How did the electron cross the road?

Apart from applications, branched nanostructures can also be used to explore fundamental issues such as the wave–particle duality of electrons. In a tetrapod transistor, an electron appears to be true to its nature.

When an electron reaches an intersection, does it hop across the road as a localized particle, or does it delocalize and materialize on the other side in a wave-like fashion? Yi Cui and co-authors¹ pose this question in Nano Letters. They find that the electron does it both ways.

In their experiment, the intersection is defined by a CdTe tetrapod — a three-dimensional nanostructure with four arms joined at equal angles to a central branch point². Electron (or hole) transport through such semiconducting branch points can be measured using single-electron transistor geometry: a tetrapod sits on a dielectric surface (Si₃N₄) prepared with a back gate electrode. Three of its arms touch the substrate and are connected to Pd electrodes. The passive fourth arm sticks out perpendicularly.

Naively, the tetrapod might be expected to behave as a single quantum dot, but from the current’s perspective, the arm–branch-point–arm connection looks more like a weakly-coupled double dot hooked up in series. Consequently, the differential conductance (dI/dV) measurements display the characteristic overlapping diamond pattern (a saw-tooth) due to discrete electron charging of the dots, and the energies involved agree with experiments on quantum dots of comparable size. This localized hopping behaviour is observed in the majority (80%) of the devices.

The remaining tetrapod transistors also exhibit a diamond pattern, but not of uniformly sized diamonds. Rather, large diamonds alternate with two or three small diamonds along the gate voltage axis. Cui et al. believe this signifies strong coupling within the arm–branch-point–arm system, such that the charge carrier can tunnel within the tetrapod, between the branch point and the arms. In other words, charge is delocalised across the entire tetrapod, though not uniformly spread. When the probability for the charge to be on the branch point is high, the transport data correspond to the large diamonds. It follows that the small diamonds correspond to the opposite case when there’s a higher probability for the charge to be on the arms.

So what determines localized and delocalized charge transport? The authors point to two possibilities: mechanical strain could affect the semiconducting properties of the tetrapod, or stacking faults could change the angles within a tetrapod. This will need to be clarified. If their interpretation is correct, it should be possible for Cui et al. to mechanically tune their devices from localized to delocalized behaviour.