Hopping conduction concentration

Impurity conduction can also be studied in compensated semiconductors, i.e. materials containing acceptors as well as donors, the majority carriers (or the other way round). For such materials, even at low concentrations, activated hopping conduction can occur (Chapter 1, Section 15), some of the donors being unoccupied so that an electron can move from an occupied to an empty centre. Here too a metal-insulator transition can be observed, which is certainly of Anderson type, the insulating state being essentially a result of disorder. 

This increase of electrical resistivity in GaN Mg crystals is related to a drastic decrease in free electron concentration. The temperature dependence of resistivity for these samples is typical for hopping conductivity [24] which suggests that the Fermi level lies within the gap. The optical absorption data... 

It is quite clear from the above that noticeable hopping conductivity can exist when there is a large density of localized states (traps for electrons) only, which can be provided by initial structure defects or by radiation damages. As far as hopping parameters (and possible free electron concentration) do depend on temperature to a large extent, the temperature increase will lead to a redistribution of internal electric fields and currents. The results of some pertinent experiments are presented below. 

Surface morphology and electrical conduction in laser beam deposited perylene based thin films were investigated. It is found that the peak-to-peak value of the surface relief significantly increases with an increase of the substrate temperature at the deposition. Measuring of electrical properties by cyclic thermal desorption method shows that the hopping conductivity mechanism is realized in the films. The conductivity is intrinsic or impurity depending on the concentration of the adsorbed oxygen. 

In this paper, we compare experimental data on morphology of the vacuum deposited PTCDI films and their electrical conduction. As known [2], the conduction of PTCDI films is strongly influenced by adsorption of the atmospheric oxygen. Therefore, the measured absorbed oxygen concentration dependencies of conductivity, activation energy and turmel faetor are represented and then conqjared with the theoretical calculations based on the two-level model of the hopping conductivity [3]. 

The two-level model of hopping conductivity allows calculating from the set of experimental data the fundamental microscopical parameters of hopping conductivity - the electron localization radius and the concentration of localization centers corresponding to the intrinsic and impurity states [3]. 

How strongly a high defect concentration affects the temperature dependence of the mobility can be seen from the comparison of the experimental results for a perylene crystal with a concentration of 0.17% traps of depth Et = 270 meV (Fig. 8.33). Even near room temperature, the mobility ii decreases steeply with decreasing temperature. In this crystal with defects, hopping conductivity occurs even in the temperature region near 300 K. 

The conduction-electron conductivity is proportional to the concentration of electrons in the conduction band, which, under equilibrium, is proportional to the ratio of concentrations [Di ]/[Di, as can be deduced from the mass action law for the reaction D, -F e -o- D,. The concentration of the electrons in the conduction band may be quite low, though both the ionic defects concentrations may be high. Then, the hopping conductivity may be higher than the conduction-electron conductivity. Not only impurities but also native defects with variable charged states allow hopping conduction in a defect band [32]. 

The data of Table 17 show the strong reaction enhancements of the specific catalysts impart under microwave heating to all of reactive systems examined. The gelation and vitrification times were lowered to one-eighth to one-tenth of those under hot-air heating with the same catalyst and its concentration. An ion-hopping conduction mechanism was recognized as the dominant source of the microwave absorption capacities of these catalysts [2]. 

The possibility of utilizing polymer-nanocomposites for the manufacture of gas and vapor sensors was studied in our laboratory in 1992 [40]. The specificity of nanocomposites, which makes them attractive as a gas sensor material, is the existence of a hopping conductivity between the nanoparticles through the polymer in a range of concentrations close to the percolation threshold (see Sect. 2.3). Since the absorption and partial dissolution of the gas or vapor molecules in polymer matrix changes its properties, it is possible to monitor these changes measuring electrophysical characteristics of the composites such as conductance and capacitance. The important point here... 

The introduction of ammonia impurities changed the sensor conductivity by 4-8 orders of magnitude due to the absence of bulk shunt resistance. The conductivity was found to be proportional to the square of ammonia impurity concentration and the 1-V curves of the films were logarithmic, which is typical for the hopping conduction mechanism. By changing the preparative conditions used to produce the films, sensors for the detection of ethanol and water vapors in air were also manufactured. 

For the range of filler concentrations above that, corresponding to formation of infinite cluster with hopping conductivity and before the true percolation in the system, the following expression for conductivity, obtained for conductivity through infinite cluster with correlation length has been used [59] ... 

Silva, (., Ribeiro, S Lanceros-Mendez, S., and Simoes, R. (2011) The influence of matrix mediated hopping conductivity, filler concentration, aspect ratio and orientation on the electrical response of carbon nanotube/polymer nanocomposite. Composite Science and Technology, 643,... 

---