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Electronically Configurable Molecular-Based Logic Gates C. P. Collier, E. W. Wong, M. Belohradský, F. M. Raymo, J. F. Stoddart, P. J. Kuekes, R. S. Williams, and J. R. Heath

Supplementary Material

Here we present evidence, both from experiments and from device modeling, that the solution phase oxidation/reduction properties of the rotaxane molecular compounds translate into solid state device properties.

As a starting point, we present the oxidation/reduction properties of the rotaxanes in solution in the form of cyclic voltammograms in Fig. 1S. This measurement is the solution phase analog to our current-voltage scans shown in Fig. 3A of the report. The resonant electronic states measured in solution serve as input parameters for fitting the electrochemical behavior of the solid-state devices. Before we model this device, it is useful to point out the qualitative similarities between the solution phase measurements and the device properties. First, note that oxidation is irreversible. Previous electrochemical studies on closely related rotaxane compounds showed irreversible oxidation features as well (1s). This is the basis of our solid-state switch. Second, notice that the peaks in the oxidation and reduction states are separated by about 1.5 to 2 V in the solution-phase measurements. This is also consistent with what is measured in the solid-state devices. In Fig. 3B of the report, the peaks in the NDOS are separated by about 1.5 V. The observation that the solution-phase voltage separation is greater than the solid-state separation implies that the Ti/Al electrode stabilizes the ionized molecular states. This is expected from a metal electrode, which can form an image charge that will lower the ionization energies of molecular species that are in electrical contact with the metal (2s).

As a first step in device modeling, we consider the device symmetry. From Fig. 1 of the report, it is clear that the insulating Al₂O₃ tunneling barrier is by far the rate-limiting step toward current flow. This means that once electrons migrate through the Al₂O₃ barrier, they quickly pass to the Ti/Al electrode. A model incorporating one tunneling barrier is thus sufficient to describe these devices. Since the oxidation process irreversibly alters (opens) the device, we present a model for resonant tunneling through the reduction states only.

In Fig. 2S we present the 1-D, single-barrier potential in the model. The bottom electrode has negative-bias and the top electrode is grounded. The rotaxanes are sandwiched between the tunneling barrier and the top electrode. The energy levels corresponding to the reduction states from solution phase voltammetry are drawn as thin lines above the Fermi level of the top electrode. The tunneling barrier is estimated to be 2.5 nm.

The tunneling current is given formally by (3s)

(S1)

Here, the "l" and "r" subscripts refer to the left and right hand side of the schematic, or the bottom and top electrode, respectively. T(E) is the transmission coefficient in what is commonly known as the WKB approximation. I(V) is evaluated at one point: midway through the barrier. The terms h_l(E) and h_r(E) are the total density-of-states (DOS) of the two sides of the device. F_l(E) and F_r(E) are Fermi functions. In the absence of the rotaxanes, they are assumed to be constant (the DOS of metals at the Fermi level are essentially constant with respect to bias voltage).

In our case, there are two contributions to the tunneling current: one is due to the resonant electronic states of the rotaxanes, and the other is a nonresonant, "background" contribution, which is always present. This nonresonant contribution explains tunneling through Al₂O₃ for example. With this in mind, Eq. S1 can be expressed as

(S2)

where h_rotaxane(E) represents the DOS corresponding to the rotaxane reduction energy levels. For h_rotaxane(E), we use two gaussians, one for each of the 2-electron reduction features. As a starting point to the fit, we utilize the peak positions and widths from the voltammetry measurements, calibrated against the Fermi level of the aluminum electrode (4s).

The following adjustable parameters were used to fit the data: barrier height, barrier width, rotaxane peak positions, peak widths (all the same) and an overall linear scaling factor. Fig. 3S shows the resulting DOS of the solid-state device from the fitted parameters.

As control experiments, we also fit nonresonant tunneling data for long-chain carboxylic acids, such as eicosanoic acid. For that calculation, we utilized the same model with the exception that the resonant contribution from the rotaxane (h_rotaxane of Eq. S2) is not included.

The fitted barrier width for both the resonant and non-resonant case was ~2.5 nm, and the barrier height ~2.2 eV. The overall magnitude of the non-resonant tunneling current for the two cases is similar. The differences between the two devices is the resonant tunneling contribution in the rotaxane device. This is shown in Fig. S4, where we compare the tunneling currents of the nonresonantly tunneling amphiphile device directly with the resonantly tunneling rotaxane device. Note that near 0 V both devices are similar. However, near -0.5 V the rotaxane energy levels become resonant with the Al electrode and the current in that device increases exponentially, relative to the control device.

References and Notes

1s. D. B. Ambalino et al., New J. Chem. 1998, 959 (1998).

2s. S. M. Sze, Physics of Semiconductor Devices (Wiley, New York 1981), section 5.3.

3s. ------, ibid., chapter 9.

4s. The reduction potential of molecules in the solution phase was referenced relative to the SCE electrode. To convert these values to voltages referenced relative to the Fermi level of aluminum, we followed the procedure found in A. J. Bard and L. R. Faulker, Electrochemical Methods (Wiley, New York, 1980), p. 634. See also R. Gomer and G. Trypson, J. Phys. Chem. 66, 4413 (1977).

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Medium version  |  Fig. S1. Cyclic voltammagram of the R(0) (rotaxane) compound in acetonitrile. The working electrode is defined relative to a standard calomel electrode (SCE). Peaks I and II are each 2-electron reduction features, while peak III is the oxidation feature. Separate oxidation and reduction scans were combined to produce this figure. Arrows indicate scan directions.

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Medium version  |  Fig. S2. A representation of the 1-D, single barrier tunneling model used to describe the solid-state current-voltage behavior of the rotaxane devices. I = Al bottom electrode; II = Al₂O₃ tunneling barrier; III = rotaxane energy levels, and IV = the top Ti/Al top electrode. The Fermi level of the Al electrodes (-4.26 eV) are shown at both ends of the figure. We show the two rotaxane reduction states for each peak in the voltammetry (Fig. S1), because each peak is actually a 2-electron reduction wave. Recall that the rotaxane has four cationic sites, each of which can be reduced. Only in the R(1) compound are these four states resolved, and then the splitting between the closely spaced pairs of states is only about 0.1 V. The three curves correspond to the shape of the potential barrier at three different applied voltages.

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Medium version  |  Fig. S3. Calculated DOS (red curve) for the negative bias current-voltage scan of the solid-state rotaxane devices, from the fitted parameters in Eq. S2. The shift and broadening of the two electron reduction features (fitted Gaussian blue curves) relative to the solution phase redox states (Fig. S1) is analogous to line broadening that is observed when a molecule in the solid-state is probed by NMR. Note that the peak-to-peak separation between the fitted curves (~0.4 V) is close to that measured by solution phase voltammetry (~0.5 V) (Fig. S1).

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Medium version  |  Fig. S4. Semi-log plot of tunneling current versus bias voltage for the solid-state rotaxane device and one consisting of a carboxylic acid as the molecular layer. The fits from the resonant and nonresonant tunneling models are shown.

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