NANO LETTERS
Resistance of Alkanethiol Molecular Wires
2003 Vol. 3, No. 11 1521-1525
Chao-Cheng Kaun* and Hong Guo Center for the Physics of Materials and Department of Physics, McGill UniVersity, Montreal, Quebec, Canada H3A 2T8 Received August 4, 2003; Revised Manuscript Received September 9, 2003
ABSTRACT We use a first-principles technique to calculate the length dependence of resistance of alkanethiol wires in the metal−alkanethiol−metal configuration. The current−voltage characteristics of the wires are found to be largely linear, and the small bias resistance increases exponentially with the molecule length. We also investigate the effects of changes at the metal−molecule junction, including the contact geometry, endgroups, and junction distance. We compare theoretical results with recently reported experimental data.
A prototypical self-assembled monolayer (SAM) that has received considerable attention is the alkanethiol film formed on Au surfaces.1 These SAMs are relatively easy to make and their charge transport properties have been studied by several laboratories.2,3 Recently, by contacting the SAM with a conducting atomic force microscope (AFM) tip,4-7 or by forming a molecular moiety between two metal electrodes,8 current-voltage (I-V) characteristics and conductance of the SAMs have been measured. The metal-alkanethiolmetal configuration can be thought of as being a model of molecular wire, which is important to the research field of molecular electronics.9,10 Such a device is becoming even more interesting because different laboratories reported transport data that were quantitatively consistent with each other.4-7 This consistency of measured data strongly suggests that the intrinsic transport properties of the alkanethiol SAM have been probed. Indeed, a very serious issue concerning molecular electronics is that experimental data are often dominated by details of the metal-molecule contacts that are difficult to control, rendering interpretation of data problematic. Alkanethiol SAMs, on the other hand, have very large resistance to dominate the electron transparency of the metal-alkanethiol-metal device. This is, presumably, a reason that different laboratories could produce quantitatively similar results.4-7 Moreover, by measuring the length dependence of resistance of the wires,4-7 one can extract a quantity that is the rate of resistance increase, and this quantity is independent of the number of molecules inside the metal-alkanethiol-metal junction. Such a measurement removes the difficulty of not knowing how many molecules are there during the transport measurement, hence providing another handle to the interpretation of the measured data. * Corresponding author. E-mail:
[email protected]. 10.1021/nl0346023 CCC: $25.00 Published on Web 09/27/2003
© 2003 American Chemical Society
Given the experimental progress in producing consistent data on the alkanethiol molecular wires, which provide a good testing ground for theoretical investigation, we believe it is timely and important to address the following question: can one make parameter-free quantitative predictions that can be directly compared with the measured data? In other words, are the existing theoretical and numerical tools adequate in providing a quantitative understanding to experiments? This issue is highlighted by ab initio analysis of conjugated molecule tunnel junctions where theory11 and experimental data12 differ by orders of magnitude. Conjugated systems are more difficult to control experimentally because the molecules typically have small resistance, therefore the contact resistance becomes important. Since the problem of controlling metal-molecule contact has not been systematically solved experimentally, it has been rather rare to see consistent transport data between different labs on conjugated molecular wires.13 Therefore, instead of investigating conjugated molecular wires, in this paper we will focus on the metal-alkanethiolmetal wire, and for this system we provide a positive answer to the above question. In particular, we focus on the following experimental findings on the metal-alkanethiolmetal system:4 (i) for bias voltages between (0.3 V, the I-V curves are almost linear; (ii) the resistance of the alkanethiol chains involving 4 to 8 carbons (C4-C8) is in the range of 0.2 MΩ to 200 MΩ at a load of 1 nN in the conducting AFM study; (iii) the resistance roughly scales as R ) Ro exp(βn), where β ≈ 1.0 per carbon at low loads (less than 10 nN) and n is the number of carbon atoms. Existing studies3-5,8 of metal-alkanethiol-metal devices have already provided a qualitative explanation of the exponential length dependence of resistance using models involving some phenomenological parameters. In the calcu-
Figure 1. (a) Schematic illustration of the Au-molecule-Au junction. The simulation box (device) is indicated by the scattering region, which includes a portion of the infinitely long electrodes and the alkanethiol molecule. The distance of S-Au (surface) and H-Au is 4.0 a.u. Five alkanethiol molecules are studied: CH3(CH2)nS, n ) 3 to 7. (b) Schematic illustration of an Alalkanethiol-Al wire. The contact layer of Al atoms to the molecule is “tempered”.
lations to be reported below, we use the first-principles computation package,14 McDCAL, which is based on the Keldysh nonequilibrium Green’s functions (NEGF) combined with density functional theory (DFT). This software enables us to calculate the charge density for open quantum systems under a bias voltage entirely self-consistently without phenomenological parameters. We therefore provide qualitative as well as quantitative analysis of the transport properties to the metal-alkanethiol-metal junction. In addition, our technique14 not only can determine how conduction channels arise from the molecular orbitals11,16 inside the scattering region but also from which bands of the electrode.17 The NEGF-DFT ab initio technique has been documented in ref 14, and we refer interested readers to it. Very briefly, the Kohn-Sham (KS) wave function is expanded in terms of the s,p,d atomic basis set, the charge density is calculated by NEGF, which takes into account the external bias voltage and the device transport boundary condition, and the contribution of device leads is calculated and included in the KS potential via self-energies. After the KS potential is obtained self-consistently, we calculate transport properties of the device using the Landauer formula,18 in which the transmission coefficient is calculated from the Green’s functions.14,18,19 Since the experimental devices4 involve many material and fabrication details that are unknown, such as the contact geometry and quality and the number of molecules sandwiched between the two leads, we begin by assuming a plausible atomic configuration. In particular, we consider the device model shown in Figure 1 where an alkanethiol chain20 is contacted by two atomic scale metallic electrodes extend1522
Figure 2. (a) I-V characteristics of Au-alkanethiol-Au junctions as a function of the number of carbons in the alkanethiol chains. (b) Semilog plot of resistance versus number of carbon in the alkane chains. Filled circles: Au-alkanethiol-Au (fitted by solid line, Ro ) 24 kΩ, β ) 0.95); empty circles: for Al-alkanethiol-Al device where an Al unit cell has 18 Al atoms oriented in the (100) direction (dotted line, Ro ) 65 kΩ, β ) 1.0); empty triangles: still for Al-alkanethiol-Al device but with a larger lead tempered at the Al-molecule contact [see Figure 1b] (dashed line, Ro ) 105 kΩ, β ) 0.95); filled square: Au-alkanedithiol-Au (long dashed line, Ro ) 1.5 kΩ, β ) 0.95); filled triangles: Au-alkanethiol(CF3)-Au (dot-dashed line, Ro ) 250 kΩ, β ) 0.95).
ing to reservoirs at z ) (∞, where bias is applied and current collected.21 We investigate the conducting behavior of the chain with different number of carbons. The molecule-lead distance is fixed to be a constant for all the systems we studied: the distance of the S-Au (from the sulfur atom to the surface of Au lead) and the H-Au is 4.0 au. Since the precise distance during charge transport is unknown, we choose these distances to be close to the equilibrium bond length suggested in the literature.22 Figure 2a plots the calculated I-V curves for the Aualkanethiol-Au wires [device in Figure 1a]. They are almost linear over the range of the bias voltage we applied. As the number of carbon atoms increases, the current decreases. The linear I-V curves give a resistance that is plotted in Figure 2b in a semilog form (resistances calculated at 0.1 V bias voltage), shown by the filled circles. The roughly linear increase of R in the semilog plot suggests a rapid increase in Rn as the number of carbon atoms, n, increases. We obtain Rn ≈ Ro exp(βn), where Ro ) 24 KΩ and β ≈ 0.95 per carbon. The corresponding experimental data were reported4 to be β ≈ 1.0 at low AFM loads (
