VOLUME 9, NUMBER 11, NOVEMBER 2009 Copyright 2009 by the American Chemical Society
Anomalous Temperature Dependent Transport through Single Colloidal Nanorods Strongly Coupled to Metallic Leads Hadar Steinberg,†,‡ Yigal Lilach,‡ Asaf Salant,†,‡ Omri Wolf,‡,§ Adam Faust,†,‡ Oded Millo,‡,§ and Uri Banin*,†,‡ Institute of Chemistry, Racah Institute of Physics, and The Center for Nanoscience and Nanotechnology, The Hebrew UniVersity, Jerusalem 91904, Israel Received June 15, 2009; Revised Manuscript Received August 11, 2009
ABSTRACT We report wiring of individual colloidal nanorods (NRs), 30-60 nm long by 3.5-5 nm diameter. Strong electrical coupling is achieved by electron beam induced deposition (EBID) of metallic lines targeting NR tips with nanometric precision. At T ) 4 K many devices exhibit smooth I(V) curves with no sharp onset features, which remarkably fit a Fowler-Nordheim tunneling model. All devices exhibit an anomalous exponential temperature dependence of the form I ∼ exp(T/T0). This irregular behavior cannot be explained by any hopping or activation model and is interpreted by accounting for the lowering of the NR conduction band due to lattice dilation and phonon coupling.
Control of size, shape, and composition of colloidal nanocrystals (NCs) allows energy-band engineering, evidenced by numerous optical and STM1,2 investigations, and found useful in a variety of optical applications.3-6 Effective electrical coupling to NCs is challenging due to their ligandmolecule coverage and their small dimensions. Fabrication of nanometric-sized electrode gaps, for example, was useful in studies of individual molecules which covalently bond to the electrodes.7 NCs deposited within, or above, such gaps8 are usually displaced from the electrode by a tunneling barrier associated with resistance RT. When RT . h/e2, e being the * Corresponding author,
[email protected]. † Institute of Chemistry. ‡ The Center for Nanoscience and Nanotechnology. § Racah Institute of Physics. 10.1021/nl901912e CCC: $40.75 Published on Web 08/19/2009
2009 American Chemical Society
electron charge and h Planck’s constant, the device is considered weakly coupled to the leads,9 and its conductance is dominated by charging energy and resonant tunneling into discrete states. For electrical applications, nanorods (NRs) of a few nanometers in diameter and tens of nanometers length are of special interest since they are among the smallest physical systems which retain quasi-one-dimensional solid-state structure.10 Devices fabricated by deposition of metallic leads directly over the tips of NRs using the multistep electron-beam-lithography technique do exhibit better contacts, but are still characterized by charging physics.11-13 Strongly coupled electrical contacts to NCs will allow to investigate their intrinsic transport properties and the nature
Figure 1. Wiring a single nanorod using EBID. (a) Scanning electron micrograph of a 60 × 3.5 nm long CdSe nanorod wired by EBID tungsten wires. Inset: Same rod, before wiring. Bars are 70 nm. (b) Schematic of NR (green) with remaining ligand molecules (wavy lines). Disordered W atoms (blue circles) with C contamination (black circles) are deposited on the tips. (c) Device schematic. Highly doped Si substrate serves as back-gate. Thermal oxide surface (gray) is 25 nm thick. Ti-Au electrodes are fabricated by standard electron-beam lithography. NRs (red) are deposited by drop-casting. A single rod is connected by tungsten EBID lines (light blue) which extend to the Au electrodes.
of the nanoscale metal-semiconductor interface.14 One possible approach, developed recently, employs growth of Au tips, resulting in hybrid particles named “nano-dumbbells” (NDBs)15 and their subsequent electrostatic trapping.16 Here we focus on an alternative approach for contacting individual nanorods (NRs) as short as 30 nm to external electrodes providing strong electrical coupling, based on electron beam induced deposition (EBID) of metallic lines. EBID is a high-resolution single-step process where an electron beam dissociates organometallic precursor molecules adsorbed to the surface of a sample. The metallic elements are deposited, resulting in a granular composite consisting of fused metal nanocrystals embedded in a matrix of amorphous carbon, residue from the precursor molecules.17 EBID was previously used to wire carbon nanotubes18 and is an appealing approach for wiring small colloidal nanorods since the precursor could be adsorbed around the NR tip and form a contact enveloping the NR from all directions (Figure 1b). We developed an alignment procedure for precisely depositing EBID lines onto NR tips by using lithographically defined markers. We have fabricated over 60 devices, most with CdSe NRs, five with NDBs,15 and two with CdS NRs. The NRs were 30-60 nm long and 3.5-5 nm in diameter; synthesis details appear in the materials and methods section in the Supporting Information. A schematic of a device is presented in Figure 1c: NRs are dissolved in toluene and drop-cast onto the surface of a substrate consisting of highly doped Si covered by a thermal oxide layer (25 nm thickness), on which Ti/Au electrodes are patterned by conventional electron beam lithography (EBL). Individual nanorods can be located in the 1 µm gap between the electrodes using SEM (scanning electron microscopy) and singled out for contacting. A SEM image of a wired 60 × 3.5 nm CdSe NR is presented in Figure 1a, with an image of the same NR prior to the EBID deposition step in the inset. EBID lines are deposited at its tips with nanometric precision, extending to the predeposited Au electrodes which are not 3672
Figure 2. I(V) curves of wired CdSe NRs (top, both panels) and dI/dV (bottom). (a) 55 × 3.5 nm CdSe NR characterized by a gap and sharp onset: annotation, conduction band separated from the leads by barriers and tilted by the source-drain field; horizontal line, energy of localized state; dashed orange line, tunneling electrons. (b) Smooth I(V) of a 45 × 3.5 nm NR: annotation, diagram of Fowler-Nordheim tunneling through the barrier when source-drain field is applied to the conduction band.
shown in the image. We use a W(CO)6 precursor to deposit W lines. Optimal performance is obtained when the lines are formed by a single sweep of the electron beam. Resistance is characterized by spanning a continuous line between the Au electrodes, and typically R ) 200-500 kΩ at T ) 4 K for a 1 µm × 10 nm line (supplementary Figure 2 in Supporting Information). The resistance is only weakly dependent on length and is therefore attributed to the Au/W interface. Typical current voltage (I(V)) curves of wired devices are shown at the top of both panels in Figure 2, while the corresponding differential conductance (dI/dV vs V) characteristics are presented below. We note that the NR resistance is orders of magnitude higher than the W wire resistance for all source-drain voltages VSD and that control Nano Lett., Vol. 9, No. 11, 2009
junctions in which no NR is connected conduct about 10-12 A at V ) (3 V (supplementary Figure 1 in Supporting Information). The NRs exhibit multistable behavior, an effect we associate with local charging dynamics on their surface, and will be addressed elsewhere. This multistable behavior is averaged out by integrating for 1 s while waiting at each VSD. Two types of I(V) curves are identified: The first, presented in Figure 2a, is characterized by a gap, the size of which may vary between different NRs, flanked by sharp onsets of conductance at both positive and negative sides. The conductance onsets resemble those observed in scanning tunneling spectroscopy data2,19 and thus indicate weak coupling or strong tunneling barriers between the W wire and the NR. The peak observed at the onset of current at positive bias may be due to resonant tunneling to a state localized by the presence of tunneling barriers (annotation in the figure). However, here we address NRs strongly coupled to leads, as demonstrated by Figure 2b where the I(V) curve of a 45 × 3.5 nm CdSe NR is plotted. The quality of the contact could be appreciated when analyzing these I(V) curves, where no sharp features or well-defined gap is detected. Similar curves were also observed for other CdSe rods and the other types of NRs studied (supplementary Figure 3 in Supporting Information) suggesting a common transport mechanism. This result can be quantitatively reproduced by a simplified model (annotation in the figure) where a semiconductor is coupled on both sides to metallic leads. The conduction band is offset from the chemical potential of the metal by energy U ) φ - χ, where in the simplest approximation φ is the metallic chemical potential and χ is the semiconductor electron affinity. Application of bias between the source and drain, VSD, tilts the band structure, forming a triangular tunneling barrier. The device conductance can be evaluated by calculating the tunneling through this triangular barrier using the WKB approximation.20 This results in the Fowler-Nordheim formula for current density J, which at low temperatures reads
(
J ) sgn(VSD)
)( )
e3mM VSD 8πhmSCU L
2
(
exp -
4√2 √mSC U3/2L 3 pe |VSD |
)
(1)
where L is the distance between the leads (see below) and mM and mSC are the effective masses at the metal and semiconductor, respectively. It is convenient to rewrite the exponential factor by introducing an effective voltage VFN, defined as VFN )
4√2 √mSC 3/2 U L 3 pe
(
J ∼ VSD2 exp -
VFN |VSD |
(2)
)
The fit to the experimental current was performed using the relation I ) JAeff, Aeff being the effective contact cross section (see below). This fit uniquely determines both the values of VFN and the prefactor. VFN evidently represents the Nano Lett., Vol. 9, No. 11, 2009
Figure 3. Fowler-Nordheim model: (a) I(V) of 45 × 3.5 nm CdSe rod (blue), fit to model (green) (eq 2), with VFN ) 0.8 V. (b) Same as (a), on a semilogarithmic scale. (c) NR statistics: Histogram of values of the parameter VFN for different NR devices. (d) Conduction-band offset U vs rod length L for VFN found in (a), eq 2. Dashed red lines: Upper and lower U values for plausible values of L.
typical voltage scale of the I(V) curve. In Figure 3a we plot an I(V) curve measured on the 45 × 3.5 nm rod and compare it to the result of eq 2. The experimental data, plotted in blue, agree well with the model calculation, plotted in green. In Figure 3b the same data are presented in a semilogarithmic plot, revealing that the model also agrees with the data down to the noise threshold of the system. The value of VFN ) 0.8 V found in this particular sample is typical, as we can see in Figure 3c where a histogram of 19 samples, each exhibiting Fowler-Nordheim characteristics, is compiled. Supplementary Figure 3 (Supporting Information) depicts a collection of I(V) curves of several NRs, all showing remarkable fit to the model. Note that although the I(V) curve uniquely defines VFN, neither L nor U can be extracted independently from the model. The curve in Figure 3d presents the pairs of (U,L) values corresponding to VFN ) 0.8 V, with the dashed red lines marking the range in U corresponding to feasible values of L. One could assume the value of L to be the length of the rod, but it is most likely that the tungsten lead contacts perturb inward to the NR, resulting in a shorter effective length, of around 40 nm, yielding a value of U ∼ 40 meV for the CdSe-W interface. Although the bulk electron affinity of CdSe is 4.95 V,21 accounting for confinement yields an effective value of χCdSe ) 4.5-4.3 V,10 depending on the NR diameter. Given that for tungsten φW ∼ 4.5 V,22 we expect 0 < U < 0.1 V, and the value we find is plausible. Another important parameter is the effective wire-NR contact area, Aeff, found to be here ∼10-18 m2. This appears to be smaller than the nominal active contact area, probably reflecting the granularity of the tungsten wires that results in small effective contact regions. The above discussion suggests that the NR indeed couples strongly to the W leads. We find no systematic difference between NRs and NDBs, suggesting that the W deposition circumvents the Au tips, since it is not possible to specifically address only the Au tips through the EBID approach. We now turn to discuss the temperature dependence of the conductance. The I(V) curves presented in Figure 4a, 3673
Figure 4. Temperature dependence of a 30 × 5 nm CdSe-Au NDB: (a) I(V) curves taken at T ) 4.4-191 K. (b) Full circles: -I (log scale) vs T at VSD ) -0.55 V (blue), -0.7 V (green), -0.85 V (red), -1 V (light blue). These voltages are marked by vertical dashed lines in (a). Lines: Fit to FN model, assuming L ) 25 nm, U0 ) 95 meV, and R ) 0.35 meV/K. (c) R vs L of several NRs which exhibit the same phenomenology. The sample in (b) is the green data set, with the black circle marking the values of L and R used in (b). (d) -I vs 1/T at VSD ) -1 V, on a semilogarithmic scale. The deviation from a straight line is inconsistent with simple thermal activation model.
taken at temperatures between 4 K and 191 K for a 35 nm long NDB, show that the current increases with temperature. The electrical conductivity (at high enough VSD values) does not conform to any thermal activated mechanism, neither to simple activation, where I ∼ exp(-EA/T), EA being the activation energy, nor to any variable-range-hopping model,23 where I ∼ exp((-T0/T)γ), for any positive γ < 1. For example, the I(VSD ) -1) vs 1/T plot deviates strongly from the straight line expected for simple activation (Figure 4d). On the other hand, the conductivity exhibited an unusual σ ∼ exp(T/T0) behavior (over a wide parameter range), as depicted by the I vs T traces for several bias voltages plotted on a semilogarithmic scale in Figure 4b. As will be discussed in the following, we can account for this anomalous temperature dependence, including the deviation from linearity observed at low temperatures, by the reduction with increased temperature of the CdSe energy gap that affects, in turn, the tunneling barrier within the framework of the Fowler-Nordheim model above. Temperature-related changes in the band structure of semiconductors are well-known. Specifically, the energy gap of CdSe is reduced by approximately 80 meV between 4 and 300 K. This effect, which appears in many semiconducting materials, is associated with lattice dilation and coupling of charge carriers to phonons.24 The typical behavior takes the phenomenological form compiled by Varshni25 Eg ) Eg(T ) 0) - RT2 /(T + β)
(3)
where R and β are material-specific parameters. For CdSe colloidal NRs R ) 0.3-0.4 meV/K, and β ≈ 120 K, as extracted from optical measurements.26 We introduce this effect into the Fowler-Nordheim model, eq 1, and obtain I∼
3674
( )( ) 1 VSD UT L
2
(
exp -
)
4√2 √mSC L U 3/2 ; 3 pe |VSD | T UT ) U0 - RT2 /(β + T)
(4)
where U0 is the conduction band offset at T ) 0. The model, depicted by lines in the figure, fits the data remarkably well for an appreciable range in VSD. The particular curves appearing in the figure were all calculated as follows: First, the I(V) curve at T ) 4 K was fit to eq 1. For a reasonable effective length L ) 25 nm we find U0 ) 95 meV. We then used eq 4 to fit the I(T) curves for all VSD values, with β ) 120 K and R ) 0.32 meV/K, the latter being a fitting parameter. We note in passing that a close look at the exponential part of eq 4 suggests that the temperature dependence will be stronger for smaller VSD, as indeed portrayed in Figure 4b. Successful fits can be obtained for a range of R vs L pairs, as shown in Figure 4c, where R vs L of several samples is reported. Remarkably, three CdSe samples of length 30-40 nm, including the NDB whose data is presented in panels a and b, exhibit very similar values. Taking the effective length to be L ) 20-30 nm, which is likely, given that the NRs and NDB are 30-40 nm long, we find R ) 0.3-0.4 meV/K, spanning the values extracted from optical measurements of the gap of CdSe rods.26 This consistency seems appealing, but one should keep in mind that eq 3 pertains to the entire gap, whereas the Fowler-Nordheim tunneling process here depends only on the change of U associated with the conduction band. Interestingly, it appears as if the change in the Fowler-Nordheim barrier takes place predominantly by shifting the CdSe conduction band edge with respect to the tungsten Fermi level. Further support to the validity of our model is provided by the data set extracted (using the suitable material-dependent parameters) from measurements acquired on a 50 nm CdS NR (supplementary Figure 4 in Supporting Information), which is shifted to the right (higher L values) in Figure 4c. It is important to note that for the expected effective length of ∼40 nm, the corresponding R value is 0.39 meV/K, typical of CdS.27 Evidently, the model discussed herein cannot be applicable for low VSD, for which the band-tilting is insufficient for Nano Lett., Vol. 9, No. 11, 2009
significant Fowler-Nordheim tunneling. In this regime we find evidence of a parallel conduction mechanism exhibiting hopping-like thermally activated characteristics. In summary, we present here a new route for wiring individual semiconductor nanorods, using electron beam induced deposition, allowing us to achieve strong electrical coupling to the leads. The I-V characteristics measured on W wired CdSe nanorods could be well accounted for by the Fowler-Nordheim tunneling mechanism. The conductance of these devices exhibited a unique ln σ ∝ T temperature dependence that can be explained by the effect of band gap reduction with temperature. The remarkable precision and quality of coupling provided by EBID electrodes, as demonstrated here, could facilitate further electrical transport studies of a large variety of colloidal nanometric objects. Specifically, one may pursue the present research and contact other nano-objects, including hybrid core-shell NCs28 and magnetically doped NRs for various nanophotonic and spintronic applications.29 Acknowledgment. The authors wish to acknowledge the help given by the staff of the Unit for Nanofabrication of the Center for Nanoscience and Nanotechnology in the Hebrew University, Jerusalem, headed by Dr. S. Eliav. We further acknowledge the help of E. Elmelem, G. Menagen, and Y. Shemesh in synthesis. The research was supported in part by the US-Israel Bi-National Science Foundation (BSF) (UB) and the Israel Science Foundation, Centers of Excellence Program Grant #481/07 (OM). O.M. acknowledges support from the Harry de Jur Chair in Applied Science. U.B. thanks the Alfred and Erica Larisch Memorial Chair in Solar Energy for support. Supporting Information Available: Figures showing background current when a NR is absent, EBID W line characterization, a selection of I(V) curves fit to the FN model for various NRs, and temperature dependence of a 50 nm CdS NR and discription of the materials and methods used. This material is available free of charge via the Internet at http://pubs.acs.org.
Nano Lett., Vol. 9, No. 11, 2009
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