Clock profile definition

Propagation analysis for molecular FCN neural networks

(a) (b)

Fig. 5.10: Charge distribution plot of the propagation across an eighteen molecules wire and connection with a second neuron across an interface cell α = 1V

Fig. 5.11: Voltage trend analysis across a N = 18 molecular wire with interface cell at the end. Voltages at the end of the molecular chain are extremely low.

Propagation analysis for molecular FCN neural networks

As a consequence, the clock signal is going to take different intermediate values between the extremes -2_nm^V and +2_nm^V .

In a first approximation, the analyzed clock signals are those reported in figure5.12. For simplicity and preliminary evaluation of possible achievable behavior, the involved wire divides into just two clock regions.

Fig. 5.12: First ideal clock signals

It is important to remark that the proposed profile is just a first approximation to move out from ideality. The step variation is present only on the falling edge of each signal, which have a shift in phase one to the other. The outcomes of the first simulation are reported in figure 5.13. The input voltage is 0.3V, and the number of molecules present in the wire equals 14. The molecules are all bis-ferrocenes. Notice that with the ideal clock configuration, the consequences of border effects would be evident and, therefore, a substantial reduction of the voltage at the end of the wire. In the results reported in5.13 it is evident that thanks to the presence of the slower variation of the clock signals, the propagation is sustained, and the molecules in the wire have maximum charge separation.

It is interesting to notice that the propagation properly occurs in this case. Due to the usual reasons, some border effects are still present on the last molecule. In figure 5.13d it is important to notice that, even if the first clock region in the wire is turned off, the molecules in the second one are capable of maintaining their charge distribution. This is the main effect of introducing the intermediate values in the clock. Moreover, comparing this result with the one reported in figure5.13b, it is possible to notice a reduction in the border effect.

From this first analysis, the idea of avoiding turning off immediately the first clock signal seems to be engaging to maintain and stabilize the information along the wire. Diffe-rent simulations were performed involving diffeDiffe-rent wire lengths. However, remarkable differences with the case reported cannot be highlighted.

Propagation analysis for molecular FCN neural networks

(a) (b)

(c) (d)

Fig. 5.13: Vin= 0.3V , N = 14, d = 1nm

5.2.1 More realistic clock profile

As already said, the clock signal waveforms introduced in the previous section are highly idealized. It is important to understand if the benefits pointed out so far can also be confirmed with the introduction of a more realistic clock, in which a finite number of steps characterizes both the falling and rising edges of the clock signals. The updated clock signals are reported in the graphs 5.14aand5.14b.

The two figures differ mainly in the number of steps introduced in the transition. In-deed, the waveforms in5.14aare characterized by steps of height 0.5_nm^V , while in the other case those are equal to 0.1_nm^V . The results found in the two situations can be considered comparable; for this reason, to improve the computational time of each simulation, only the results related to the use of the first signal will be presented. An important aspect to be noticed is the scale of the x-axis of the plots. These show the steps multiplied by 10 for plotting easiness. The simulation results proposed in this section are referred to by the step number, from which the values of the two clock signals at that time instant can

Propagation analysis for molecular FCN neural networks

(a) (b)

Fig. 5.14: Complete clock waveforms

be derived.

The first proposed simulation has the following characteristics:

• N = 18 bis-ferrocene molecules

• intermolecular distance equal to 1nm

• Vin= 0.3V . Notice that with clock signal showing vertical transitions, such a value would not provide the saturation of the molecules in the wire.

The results are reported in figures 5.15a-5.15d. The first plot in figure 5.15a repre-sents the first time instant, in which only the clock region number one is active. On the last molecule there is a strong influence of the border effects. In 5.15b the second clock region activates, and its effects are visible on the voltages present in the first zone. The wire then saturates when all the molecules are subjected to a clock field equal to 0_nm^V , whose plot, in terms of charge distribution across the dots, is reported in figure 5.16. It is interesting to notice a lower charge separation due to the reduced value of the elec-tric field at that time step. Then, in figure5.15dis reported the last propagation step, in which it is possible to appreciate a useful polarization on the last cell of the molecular wire.

Propagation analysis for molecular FCN neural networks

(a) Step 1 (b) Step 4

(c) Step 5 (d) Step 9

Fig. 5.15: Vin= 0.3V , d = 1nm, N = 18

Fig. 5.16: First simulation: charge distribution for CK1 = CK2 = 0_nm^V

Propagation analysis for molecular FCN neural networks

Overall, it is possible to consider these first results satisfactory. We tested different input voltage values, such as 0.1V, obtaining the same results as those reported above.

This implies that the behavior of a wire clocked in this way is independent of the input voltage level. Once again, the final result is a binary wire. Therefore, it was not possible to obtain the analog solution for any input.

Another critical value is the polarization of the last cell of the wire, being this the one in contact with the linked neuron. Also, in this case, the values are almost equal indepen-dently of the number of molecules present in the molecular chain.

Summing up the results presented, it is possible to state that the best solution for infor-mation propagation is a digital one. The slow variation of the clock allows reaching the saturation for any values at the input with an intermolecular distance equal to 1nm.