Length Matters: Keeping Atomic Wires in Check
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Length Matters: Keeping Atomic Wires in Check Brian Cunningham, Tchavdar N. Todorov and Daniel Dundas Atomistic Simulation Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, U.K. ABSTRACT Dynamical effects of non-conservative forces in long, defect free atomic wires are investigated. Current flow through these wires is simulated and we find that during the initial transient, the kinetic energies of the ions are contained in a small number of phonon modes, closely clustered in frequency. These phonon modes correspond to the waterwheel modes determined from preliminary static calculations. The static calculations allow one to predict the appearance of non-conservative effects in advance of the more expensive real-time simulations. The ion kinetic energy redistributes across the band as non-conservative forces reach a steady state with electronic frictional forces. The typical ion kinetic energy is found to decrease with system length, increase with atomic mass, and its dependence on bias, mass and length is supported with a pen and paper model. This paper highlights the importance of non-conservative forces in current carrying devices and provides criteria for the design of stable atomic wires. INTRODUCTION With the miniaturization of electronic devices, stability issues and failure due to large current-induced forces (CIF)—as a result of the huge current densities flowing—become a central issue. One particular component of the CIF is the electron wind force [1,2], which has received a lot of attention recently due to its non-conservative nature [1,3-5]. Non-conservative forces (NCF) could cause adverse effects in nanoscale devices. For example, NCF (as opposed to Joule heating) may be the primary mechanism behind certain electromigration phenomena and anomalous heating in atomic wires [6]. However, NCF may also be exploited constructively, for example, in the development of a nanoscale engine [7]. Long defect free atomic wires are prime candidates for observing certain properties and characteristics of NCF. The reason is the dense vibrational mode frequency spectra of these systems [8] together with their high conductivity. It is shown in [3,8] that current can couple near degenerate modes to create new modes that grow in time (referred to as waterwheel modes). In this paper we employ two methods for investigating NCF: a Landauer steady-state approach; and non-equilibrium, non-adiabatic molecular dynamics (MD) simulations. We investigate the normal modes under bias in the Landauer steady-state [9], and as we shall see, this allows us to predict the outcome of the MD. In the MD, we find that as a result of the competition between NCF and electronic friction, the typical kinetic energy of an ion (and hence effective temperature) attained under the above non-equilibrium conditions decreases with system length but increases with atomic mass. A simple model to support the findings is given in the results. METHOD The types of systems investigated are illustrated in figure 1. A device re
