Voltage analysis of the drivers only layout

With the weights just calculated, it is interesting to make some first trials applying to the molecular structure the equation 3.2.

To accomplish this task, the procedure was the following: one of the three interfaces is subjected to a sweep in the input voltage values while fixed voltages influence the other two. The weight formula is evaluated in its ideal form on the whole voltage range. In this way, it was possible to understand whether or not the model works and find some critical regions in which the structure cannot correctly operate as a neuron of an ANN.

To compare the obtained results with those calculated with the ideal formula, it is possible to consider the voltage at the output of the left molecule of the central cell. In the proposed graph, the dummy molecule voltage is also present. It is helpful to have an idea of the voltage that will influence the first molecules of the output wire, which will be positioned in the next steps in the same position as the dummy molecule.

The first example is characterized by:

• Interface m3: input voltage sweep from -2V to 2V. α = 1V

• Interface m2: Vin2 = 0.5V, α = 2V

• Interface m1: Vin1 = 0V, α = 2V . This interface is going to be non influent in this first example.

The results are reported in figure 4.7.

From this first simulation, some interesting analyses can be provided. Looking at the graph reported in figure4.7b, it is possible to notice that in the region in which the out-put voltage on the central cell has a linear variation, the difference with the ideal curve obtained through the application of equation 3.2 is relatively small. This linear region falls approximately within -0.5V and 1V. For lower or higher values the voltage on the molecule saturates due to the saturation of the charge distribution within the dots. In figure 4.7cis reported the error curve; this shows minimal values in the linear region and then increases in magnitude at the extreme of the input voltage range.

The error increases because the adopted model does not consider the molecules satura-tion, meaning that the voltage prediction works well until the charge distribution is not maximized.

Another point is that the obtained voltage curve is not symmetric to zero but shifted towards positive values. This behavior is due to the presence of the fixed voltage provided by interface m2, which is a positive one. Therefore it enhances the polarization of the central cell when the interface m3 has the same configuration and reduces it when the charge distributions are opposite within the two drivers.

As a second example consider the following one:

• Interface m3: Vin3 =0.7V, α = 1.5V

• Interface m2: voltage sweep from -2V up to 2V. α = 1V

• Interface m1: Vin1 = -0.8V, α = 2.5V

Interface analysis and weight evaluation

(a) (b)

(c)

Fig. 4.7: Simulation results. 4.7arepresents a snapshot of layout and the polarization on the involved molecules. 4.7bshows the output voltage curves. 4.7creports the error curve:

difference between the ideal output voltage and the one obtained on the first molecule of the cell

The simulation results are reported in figures 4.8. In this case, it is possible to notice an error higher than in the previous simulation but still relatively small in the same input voltage range. Therefore, once again, when the central cell is working in its linear region, Vout tends to follow quite well its ideal behavior.

The interesting point is that the shift toward positive values is even more evident than in the previous example; the output voltage curve is completely asymmetric to Vout = 0V . Notice in figure4.8athat, besides two interfaces configured as logical ‘1’, the central cell has the charge not distributed. It means that the influence of m3, which is quite strong in this case, is such that it counteracts the contributions of the other two. An actual inversion of the majority voter behavior is not present but the result strongly opens to the possibility.

Interface analysis and weight evaluation

(a) (b)

(c)

Fig. 4.8: Simulation results. m3: α = 1.5V Vin3 = 0.7V , m2 = sweep, m1: α = 2.5V Vin1 = −0.8V

At last, consider the following situation:

• Interface m3: Vin3 = -0.8V, α = 3V

• Interface m2: Vin2 = -1V, α = 2V

• Interface m1: Input voltage sweep. α = 1.5V

The presented one is an extreme situation involving molecules with high saturation voltages. However, the results are useful to highlight the point; these are reported in figures 4.9. In 4.9b, it is clear how the output voltage shifts toward negative values.

The maximum positive value that this combination of voltages and interface molecules provides is close to 0V. It is also interesting to notice the polarization curve of the central cell, noticing how it is almost completely on the positive side of the y-axis. This means that one of the two logical configurations is prevailing upon the other for this circuit.

However, although two interfaces have the same configuration when m1 has the opposite

Interface analysis and weight evaluation

one, the output voltage will be slightly positive. Therefore, it is also possible to state that the voltage inversion will be stronger by using molecules with lower α on interface m1.

This can be considered as the first example of inversion of the usual working behavior of the majority voter. In the following of this work, other examples will be reported.

In conclusion, the main result that can be highlighted is the possibility of predicting with a small error the behavior of the central cell of the neuron whenever the combination of interfaces and input voltages avoids cell saturation. Once the charge distribution is maximum in the cell, the mathematical equation used to describe the single neuron cannot properly track the behavior, which is restricted to the molecular implementation and not native to neural networks. In the proposed examples, the errors in the useful region are quite small, but besides the detailed result analysis, it is interesting to notice how the sign of the predicted voltage is always the correct one. This last consideration will be extremely useful and analyzed in-depth in the following.

(a) (b)

(c)

Fig. 4.9: Simulation results. m3: α = 3V Vin3 = −0.8V , m2: α = 2V , Vin2 = −1V , m1:

sweep

Interface analysis and weight evaluation

4.3 Toward a complete structure: the additional cel l