Electron mobility temperature dependence

The mobility of electrons and holes is affected by two main scattering mechanisms chemical impurities and lattice scattering. The mobility temperature dependence due to... 

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. 

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... 

Referring to results obtained in study [16], we can assume that the conductivity of crystals in sintered ZnO film increases due to increase in number of conductivity electrons in the surface layer. Taking the sample mobility of electrons fd as 10 cm -s -V the temperature dependence being T (the data borrowed from [21]) one estimate the value A[e] from the following expression Acr = A[e, where Acr is the con-... 

Dodelet and Freeman, 1975 Jay-Gerin et ah, 1993). The main outcome from such analysis is that the free-ion yield, and therefore by implication the (r(h) value, increases with electron mobility, which in turn increases with the sphericity of the molecule. The heuristic conclusion is that the probability of inter-molecular energy losses decreases with the sphericity of the molecule, since there is no discernible difference between the various hydrocarbons for electronic or intramolecular vibrational energy losses. The (rth) values depend somewhat on the assumed form of distribution and, of course, on the liquid itself. At room temperature, these values range from -25 A for a truncated power-law distribution in n-hexane to -250 A for an exponential distribution in neopentane. 

From the measured mobilities, certain general systematics can be observed. Of these, the dependences of mobility on temperature and molecular srtucture, which are of obvious importance, will be discussed in the following subsections. In n-alkanes, at and around room temperatures, the electron mobility gradually falls with the carbon number, but it becomes nearly constant at n > 7. One interpretation attributes this to electron scattering by a finite part of the alkane... 

Theories of electron mobility are intimately related to the state of the electron in the fluid. The latter not only depends on molecular and liquid structure, it is also circumstantially influenced by temperature, density, pressure, and so forth. Moreover, the electron can simultaneously exist in multiple states of quite different quantum character, between which equilibrium transitions are possible. Therefore, there is no unique theory that will explain electron mobilities in different substances under different conditions. Conversely, given a set of experimental parameters, it is usually possible to construct a theoretical model that will be consistent with known experiments. Rather different physical pictures have thus emerged for high-, intermediate- and low-mobility liquids. In this section, we will first describe some general theoretical concepts. Following that, a detailed discussion will be presented in the subsequent subsections of specific theoretical models that have been found to be useful in low- and intermediate-mobility hydrocarbon liquids. 

Table 10.4 lists the values of trap density and binding energy obtained in the quasi-ballistic model for different hydrocarbon liquids by matching the calculated mobility with experimental determination at one temperature. The experimental data have been taken from Allen (1976) and Tabata et ah, (1991). In all cases, the computed activation energy slightly exceeds the experimental value, and typically for n-hexane, 0/Eac = 0.89. Some other details of calculation will be found in Mozumder (1995a). It is noteworthy that in low-mobility liquids ballistic motion predominates. Its effect on the mobility in n-hexane is 1.74 times greater than that of diffusive trap-controlled motion. As yet, there has been no calculation of the field dependence of electron mobility in the quasi-ballistic model. 

Holroyd (1977) finds that generally the attachment reactions are very fast (fej - 1012-1013 M 1s 1), are relatively insensitive to temperature, and increase with electron mobility. The detachment reactions are sensitive to temperature and the nature of the liquid. Fitted to the Arrhenius equation, these reactions show very large preexponential factors, which allow the endothermic detachment reactions to occur despite high activation energy. Interpreted in terms of the transition state theory and taking the collision frequency as 1013 s 1- these preexponential factors give activation entropies 100 to 200 J/(mole.K), depending on the solute and the solvent. 

Fig. 9 Temperature dependence of (a) electron and (b) hole mobilities of an EHO-OPPE film (1=8 pm) measured at =2.0-10 (squares), 3.0-10 (circles), and 4.0-10 Vcm" (triangles). Reproduced with permission from [61]...

These different modes of transport result in a dissimilar temperature dependence of the charge carrier mobility, and this often provides a convenient means to investigate which transport regime may apply. In this chapter, due attention is therefore given to experimental approaches that allow for an investigation of the transport mechanism, and concomitantly of the underlying electronic structure. 

Fig. 11 Temperature dependence of the hole mobility in PMPSi at different electric fields. Full curves are calculated using the theory by Fishchuk et al. [70], The fit parameters are the width a of the density of states distribution, the activation energy (which is p/2), the electronic exchange integral J, and the intersite separation a. From [70] with permission. Copyright (2003) by the American Institute of Physics...

Gambino S, Samuel IDW, Barcena H, Bum PL (2008) Electric field and temperature dependence of the hole mobility in a bis-fluorene cored dendrimer. Org Electron 9 220... 

An interesting example of a diffusion-controlled reaction is electron attachment to SFg. Early studies showed that in -alkanes, k increases linearly with over a wide range of mobilities from 10 to 1 cm /Vs [119]. Another study of the effect of electric field E) showed that in ethane and propane, k is independent of E up to approximately 90 kV/cm, but increases at higher fields [105]. This field is also the onset of the supralinear field dependence of the electron mobility [120]. Thus over a wide range of temperature and electric field, the rate of attachment to SFg remains linearly dependent on the mobility of the electron, as required by Eq. (15). 

The deformation potential model seems to provide a suitable framework to understand the quasi-free electron mobility in nonpolar liquids. Already several extensions or modifications on this theory have been proposed, and the dependence on temperature and pressure seems to be adequately explained. However, several authors have taken dilferent approaches to the problem showing that a consensus in our understanding has not yet been reached. 

Thus considerable support exists to support the two-state model of electron transport. The magnitude of the mobility is dependent on many factors including Fq, qf, AGsoin(e), temperature, pressure, and other factors. Presumably, differences in these factors can... 

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