The first experimental SET transistors were fabricated by T. Fulton and G. Dolan [35] and L. Kuzmin and K. Likharev [71] already in 1987. The effect of the gate electrode is that the background charge

The formulas derived in Section 2.7 for the double junction can be modified to describe the SET transistor. Substituting in (2.33), the new voltages across the junctions are

with . The electrostatic energy has to include also the energy stored in the gate capacitor, and the work done by the gate voltage has to be accounted for in the free energy. The change in free energy after a tunnel event in junctions one and two becomes

At zero temperature only transitions with a negative change in free energy, or , are allowed. These conditions may be used to generate a stability plot in the

The shaded regions correspond to stable regions with an integer number of excess electrons on the island, neglecting any non-zero background charge. If the gate voltage is increased, and the bias voltage is kept constant below the Coulomb blockade, , which is equivalent to a cut through the stable regions in the stability plot, parallel to the x-axis, the current will oscillate with a period of

Increasing the bias voltage will increase the line-width of the oscillations, because the regions where current is allowed to flow grow at the expense of the remaining Coulomb blockade region. Thermal broadening at higher temperatures or a discrete energy spectrum change the form of the oscillations considerably. Coulomb oscillations have been theoretically investigated by C. Beenakker [15].