arXiv subjects

Magnus Paulsson

Publications and source records attributed to Magnus Paulsson.

18 recordsLinked to original sources

arXiv2018

STM contrast of a CO dimer on a Cu(1 1 1) surface: a wave-function analysis

We present a method used to intuitively interpret the STM contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.

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arXiv2018

Theory of vibrationally assisted tunneling for hydroxyl monomer flipping on Cu(110)

To describe vibrationally mediated configuration changes of adsorbates on surfaces we have developed a new theory to calculate both reaction rates and pathways. The method uses the T-matrix to describe excitations of vibrational states by the electrons of the substrate, adsorbate and tunneling electrons from a scanning tunneling probe. In addition to reaction rates, the theory also provides the reaction pathways by going beyond the harmonic approximation and using the full potential energy surface of the adsorbate which contains local minima corresponding to the adsorbates different configurations. To describe the theory, we reproduce the experimental results in [T. Kumagai \textit{et al.}, Phys. Rev. B \textbf{79}, 035423 (2009)], where the hydrogen/deuterium atom of an adsorbed hydroxyl (OH/OD) exhibits back and forth flipping between two equivalent configurations on a Cu(110) surface at $T = 6$ K. We estimate the potential energy surface and the reaction barrier, $\sim$160 meV, from DFT calculations. The calculated flipping processes arise from i) at low bias, tunneling of the hydrogen through the barrier, ii) intermediate bias, tunneling electrons excite the vibrations increasing the reaction rate although over the barrier processes are rare, and iii) higher bias, overtone excitations increase the reaction rate further.

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arXiv2018

Scanning tunneling microscopy current from localized basis orbital density functional theory

We present a method capable of calculating elastic scanning tunneling microscopy (STM) currents from localized atomic orbital density functional theory (DFT). To overcome the poor accuracy of the localized orbital description of the wave functions far away from the atoms, we propagate the wave functions, using the total DFT potential. From the propagated wave functions, the Bardeen's perturbative approach provides the tunneling current. To illustrate the method we investigate carbon monoxide adsorbed on a Cu(111) surface and recover the depression/protrusion observed experimentally with normal/CO-functionalized STM tips. The theory furthermore allows us to discuss the significance of $s$- and $p$-wave tips.

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arXiv2018

Analysis of STM images with pure and CO-functionalized tips: A first-principles and experimental study

We describe a first principles method to calculate scanning tunneling microscopy (STM) images, and compare the results to well-characterized experiments combining STM with atomic force microscopy (AFM). The theory is based on density functional theory (DFT) with a localized basis set, where the wave functions in the vacuum gap are computed by propagating the localized-basis wave functions into the gap using a real-space grid. Constant-height STM images are computed using Bardeen's approximation method, including averaging over the reciprocal space. We consider copper adatoms and single CO molecules adsorbed on Cu(111), scanned with a single-atom copper tip with and without CO functionalization. The calculated images agree with state-of-the-art experiments, where the atomic structure of the tip apex is determined by AFM. The comparison further allows for detailed interpretation of the STM images.

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arXiv2016

Influence of atomic tip structure on the intensity of inelastic tunneling spectroscopy data analyzed by combined scanning tunneling spectroscopy, force microscopy and density functional theory

Achieving a high intensity in inelastic scanning tunneling spectroscopy (IETS) is important for precise measurements. The intensity of the IETS signal can vary up to a factor three for various tips without an apparent reason accessible by scanning tunneling microscopy (STM) alone. Here, we show that combining STM and IETS with atomic force microscopy enables carbon monoxide front atom identification, revealing that high IETS intensities for CO/Cu(111) are obtained for single atom tips, while the intensity drops sharply for multi-atom tips. Adsorbing the CO molecule on a Cu adatom [CO/Cu/Cu(111)] such that it is elevated over the substrate strongly diminishes the tip dependence of IETS intensity, showing that an elevated position channels most of the tunneling current through the CO molecule even for multi-atom tips, while a large fraction of the tunneling current bypasses the CO molecule in the case of CO/Cu(111).

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arXiv2013

Isotope effect in acetylene C$_2$H$_2$ and C$_2$D$_2$ rotations on Cu(001)

A comprehensive analysis of the elementary processes behind the scanning tunneling microscope controlled rotation of C$_2$H$_2$ and C$_2$D$_2$, isotopologues of a single acetylene molecule adsorbed on the Cu(001) surface is given, with a focus on the isotope effects. With the help of density-functional theory we calculate the vibrational modes of C$_2$H$_2$ and C$_2$D$_2$ on Cu(001) and estimate the anharmonic couplings between them, using a simple strings-on-rods model. The probability of the elementary processes -- non-linear and combination band -- are estimated using the Keldysh diagram technique. This allows us to clarify the main peculiarities and the isotope effects of the C$_2$H$_2$ and C$_2$D$_2$ on Cu(001) rotation, discovered in the pioneering work [Stipe et al., Phys. Rev. Lett. 81, 1263 (1998)], which have not been previously understood.

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arXiv2013

Rotation of a single acetylene molecule on Cu(001) by tunneling electrons in STM

We study the elementary processes behind one of the pioneering works on STM controlled reactions of single molecules [Stipe et al., Phys. Rev. Lett. 81, 1263 (1998)]. Using the Keldysh-Green function approach for the vibrational generation rate in combination with DFT calculations to obtain realistic parameters we reproduce the experimental rotation rate of an acetylene molecule on a Cu(100) surface as a function of bias voltage and tunneling current. This combined approach allows us to identify the reaction coordinate mode of the acetylene rotation and its anharmonic coupling with the C-H stretch mode. We show that three different elementary processes, the excitation of C-H stretch, the overtone ladder climbing of the hindered rotational mode, and the combination band excitation together explain the rotation of the acetylene molecule on Cu(100).

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arXiv2011

Vibrationally induced flip motion of a hydroxyl dimer on Cu(110)

Recent low-temperature scanning-tunneling microscopy experiments [T. Kumagai et al., Phys. Rev. B 79, 035423 (2009)] observed the vibrationally induced flip motion of a hydroxyl dimer (OD)2 on Cu(110). We propose a model to describe two-level fluctuations and current-voltage characteristics of nanoscale systems which undergo vibrationally induced switching. The parameters of the model are based on comprehensive density-functional calculations of the system's vibrational properties. For the dimer (OD)2 the calculated population of the high and low conductance states, the I-V, dI/dV, and d2I/dV2 curves are in good agreement with the experimental results and underlines the different roles played by the free and shared OD stretch modes of the dimer.

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arXiv2008

Unified description of inelastic propensity rules for electron transport through nanoscale junctions

We present a method to analyze the results of first-principles based calculations of electronic currents including inelastic electron-phonon effects. This method allows us to determine the electronic and vibrational symmeties in play, and hence to obtain the so-called propensity rules for the studied systems. We show that only a few scattering states -- namely those belonging to the most transmitting eigenchannels -- need to be considered for a complete description of the electron transport. We apply the method on first-principles calculations of four different systems and obtain the propensity rules in each case.

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arXiv2007

Transmission eigenchannels from non-equilibrium Green's functions

The concept of transmission eigenchannels is described in a tight-binding nonequilibrium Green's function (NEGF) framework. A simple procedure for calculating the eigenchannels is derived using only the properties of the device subspace and quantities normally available in a NEGF calculation. The method is exemplified by visualization in real-space of the eigenchannels for three different molecular and atomic-wires.

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arXiv2007

From tunneling to contact: Inelastic signals in an atomic gold junction

The evolution of electron conductance in the presence of inelastic effects is studied as an atomic gold contact is formed evolving from a low-conductance regime (tunneling) to a high-conductance regime (contact). In order to characterize each regime, we perform density functional theory (DFT) calculations to study the geometric and electronic structures, together with the strength of the atomic bonds and the associated vibrational frequencies. The conductance is calculated by first evaluating the transmission of electrons through the system, and secondly by calculating the conductance change due to the excitation of vibrations. As found in previous studies [Paulsson et al., Phys. Rev. B. 72, 201101(R) (2005)] the change in conductance due to inelastic effects permits to characterize the crossover from tunneling to contact. The most notorious effect being the crossover from an increase in conductance in the tunneling regime to a decrease in conductance in the contact regime when the bias voltage matches a vibrational threshold. Our DFT-based calculations actually show that the effect of vibrational modes in electron conductance is rather complex, in particular when modes localized in the contact region are permitted to extend into the electrodes. As an example, we find that certain modes can give rise to decreases in conductance when in the tunneling regime, opposite to the above mentioned result. Whereas details in the inelastic spectrum depend on the size of the vibrational region, we show that the overall change in conductance is quantitatively well approximated by the simplest calculation where only the apex atoms are allowed to vibrate. Our study is completed by the application of a simplified model where the relevant parameters are obtained from the above DFT-based calculations.

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arXiv2006

Inelastic transport theory from first-principles: methodology and applications for nanoscale devices

We describe a first-principles method for calculating electronic structure, vibrational modes and frequencies, electron-phonon couplings, and inelastic electron transport properties of an atomic-scale device bridging two metallic contacts under nonequilibrium conditions. The method extends the density-functional codes SIESTA and TranSIESTA that use atomic basis sets. The inelastic conductance characteristics are calculated using the nonequilibrium Green's function formalism, and the electron-phonon interaction is addressed with perturbation theory up to the level of the self-consistent Born approximation. While these calculations often are computationally demanding, we show how they can be approximated by a simple and efficient lowest order expansion. Our method also addresses effects of energy dissipation and local heating of the junction via detailed calculations of the power flow. We demonstrate the developed procedures by considering inelastic transport through atomic gold wires of various lengths, thereby extending the results presented in [Frederiksen et al., Phys. Rev. Lett. 93, 256601 (2004)]. To illustrate that the method applies more generally to molecular devices, we also calculate the inelastic current through different hydrocarbon molecules between gold electrodes. Both for the wires and the molecules our theory is in quantitative agreement with experiments, and characterizes the system-specific mode selectivity and local heating.

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arXiv2006

Inelastic fingerprints of hydrogen contamination in atomic gold wire systems

We present series of first-principles calculations for both pure and hydrogen contaminated gold wire systems in order to investigate how such impurities can be detected. We show how a single H atom or a single H2 molecule in an atomic gold wire will affect forces and Au-Au atom distances under elongation. We further determine the corresponding evolution of the low-bias conductance as well as the inelastic contributions from vibrations. Our results indicate that the conductance of gold wires is only slightly reduced from the conductance quantum G0=2e^2/h by the presence of a single hydrogen impurity, hence making it difficult to use the conductance itself to distinguish between various configurations. On the other hand, our calculations of the inelastic signals predict significant differences between pure and hydrogen contaminated wires, and, importantly, between atomic and molecular forms of the impurity. A detailed characterization of gold wires with a hydrogen impurity should therefore be possible from the strain dependence of the inelastic signals in the conductance.

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arXiv2005

Modeling inelastic phonon scattering in atomic- and molecular-wire junctions

Computationally inexpensive approximations describing electron-phonon scattering in molecular-scale conductors are derived from the non-equilibrium Green's function method. The accuracy is demonstrated with a first principles calculation on an atomic gold wire. Quantitative agreement between the full non-equilibrium Green's function calculation and the newly derived expressions is obtained while simplifying the computational burden by several orders of magnitude. In addition, analytical models provide intuitive understanding of the conductance including non-equilibrium heating and provide a convenient way of parameterizing the physics. This is exemplified by fitting the expressions to the experimentally observed conductances through both an atomic gold wire and a hydrogen molecule.

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arXiv2004

Electrostatic potential profiles of molecular conductors

The electrostatic potential across a short ballistic molecular conductor depends sensitively on the geometry of its environment, and can affect its conduction significantly by influencing its energy levels and wave functions. We illustrate some of the issues involved by evaluating the potential profiles for a conducting gold wire and an aromatic phenyl dithiol molecule in various geometries. The potential profile is obtained by solving Poisson's equation with boundary conditions set by the contact electrochemical potentials and coupling the result self-consistently with a nonequilibrium Green's function (NEGF) formulation of transport. The overall shape of the potential profile (ramp vs. flat) depends on the feasibility of transverse screening of electric fields. Accordingly, the screening is better for a thick wire, a multiwalled nanotube or a close-packed self-assembled monolayer (SAM), in comparison to a thin wire, a single-walled nanotube or an isolated molecular conductor. The electrostatic potential further governs the alignment or misalignment of intramolecular levels, which can strongly influence the molecular I-V characteristic. An external gate voltage can modify the overall potential profile, changing the current-voltage (I-V) characteristic from a resonant conducting to a saturating one. The degree of saturation and gate modulation depends on the metal-induced-gap states (MIGS) and on the electrostatic gate control parameter set by the ratio of the gate oxide thickness to the channel length.

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arXiv2004

High-Field, Quasi-Ballistic Transport in Short Carbon Nanotubes

Single walled carbon nanotubes with Pd ohmic contacts and lengths ranging from several microns down to 10 nm are investigated by electron transport experiments and theory. The mean free path (mfp) for acoustic phonon scattering is estimated to be lap~300 nm, and that for optical phonon scattering is lop~15 nm. Transport through very short (~10 nm) nanotubes is free of significant acoustic and optical phonon scattering and thus ballistic and quasi-ballistic at the low and high bias voltage limits respectively. High currents of up to 70 uA can flow through a short nanotube. Possible mechanisms for the eventual electrical breakdown of short nanotubes at high fields are discussed. The results presented here have important implications to high performance nanotube transistors and interconnects.

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arXiv2002

Current-voltage Characteristics of Molecular Conductors: Two versus Three Terminal

This paper addresses the question of whether a ``rigid molecule'' (one which does not deform in an external field) used as the conducting channel in a standard three-terminal MOSFET configuration can offer any performance advantage relative to a standard silicon MOSFET. A self-consistent solution of coupled quantum transport and Poisson's equations shows that even for extremely small channel lengths (about 1 nm), a ``well-tempered'' molecular FET demands much the same electrostatic considerations as a ``well-tempered'' conventional MOSFET. In other words, we show that just as in a conventional MOSFET, the gate oxide thickness needs to be much smaller than the channel length (length of the molecule) for the gate control to be effective. Furthermore, we show that a rigid molecule with metallic source and drain contacts has a temperature independent subthreshold slope much larger than 60 mV/decade, because the metal-induced gap states in the channel prevent it from turning off abruptly. However, this disadvantage can be overcome by using semiconductor contacts because of their band-limited nature.

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arXiv2002

Resistance of a Molecule

In recent years, several experimental groups have reported measurements of the current-voltage (I-V) characteristics of individual or small numbers of molecules. Our purpose in this chapter is to provide an intuitive explanation for the observed I-V characteristics using simple models to illustrate the basic physics. In contrast to the MOSFET, whose I-V is largely dominated by classical electrostatics, the I-V characteristics of molecules is determined by a more interesting interplay between nineteenth century physics (electrostatics) and twentieth century physics (quantum transport) and it is important to do justice to both aspects. We start with a qualitative discussion of the main factors affecting the I-V characteristics of molecular conductors, using a simple toy model to illustrate their role. Including the effects of: (1) Shift in the energy level due to charging effects and (2) broadening of the energy levels due to the coupling to the two contacts we obtain realistic I-V plots, even though the toy model assumes that conduction takes place independently through individual molecular levels. In general, however, the full non-equilibrium Green's function (NEGF) formalism is needed. Here, we describe the NEGF formalism as a generalized version of the one-level model. This formalism provides a convenient framework for describing quantum transport and can be used in conjunction with ab initio or semi-empirical Hamiltonians. A simple semi-empirical model for a gold wire serves to illustrate the full NEGF formalism. This example is particularly instructive because it shows the lowest possible "Resistance of a 'Molecule'" per channel.

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