Semiconductor Physics Group

Department of Physics

Semiconductor Physics Group

Coulomb Blockade

Coulomb Blockade in a Quantum Dot

By using the split-gate techniques pioneered in the Semiconductor Physics Group, one can form tunnel barriers which isolate a puddle of electrons, often called a "dot", from the leads. To add one electron to the dot costs a "charging energy" e2/C. The total capacitance of a sub-micron-sized dot to the surrounding gates and leads can be very small, less than 1 fF (10-15 F), so this energy is greater than the thermal energy for temperatures of a few Kelvin or less. Thus at such temperatures, transport through the dot is determined by Coulomb charging. Smaller dots can give even higher temperatures of operation.

For an electron to tunnel onto the dot, when the applied bias is small, there must be no net energy cost of adding an electron. Thus tunnelling can only occur when the size of the dot is such that it would be neutral if it contained an integer N plus a half electrons. Since it can only contain an integer number, the net charge on the dot will be ±e/2, depending on whether there are N or N+1 electrons in the dot. The charging energy is then (±e/2)2/C, which is the same in both cases. Hence changing the number of electrons in the dot between N and N+1 costs no energy, so electrons can flow on and off the dot with ease, and a current can flow. If the size of the dot is changed slightly, the charging energy in the two cases is no longer the same, and so the current falls to zero, only rising again when the size of the dot has changed by one electron. This is called the Coulomb Blockade (CB) of tunnelling. Sweeping a gate (shown in red in the figure) changes the size of the dot and thus the conductance between the leads (source and drain) has periodic peaks rising from zero to a value which may be as high as 2e2/h.

This effect can be seen in metal and semiconductor dots. In the latter, the quantum-mechanical energy levels of the electrons are also important, as their wavelength is comparable to the size of the dot, thus the term "quantum dot" is used. The number of electrons in a semiconductor dot can also sometimes be reduced all the way to zero, close to which the spacing of CB peaks becomes less regular as the energy spacing of the electronic states, and the mutual Coulomb interactions of the electrons in the dot, cannot be ignored.

Coulomb blockade has many applications; in particular we are using it to obtain a current standard.