A new theoretical model for inelastic tunneling in realistic systems : comparing STM simulations with experiments

Abstract

This thesis has been dedicated to modeling the electron transport in tunnel junctions in order to efficiently describe and predict inelastic effects that occur when electrons pass a tunnel junction. These inelastic effects can be considered at several levels of sophistication, from very simple to very complex. The main innovation in this thesis is the development of the lowest order in inelastic tunneling (LOIT) approach. This approach has been employed to predict inelastic electron tunneling spectroscopy (IETS) intensities of vibrational modes in three different systems of increasing complexity. The thesis can be divided into three parts. The first part, which contains Chapters 1 and 2, serves as an introduction to STM imaging and inelastic effects in tunnel junctions. Chapter 1 introduces the reader to a debate in biology in which IETS could be the key tool to determine the physical mechanism of smell. The possible link between smell and IETS is explained and a roadmap for future research is outlined which might help answer the question whether our nose detects odors by measuring vibrations of molecules with tunneling electrons. Since all IETS experiments and modeling are performed using a scanning tunneling microscope (STM), Chapter 2 describes the processes of STM, scanning tunneling spectroscopy (STS) and IETS in simple terms and presents the details of the STM experiments. The second part, Chapters 3 and 4, presents in full detail the modeling of the electron transport in a realistic STM experiment, where Chapter 3 is devoted to the description of elastic transport and Chapter 4 to including inelastic effects. The ab initio method described here requires density functional theory (DFT) and Green's functions calculations, which are both introduced in Chapter 3. The crucial interactions between tip and sample are described by Slater-Koster (SK) functions fitted to DFT calculations. Three parameterization schemes are presented in Chapter 3. In Chapter 4 a two-level system within a one-dimensional model is introduced to describe in more detail the STM setup and to investigate which ingredients are necessary to correctly describe IETS intensities. To obtain correct IETS signals it is crucial to take the inelastic tunneling terms – i.e. the interactions between tip and sample under excitation of a vibrational mode – into account. These inelastic tunneling terms are included up to lowest order in the introduced LOIT approach, which is described in detail. Within the tunneling regime, inclusion of these terms up to lowest order represents an accurate approximation and reduces drastically the computational cost for this type of calculations. The third and last part of the thesis, which contains Chapters 5-8, concerns the results obtained by employing the LOIT approach to realistic systems for which experimental data is available. Chapter 5 describes IETS on a CO molecule adsorbed onto Ag(110). The simulated STM images reproduce the experimental fact that a tip which is terminated with a CO molecule leads to a protrusion in the imaging of a CO molecule on the surface, and a clean tip leads to a dip in the imaging of a CO molecule. Next, inelastic spectra are simulated by combining the LOIT method with the wide band limit (WBL). In agreement with the experiment, the hindered rotation modes contribute the most, and, depending on the used tip, also the metal-CO stretch mode. Using full Green's functions leads to problems in convergence in k-grid size and hence the wide band limit must be assumed. Furthermore, propensity rules are explored, which can be used to simply predict IETS intensities. The IETS intensity of a given vibrational mode is large if i) the inelastic tunneling matrix elements are large, ii) the corresponding AOs contribute to the elastic current and iii) there is no destructive interference. Chapter 6 describes IETS on a monolayer of NO on Rh(111). It is found that NO molecules are imaged as a protrusion if an NO molecule is adsorbed in upright position on the tip. The simulated STM images suggest that without such a tip NO molecule, the probability is low for the tunneling electrons to traverse the surface NO molecules. The LOIT+WBL approach gives qualitatively correct predictions for which vibrations are excited. In this system the measured peaks around ±18 mV are assigned to a convolution of the out-of-phase ?(Rh-NO) and several R(N-O) modes and the peaks around ±55 mV to a convolution of the surface in phase ?(Rh-NO) and tip ?(W-NO) modes. Both in Chapter 5 and in Chapter 6 the IETS intensities depend crucially on the used tip. The low intensity of inelastic effects in the curves obtained with the tips without an NO molecule adsorbed upright is consistent with the low probability of tunneling through the orbitals of the surface NO molecules for these tips. Chapters 7 and 8 deal with the more complex system of a self assembled thiophenol monolayer on Ag(111). Because the full details of a junction are important to describe the IETS signals, the structure of the monolayer is first studied in Chapter 7. From the results of STM and low energy electron diffraction (LEED) experiments and simple LEED modeling, an adsorption model is proposed with six molecules and 17 Ag atoms per layer in the unit cell. It is shown that the optimal structure of the monolayer obtained by DFT depends critically on the initial configuration and the used approximation to incorporate Van-der-Waals interactions. DFT could therefore not be used to determine accurately geometric parameters such as the adsorption site, ring tilt angle or S-C bond angle. Also the STM simulations could not be used to determine which surface geometry corresponds to the experiments, although they justify the wide variety of experimental STM images and reproduce the most robust features. The vibrational modes calculated with DFT for the large unit cell are nearly identical to those calculated for a small model unit cell and reproduce reasonably well those measured with high resolution electron energy loss spectroscopy (HREELS). This suggests that the vibrational modes are not very sensitive to the details of the adsorption geometry of the molecules. Chapter 8 describes a well-reported narrow reduction in the density of states (DOS) around the Fermi energy, termed zero-bias anomaly (ZBA), in thiol-bound molecular junctions. A few possible explanations are reviewed in Chapter 8. First, the suggestion that the ZBA is part of the single-particle DOS is discarded by means of DFT calculations, and next a many-body explanation which includes umklapp processes is also discarded by means of experimental photoemission spectroscopy. The excitation of low energetic vibrations, as calculated with the LOIT+WBL approach, does lead to a pseudogap in the conductance at low voltages, although the found intensity is too low for realistic tip-sample distances. By moving the tip closer, the IETS intensity increases, although it is questionable if the transport still takes place in the tunneling regime then. In conclusion, for junctions in which the transport takes place in the tunneling regime, the LOIT+WBL approach is an efficient method to calculate IETS intensities. The efficiency of the method allows for treating highly complex systems such as the STM setup. The limiting factor in an ab initio implementation of the method is the time required to accurately perform the DFT calculations to obtain the ground state geometry, electronic structure and vibrational modes. The relative IETS intensities calculated with this method are correct and the absolute values have the correct order of magnitude. Outlook Details of simulated STM images as well as accurate values for IETS intensities depend critically on two so far unknown factors: the SK parameters and the details of the tip. The amount of atoms taken into account in the DFT calculations to which the SK parameters are fitted represent a tradeoff between accuracy (many atoms) on the one hand and efficiency and transferability (few atoms) on the other hand. It is thus necessary to develop a more robust yet accurate parameterization scheme, allowing the correct description of both STM images and IETS curves. The tips used in experiments can differ significantly from one experiment to another. This can be modeled by varying the metal termination, the adsorbates and/or their adsorption sites in the DFT calculations and by rotating the tip axes in the Green's functions calculations. However, in order to prevent from drowning in a sea of possibilities, it is important to i) experimentally make stable tips, including controlled atom transfer, and ii) identify the most important characteristics of tip terminations that determine the transport in an STM junction and model only a limited number of them. The implementation of the LOIT approach in the STM simulations helps in determining this robust yet accurate SK parameterization scheme and in selecting characteristic tips and brings as a result modeling of molecular transport junctions a step forward. Furthermore, since the LOIT approach is a relatively cheap method to detect which vibrations are excited in molecules, IETS spectra of more complex molecules can be better understood. This can be helpful to better choose systems to test the vibrational odor recognition theory and to predict odor intensities.