Article pubs.acs.org/JPCC
First Principles Study of Electron Tunneling through Ice Clotilde S. Cucinotta,* Ivan Rungger, and Stefano Sanvito School of Physics and CRANN, Trinity College, Dublin 2, Ireland ABSTRACT: With the aim of understanding electrochemical scanning tunnel microscopy experiments in an aqueous environment, we investigate electron transport through ice in the coherent limit. This is done by using the nonequilibrium Green’s functions method, implemented within density functional theory, in the self-interaction corrected local density approximation. In particular, we explore different ice structures and different Au electrode surface orientations. By comparing the decay coefficient for different thicknesses to the ice complex band structure, we find that the electron transport occurs via tunneling with almost one-dimensional character. The slow decay of the current with the ice thickness is largely due to the small effective mass of the conduction electrons. Furthermore, we find that the calculated tunneling decay coefficients at the Fermi energy are not sensitive to the structural details of the junctions and are at the upper end of the experimental range for liquid water. This suggests that linear response transport measurements are not capable of distinguishing between different ordered ice structures. However, we also demonstrate that a finite bias measurement may be capable of sorting polar from nonpolar interfaces due to the asymmetry of the current−voltage curves for polar interfaces.
However the same argument was excluded in ref 5, where it was instead proposed that the remarkably small tunnel barrier through water is simply due to the electronic structure of the metal−water junction. In the same paper, the one-dimensional (1D) nature of the tunneling process over a wide range of distances was confirmed. Finally for short tip-to-sample separations, Φ is found to depend strongly on the voltage polarity,5,6 a fact which is likely due to a realignment of the water molecules in the STM electric field. In recent computational simulations of such systems, the one electron pseudopotential model of Barnett et al.8 has been used to describe the interaction of the hydrated electron in water with the environment.9 It was found that, for large electric fields, the water structure in a junction geometry depends on the bias. In this regime, electron tunneling through ordered molecular barriers is found to depend on the tunneling direction, in contrast to earlier predictions based on the continuum dielectric model.10 In both such simulations, it was assumed that the electron transmission time through water is short enough so that nuclear motion in the molecular barrier can be disregarded. This is justified by the fact that typical tunneling times are of about 1 fs for a 5 Å tip−sample separation.9 Transmission of electrons through resonant levels in the molecular barrier would cause the interaction times between nuclear and electronic motions to be longer, and the static barrier approximation would consequently break down.
Electron tunneling in water is an important phenomenon, which relates to the different types of electron transfer processes that can occur in an aqueous environment. It is also at the foundation of electrochemical scanning tunneling microscopy (EC-STM), which has become an important tool for investigating both the surface structure of the electrodes and possible reactions at electrochemical interfaces.1−3 The fundamental mechanism of the EC-STM operation in aqueous solution and in particular the electron tunneling process through the interfacial water layer however is still not completely understood. An early study of Binggeli et al.4 on the dependence of the tunneling current on the distance between the STM tip and the sample in an electrolytic solution has shown that the tunneling distance in aqueous solutions is substantially longer than that measured in vacuum. Such electrochemical STM experiments4,5 have observed that the dependence of the tunneling conductance, G, on distance follows approximately the expected exponential behavior G = G0e−2κd, where G0 is a prefactor, d is the tip-to-sample distance, and κ is the decay 1
coefficient. This is usually approximated as κ = (2m0/ℏ2) /2√Φ, with m0 being the free electron mass and Φ the apparent barrier height. As such, by measuring κ, it is possible to infer Φ.5,6 Experimental results for Φ in water and in vacuum usually range between 0.1−2 eV and 3−5 eV,4,5 respectively. Furthermore, usually the tunneling current seems to depend on the tip used, the electrochemical conditions, and possible impurities.5 It has also been suggested that the lower value of the tunneling barrier with respect to vacuum could be due to elastic deformation of the STM junction caused by the tip pressure, which would change the actual gap distance.7 © 2012 American Chemical Society
Received: May 28, 2012 Revised: August 28, 2012 Published: September 20, 2012 22129
dx.doi.org/10.1021/jp3051774 | J. Phys. Chem. C 2012, 116, 22129−22138
The Journal of Physical Chemistry C
Article
Figure 1. (Color online) Relaxed structures of the studied Au/ice interfaces. We label the various junctions as αβγ/n−Σ where αβγ indicate the Au surface orientation [either (111) or (110)], n labels the crystal symmetry of the ice (c = cubic; h = hexagonal), and Σ indicates whether the ice surface is polar (P) or nonpolar (NP). Note that, despite the apparences, in the hexagonal ice structures, there are no two hydrogen atoms in the H bond of hexagonal ice. Color code: Au = large yellow (light gray) spheres; H = small light blue (light gray) spheres; O = medium red (dark gray) spheres.
tally determined Φ is due to the fact that the electron effective mass near the ice conduction band minimum is about a factor of two smaller than the bare electron mass. Once this is taken into account, no disagreement is found between theory and experiments, and the 1D model for tunneling provides a good description of the STM data. The paper is organized as follows. In the next two sections, we describe the computational methods used and the strategy adopted to construct the Au/ice/Au structures. We then move to present the electronic transport properties for the different interfaces considered and compare the results for the barrier heights to available experimental data for liquid water. Finally, we present our conclusions.
In a subsequent work,11 performed with a more refined model for the potential and the system, it was stated that the transmission probabilities could not be described by simply using a 1D rectangular barrier. Furthermore, it was claimed that different water configurations scatter tunneling electrons in different ways. It was also found that, in the deep tunneling regime (>1 eV below the barrier), the width of the electron current distribution with the water configurations is rather narrow and that, in this energy region, nuclear motion is slow relative to the time that the electron spends in the barrier. This contrasts with the resonance region (
