Contact resistance, temperature

There is a discontinuity in temperature at the gas diffusion layer-bipolar plate interface due to contact resistance. Temperature T3 is then ... 

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. 

Around 1936, the existence of a very considerable thermal resistance at the interface between liquid helium and solids was discovered (Kapitza resistance Rk) [50], A similar effect (contact resistance Rc) is present in any contact between two materials. In the presence of a heat flux across the boundary, this thermal resistance causes a temperature discontinuity (see Fig. 4.2). 

At milli-kelvin temperatures, the problem of contact resistance between helium and solids becomes more complex. Thermal transfer phenomena take place involving spins and thermal resistance of sintered materials. The understanding of the thermal transport at very low temperature is of the utmost importance, also from a technical point of view, since helium is the working substance in dilution refrigerators (see Chapter 6). 

Only at very low temperatures (T< 100 mK) [71], the measurements of contact resistance are in good agreement with the mismatch theory. 

The study of the contact resistance Rc between solids can be carried out over a temperature range (from milli-kelvin up to hundreds kelvin) much larger than in the case of the Kapitza resistance Rk (below 4K). It is hence possible to evidence effects, such as dispersion and inelastic phonon scattering, which are absent at low temperatures. 

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... 

If the contact resistance is Rc = 5 x 103 T l [K/W], the time constant r = cA x Rc, due to the contact at the mean temperature of 60 mK, is 120s. Hence the sample temperature lags the bath temperature with a delay of about 120s. 

Ge resistors are specifically produced for low-temperature thermometry carbon and Ru02 resistors are commercial products for electronics. Pure carbon is not a semiconductor. The negative slope R(T) is due to the production process which consists in pressing and sinterization of carbon particles with glue. The resulting resistance is probably determined by the contact resistance between the particles. The cost of the carbon resistor thermometer is very low. Manufacturers such as Speer, Allen-Bradley and Matsushita have produced in the past carbon resistors for many years. Most of firms have now ceased manufacture, although their products may still be found in the storerooms of research laboratories. 

The small power needed to measure the resistance of the thermometer brings the thermometer at a temperature over that of the support surface. Such overheating is due to the contact resistance at the interface (see Chapter 4). A typical value of the contact resistance is ... 

Equation (9.15) is sometimes optimistic. Thermometer overheating as a function of temperature and contact resistance can be experimentally found, varying the power supplied to the thermometer while keeping constant the support temperature. This is shown in Fig. 9.9 for an RuOz thermometer. Note that a measuring power of 5 x 10 12W at 20 mK produces an overheating of 12mK ... 

The contact resistance may change when the thermometer is moved from a position to another. Hence the accuracy of resistance temperature measurements below about 25 mK... 

The simplest experimental arrangement (two-probe method) uses two thermometers one on the thermal bath at Ts, the second on the warm end of the sample together with the heater (see Fig. 11.1). Such configuration can be used when one is sure that contact resistances are negligible compared with the sample thermal resistance. This is seldom the case at very low temperature. A sample bath (and sample support) temperature drop ... 

The thermal resistance between the ends of the sample and the copper blocks must be negligible compared with the thermal resistance of the sample. This assumption must be verified especially for short samples at low temperature where the contact resistance is higher. For this reason, a second measurement of the thermal conductivity of Torlon in the 4.2-25 K range was carried out. The second sample had a different length (L = 24.51 mm) and the same section A. This additional measurement gave the same value of k within 2%. Moreover, we see from Fig. 11.15 that data of thermal conductivity at 4.2 K well join data at lower temperatures (within 3%) obtained on a sample of much smaller geometrical factor and with a different method (integrated thermal conductivity method) and a different apparatus [38], Finally, at room temperature, we find k = 0.26 W/mK, which is the data sheet value. 

The relation between 7 (7) and Ts(t) can be formally obtained for small temperature changes if all the circuit parameters, in particular the contact resistances, are known. 

In the methods reported above, the temperature change AT used to measure the heat capacity C(T) was supposed to be so small that the time constant r = R C could considered constant in the AT interval. Let us consider, for example, the thermal discharge of a system with heat capacity C(T) a T and thermal conductance to the bath G(T) a T3 (e.g. a metal sample and a contact resistance to the bath at rB). A AT/TB = 10% gives a At/t = 20% over the interval AT, that is a time constant definitely not constant. 

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. 

The carrier-phonon decoupling and the contact resistance between T and A increase the rise time of the pulse when the temperature is lowered. 

Figure 15.8 shows the thermal scheme of one detector there are six lumped elements with three thermal nodes at Tu T2, r3, i.e. the temperatures of the electrons of Ge sensor, Te02 absorber and PTFE crystal supports respectively. C), C2 and C3 are the heat capacity of absorber, PTFE and NTD Ge sensor respectively. The resistors Rx and R2 take into account the contact resistances at the surfaces of PTFE supports and R3 represents the series contribution of contact and the electron-phonon decoupling resistances in the Ge thermistor (see Section 15.2.1.3). 

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. 

In contrast with this, Liu, Ko, and Liao [13] and Liu et al. [14] reported the fabrication of CFPs that were carbonized at temperatures between 1,300 and 1,400°C. Carbon black particles or graphite powder can also be added to the resin-based solution that is impregnated in the paper in order to improve the electrical conductivity (and decrease contact resistance) of the CFP. By adding these particles, it is not necessary to perform the final carbonization or graphitization step in order to achieve high conductivity in the paper [9,13]. 

Pesavento PV, Chesterfield RJ, Newman CR, Frisbie D (2004) Gated four-probe measurements on pentacene thin-fihn transistors contact resistance as a function of gate voltage and temperature. J Appl Phys 96(12) 7312-7324... 

Different nickel deposits show a great variety of contact resistance values. This is particularly so after the deposits have been exposed to the atmosphere for an extended period of time. The differences between these values may be best explained in terms of variations in plated texture. Nickel electrodeposits with polycrystalline nature have been observed to behave as single crystals ( ) when their grains were oriented such that the (100) plane was parallel to the surface. Not surprisingly, the oxidation rate in (lOO)-oriented single crystals is self-limiting at ambient temperature. 

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