We consider the transport of electrons through a molecular
system by modeling it as a one electron elastic scattering
problem. The molecule acts as a defect between two metallic
reservoirs of electrons. An electron incident from the source
lead with an energy E, has a transmission probability T(E)to scatter through the molecule into the drain lead. A
schematic of the model system is shown in Fig. 2.1. By
determining the transmission probability for a range of
energies around the Fermi energy
of the source
lead, the finite temperature, finite voltage,
Landauer formula can be used to calculate the
transmitted current I as a function of the bias voltage, V,
applied between the source (left lead) and drain (right lead)
![\begin{displaymath}I(V) = \frac{2e}{h} \int_{-\infty}^{\infty}
dE\:T(E)\left( \f...
...E-\mu_{s})/kT] + 1} -
\frac{1}{\exp[(E-\mu_{d})/kT]+1} \right)
\end{displaymath}](img3.gif) |
(1) |
The two electro-chemical potentials 
and  ,
refer to the source and drain, respectively. They are defined
to be,
and
 .
The differential conductance is then
given by the derivative of the current with respect to voltage.
|