conditions) that IPIT )
2e h
[∫
Ef
Ef-pω
∫
Ef+pω
Ef
Figure 6. Average values of conductance enhancement and their distributions, measured for 20 contacts. Each contact was probed by three lasers with the indicated photon energies. The intensity of the lasers was 7 mW. The continuous lines are calculated from eq 1, using R in the range between 0.25 to 2.0 (in steps of 0.25).
maximum enhancement at 658 nm is for R ∼ 1, which for the laser power that was used (7 mW) corresponds to an effective enhancement of the laser field of ∼100. This value is in good agreement with theoretical expectations for plasmonic field enhancement in Au bow-tie junctions with similar structure to our contacts.1-7 Figure 6 also plots the distribution of measurements for the 532 nm (2.33 eV) laser. In this case, the measured enhancement appears to be larger than the theoretical calculation for a PAT mechanism. Partial explanation could be due to limitations of the theoretical model itself, as explained in ref 11. However, since at this wavelength the absorption of Au is not negligible anymore (reflectance ∼ 0.64), enhancement of conductance could also result from a PIT, which is simply a process that requires excitation of electrons in the metals (formation of hot carriers). These electrons then cross the contact with a probability value depending on the transmission coefficients. The lifetime of the excited electrons in these states, typically in the range of few femtoseconds, and their excitation cross section determine the magnitude of this contribution. To validate this argument, we reanalyze the results at 532 nm in the following way. Since the “skin depth” of light into Au is in the order of 15 nm,38 we assume based on the structure of the contacts excitation of hot electrons in the thin Au lead only. We note that taking into account excitation on both leads will not change the overall picture but will make the calculations more cumbersome. We further assume that all allowed energy-conserving transitions are of equal probability. As a result of optical excitation, a new energy distribution function for electrons, f*(E), is established at the thin lead. It would be a reasonable approximation to assume that the distribution function is reduced by a fraction θ in the energy range Ef - pω < E < Ef and augmented by the same amount in the range Ef < E < Ef + pω, where Ef is the Fermi energy. The parameter θ is taken to be directly proportional to the light intensity, F. The net current through the contact is given by Nano Lett., Vol. 9, No. 4, 2009
[fL(E)(1 - θ) - fR(E)]τ(E)dE +
]
(fL(E) + θfL(E - pω) - fR(E))τ(E)dE
(3)
The magnitude of θ can be extracted from the experimental results. According to Figure 6, the average measured conductance with the 532 nm laser is roughly ∼0.05G0 above the highest theoretical estimation, calculated for R )2. We note that above this value of R, the conductance according to eq 1 starts to decrease because of the behavior of the Bessel argument. The ∼0.05G0 conductance difference can be translated into current, by multiplying it with the small bias value that was used in the experiments, 30 mV, resulting in ∼1 × 10-7A. This value is plugged into eq 3 as IPIT. The integrals are evaluated numerically using the same set of theoretical transmission values from Figure 4. The fraction θ is found to be ∼10-3. The expected value for θ/F can be estimated from data on the optical properties of Au. It can be expressed by θ β ) σt(1 - r) ) t(1 - r) F n
(4)
where σ is the cross section for photogeneration of hot electrons in Au, t is the mean free time of a photoexcited electron, β is the light absorption coefficient, n is the volume concentration of electrons in Au, and r is the reflectivity. For β, n, and r, we take the values39 5 × 105 cm-1, 6 × 1022 cm-3, and 0.64, respectively, while t is estimated to be 10-14 sec.40 Using these values, we obtain θ/F ) 2 × 10-32 cm2 sec. The flux of photons, F, under irradiation of 7 mW and energy per photon of 2.33 eV (532 nm) is ∼1024 photons cm-2 sec-1. This flux is enhanced at the contact due to field enhancement by plasmons. Examination of the other wavelengths in Figure 6 suggests that an R ()eVω/pω) value of 1 describes quite reasonably this field enhancement. Thus, for 2.33 eV (pω) photons, Vω is ∼2 V. A 7 mW flux corresponds to an electrical field of ∼2 mV/1 nm. With a mean free path of electrons in Au of ∼10 nm, a 20 mV potential is then dropped across a segment of Au, on both sides of the contact, in which the transport of electrons is ballistic. Therefore, field enhancement is roughly 100, within agreement with other experiments,41 corresponding to flux enhancement of 10 000 (1002). Thus the effective flux at the contact is ∼1028 photons cm-2 sec-1. Using this value in combination with the above estimated value for θ/F, results in θ∼2 × 10-3, in excellent agreement with θ calculated from the experimental results. Importantly, performing the same calculation for the 781 nm laser (using the relevant 1619
Figure 7. A comparison between conductance-enhancement as a function of laser power for a certain contact, under irradiation with two wavelengths. The linear behavior for 532 nm suggests a PIT mechanism. The nonlinear behavior of 781 nm suggests a PAT mechanism.
optical parameters, that is, almost total reflectance), results in a θ value that is 2 orders of magnitude lower than the above value, which suggests that at this wavelength the PIT (generation of hot electrons in the leads) mechanism is much less important. Further support for the important role of PIT under the 532 nm laser is also revealed in Figure 7, which depicts the change of conductance enhancement with increasing laser power. With 532 nm, the change is linear with power in agreement with a PIT mechanism for which according to eqs 3 and 4 the current varies linearly with θ, which in turn is linear with the laser flux, F. In conclusion, we have presented transport measurements of highly stable 1G0 MQPCs, made of Au, under lasers irradiation. The effect of light appears to be wavelengthdependent. When absorption of photons is negligible, conductance enhancement can be explained by invoking a photoassisted transport mechanism and enhancement of the oscillating lasers field by local plasmons. When absorption of photons is not negligible photoinduced transport appears to be the dominant transport mechanism. The results are important for future interpretation of light effects on the conductance of molecular junctions. Acknowledgment. Support was given by the GIF foundation, Wolfson fund, and the James Franck program. G.N. thanks the converging technologies program via the ISF for a fellowship. References (1) Novotny, L. Prog. Opt. 2007, 50, 137. (2) Krozier, K. B.; Sundaramurthy, A.; Kino, G. S.; Quate, C. F. J. Appl. Phys. 2003, 94, 4632. (3) Sundaramurthy, A.; Crozier, K. B.; Kino, G. S.; Fromm, D. P.; Schuck, P. J.; Moerner, W. E. Phys. ReV. B. 2005, 72, 165409. (4) Mu¨lschlegel, P.; Eisler, H.-J.; Martin, O. J. F.; Hecht, B.; Pohl, D. W. Science 2005, 308, 1607.
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NL803888Q
Nano Lett., Vol. 9, No. 4, 2009
