LETTER pubs.acs.org/NanoLett
Accurate Determination of Plasmonic Fields in Molecular Junctions by Current Rectification at Optical Frequencies Rani Arielly, Ayelet Ofarim, Gilad Noy, and Yoram Selzer* School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel ABSTRACT: Current rectification, i.e., induction of dc current by oscillating electromagnetic fields, is demonstrated in molecular junctions at an optical frequency. The magnitude of rectification is used to accurately determine the effective oscillating potentials in the junctions induced by the irradiating laser. Since the gap size of the junctions used in this study is precisely determined by the length of the embedded molecules, the oscillating potential can be used to calculate the plasmonic enhancement of the electromagnetic field in the junctions. With a set of junctions based on alkyl thiolated molecules with identical HOMOLUMO gap and different lengths, an exponential dependence of the plasmonic field enhancement on gap size is observed. KEYWORDS: Molecular junctions, rectification, photoassisted tunneling, plasmons
S
urface plasmons (SPs) are coherent oscillations of conductive electrons in a skin layer of metal capable of producing strong electromagnetic fields in the near-field region.1,2 SP fields that can be formed in ∼1 nm gaps between metal surfaces are of particular importance as they are imperative for numerous applications such as single molecule Raman3,4 and fluorescence spectroscopies,5 Raman probing of molecular junctions,6,7 and prospect control of molecular junctions by processes such as coherent steering and destruction of tunneling, photoassisted transport, and current ratcheting.817 Notwithstanding their high importance, exact determination of the magnitude of plasmonic fields in ∼1 nm scale gaps is very challenging because of the small regions in which they occur. Approaches to determine these fields using methods such as surface-enhanced Raman spectroscopy rely (probably in many cases) on erroneous estimations of the number of molecules that contribute to the signal, in order to calculate the enhancement. A recent promising alternative approach is to determine the effective field in nanogaps by the magnitude of current rectification, i.e., by measuring the additional dc current that is formed in various nanojunctions such as metal quantum point contacts,18,19 metal plasmonic tunneling gaps,20 and graphene nanoconstrictions21 upon laser irradiation. The accuracy of this approach is somewhat obstructed since the size and shape of the metal gaps in each of these cases are not accurately known. Here we employ current rectification in molecular junctions to determine optical fields in nanoscale metal gaps under laser irradiation. In contrast to previous studies, the size of the gaps in the junctions can be varied and is precisely determined by the embedded molecules, thus enabling unequivocal determination of plasmonic field enhancements in nanogaps that are 12 nm in scale. Current rectification is described quantum mechanically by the photoassisted transport (PAT) theory, first introduced by r 2011 American Chemical Society
Tien and Gordon.22 According to this model, under irradiation a certain fraction of the tunneling charge across a gap undergoes inelastic scattering events in which photons with energy pω are either emitted or absorbed as a result of interaction with the oscillating (SP) field. The SP field can be described as an ac voltage bias Vac cos(ωt) added to the dc applied bias Vdc, producing a dc current described by22 n¼∞ eVac Idc ¼ Jn 2 ð1Þ Idc ðVdc + npω=eÞ pω n¼ ∞
∑
where Jn is a Bessel function of the nth order. Expanding to lowest order in the signal voltage, the incremental dc current [Idc Idc(Vac = 0)] is ! 1 2 Idc ðVdc + pω=eÞ 2Idc ðVdc Þ + Idc ðVdc pω=eÞ ΔIdc ¼ Vac 4 ðpω=eÞ2 ð2Þ We note that under conditions in which the conductance varies slowly on a voltage scale of pω/e, the expression in brackets reduces to a simple second derivative of Idc 1 d2 Idc ΔIdc ¼ Vac 2 4 dVdc 2
ð3Þ
As described below we realize the necessary conductance conditions to make eq 3 applicable by employing junctions comprising of thiolated alkyl chains, with (chain length independent) Received: May 6, 2011 Revised: June 13, 2011 Published: June 16, 2011 2968
dx.doi.org/10.1021/nl201517k | Nano Lett. 2011, 11, 2968–2972
Nano Letters
Figure 1. Suspended wire molecular junctions (SWMJ). (a) Typical IV curves of junctions with C8 (blue) and C12 (red). Inset: a SEM picture of a SWMJ. A junction is formed between one of the ends of the molecule-covered Au nanowire and the underneath pad. (b) Histograms of log(R), the resistance of the junctions determined at 0.1 V, for the different molecules. The trend shows average resistance increase by approximately an order of magnitude for every addition of two CH2 units.
Figure 2. Characterization of SWMJ junctions. (a) Histograms of transition voltage, VT, values determined for junctions based on the indicated molecules. (b) IETS of a junction with thiolated alkyl chain (C10) measured at 5 K using an ac amplitude of 20 mV. Peaks of different characteristic vibrational modes are marked with arrows. Junctions with C8 and C12 give similar results.
HOMOLUMO gaps that are larger than twice the energy of photons used. “Suspended-wire” molecular junctions (SWMJ) were fabricated by trapping Au nanowires, ∼200 nm in diameter, capped with selfassembled monolayers of either 1-octanethiol (C8), 1-decanethiol (C10), or 1-dodecanethiol (C12), onto lithography-defined Au leads using a dielectrophoresis technique (see inset in Figure 1a).23 The nanowires which are completely covered with a molecular layer could potentially form two molecular junctions in each SWMJ, only one junction per suspended nanowire (and a short on the other end), and a complete short circuit. The latter option was easy to sort out, and for the former two, transition voltage spectroscopy (TVS) and inelastic electron tunneling spectroscopy (IETS) were used in order to confirm the molecular nature of the junctions and their number per structure. TVS refers to a FowlerNordheim analysis of IV curves, i.e., plots of ln(I/V2) versus 1/V, revealing minimum points at transition voltage (VT) values that are characteristic of the molecules under study.24 Figure 2a shows histograms of VT values for the different molecules. Within agreement with previous results,25 all alkyl chains based junctions have a common value of VT = 1.15 ( 0.05 V.
LETTER
IETS measurements were done at 5 K using a standard lock-in technique (Figure 2b) revealing typical vibrations in both bias polarities.26 Prior to the measurements under the laser, approximately 100 junctions were measured by both IETS and TVS at 5 K. These measurements ascertain the applicability of TVS as an analytical tool to verify the molecular nature of junctions. The TVS curves of the molecule used here were found to be temperature independent. The agreement of measured VT values with previous results, and the lack of shift in the IETS peaks (within an error of (2 mV) from the expected values prove that there is no potential divider, i.e., two molecular junctions, in the SWMJs. The reason for this unique observation of essentially always one junction per SWMJ structure still needs to be resolved and is currently under study. Laser irradiation of selected junctions under ambient conditions was done through a microscope with maximum intensity of ∼6.5mW/μm2 and laser polarization parallel to the nanowires using a wavelength of 658 nm (1.89 eV). Finite-difference time-domain (FDTD) simulations provide insight to the role of plasmons in the SWMJ (Figure 3). Propagating surface plasmons can be launched in the nanowires only when the excitation laser is incident on their end. The dispersion curves of metalinsulatormetal structures, with insulator thicknesses and dielectric parameters similar to the molecules used here, were recently calculated.27,28 In agreement with these calculations we find that the characteristic SP wavelength in the junctions is ∼50 nm and that their propagation length is several hundreds of nanometers. Thus, a substantial area of each junction (which is typically
