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The Single Electron Box
Figure 1: Single-Electron Box
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A Single-Electron Circuit is described by means of a configuration file, containing also the simulation parameters, named circuit.crc. The first step consists in drawing the circuit diagram as in Figure 1 and numbering each node, starting from the islands and then continuing with the external voltage sources1. In this way, we have a reference frame to indicate the position of each element. The configuration file begins with the parameter section. If you want introduce comments, you can do it by inserting a pound sign # as the first character of the line.
The parameters we must supply are the temperature in kelvins, the seed for the random number generator, which must be a negative integer, the number of steps into which we want to divide the simulation, the number of averages we want to perform for each step, the number of external voltage sources, the number of tunneling junctions and the number of islands. The parameter order is not important. The syntax is instead important: a parameter is indicated with a capital ``P'' followed by an identification number, then the capitalized name of the parameter and, finally, its value.
Figure 2: Parameter section in the input file.
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In our example, the parameter section is shown in Figure 2 where the temperature is  K the number of ``time steps'' is  and the number of averages 10000.
The second section in the circuit description file lists the tunneling junctions, and their location. A junction is indicated with a capital ``T'' followed by an identification number and by the numbers of the nodes between which it is located. The node with the lower number must be indicated first. Finally, the junction capacitance values are expressed in attofarads and the junction resistance values in ohms.
Figure 3: Tunneling junctions section in the input file.
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In the Single-Electron Box we have only one tunneling junction between the island ``1'' and the voltage source terminal ``2'', as in Figure 1. If the capacitance value is  and the resistance is  , the relevant section in the input file looks like Figure 3. The next section is the one for capacitors. A capacitor is labelled with a capital ``C'' followed by the identification number. Then the numbers of the two nodes between which it is located are listed, with the lower one first. Finally, the capacitance value in attofarads is indicated.
Figure 4: Capacitor section in the input file.
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In our simple example we have only one capacitor between island ``1'' and the voltage source terminal ``3'' (see Figure 1). If the capacitance value is  , the relevant section in the input file looks like Figure 4.
The last section is devoted to the external voltage sources. In our Montecarlo code only linearly time-varying voltage sources can be used. A voltage source is labelled with a capital ``V'' followed by the identification number. Then the numbers of the two nodes between which the voltage source is connected are listed. At present only voltage sources connected between a node and the ground are implemented, thus the second node number will always be 0. The description of each voltage source is completed with the starting and final values, expressed in volts.
Figure 5: Voltage source section in the input file.
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In the circuit of Figure 1 we have two voltage sources. We can decide to keep one constant, for instance  , and to linearly vary  . The description in the input file will be that of Figure 5.
Figure 6: circuit.crc file.
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Now we have all the necessary elements of our input file. For the sake of clarity, the whole circuit.crc file has been reported in Figure 6. The program is started by running the executable script montecarlo.x. Three output files are generated:
Figure 7: Coulomb Blockade
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The first is charges.out, where the first entry of each line is the time in arbitrary units, the second is the charge in electron units on the first island, the third the charge on the second island, and so on. The second file is current1.out, where the first entry is the time, the second entry is the current in amperes through the first tunneling junction, and so on up to the third tunneling junction. From the fourth to the sixth tunneling junctions, currents are reported in the third file, current2.out, where the first entry is the time, the second the current through the fourth tunneling junction, and so on.
For the sake of completeness, in Figure 7 a plot from charges.dat is reported, in which a Coulomb Blockade effect is shown. |
