7.4.1 Considerations for current measurements
Current leakage occurs through stray resistance paths when the voltage sources in close prox-imity to the measuring circuit, thus, affecting current measurements (Keithley Instruments, 2004). In order to reduce the possibility of current leakage, a Keithley 6517B electrometer is used as both the voltage source and the current meter by employing the Meter-Connect
Figure 7.11: Top view of the two-terminal fixture. Dimensions are in mm
option. This internally connects the voltage source to the ammeter. A disadvantage of em-ploying the Meter-Connect option is the potential for an increase in noise in the voltage source due to an input amplifier. Therefore, a Keithley 2100 digital multimeter was con-nected in parallel to the circuit to monitor the voltage burden of the current meter during the test period. Voltage burden is the voltage drop across the input terminals that is caused by the internal R of the current meter. The internal resistance of the multimeter is set to
>109 Ω to prevent drawing current from the circuit.
Input bias current arises from an offset current flowing through the ammeter, and only ideal ammeters have zero input bias current. This could potentially affect low current measure-ments. The input bias current for a Keithley 6517B, as used in our work, is rated as less than 3 fA (Keithley Instruments, 2009). As currents measured with the fixture are typically between 10−4 A and 10−2 A, this error is negligible.
The device connections are crucial to minimise the signal loss between the instrumentation and the test fixture. A triaxial cable is typically used with a source measurement unit (e.g. an electrometer). It has two layers of shielding and insulation, protecting the center conductor from electrostatic interference. However, friction between the conductor and the insulator in the cable through flexing or movements, may generate triboelectric currents that can affect ρ measurements (Keithley Instruments, 2004). A low noise cable, Model 237-ALG-2 triaxial
cable with an internal graphite coating, is used to prevent errors due to such effects. The triaxial cable was secured in a fixed location during tests, in order to inhibit movement that could generate triboelectric voltages. The test fixture was connected to safety earth through the triaxial cable.
Extraneous currents can be internally generated in the test circuit, leading to errors in measurements. Undesirable currents can be introduced through contamination from body oils, salt, solder flux and moisture (Keithley Instruments, 2004). Such error was minimised by ensuring (1) the fixture is of rigid construction and made from insulating and water-resisting materials (i.e. PVC) and (2) maintaining clean fixture terminals. The latter was achieved by avoiding manual handling with bare hands, and using compressed air to remove any foreign matter between the conductive elastomer and the specimen.
The measuring devices were controlled remotely using a custom LabVIEW interface. The software is used to set input parameters, to perform zero checks on the devices, and to record data files. The zero checks, conducted prior to R measurements, reconfigure the measuring devices to shunt the input signal to low.
Contact resistances in the fixtures come from several sources: (1) contact of the terminals with the specimen, (2) copper plate and conductive elastomer interface, (3) oxide layers on copper, (4) connections between the triaxial cable and the terminals (i.e soldered and brass-ring terminal junctions), and (5) connecting wires. Sources (1) and (2) were limited by with the application of consistent pressure using compression springs. Further investigation into the magnitude of contact resistances (1) and (2) will be presented in Section 7.5. Formation of an oxide layer on the surfaces of the copper is inevitable, and hence, care was taken to prevent puncture of the oxide layer to attain repeatable measurements. All soldered junctions and crocodile clip connections were insulated using PVC electrical tape. Connecting wires were crimped to insulating ring terminals.
7.4.2 Temperature effects
Thermoelectric electromagnetic fields (EMF) are the voltages that arises from the differ-ent materials connected within a circuit and the temperature differences at the connections (which are dependent on the type of material) (Keithley Instruments, 2004). This introduces
errors into the voltage measurements. As the custom test fixture was constructed from vari-ous materials, care was taken to minimise this error with practical steps such as warming up the test instruments prior to use. The sum of all the connections in the circuit provides the total EMF voltage. One method to address thermoelectric EMF is to perform the first mea-surement and then reverse the voltage source, Vs to read the second measurement (Keithley Instruments, 2004). This test was conducted on the test fixture and will be presented in the Section 7.5.1.1. By reversing Vs, the polarity of the signal of interest is reversed but the EMF voltages remain unchanged. Therefore, averaging the first and second measurements cancels the EMF voltages.
Temperature is known to affect current measurements through, for instance, the contraction or expansion of the fixture materials or connections with measuring devices. Hence, prior to performing ρ measurement, all measuring devices were switched on for a minimum of an hour to attain thermal stability. All measuring devices and the fixture were kept away from direct sunlight. Resistivity measurements were performed between 16◦C and 18 ◦C.
Device heating affects ρ measurements as high current density in a specimen can increase or decrease the resistance of a specimen, depending on the material. Assuming a closed system, electrical power, P that can be converted to heat within a specimen is given by
P = I2R (7.12)
Following the relationship in Eq. 7.12, if the current flowing through the specimen increases, the power dissipated will increase the square of the current. Therefore, the most effective way to minimise heating effects is to use a smaller current through the specimen.