Measured mobilities

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... 

In comparing the results of the quasi-ballistic model with experiment, generally pq[ = 100 cn v s-1 has been used (Mozumder, 1995a) except in a case such as isooctane (Itoh et al, 1989) where a lower Hall mobility has been determined when that value is used for the quasi-free mobility. There is no obvious reason that the quasi-free mobility should be the same in all liquids, and in fact values in the range 30-400 cmV -1 have been indicated (Berlin et al, 1978). However, in the indicated range, the computed mobility depends sensitively on the trap density and the binding energy, and not so much on the quasi-free mobility if the effective mobility is less than 10 crr v s-1. A partial theoretical justification of 100 cm2 v 1s 1 for the quasi-free mobility has been advanced by Davis and Brown (1975). Experimentally, it is the measured mobility in TMS, which is considered to be trap-free (vide supra). 

The straight line confirms that the excluded dead volume must not only be used for measuring mobile phase velocities but in kinetic studies of LC columns and LC column design it must also be employed for the measurement of capacity factors. 

Fig. 2. The relationship of the true mobility ft to the measured mobility — R0a0 at various values of resistivity p0. These curves hold only for samples with negative Hall coefficients, the usual case. [From Look (1980).]...

Another point in favor of the simpler, but less accurate, fluid approach is that discharge diagnostics are still quite primitive. In studies of electron and ion swarms, experimentalists routinely measure mobilities and diffusiv-ities with a precision in the order of a few percent. A sophisticated model must be used to properly interpret such experiments. However, for discharges, even relative concentration profiles for a few of the dozens of important neutral and charged species are difficult to attain. Thus, an overly complex and expensive model is probably inappropriate, and the fluid model is a good compromise at present. 

These include, again in the approximate order of decreasing usefulness, (a) optical spectroscopy, (b) density measurements, (c) NMR (Knight shifts), (d) conductivity measurements (mobilities and temperature coefficients), (e) ESR, and (f) thermochemistry. There is every reason to believe that in the future other techniques will be applied to these studies, and that a number of subtle features of the solutions will be uncovered. 

Fig. 3 Visualisation of a future monitoring concept linking all available monitoring tools, fixed site measurements, mobile and flexible measurements, modelling and satellite observations...

The effect of field variations on measured mobility are considerable and discussion of this in terms of double layer relaxations provides the major thrust of Stotz paper. When the field is applied to a particle and its double layer, the particle moves in one direction relative to the double layer and there is, therefore, an induced asymmetry. The relaxation time required to restore the original symmetry can be defined as... 

The structures of Si clusters derived from various optimizations ( 3) were vetted by comparisons with experiments ( 2). Table 1 presents calculated and measured mobilities for lowest-energy Sin cations and anions. 

Table 1. Computed cohesive energies (PWB 88) and mobilities of low-energy isomers for Sin (n < 20) neutrals, cations, and anions vs. measured mobilities (in He at 298 K, Ref. [16,44]), and calculated binding energies for Si + vs. CID data (Ref. [20]). Global minima are in bold. Multiple features observed for Sin cations (n > 17) are ranked by decreasing abundance.

Pentacene routinely yields field-effect transistor (FET) devices with reliable hole mobility of 1 cm2 V-1 s 1 [6], with mobility > 3 cm2 V-1 s-1 reported for thin-film devices on polymer gate dielectrics [9]. For transistors fabricated on single crystals of pentacene, the measured mobility approaches 60 cm2 V-1 s 1 [10]. 

The first successful application of this method was reported by Mullen and coworkers [18]. The removal of their solubilizing group occurs thermally at temperatures as low as 180 °C, yielding pentacene and a volatile tetrahalobenzene. The tetrachloro compound 4 (Fig. 3.3) formed good-quality films from spin-cast solution, and heating the film of the soluble precursor at 200 °C for 5 s yielded the desired acene film. FET properties for devices made from solution-cast films were quite good - measured mobilities were as high as 0.2 cm2 V-1 s-1 with on/off current ratios of 106. 

The maxima of the mobilities around 50-100 K are caused by the onset of ionized impurity scattering. The highest measured mobility at about 80 K is... 

Nunes et al. wanted to find out whether transistors made with PHS and other organic dielectrics could show the excellent performance already reported for the pentacene transistors. This will help to determine whether other polymers with improved characteristics can be found. They investigated the effect of PHS on important device characteristics, threshold voltage and subthreshold slope. The dielectrics they investigated and their dielectric properties are shown in Fig. 6.22. Measured mobilities in transistors fabricated... 

This result is useful in understanding the variation of the field dependence of the TOF measured mobility from sample to sample, following the carrier density gradients (Fc dn/cbc). For example, the role of the diffusion carrier stream would explain the field dependence of jx in single crystals whenever their near-surface layer is strongly populated... 

Note that the measured mobility should be corrected for changes of physical properties of the BGE solution upon addition of ligands. Normally the viscosity increases when significant amounts of additives are dissolved. In these cases a correction must be made which takes such changes into account, e.g., by using marker compounds that do not interact with the ligands. 

Returning to the expressions for the mobility given by Eqs. (3.18) and (3.20), it must be stressed that the thickness and field dependences are artifacts of the time-of-flight experiment and are not intrinsic properties of the mobility, which is only time-dependent. The artifact arises because the transit time changes with the sample thickness or applied field and the measurement of the mobility Hu(0 then applies to a different time. It is also of note that the measured mobility in Fig. 3.13... 

The standard method for measuring mobilities in materials with long dielectric relaxation times is the time-of-flight photocurrent technique, first described by Haynes and Shockley (1951) and Lawrance and Gibson (1952). This method was developed in considerable detail during the 1950s and 1960s by Brown... 

Figure 3 A typical time-of-flight configuration for measuring mobilities of polymers.

During the past two decades, time-of-flight photocurrent measurements have become the conventional method for studies of transport phenomena in organic solids. The limitations of the technique are that it is difficult to measure mobilities in the presence of trapping and thfc need for relatively thick samples. 

The major advantages of the HTOF technique are that it is not subject to trapping constraints nor the restrictions concerning the absorption depth of conventional photocurrent transient measurements. The principal limitation is that it is limited to photorefractive materials. Malliaras et al. (1995) used the HTOF method to measure mobilities of ternary mixtures of poly(N-vinylcarbazole), 2.4.7-trinitro-9-fluorenone, and 4-(hexyloxy)nitrobenzene. Results obtained by the HTOF method were in good agreement with those obtained by conventional photocurrent transient measurements. 

Hattori et al. (1993) measured mobilities of a series of aiylamine derivatives doped into a PC. The results were compared to ionization potentials and the calculated differences of the electron densities of the donor molecules in their neutral and cation radical states. While there was no apparent correlation between the mobilities and the ionization potentials, the mobilities decreased as the difference in electron density distribution increased. 

Hara et al. (1985) measured mobilities of pyrolyzed films of poly(N,N -/ , //-oxydiphenylene pyromellitimide) (polyimide). The properties of polyimides are known to be strongly dependent upon the pyrolysis temperature. Both electrons and holes are mobile in polyimide. Depending on the pyrolysis temperature, the mobilities were in the range of 10-7 to 10-3 cm2/Vs. 

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