Semiconductors temperature dependence

Electronic hole will be formed on Cr" " sites, and the conduction mechanism is a small polaron hopping process via Cr" " sites. The electronic conductivity is about 10-100 Scm at 1,273 K in air [22,23]. The electronic conductivity increases with increasing temperature, suggesting the semiconductor temperature dependence. An increasing of the Ca concentration in Lai xCaxCr03 8 enhanced the electronic conductivity due to the increase of Cr" " concentration. There are some deviations of the electrical conductivity among the examined alkaline earth elements Ca-doped LaCr03 shows the... 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

Materials are usually classified according to the specific conductivity mode, eg, as insulators, which have low conductivity and low mobihty of carriers. Metahic conductors, which include some oxides, have a high conductivity value which is not a strong (exponential) function of temperature. Semiconductors are intermediate and have an exponential temperature dependence. Figure 1 gives examples of electrical conductivities at room temperature for these various materials. 

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. 

A celebrated derivation of the temperature dependence of the mobility within the hopping model was made by Miller and Abrahams 22. They first evaluated the hopping rate y,y, that is the probability that an electron at site i jumps to site j. Their evaluation was made in the case of a lightly doped semiconductor at a very low temperature. The localized states are shallow impurity levels their energy stands in a narrow range, so that even at low temperatures, an electron at one site can easily find a phonon to jump to the nearest site. The hopping rate is given by... 

We note a temperature dependence of the zero field mobility as exp[—( F()/F)2], a behavior which is indeed encountered in real organic semiconductors, and differs from both Millers-Abrahams fixed range and Moll s variable range hopping models. 

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). 

With respect to the physical properties mentioned, band-structure calculations have attracted considerable interest, e.g., for SbSBr, SbSI, and SbSel (234). For the compounds having reference 22i in column 4 of Table XXIX, a temperature-independent diamagnetism has been found, with values of about 10 cm" g between 77 and 340 K. A small temperature-dependence is exhibited by BiTel, a narrow-gap semiconductor (41). The anisotropy of the magnetic susceptibility has been studied for SbSI, BiSel, and BiTel (41, 420). 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

Temperature-dependent resistivity data (In p vs 1/T) for both Eu3lnP3 and Eu3ln2P4 are shown in Pig. 11.3 and indicate that they are semiconductors. The room-temperature resistivities are on the order of 1-100 cm. Band gaps were determined by fitting the data from about 130-300 K to the relationship. In p= Eg/ Ik T + f, providing a band gap. Eg, of approximately 0.5 eV for both samples. Since these two compounds can be rationalized as electron-precise Zintl phases, semiconducting behavior is expected. 

Semiconductors have a considerably smaller band gap (e.g. silicon 1.17 eV). Their conductivity, which is zero at low temperatures but increases to appreciable values at higher temperatures, depends greatly on the presence of impurities or, if added advertently, dopants. This makes it possible to manipulate the band gap and tune the properties of semiconductors for applications in electronic devices [C. Kit-tel. Introduction to Solid State Physics (1976), Wiley Sons, New York N. Ashcroft and N.D Mermin, Solid State Physics (1976), Saunder College]. 

AU these features—low values of a, a strong temperature dependence, and the effect of impurities—are reminiscent of the behavior of p- and n-type semiconductors. By analogy, we can consider these compounds as ionic semiconductors with intrinsic or impurity-type conduction. As a rule (although not always), ionic semiconductors have unipolar conduction, due to ions of one sign. Thus, in compounds AgBr, PbCl2, and others, the cation transport number is close to unity. In the mixed oxide ZrOj-nYjOj, pure 0 anion conduction t = 1) is observed. 

In general, the peculiarities of the surface effects in thin semiconductors, for which application of semi-infinite geometry becomes incorrect were examined in numerous papers. As it has been shown in studies [101, 113, 121 - 123] the thickness of semiconductor adsorbent becomes one of important parameters in this case. Thus, in paper [121] the relationship was deduced for the change in conductivity and work function of a thin semiconductor with weakly ionized dopes when the surface charge was available. Paper [122] examined the effect of the charge on the temperature dependence of the work function and conductivity of substantially thin adsorbents. Papers [101, 123] focused on the dependence of the surface conductivity and value of the surface charge as functions of the thickness of semiconductor and value of the surface band bending caused by adsorption and application of external field. 

Schematic representation of how doping can lead to (a) w-type and (b) / -type semiconductors. Note that the exact position of the Fermi level is temperature-dependent.

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)... 

We will first describe the results obtained for n-type GaAs doped with silicon and then those on p-type GaAs and InP, trying to show how the spectroscopic results correlate with the electrical measurements to provide a consistent picture of the neutralization of dopants by hydrogen in III-V semiconductors. After considerations on the temperature dependence of the widths and positions of the H-related lines, we will discuss the occurrence and origin of other vibration lines associated also with hydrogen in as grown bulk and epitaxial III-V compounds. 

Another semiconducting fulleride salt, [Ru(bpy)3](C5o)2 with bpy = 2,2 -bipyridine, crystallizes on the Pt electrode surface out of dichloromethane solutions saturated with [Ru(bpy)3]PF5 within a few minutes [79]. The NIR spectra of benzonitrile solutions of this salt demonstrate that the only fulleride anion present is 55 . The temperature dependence of the conductivity is typical for a semiconductor, with the room temperature conductivity being 0.01 S cm and the activation energy 0.1 kj mol (0.15 eV). It was postulated that there is an electronic overlap between the two ions of this salt leading to a donation of electron density from the 55 to the ligand orbitals in the [Ru(bpy)3] " AI 0.7) [79]. 

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