Local Heating in Nanoscale Conductors

Abstract

We report first-principles calculations of local heating in nanoscale junctions formed by a single molecule and a gold point contact. Due to the lower current density and larger heat dissipation, the single molecule heats up less than the gold point contact. We also find that, at zero temperature, a threshold bias Vonset of about 6 mV and 11 mV for the molecule and the point contact, respectively, is required to excite the smallest vibrational mode and generate heat. The latter estimate is in very good agreement with recent experimental results on the same system. At a given external bias V below Vonset, heating becomes noticeable when the background temperature is on the order of ∼ e(Vonset − V )/kB. Above Vonset, local heating increases dramatically with increasing bias but is also considerably suppressed by thermal dissipation into the electrodes. The results provide a microscopic picture of current-induced heat generation in atomic-scale structures.

Inelastic Current-Voltage Characteristics of Atomic and Molecular Junctions

“…We assume that the phonon distribution is at equilibrium at all (small) biases, thus neglecting local heating. [5] We have previously shown that for small biases this effect is small, provided good thermal contacts exist between the nanostructures and the bulk electrodes. [5] The many-body Hamiltonian of the system is (atomic units are used throughout this paper) [5] …”

“…We assume that the phonon distribution is at equilibrium at all (small) biases, thus neglecting local heating. [5] We have previously shown that for small biases this effect is small, provided good thermal contacts exist between the nanostructures and the bulk electrodes.[5] The many-body Hamiltonian of the system is (atomic units are used throughout this paper) [5]where H el is the electronic part of the Hamiltonian;iµ is the ionic contribution where q iµ is the normal coordinate and ω iµ is the normal frequency corresponding to the i-th ion and µ-th component; finally, H el−vib describes the electron-ion interaction and has the following form:where α = L, R; a α E and b jν are the electron and phonon annihilation operators, respectively, satisfying the usual commutation relations. A iµ,jν are the matrix elements of…”

“…However, the modes of a realistic junction are not necessarily purely transverse or purely longitudinal with respect to the direction of current flow. [5,6,7] Therefore, the inelastic current-voltage (I-V) characteristics are likely to depend strongly on the detailed atomic structure of the full system. This is particularly relevant for molecular junctions for which the contact geometry between the molecule and the bulk electrodes is difficult to control in experiments.…”

“…A iµ,jν are the matrix elements of the transformation from cartesian coordinates to normal coordinates, and J iµ,αβ E1,E2 is the electron-phonon coupling constant which can be directly calculated from the scattering wave-functions [5] …”

The influence of vibronic coupling on the shape of transport characteristics in inelastic tunneling through molecules

“…Recently, the polaron formation on the molecule was also suggested as a possible mechanism for generating the negative differential resistance (NDR effect) and hysteresis behaviour of the V I − dependence [40]. Moreover, the problem of localized electron-phonon interactions is closely connected to the problem of local heating in current carrying molecular junctions [41,42].…”