Solving rate equations for electron tunneling via discrete quantum states

Abstract

We consider the form of the current-voltage curves generated when tunneling spectroscopy is used to measure the energies of individual electronic energy levels in nanometer-scale systems. We point out that the voltage positions of the tunneling resonances can undergo temperature-dependent shifts, leading to errors in spectroscopic measurements that are proportional to temperature. We do this by solving the set of rate equations that can be used to describe electron tunneling via discrete quantum states, for a number of cases important for comparison to experiments, including (1) when just one spin-degenerate level is accessible for transport, (2) when 2 spin-degenerate levels are accessible, with no variation in electron-electron interactions between eigenstates, and (3) when 2 spin-degenerate levels are accessible, but with variations in electron-electron interactions. We also comment on the general case with an arbitrary number of accessible levels. In each case we analyze the voltage-positions, amplitudes, and widths of the current steps due to the quantum states.

Coulomb blockade in molecular quantum dots

“…In this case, approximate current steps (or conductance peaks) can even merge due to the mentioned phenomenon (compare the curves for U = 0.5). Additionally, the temperature-generated shifting of resonances (current steps or conductance peaks) [17] should be noted. However, this effect seems to be negligibly small for MQD-based junctions within a reasonable range of model parameters.…”

“…Here we present a standard rate-equation approach to transport via discrete energy states [7,[14][15][16][17]. This was used in section 2 to develop the presented model.…”

“…In this case, all the cotunneling processes can be neglected and the current is accurately described by lowest-order perturbation theory. In these conditions, transport can be analyzed in the sequential-tunneling picture using a rate-equation approach [7,[14][15][16][17]. In other words, the current flowing through the device is a strict consequence of sequential electron transition, whereby the molecular quantum dot is successively charged and discharged by the tunneling process.…”

Theory of High Bias Coulomb Blockade in Ultrashort Molecules

“…It is interesting to note that most theoretical efforts in molecular conduction have been in the ballistic SCF regime, in which relaxation effects due to electron-phonon interaction are not taken into account. Our paper is thus a concrete attempt towards CI based transport in the sequential tunneling regime [19], [40] and neglects effects of electron-phonon interactions. These interactions could technically be included within the same framework [17], [18] as already noted.…”

Rate-equation calculations of the current flow through two-site molecular device and DNA-based junction

“…Later, Zwolak and Di Ventra using the same method have predicted that a spin-valve behavior can be observed in experiments with ferromagnetic electrodes [29]. The main purpose of this work is to perform the calculations within the rate-equation approach [30][31][32][33][34] to study the influence of a few important factors on incoherent transport through a two-site molecular device as well as a DNA-based junction, namely: (i) the strength of the molecule-electrode coupling, (ii) the asymmetry of the contact, (iii) the length of DNA molecule, and (iv) the temperature of the system under investigation. It should be also noted that the mentioned method was used earlier to calculate numerically the I − V dependences of DNA-based devices [35][36][37][38].…”