Contact resistance, temperature dependent

Early transport measurements on individual multi-wall nanotubes [187] were carried out on nanotubes with too large an outer diameter to be sensitive to ID quantum effects. Furthermore, contributions from the inner constituent shells which may not make electrical contact with the current source complicate the interpretation of the transport results, and in some cases the measurements were not made at low enough temperatures to be sensitive to 1D effects. Early transport measurements on multiple ropes (arrays) of single-wall armchair carbon nanotubes [188], addressed general issues such as the temperature dependence of the resistivity of nanotube bundles, each containing many single-wall nanotubes with a distribution of diameters d/ and chiral angles 6. Their results confirmed the theoretical prediction that many of the individual nanotubes are metallic. 

Instruments based on the contact principle can further be divided into two classes mechanical thermometers and electrical thermometers. Mechanical thermometers are based on the thermal expansion of a gas, a liquid, or a solid material. They are simple, robust, and do not normally require power to operate. Electrical resistance thermometers utilize the connection between the electrical resistance and the sensor temperature. Thermocouples are based on the phenomenon, where a temperature-dependent voltage is created in a circuit of two different metals. Semiconductor thermometers have a diode or transistor probe, or a more advanced integrated circuit, where the voltage of the semiconductor junctions is temperature dependent. All electrical meters are easy to incorporate with modern data acquisition systems. A summary of contact thermometer properties is shown in Table 12.3. 

Figure 14-25. Arrhenius plot of the temperature-dependent mobility of 8T evaporated lilm. Data were recorded at various gale voltages and corrected for the contact scries resistance (taken from Ref. [ 1241).

More recently, the Thiais group reported on temperature-dependent mobility of 6T and 8T down to 10 K [ 124]. In this case, the mobility was estimated from the linear regime and corrected for the contact resistance. Data for 8Tare shown in Figure 14-25. 

Debye phonon velocity) and lower in the case of very dissimilar materials. For example, the estimated Kapitza resistance is smaller by about an order of magnitude due to the great difference in the characteristics of helium and any solid. On the other hand, for a solid-solid interface, the estimated resistance is quite close (30%) to the value given by the mismatch model. The agreement with experimental data is not the best in many cases. This is probably due to many phenomena such as surface irregularities, presence of oxides and bulk disorder close to the surfaces. Since the physical condition of a contact is hardly reproducible, measurements give, in the best case, the temperature dependence of Rc. 

A system reaches the thermal equilibrium in a time that depends on its heat capacity, on the thermal conductance of the various parts and on the thermal contact resistance. The latter contribution becomes more important as the temperature decreases. The ideal... 

The resistance thermometry is based on the temperature dependence of the electric resistance of metals, semiconductors and other resistive materials. This is the most diffused type of low-temperature thermometry sensors are usually commercial low-cost components. At very low temperatures, however, several drawbacks take place such as the low thermal conductivity in the bulk of the resistance and at the contact surface, the heating due to RF pick up and overheating (see Section 9.6.3)... 

Since C had a cubic dependence on T and G was mainly due to the contact resistance, r was almost constant over the measurement temperature range and close to 10 s. 

For R3j a l/T4 dependence on temperature was chosen as a representative average between the l/T3 (contact resistance) and 1/r4 5 (electron-phonon decoupling) scaling. 

The cool-down process of the cold-start experiment also provides an opportunity to obtain the membrane proton conductivity as a function of temperature at a known water content. Note that the temperature dependence of proton conductivity with low membrane water content is of particular interest here as PEFC cold start rarely involves fully hydrated membranes after gas purge. In addition, unlike PEFCs operated under normal temperatures, the membrane resistance under low water content and low temperature typical of cold start conditions is much greater than the contact resistance, making in-situ measurements of the membrane proton conductivity in a PEFC a simple but accurate method. 

Temperature and pressure measurements during freeze-drying are difficult tasks. Thermal elements (Th) and temperature-depended electrical resistance (RTD) systems measure only their own temperature and that of their surroundings only if they are in very close contact with them. Furthermore, they heat themselves and their surroundings by the current flow through the sensors. Also, they influence the crystallization of the product in their surroundings ... 

Figure 12 (a) Temperature dependence of the longitudinal resistivity of (TMTSF)2PF6 obtained with the clamped contact technique. (From W. Kang, private communication, and O. Traetteberg, Thesis, Univ. Orsay, 1993.) (b) The conductivity anisotropy is temperature independent as long as the transverse motion remains incoherent. Data for (TMTSF)2PF6 under 12 kbar. (After Ref. 6.)... 

---