Electrical transport measurements are a basic material characterization technique that provides insight into the scattering mechanisms and the band structure of solid-state materials. Macroscopic carrier transport, as described by quantum mechanics, is one of the most fundamental concepts for electronic material properties with prominent, gate-tunable effects in low-dimensional systems and at low temperatures.
The figure below shows typical 2- and 4-terminal measurement configurations in a gated geometry. Electrical, optical, or thermal excitations are applied to the sample and converted to voltage (V) or current (I) signals. These measurements are often performed at low frequencies with significant background noise. The resistance and conductance of the sample are derived from the V and I signals as functions of an external parameter such as temperature, gate voltage, or magnetic field strength.
The choice of a measurement strategy depends on the impedance and the geometry of the sample. AC techniques using lock-in amplifiers offer higher sensitivity, signal-to-noise ratio and dynamic range as well as faster measurements compared to DC measurements, which are also prone to large systematic errors.
These measurements are typically performed at constant voltage to quantify the conduction through the device under study. An example of such a measurement is that of the conductance through a carbon nanotube or a nanowire, where a constant voltage is applied to the sample and the conductance is calculated as I(measured)/V(applied). 2-terminal measurements are simple to perform and are used in the following scenarios:
The contact resistance can be neglected with respect to the sample resistance.
The sample is externally excited by optical or other means.
These measurements are performed at a constant current, and the resistance of the device is calculated as a voltage drop across a portion of the sample divided by the current.
The constant current is supplied using either a constant current source or a current-limiting resistor; in the latter case, the resistance of the current-limiting resistor needs to be much larger than the sample resistance (impedance).
4-terminal measurements can be performed in the Hall bar or the Van der Paw geometry. Compared to 2-terminal measurements they are more complex to set up, and they are the preferred choice if one of the following conditions applies:
- The impedance of the sample is small.
- It is necessary to exclude the large contact resistance from the material's properties.
With the MFLI Lock-in Amplifier (upgraded with the MF-MD Multi-Demodulator option), a single piece of equipment performs all the required tasks: measure the current through the sample, when using a current-limiting resistor, and the voltage drop across the sample, as well as apply a DC bias-voltage for gating the sample (in the case of gate-dependent transport). DC and AC excitations are externally mixed such that the potential is applied across the source-drain electrodes.
For gated structures, it is common to reconstruct a two-dimensional plot of the conductance as a function of source-drain and back-gate voltage: this is often time-consuming, because the measurements are performed at low frequencies where significant noise slows down the measurement due to long time constants. Removing some of the leading noise sources – including ground loops – and tuning the measurement frequency away from the background noise benefits greatly this type of measurement.
The Benefits of Choosing Zurich Instruments
- A single MFLI 500 kHz Lock-in Amplifier allows you to fully characterize your sample: you can measure simultaneously I and V at DC and AC thanks to the MF-MD field-upgradeable option.
- Use the built-in analog adder to mix and output DC and AC voltage biases.
- With the API Sweeper functionality, it is also possible to integrate multiple gate voltage sweeps.
- You can perform noise measurements with the MF-DIG Digitizer option: obtain time- and frequency-domain signals at both I and V inputs.
- The battery-powered MFLI enables low-noise measurements and allows you to remove ground loops.
- The measurement speed and the signal-to-noise ratio can be improved thanks to the integrated toolset for built-in time- and frequency-domain analysis provided by LabOne®.