Semiempirical model for nanoscale device simulations

We present a semiempirical model for calculating electron transport in atomic-scale devices. The model is an extension of the extended Hückel method with a self-consistent Hartree potential that models the effect of an external bias and corresponding charge rearrangements in the device. It is also possible to include the effect of external gate potentials and continuum dielectric regions in the device. The model is used to study the electron transport through an organic molecule between gold surfaces, and it is demonstrated that the results are in closer agreement with experiments than ab initio approaches provide. In another example, we study the transition from tunneling to thermionic emission in a transistor structure based on graphene nanoribbons.

Figure 1

(Color online) Geometry of a nanodevice consisting of a dithiol-triethynylene-phenylene molecule attached to two $\left(3\times 3\right)$ (111) gold electrodes. The left and right electrode regions are illustrated with wire boxes, and the properties of these regions are obtained from a calculation with periodic boundary conditions in all directions. The region between the two electrodes is the central device region, which is described with open boundary conditions in the transport direction and periodic boundary conditions in the directions perpendicular to the transport direction.

Figure 2

(Color online) The upper plot shows the transmission spectrum of the symmetric Tour wire device, calculated with the EH-SCF model for three different $k$-point samplings. The lower plot shows transmission spectra calculated with a $\left(2\times 2\right)$ $k$-point sampling using different models: EH-SCF (solid), EH without the Hartree term (dotted), and DFT-LDA (blue dashed). Energies are given relative to the Fermi level of the gold electrodes.

Figure 3

(Color online) Geometry of the asymmetric system. The Tour wire is attached to the left gold electrode through a thiol bond while the right end of the molecule is hydrogen terminated and there is no chemical bond to the right gold electrode.

Figure 4

(Color online) $I\text{−}V$ characteristics of the symmetric (upper figure) and asymmetric (lower figure) Tour wire devices. The positive current direction is from left to right.

Figure 5

(Color online) Voltage drop of the symmetric and asymmetric Tour wire systems along a line that goes through the two sulfur atoms in the symmetric system, for an applied bias of $+1\text{V}$. The inset shows the voltage drop in the asymmetric system subtracted from the voltage drop in the symmetric system. Both plots show results calculated with the EH-SCF (solid) and DFT-LDA (dashed) models.

Figure 6

(Color online) Graphene nanotransistor consisting of two metallic zigzag nanoribbons connected by a semiconducting armchair ribbon. The nanoribbons are passivated with hydrogen, and the width of the ribbons are is $7\text{Å}$. The device is sitting on top of a dielectric and the transport is controlled by an electrostatic backgate. The contour plot illustrates the Hartree potential for a gate potential of $-1\text{V}$.

Figure 7

Zero-bias transmission spectrum for the short (dashed) and long (solid) graphene devices. Energies are relative to the Fermi level of the electrodes.

Figure 8

(Color online) The tunneling current for a source-drain voltage of 0.2 V, as a function of the gate potential for the long (solid) and short (dashed) graphene devices, respectively. Three different values of the electron temperature in the electrodes were considered: 150, 300, and 450 K. The dotted lines illustrate the $1/k_{\text{B}}T$ slope for the different temperatures.