With nanoscale materials and devices comes the widespread promise of benefit to mankind—everything from enhancing the properties of everyday materials and electronic products to sustainable energy, environmental remediation, and nano-biosystems, medical, and health applications. However, before these technologies can be realized, researchers must master a variety of low power, low voltage, and low resistance measurement techniques to characterize graphene, carbon nanotubes, and other nano-materials and nano-devices effectively so that others may appropriately apply the technology outside of the laboratory.

Test and measurement guidelines
Characterizing the electrical properties of delicate nanoelectronic devices and materials requires instruments and measurement techniques that are optimized for low power levels and high measurement sensitivity. Here are some test and measurement best practices to obtain optimal results.

Choose the right instrumentation. Review the specifications of the source and measuring instrumentation to make sure they have the required sensitivity and capability to limit the current and voltage to avoid damaging the devices.

Provide sufficient settling time. Because nano-device measurements often involve measuring low current, it is important to allow sufficient settling time to ensure the measurements are stabilized after a current or voltage has been applied.

Minimize noise in measurements. Noise may be introduced from a variety of sources including particle collisions, defects, ac pick-up, and electrostatic interference. Noisy measurements result when a noise signal couples to the signal being measured. This can result in inaccurate or fluctuating measurements.

The most common form of external noise “pick-up” is line cycle pick-up from ac power through the instrument and the surrounding environment. Millivolts of noise on measurements are not uncommon. If available, use the measuring instrument’s line cycle integration feature to “average out” the line-cycle noise. Conductive shields, correct terminations, and proper twist rates of signal wires are also mitigating steps for radiative line cycle noise pick-up.

Electrostatic interference is a cause of noisy low current measurements, which can be due to either dc or ac electrostatic fields. An electrostatic shield surrounding the device can help minimize the effects of these fields. The shield can be a simple metal box that encloses the test circuit. The shield should be connected to the measurement circuit LO terminal, not necessarily Earth ground. Figure 1 shows the difference between an unshielded (blue curve) and shielded (purple) low current measurements on a graphene FET. In addition to shielding the device, it is important to use shielded cables.

Figure 1. Shielded (purple) and unshielded (blue) low current measurements on graphene FET.

Minimize thermoelectric voltages. Thermoelectric voltages, which are generated when different metals in the circuit are at different temperatures and when conductors are made of dissimilar materials that are joined together (the basis for the thermocouple), are a common source of error when making low voltage and low resistance measurements. There are several steps that can reduce these voltages. Whenever possible, construct test circuits using the same materials for interconnects. Minimize temperature gradients within the test circuit by placing corresponding pairs of junctions in close proximity. Allow the test equipment to warm up and reach thermal equilibrium. Finally, always use an offset compensation method such as the current-reversal method to eliminate unwanted voltage offsets, or the delta method to eliminate offsets and low frequency noise.

Minimize contact resistance. Excessively high contact resistance can make it difficult to obtain repeatable and useable results. Minimizing the effect of contact resistance on measurements is also critical in nano-characterization. J. A. Robinson et al at Pennsylvania State University is doing work with gold-titanium contacts to graphene and has achieved impressive results using a method to achieve low contact resistivities with a plasma treatment and an annealing process.

Figure 2. (a) The transfer length method allows assessing the magnitude of the resistance (b) of a test circuit’s contacts.

The transfer length method illustrated in Figures 2a and 2b allows assessing the magnitude of the resistance of the test circuit’s contacts. The blue rectangles shown are the metalized contacts on the sample. Voltage measurements are made across the contacts with increasing distance between the contacts and a curve of resistance versus distance is created (Figure 2b). The Y-intercept is equal to twice the contact resistance. From the slope, it’s possible to derive the sheet resistance. The value ρ is the sheet resistivity. More information on this technique can be found in Semiconductor Material and Devices by Dieter Schroder.

Measurement configurations
One of the most common nano-device structures researched is the field-effect transistor (FET). The channel of the nano-FET can be graphene, a carbon nanotube, or nano-wire. The transfer characteristics are determined using I-V measurements.

Figure 3. I-V measurement configuration for measuring transfer characteristics of graphene FET.

Figure 3 illustrates a configuration for measuring a graphene FET. In this setup, a source measure unit (SMU) is connected to the drain terminal and another SMU is connected to the back-sided gate terminal. An SMU is an instrument that can source and measure both current and voltage. The source terminal of the FET is connected to common. With this setup you can sweep the drain voltage and measure the resulting drain current as a function of the gate voltage. It is also possible to measure the drain current as a function of the gate voltage at a constant drain voltage. To avoid damaging the device, it is important to limit the compliance current of the voltage source to about 10 microamps or so.

Figure 4. Measurement of IDS vs. VGate with VDS constant for a graphene sample in a FET-type structure.

Figure 4 shows the results of measuring the drain current as a function of gate voltage of a graphene FET. Drain current flows for both positive and negative gate voltages, indicating both electron and hole conduction.

Figure 5. Setup for measuring resistance as a function of electric field effects on a graphene-based structure.

Figure 5 illustrates an alternative approach for a setup for measuring resistance as a function of electric field effects on a graphene-based FET structure. While the gate voltage is swept, a constant current is applied to the graphene and the resulting voltage is measured in a 4-wire configuration. The source current needs to be kept low as well to minimize power dissipation. From the source current and measured voltage drop across the graphene, the resistance is calculated.

Figure 6. Longitudinal resistance of a graphene layer on a silicon substrate as a function of the substrate voltage.

Figure 6 is a plot of the longitudinal resistance of a graphene layer on a silicon substrate as a function of the substrate voltage, which illustrates graphene’s ambipolar property—it conducts when either electrons or holes are induced into it. The large slope on each side of the peak (Dirac point) indicates a rapid decrease in resistance as the magnitude of the gate voltage increases. The data illustrated were taken using Keithley’s Model 2636A two-channel System SourceMeter® instrument at room temperature on a sample of graphene with gold metallization and wires connected to the gold.

Graphene absorbs moisture easily, which can produce a shift in the Dirac point (the top of the curve). If it seems likely that a shift in the curve is due to moisture absorption rather than experimental controls, annealing the samples can remove the moisture.

Figure 7. I-V measurement setup for a CNT FET.

A FET device structure can also be constructed using a carbon nanotube as shown in Figure 7. This measurement configuration is similar to the graphene-based FET. Again, rather than separate sources and meters, two SMUs are used with the configuration to source voltage and measure current. The gate voltage is swept in nominal increments and held constant while the drain source voltage is swept and drain source current is measured, resulting in a set of characteristic dc I-V curves for the transistor.

The results of generating a FET family of curves on a carbon nanotube (CNT) transistor are shown in Figure 8. In this test, drain current was plotted as a function of drain voltage while the gate voltage is stepped. These measurements were generated using Keithley’s Model 4200-SCS Semiconductor Characterization System.

Figure 8. Family of curves of CNT FET generated using two SMUs.

In addition to performing I-V measurements on nano-FET structures, materials like graphene are often characterized by resistivity and Hall voltage.

Figure 9 is a configuration for measuring both the Hall voltage and the longitudinal voltage on a Hall bar structure. The combination of an applied magnetic field perpendicular to the plane of the sample and a longitudinal current establishes the Lorentz force, which creates current flow perpendicular to both the magnetic field and the source current. The result is the Hall voltage, which is a signal on the millivolt level or lower. A very low test current is required to avoid exposing the test structure to damage due to excess self-heating. The recommended current levels range from 100 microamps to 1 milliamp maximum. These low-level test currents and small voltages for both the longitudinal resistance and the Hall effect measurement require the use of a sensitive current source and a voltmeter with nanovolt sensitivity.

Figure 9. Configuration for measuring both the Hall voltage and the longitudinal voltage on a Hall bar structure.

Figure 10 plots the results of a quantum Hall effect measurement. The red curve is effectively the Hall voltage. Note the plateaus in that curve, which occur at conductivity levels that are multiples of 2e2/h (the charge of an electron divided by Planck’s constant). Given that this number can be derived very accurately, graphene is now being studied as a possible metrology standard for the unit of resistance.

Figure 10. Quantum Hall effect results taken from a graphene sample.
(Reference: Neto et al., The Electroni Properties of Graphene, Reviews of Modern Physics, vol. 81, Jan-March 2009.)

At the Hall plateaus, note that the longitudinal resistance can reach 0, indicating that the graphene can attain extreme levels of conductivity. Therefore, the developed voltage is very small and can be significantly less than microvolts.

Good quality measurements of graphene, graphene-based devices, and other nanoscale structures depend on a variety of factors, including using instrumentation with sufficient sensitivity, proper measurement contacts, appropriate measurement techniques, methods to reduce external noise, and the minimization of the power dissipated in the device under test. Paying attention to each of these factors will ensure the best low power, low voltage, and low resistance measurement results for devices and materials.

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What is graphene?

Graphene is among the most popular nanomaterials of today. Its discoverers, Drs. Andre Geim and Konstantin Novoselov of the Condensed Matter Physics Lab at the University of Manchester, were awarded the 2010 Nobel Prize in Physics for their work. As a single atomic-layer thick crystal of carbon that can exist at room temperature, graphane is the ultimate thin film. It’s a two-dimensional honeycomb lattice with no atomic defects. Before Geim and Novoselov demonstrated graphene’s existence in 2004, physicists did not believe that a single atomic layer of a substance could exist in crystalline form.

Graphene exhibits a breaking strength 200 times greater than steel, with a tensile strength of 19,000,000 psi, yet it forms highly flexible bonds and can withstand substantial deformation. From an electronics engineering perspective, it provides both very high electrical conductivity and thermal conductivity; electrons travel through it unimpeded and behave according to quantum electrodynamic principles. These properties, combined with its high optical transparency, have made graphene a good candidate for use in creating transparent conducting electrodes for applications like touchscreens, liquid crystal displays, organic photovoltaic (solar) cells, and organic light-emitting diodes. Its high mobility has lead many to declare it the natural successor to silicon for the semiconductor devices of the future.

The list of potential applications for graphene in electronics alone is seemingly limited only by the imagination. IBM researchers recently reported that they were able to create graphene transistors with an on–off rate of 100 GHz with the same equipment used to create silicon transistors.

Ultra-thin transparent graphene films are also being studied for use as alternatives to indium tin oxide (ITO) and other materials as window electrodes in photovoltaic devices like high-efficiency solar cells, as well as their use in the fabrication of flat panel displays, organic light-emitting diodes (OLEDs), and other optoelectronic devices. Researchers at Samsung and Sungkyunkwan University, in Korea, have produced a large continuous layer of pure graphene with a diagonal dimension of 76 centimeters on top of a flexible, transparent, polyester sheet. They are working toward the development of a flexible touchscreen by using the polymer-supported graphene to make the screen’s transparent electrodes.

Like carbon and graphite, graphene has an affinity for bonding with other elements, which makes it a good choice for use in sensors because chemicals are attracted to it. Researchers are studying how graphene can be applied to sensing the presence of a variety of gases, including nitrogen dioxide (NO2), ammonia (NH3), and dintrotoluene (a precursor to trinitrotoluene or TNT, which makes it of particular interest to those developing sensors for military and homeland security applications).

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