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Local Transport Measurement Using Scanning Tunneling Potentiometry

Weigang Wang
Françoise Kidwingira
Malcolm Beasley

Conventional transport measurements are often in the form of a four-point measurement, where two electrical contacts are used to deliver current into the sample, and the voltage across two other electrical contacts is measured. In order to understand the transport properties of the sample, one often needs to compare measurement results taken under different conditions, for example, under different temperature, under different magnetic field, or under different doping. In our measurement, we are capable of comparing transport measurement results with different positions of one of the voltage-probing electrodes, i.e., the STM tip.

As seen in the Figure 1, scanning tunneling potentiometry (STP) is effectively a four-point measurement using a scanning tunneling microscope (STM). In a STP measurement, a floating current is applied through the sample via electrodes 1 and 2; a voltage is applied between the third electrode and the STM tip, which serves as the forth electrode. The voltage is so adjusted that the tunneling current between the sample and the STM tip is zero. This applied voltage which nulls the tunneling current is the data that is recorded in STP measurement. Moreover, the capability of STM to scan on nanometer scales makes STP measurement a nanoscale transport measurement. The nanoscale probing capability gives the possibility to probe transport phenomenon at the lengthscale that is relevant to the physics of the transport. The outcome of the experiment is in the form of a potential (in volts) map of the scanning area accompanied by a topographical map (obtained by conventional STM operation, in nanometers) of the same area taken almost simultaneously.

Figure 1

The objective of the project is to develop techniques necessary to make nanoscale local transport measurements, and to develop the theoretical framework that is needed to understand the measurement results, because conventional interpretation of four-point measurement as measuring the resistance of the sample across the third and forth electrodes is inadequate to understand STP measurement.

There are different lengthscales of the sample that need to be considered. Among these are the inelastic mean free path of the sample, the elastic mean free path of the sample, and the Fermi-wavelength of the sample.

Suppose the sample is homogeneous and pristine, without any defect, the measurement result from STP will be nothing but a potential map with constant gradient in the direction of the current flow. Now suppose we put in one defect into the sample that deflects electrons, as seen in Figure 2. Theories[1],[2] predict that due to the existence of the current, charge will pile up in the upstream of current flow, and depleted in the downstream of current flow, hence making a dipole potential in the STP measurement. The charge separation distance is expected to be of order the inelastic mean free path of the sample. Besides that, the scattered electrons will interfere with the incoming electrons, which brings in Friedel like quantum fluctuations. The characteristic lengthscale of the quantum fluctuations is the Fermi-wavelength of the sample.

Figure 2

If the sample is less ideal than described above, and the elastic mean free path of the sample is comparable with other parameters, the theory of STP measurement is yet to be developed. So is the case when the electrons in the sample obey novel dynamics, such as when Klein tunneling happens in graphene.

[1] Chu C.S., and Sorbello R.S., Phys. Rev. B 42, 4928 (1990).
[2] Landauer R., IBM J. Res. Dev. 1, 223 (1957).

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