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As in Ref., in the present model the approximation is made that the entire potential drop V due to the applied bias occurs within the vacuum gap between the STM tip and molecule. This is a physically reasonable approximation since this gap is the weakest electrostatic and electronic link between the source and drain electrodes in STM experiments. It is also qualitatively consistent with published self-consistent calculations such as those of Bevan (Ref.) who found that under bias the energies of the molecular levels of molecules adsorbed on a silicon surface and probed by an STM tip track the energies of the silicon band edges much more accurately than they do the electrochemical potential of the STM tip. We also note that unlike in the controversial resonant tunneling models of negative differential resistance (NDR) in molecules on silicon (Refs.) movement of a molecular level under applied bias across a silicon band edge into the silicon band gap does not occur in the present theory and there is no experimental or theoretical evidence suggesting that it may be occurring in the present system.
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The temperature T in the Fermi functions was set to 0 K in the calculations reported here.
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See the inset of Fig. 1(d) of Ref. for a representative example of the calculated densities of states of the HOMO bands for the OCH3 -styrene and CF3 -styrene molecules in a CF3 -styrene/ OCH3 -styrene heterostructure on silicon.
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See the inset of Fig. 1(d) of Ref. for a representative example of the calculated densities of states of the HOMO bands for the OCH3 -styrene and CF3 -styrene molecules in a CF3 -styrene/ OCH3 -styrene heterostructure on silicon.
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The units of current are arbitrary principally because only a small number of atomic layers of the Si substrate are included in the present model.
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The very strong current contrast in curves E and H of Fig. 6 between the OCH3 -styrene chain and all or part of the CF3 -styrene chain is due in part to the resonant electron transmission through molecules via the molecular LUMO states of the CF3 -styrene being much stronger than the tunneling mechanism responsible for electron transmission through the OCH3 -styrene molecules. Furthermore, due to the differing electrostatic dipoles of the CF3 -styrene and OCH3 -styrene molecules the silicon conduction-band edge in the surface silicon layers under the OCH3 -styrene molecules is locally higher than it is under the CF3 -styrene molecules. This tends to weaken the current through the OCH3 -styrene relative to CF3 -styrene in empty-state imaging and thus also contributes to the strong current contrast.
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In our STM experiments imaging of the CF3 -styrene/ OCH3 -styrene molecular heterowires in this very low bias regime was rarely possible, as is discussed in Sec. 3.
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Plots L and V in Fig. 4(b) of Ref. are at the same values of the bias but for a tip trajectory 0.1 nm lower that in Fig. 14 of the present paper. The lateral location of the tip trajectory for plots L, V, and H in Fig. 14 was chosen so as to maximize the calculated current along the (straight line) trajectory in plot L in both the single and triple molecular chain regions in order to accurately reflect the current contrast between different parts of the trajectory. Such optimization was not carried out in Fig. 4(b) of Ref. 8.
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We include 423 Si atoms and 936 other atoms in our density-functional calculations of the electrostatic potentials in the single-triple row CF3 -styrene heterostructure on silicon.
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