The most well-known neural processing element for artificial analog neural networks is one of the Perceptron models of Rosenblatt (1962) [15] . This model is an extension to the older neural model of McCulloch and Pitts (1943) [16] .

The perceptron forms the basic neural processing element for the artificial analog neural networks, a single layer neural network with weights and biases trained to produce a correct target vector [17] . It represents the combination of a neuron and n number of synapses. Figure 2 shows the complete perceptron.

In the literature, many types of neural networks hardware based on single-electron transistor can be found. Our work is based on a complete two-input perceptron implemented in SET technology by Van de Haar and Hoekstra [18] , which is composed of two important stage, a SET inverter performs the function of the synapse while another one perform the activation function of the neuron.

SIMON simulations are shown using an input test-pattern that enters all possible states of the neural network. We should know that the various coupling capacitances between device elements, such as the capacitance of tunnel junction, are extracted from SIMON simulator after several trials using stationary simulation. In fact, for every such time step “even number tunnel events are simulated and averaged”.

The synapse is the point of connection between neurons, it allows to store the analog weight value W_i and to multiply them by digital input signal X_i.

The basic principle of a synapse is to perform the following two functions.

・ Modify connection strength.

・ Store weight.

In the SET inverter, the analog values of W_i and X_i are represented by the voltages V_Wi and V_Xi. Figure 3 shows the SET inverter structure based synapse where V_W0 is Weight value.

The digital input signals V_X0 are set by the supervisor or by the output of another perceptron. The analog weights W_i and the digital inputs signals X_i are normalized between 0 and 1. In order to translate these digital values to voltages in the SET inverter structure, we simulate the transfer function using SIMON simulator with the parameters set as chosen in Figure 3.

The transfer function of the SET inverter based synapse is shown in Figure 4. V_X0 is set to 0 and 6 mV in or- der to obtain this simulation result.

The transfer function is approximately linear when the input voltage V_W0 evolves in the region 3.9 mV < V_W0 < 5.8 mV. In this case the structure has an inversion operation, as a consequence the analog weight value W_i = 1 is mapped to 3.9 mV and W_i = 0 is mapped to 5.8 mV.

The translation Table 1 shows the translation of parameter W_i into voltage V_Wi. Note that parameter X_i can only yield 0 or 1 in other words V_Xi can be 0 or 6 mV.

The task of the neuron is to sum all weighted analog input signals X_i and classify the summed signals by means of an activation function. The activation function is a limiting function and different activation functions are found, in fact, the most commonly used functions, are the hard-limiter and the sigmoid function [17] .

The neuron should perform the following two functions:

・ Gather input signals.

・ Classify the results.

In Figure 5, a two-input neuron based on a SET inverter structure is shown. The coupling capacitors C_C0 and C_C1 perform the summation function and the activation function is carried out by the SET inverter structure [17] .

The parameter set for the neuron is scaled with a factor 0.8 with respect to the parameter set of the synapse, in order to obtain output signals in the same voltage range.

Two important parameters can be distinguished. The first parameter is the SET junction capacitance value C_T, this parameter describes the behavior of a SET circuit operating in the single-electron transport regime. The second parameter is the tunnel resistance R_T, which is needed to describe the behavior of a SET circuit in the high current regime.

The neuron’s activation function is a hard-limiter function, as it is shown in Figure 6 the threshold voltage, which is the input voltage V_g for which the output voltage changes, is set to 3.3 mV approximately in this configuration. Which correspond to the threshold parameter S₀ = 0.55.

The perceptron developed by Rosenblatt (1957) is an artificial neuron [15] -[17] , whose activation function is a step function, it consists of multiple synapses and a neuron which is designed using the SET inverter structure. If the adder output is equal or greater than the threshold Z, then the neuron fires. If the adder output is smaller than the threshold Z then there is no neuron output.

In Equation (1), the output signal Y is expressed in terms of the input variables X_i and W_i for a general case:

Figure 7 shows a complete two-input perceptron, which is based on SET inverter structures. This perceptron was first published at the ICES2003 [17] [18] and simulated using P-Spice. Therefore, in our work special

measures had to be taken in order to simulate this circuit correctly in SIMON.

Before this perceptron can be simulated, the desired output has to be defined. In order to check if the output signal is the desired signal, a good test-set of input signals has to be created using MATLAB taking into account Equation (1). In Table 2 a test-set of input signals and the desired output of a two-input perceptron is shown.

The threshold level S₀ is assumed to be 0.35 (which is an arbitrary choice). Then the operation of the perceptron is fully tested using SIMON simulator and results are presented in Table 3. Comparing with the results obtained with P-Spice in [17] the output signal V_Y agrees with the desired output signals obtained from the test patterns of Table 2. However, these outputs are inverted with respect to the outputs obtained using MATLAB. In order to obtain a non-inverted output signal V_Y, an extra inversion stage (identical to the neuron stage of Figure 5) can be added to the perceptron of Figure 7.

A very interesting idea that brings multiple benefits to nanotechnology is to have a multi-level memory to a single electron [19] . In this context, we have tried to highlight the discrete of the charge of the electron node memory N₁.

The shapes of control signals (the weight V_Wi & the input V_Xi) are very important to observe the charge evolution “Q” versus time. We have considered in this work that the architecture works in the same way as a memory.

Figure 8 shows the shape of the charge Q(t) in the island which allows us to count the number of electrons stored in the memory node (node 1) and to know the instant t when writing or erasing.

At first, the input voltage V_X1 is zero and there is no electron at the quantum dot N₁. By applying a negative input voltage V_X1 = −6 mV, a certain number of electrons are stored inside the quantum dot and no more electrons will be transported out of there. Because of the Coulomb blockade effect and the potential barrier, the electron cannot flow back to the ground.

This result shows that the number of electrons in the memory node (the red curve for V_w1 = 9 mV) after the charging increases when the input voltages increase until it reaches 5 electrons.

After returning V_X1 to zero electrons are not lost, this property provides a great potential for the network to be used in the design of nonvolatile RAMs.

The weight V_W1 plays the role of parameters which are adjusted at the training process. As we can see in Figure 8 the number of charge stored in node N₁ depends of the value of V_W1. When the value of V_W1 is equal to 9 mV five electrons are stored in the node N₁ but when we decrease the value of the weight the number of the writing electron increase until it reach ≈19 electron for V_w1 = 1 mV. It can be seen that this memory can be con-

sidered as a smart memory because we can manipulate the number of charges stored in the memory by a learning algorithm.

This learning algorithm is used to train the network for a particular purpose, in our case achieve extraordinary storage densities at an extremely low power consumption.