Why asymmetric molecular coupling to electrodes cannot be at work in real molecular rectifiers

Every now and then one hears in the molecular electronics community that asymmetric couplings (${\mathrm{\Gamma }}_s\ne {\mathrm{\Gamma }}_t$) of the dominant level (molecular orbital) to electrodes ($s$ and $t$) which typically have shapes different from each other may be responsible for current rectification observed in experiments. Using a general single level model going beyond the Lorentzian transmission limit, in this work we present a rigorous demonstration that this is not the case. In particular, we deduce an analytical for the bias ($V$)–driven shift of the level energy $\delta {\varepsilon }_0\left(V\right)$ showing that $\delta {\varepsilon }_0\left(V\right)/V$ scales as ${\mathrm{\Gamma }}_t/W_t-{\mathrm{\Gamma }}_s/W_s$, which is merely a tiny quantity because the electrode bandwidths $W_{s,t}$ are much larger than ${\mathrm{\Gamma }}_{s,t}$. This result invalidates a previous, never deduced formula used in some previous publications that neither could be justified theoretically nor is supported by experiment. Toward the latter aim, we present new experimental evidence adding to that already inferred in earlier analyses.

Figure 1

Current rectification RR calculated in the experimentally relevant bias range using parameters (a) estimated for C8T junctions [46] and (b) modified to overestimate the RR values. See Sec. 4b for details.

Figure 2

Current rectification RR calculated in the experimentally relevant bias range using parameters (a) estimated for OPT3 junctions [45] and (b) modified to overestimate the RR values. See Sec. 4b for details.

Figure 3

The bias dependence of the occupancies $n_j$ of (a) the HOMO and the adjacent sites in (b) substrate and (c) tip electrodes computed using parameters estimated for C8T junctions and modified to overestimate the RR values. See Fig. 1 and Sec. 4b for details.

Figure 4

(a) The bias-driven MO shift ${\gamma }_{\mathrm{real}}\equiv {\gamma }_{\exp }$ deduced from transport measurements plotted against the MO coupling asymmetry parameter $\delta$ defined by Eq. (18b) reveals that the latter parameter has no impact on current rectification. (b) If Eq. (18) was correct, $\overline{\gamma }$ and ${\gamma }_{\mathrm{real}}$ would be equal, but, as shown, they are not. Numerical values underlying this figure are collected in Table 1.