Temperature dependence semiconductors, metals

Temperature The level of the temperature measurement (4 K, 20 K, 77 K, or higher) is the first issue to be considered. The second issue is the range needed (e.g., a few degrees around 90 K or 1 to 400 K). If the temperature level is that of air separation or liquefact-ing of natural gas (LNG), then the favorite choice is the platinum resistance thermometer (PRT). Platinum, as with all pure metals, has an electrical resistance that goes to zero as the absolute temperature decreases to zero. Accordingly, the lower useful limit of platinum is about 20 K, or liquid hydrogen temperatures. Below 20 K, semiconductor thermometers (germanium-, carbon-, or silicon-based) are preferred. Semiconductors have just the opposite resistance-temperature dependence of metals—their resistance increases as the temperature is lowered, as fewer valence electrons can be promoted into the conduction band at lower temperatures. Thus, semiconductors are usually chosen for temperatures from about 1 to 20 K. 

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. 

Metals and semiconductors are electronic conductors in which an electric current is carried by delocalized electrons. A metallic conductor is an electronic conductor in which the electrical conductivity decreases as the temperature is raised. A semiconductor is an electronic conductor in which the electrical conductivity increases as the temperature is raised. In most cases, a metallic conductor has a much higher electrical conductivity than a semiconductor, but it is the temperature dependence of the conductivity that distinguishes the two types of conductors. An insulator does not conduct electricity. A superconductor is a solid that has zero resistance to an electric current. Some metals become superconductors at very low temperatures, at about 20 K or less, and some compounds also show superconductivity (see Box 5.2). High-temperature superconductors have enormous technological potential because they offer the prospect of more efficient power transmission and the generation of high magnetic fields for use in transport systems (Fig. 3.42). 

In addition, Janczak [26] studied the conductivity property of complex 3 with a polycrystalline sample, and the results show that the conductivity is in the range 2.7 -2.8 x 10-2Q-1cm-1 at room temperature. Very weak temperature dependence of the conductivity and a metallic-like dependence in conductivity are observed in the range 300-15 K. Ibers and co-workers [70] investigated the electrical conductivity of partially oxidized complex 82 with a suitable single crystal and the results indicate its semiconductor nature (Ea = 0.22eV). 

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)... 

Some transition metal complexes are excellent conductors. Thin films of cyto-chrome-C3, which contains four heme moieties coordinated by protein, exhibited a high conductivity with mixed valence state (Fe /Fe ) and showed an increase in conductivity as the temperature was decreased (2 x 10 S cm at 268 K) [68-70]. The temperature dependence of conductivity in the highly conductive region is the opposite of that of semiconductors and may preclude the ionic conduction as a dominant contribution. However, since the high conductivity is realized in the presence of hydrogenase and hydrogen, the system is not strictly a single but rather a multicomponent molecular solid. 

This competition between electrons and the heat carriers in the lattice (phonons) is the key factor in determining not only whether a material is a good heat conductor or not, but also the temperature dependence of thermal conductivity. In fact, Eq. (4.40) can be written for either thermal conduction via electrons, k, or thermal conduction via phonons, kp, where the mean free path corresponds to either electrons or phonons, respectively. For pure metals, kg/kp 30, so that electronic conduction dominates. This is because the mean free path for electrons is 10 to 100 times higher than that of phonons, which more than compensates for the fact that C <, is only 10% of the total heat capacity at normal temperatures. In disordered metallic mixtures, such as alloys, the disorder limits the mean free path of both the electrons and the phonons, such that the two modes of thermal conductivity are more similar, and kg/kp 3. Similarly, in semiconductors, the density of free electrons is so low that heat transport by phonon conduction dominates. 

A more recent review of the properties of this material has been given by von Molnar and Penney (1985 see also von Molnar et al 1983, 1985). Results discussed in this article, involving the effects of disorder and electron-electron interaction, are described in Chapters 5 and 9. Briefly, the semiconductor-to-metal transition in an increasing magnetic field leads to a conductivity, at 300 mK, that increases linearly with H (von Molnar et al 1983). This is shown in Fig. 3.7. Hopping conduction is observed with an index indicating the influence of a Coulomb gap (Washburn et al 1984), and near the transition a temperature dependence of a as a+mT, with m positive (von Molnar et al 1985). 

Diffusion in ionically bonded solids is more complicated than in metals because site defects are generally electrically charged. Electric neutrality requires that point defects form as neutral complexes of charged site defects. Therefore, diffusion always involves more than one charged species.9 The point-defect population depends sensitively on stoichiometry for example, the high-temperature oxide semiconductors have diffusivities and conductivities that are strongly regulated by the stoichiometry. The introduction of extrinsic aliovalent solute atoms can be used to fix the low-temperature population of point defects. 

Neutral square coplanar complexes of divalent transition metal ions and monoanionic chelate or dianionic tetrachelate ligands have been widely studied. Columnar stack structures are common but electrical conductivities in the metal atom chain direction are very low and the temperature dependence is that of a semiconductor or insulator. However, many of these compounds have been shown to undergo partial oxidation when heated with iodine or sometimes bromine. The resulting crystals exhibit high conductivities occasionally with a metallic-type temperature dependence. The electron transport mechanism may be located either on predominantly metal orbitals, predominantly ligand re-orbitals and occasionally on both metal and ligand orbitals. Recent review articles deal with the structures and properties of this class of compound in detail.89 90 12... 

The connection between the measured conductivity (which is a macroscopic measure) and the structural parameters of the compound at the various levels is a major problem. One can say that the conduction in CPs, at least concerning its temperature dependence, is intermediate between semiconductors and metals. As in semiconductors, a decreases with decreasing T. In the overwhelming majority of cases, a steep decrease is observed ... 

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