Write down the different cases of tunneling in SET.

Write down the different cases of tunneling in SET.

Ans. When one electron tunnels onto the island through junction b. The change in stored energy is

ut

To consider current flow, assume that initially the island is charge neutral (n = 0), and that an electron tunnels onto the island through junction b. Then, for tunneling to occur, we need

vs1                                                                    ……(v)

which is plotted in fig. 3.15.

Now n = 1, and for the electron to tunnel off of the island through junction a, we need

vs2                                         ………..(vi)

which is depicted in fig. 3.16

For positive current to flow, the electron must tunnel onto the island through junction b, then off of the island . through junction  and so both conditions . need to be met, resulting in fig. 3.17.

Now if we assume that there is already one electron on the island, and another electron tunnels onto the island and through junction b, then off of the island through junction a, we obtain

vs4                                                   …………..(vii)

vs5

Considering the opposing tunneling events that is, an electron tunneling onto the island through junction a, and then off of the island through junction b, we obtain the Coulomb diamond shown in fig. 3.18, where V1= e/(2Cg)· This is also called a charge stability diagram, since tor combinations of V s and V8 lying within the shaded regions, no tunneling is allowed (l = 0) and the charge on the island will remain stable. For the center shaded region, n = 1, and, moving outwards from the center, each shaded region corresponds to an integral change in the charge.

coulamb diamond structure for a SET

By adjusting the gate voltage, we mn tune the effective Coulomb gap seen by Vs For Vg = me/2Cg, m = ± 1, i J, ±S, … ,there is no Coulomb gap; and current will flow for a small voltage Vs· However, for m = 0, ± 2, ± 4, ± 6, … , there is a maximum Coulomb gap that must be overcome in order for current to flow. The Coulomb diamond has been seen in a variety of experiments’ where both Vg and Vs are varied.

 

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