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


Image of FIG. 1.
FIG. 1.

The basic scheme of our self-consistent calculations along with a basic structure of a molecular conductor. The molecule is connected between two gold contacts with gate electrodes around it. The schematic shows the partitioning of the system into two parts: device and contacts. The device part is represented by the molecular Hamiltonian and the self-consistent potential whereas the self-energy terms describe the effects of contacts on the device. The self-consistent calculations are performed with a combination of NEGF and EHT in a two-step process.

Image of FIG. 2.
FIG. 2.

A comparison of the potential profiles for the gold-PDT-gold system (shown at the top) in our EHT-based models under the applied bias of . The dotted line shows the applied (Laplace) potential. The “” notation indicates the position of the two sulphur end groups. The bias polarity is defined as positive when the applied voltage on the left contact is positive. Same convention of bias polarity is maintained throughout this paper. The spatial features of the potential profile are captured in Huckel 3.0 whereas in our earlier models, the potential profile is assumed to be flat inside the molecule. Note that the device region only contains the PDT molecule.46

Image of FIG. 3.
FIG. 3.

A comparison of energy levels as a function of applied bias for the gold-PDT-gold system in our EHT-based models. Solid line, Huckel 3.0; dotted line, Huckel 2.0. In Huckel 1.0 the energy levels remain constant under applied bias (not shown). The electrochemical potentials for the left and right contacts are shown by and . Due to the inclusion of spatial features in Huckel 3.0 the energy levels move in a complicated but more accurate manner under applied bias whereas in Huckel 2.0, all the energy levels move in the same direction by a constant value.

Image of FIG. 4.
FIG. 4.

characteristics for the gold-ODT-gold system (shown at the top). Solid line: theoretical calculations using our Huckel 3.0 model; dots: experimentally obtained data in a nanopore setup. Two fitting parameters have been used for this match. One is which shifts the molecular energy levels and sets to . The other one is the effective number of molecules by which the current is multiplied to obtain the total current inside the nanopore. It is assumed that each molecule in the pore is strongly connected to the gold contacts on both sides and they are conducting independently of each other. In reality, one could have a lot more molecules poorly connected and conducting much less current individually.

Image of FIG. 5.
FIG. 5.

A close look of the fitting: (a) the deviation as a function of showing a clear minimum at ; (b) the deviation as a function of the effective number of molecules for the particular value of showing a best fit for around 425 well-contacted molecules. Deviation is defined as the sum of the square of the differences between the theoretical and experimental current values at every bias.

Image of FIG. 6.
FIG. 6.

(Color) (a) Energy level as a function of applied bias and (b) the corresponding transmission coefficients as a function of energy and applied bias in a color plot at . It is evident that the conduction remains in the tunneling regime with low transmission coefficients in the entire bias range.

Image of FIG. 7.
FIG. 7.

(a) Equilibrium transmission coefficient as a function of energy for three alkane dithiol molecules of different length with the same value for all three curves and (b) the curve fitting for the calculation of the decay coefficient . Our calculated value of for alkane dithiol molecules, , is comparable to experimentally observed values.

Image of FIG. 8.
FIG. 8.

Estimate of gate control for two molecules (shown on the left) as a function of oxide thickness with four gate plates around the molecule and with oxide dielectric constant . The value of is averaged over the molecular length. As both molecules are roughly of the same length gate control for both of them is almost the same. To obtain good gate control the gate electrodes need to be placed prohibitively close to the molecules .

Image of FIG. 9.
FIG. 9.

Transistor characteristics ( and curves) for molecule at oxide thickness with a number of gate and oxide dielectric constant . The values of subthreshold swing and ratio are poor. The curves show no saturation of current. Overall, molecule shows very poor transistor performance operating at .

Image of FIG. 10.
FIG. 10.

Transistor characteristics for molecule [(a) and (b)] and molecule [(c) and (d)] at oxide thickness with a number of gate and oxide dielectric constant . The value of is set to be 0.7 and for molecules and , respectively. The main difference in transistor performance between these two molecules is in the values of subthreshold swing and ratio. For molecule we obtain and which are much better for switching action compared to those of molecule ( and ). For both molecules the subthreshold swing is obtained from the curve at in the linear region between and . Both molecules show relatively low current saturation [(b) and (d)] whereas, irregular behavior (current is going down with higher ) is observed at low for molecule . Molecule also shows bipolar transistor behavior (c) as current increases in both polarities of .

Image of FIG. 11.
FIG. 11.

A comparison of the equilibrium transmission coefficients as a function of energy between molecular systems and . Transmission coefficients for molecule are much lower around due to fewer MIGS. This is the main reason for the better performance of molecule as a switching device compared to that of molecule . Besides, the HOMO-LUMO gap of molecule is much larger than that of molecule which also affects the transistor action.

Image of FIG. 12.
FIG. 12.

(Color) Energy level as a function of drain bias and the corresponding color plot of the transmission as a function of energy and drain bias for molecule at in off [(a) and (b)] and on [(c) and (d)] states. The source and drain electrochemical potentials are shown by and , respectively. At small gate bias [(a) and (b)] the current remains very low as tunneling conduction takes place through the HOMO-LUMO gap. The current level increases with high gate bias [(c) and (d)] as the HOMO level comes inside the window. However, the current then starts to saturate with increasing drain bias as no new energy levels come inside the window.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A self-consistent transport model for molecular conduction based on extended Hückel theory with full three-dimensional electrostatics