Graphene is an atomic-scale honeycomb latticemade of carbon atoms (Credit: Wikipedia) 

Before 2004, when Geim and Novoselov demonstrated the existence of graphene, a single-atomic-layer-thick crystal of carbon, physicists didn’t believe such a substance could exist. Since then, graphene has attracted tremendous research interest because of its exceptional physical and electrical properties, including remarkably high electron mobility at room temperature, high transparency, very high thermal conductivity and superior mechanical strength. Although graphene likely won’t be incorporated into high-performance integrated logic circuits as a planar channel material within the next decade, because it lacks a bandgap, many other electronic applications are in development.

 

Figure 1. (a) Measuring resistance as a function of electric field effects on a graphene-based structure and (b) longitudinal resistance of the graphene layer as a function of the silicon substrate  

Techniques for electrical characterization typically involve measuring resistance as a function of electric field effects on a graphene-based structure (Figure 1a). A low constant level of current is applied to the graphene and the resulting voltage is measured while the voltage on the substrate is varied. Graphene is highly conductive, so measured voltages are low. The results (Figure 1b) show the longitudinal resistance of the graphene layer as a function of the silicon substrate. They demonstrate graphene’s ambipolar nature; that is, that it conducts when either electrons or holes are induced into the material. The large slope on each side of the peak indicates a rapid decrease in resistance as the magnitude of the gate voltage increases, which offers evidence of graphene’s high carrier mobility.

 

                              

Figure 2. (a) Using an SMU instrument to study mobility as a function of injected charge carriers and (b) plot of the current through the sample vs. substrate voltage on a graphene sample

It’s also possible to study mobility as a function of injected charge carriers. Figure 2a illustrates the use of a source measure unit (SMU) instrument, which not only reduces the number of instruments required, but allows measuring low current, which is often easier than measuring low voltage. The test involves sweeping the gate voltage and measuring the current through the sample with a constant voltage across the sample. Figure 2b is a plot of the current versus substrate voltage on a graphene sample. Note that it’s the inverse of the plot in Figure 1b. Either measurement technique can provide good results.

Graphene demonstrates the quantum Hall effect at both extremely low temperatures and room temperature. Figure 3a illustrates a configuration for measuring both the Hall voltage and the longitudinal voltage of a Hall bar structure. The combination of an applied magnetic field perpendicular to the plane of the sample and a longitudinal current establish the Lorentz force, which creates current flow perpendicular to both the magnetic field and the source current. The result is the Hall voltage, with a magnitude of millivolts or less.

A very low current source level (100 μA to 1 mA maximum) is essential to avoid damaging the structure through overheating, so use a sensitive voltmeter to pick up the small voltages developed. Figure 3b illustrates typical quantum Hall effect results. The red curve is effectively the Hall voltage. The plateaus in the curve occur at conductivity levels that are multiples of 2e^2/h (where e is the charge of an electron and h is Planck’s constant). Because this number can be derived with high accuracy, graphene is being studied as a metrology standard for the unit of resistance. At the Hall plateaus, note that the longitudinal resistance can reach 0, indicating the graphene exhibits extremely high conductivity. As a result, the developed voltage may be just microvolts or far less.

 

Figure 3. (a) Configuration for measuring both the Hall voltage and the longitudinal voltage of a Hall bar structure and (b) typical quantum Hall effect results.  

Other measurement techniques employed for characterizing graphene-based devices include pulsed I-V, charge pumping measurements and capacitance-voltage (C-V) measurements. Although the details of these techniques are beyond the scope of this article, all demand precision instrumentation like low-level current sources, nanovoltmeters and source measurement unit (SMU) instruments. One of the most flexible options for graphene research is the semiconductor parameter analyzer, which often offer a turnkey package of hardware and software with a configurable mix of SMUs, pulse generators and other instruments, as well as built-in test routines for resistivity measurements, Hall effect characterization, DC and pulse I-V sweeps, C‑V sweeps and more.

Characterizing new graphene-based materials and devices accurately requires tools and techniques optimized for extremely low-power, low-voltage or low-resistance measurements. For example, it’s essential to minimize the power applied to microscopic devices-under-test (DUTs) to avoid raising sample temperatures, which is especially problematic in cryogenic testing, where even a millidegree of temperature variation is unacceptable. For such applications, instruments capable of sourcing sub-microamp currents accurately are essential.

Source from: R&D Magazine