A self-consistent transport model for molecular conduction based on extended Hückel theory with full three-dimensional electrostatics

Abstract

We present a transport model for molecular conduction involving an extended Hückel theoretical treatment of the molecular chemistry combined with a nonequilibrium Green's function treatment of quantum transport. The self-consistent potential is approximated by CNDO (complete neglect of differential overlap) method and the electrostatic effects of metallic leads (bias and image charges) are included through a three-dimensional finite element method. This allows us to capture spatial details of the electrostatic potential profile, including effects of charging, screening, and complicated electrode configurations employing only a single adjustable parameter to locate the Fermi energy. As this model is based on semiempirical methods it is computationally inexpensive and flexible compared to ab initio models, yet at the same time it is able to capture salient qualitative features as well as several relevant quantitative details of transport. We apply our model to investigate recent experimental data on alkane dithiol molecules obtained in a nanopore setup. We also present a comparison study of single molecule transistors and identify electronic properties that control their performance.

Semiempirical model for nanoscale device simulations

“…Examples of semiempirical transport models are methods based on SlaterKoster tight-binding parameters 6,7 and extended Hückel ͑EH͒ parameters. [8][9][10][11][12][13][14] The ab initio models have the advantage of predictive power and can often give reasonable results for systems where there is no prior experimental data. However, the use of the Kohn-Sham one-particle states as quasiparticles is questionable, and it is well known that for many systems the energies of the unoccupied levels are rather poorly described within DFT.…”

Role of contact bonding on electronic transport in metal–carbon nanotube–metal systems

“…Appropriate Pariser-Parr-Pople (PPP) type functional forms of U SC , depending on a set of semiempirical parameters, have been introduced in the TB and EH models [18,19]. However, the potential profile inside a sufficiently long CNT could be assumed to be flat with the voltage drop largely occurring at the contacts.…”

“…In equation 2 f (E, L,R ) is the Fermi-Dirac distribution of electrons in the contact at chemical potential L,R E F 0.5V [16,18] where E F is the Fermi energy of the system and V the applied potential.…”

“…In the spirit of the semi-empirical approaches applied in this work it is more appropriate to consider the E F level as a free parameter, which should vary approximately between the Fermi energy of the infinite CNT and that of the contacts [16]. An empirical estimate of the E F level can be obtained eventually by fitting experimental results [18]. Anyhow the corrections in the I-V characteristics due to charging effects under bias conditions can be evaluated by means of our approach, while in consistence to the previous discussion we have considered different values of the E F level in our calculations.…”

“…Contrarily, when E F is positioned symmetrically with the states present for E<E F and E>E F a balanced charge transfer between the device and the two pads occurs reducing sensibly the charging effects [16,18].…”