Hall mobility, measurement electrons

The main experimental elfects are accounted for with this model. Some approximations have been made a higher-level calculation is needed which takes into account the fact that the charge distribution of the trapped electron may extend outside the cavity into the liquid. A significant unknown is the value of the quasi-free mobility in low mobility liquids. In principle, Hall mobility measurements (see Sec. 6.3) could provide an answer but so far have not. Berlin et al. [144] estimated a value of = 27 cm /Vs for hexane. Recently, terahertz (THz) time-domain spectroscopy has been utilized which is sensitive to the transport of quasi-free electrons [161]. For hexane, this technique gave a value of qf = 470 cm /Vs. Mozumder [162] introduced the modification that motion of the electron in the quasi-free state may be in part ballistic that is, there is very little scattering of the electron while in the quasi-free state. 

Measurements of the Hall mobility of electrons in nonpolar liquids are few in number, but those that have been made provide information about the transport processes that is not available from drift measurements alone. The Hall mobility, nn, is obtained by measuring the deflection of electrons by a magnetic field while they are drifting in an electric field. Since the deflection occurs only while the electrons are quasi-free, nn is a measure of qf. Measurements of nu that have been done are for liquids of high drift mobility. The results for liquid argon [165] and xenon [166] show that is approximately equal to near the respective triple points. The results for TMS indicate that the ratio is close to unity... 

Figure 22 Hall mobility measurement circuit by Munoz et al. (Redrawn from the data of Munoz, R.C., Excess Electrons in Dielectric Media, Ferradini, C. and Jay-Gerrin, J.R, Eds., CRC Press, Boca Raton, 1991.)...

Experimental measurement of Hall mobility produces values of the same order of magnitude as the drift mobility their ratio r = jij/l may be called the Hall ratio. If we restrict ourselves to high-mobility electrons in conducting states in which they are occasionally scattered and if we adopt a relaxation time formulation, then it can be shown that (Smith, 1978 Dekker, 1957)... 

Hall and drift mobilities have been measured in mixtures of n-pentane and NP by Itoh et al., (1991) between 20 and 150°C. They found both mobilities to decrease with the addition of n-pentane to the extent that the Hall mobility in a 30% solution was reduced by a factor of about 5 relative to pure NR However the Hall ratio remained in the range 0.9 to 1.5. This indicates that, up to 30% n-pentane solution in NP, the incipient traps are not strong enough to bind an electron permanently. However, they are effective in providing additional scattering mechanism for electrons in the conducting state. 

For depth inhomogeneities in the free electron concentration n x) and electron mobility the Hall-effect measurement yields an effective... 

Measurements of mobility in PS suffer from the fact that the number of free charge carriers is usually small and very sensitive to illumination, temperature and PS surface condition. Hall measurements of meso PS formed on a highly doped substrate (1018 cm3, bulk electron mobility 310 cm2 V-1 s-1) indicated an electron mobility of 30 cm2 V 1 s 1 and a free electron density of about 1013 cm-3 [Si2]. Values reported for effective mobility of electron and hole space charges in micro PS are about five orders of magnitude smaller (10-3 to 10 4 cm2 V 1 s ) [PelO]. The latter values are much smaller than expected from theoretical investigations of square silicon nanowires [Sa9]. For in-depth information about carrier mobility in PS see [Si6]. 

Electrons have not been detected by optical absorption in alkanes in which the mobility is greater than 10 cm /Vs. For example, Gillis et al. [82] report seeing no infrared absorption in pulse-irradiated liquid methane at 93 K. This is not surprising since the electron mobility in methane is 500 cm /Vs [81] and trapping does not occur. Geminately recombining electrons have, however, been detected by IR absorption in 2,2,4-trimethyl-pentane in a subpicosecond laser pulse experiment [83]. The drift mobility in this alkane is 6.5 cm /Vs, and the quasi-free mobility, as measured by the Hall mobility, is 22 cm /Vs (see Sec. 6). Thus the electron is trapped two-thirds of the time. 

This theory has also been used to predict mobility for molecular liquids. Neopentane and TMS are liquids that exhibit maxima in the electron mobility at intermediate densities [46]. These maxima occur at the same densities at which Vq minimizes, in accordance with the Basak Cohen theory. The drift mobility in TMS has been measured as a function of pressure to 2500 bar [150]. The observed relative experimental changes of mobility with pressure are predicted quite well by the Basak-Cohen theory however, the predicted value of /i ) is 2.5 times the experimental value at 1 bar and 295 K. In this calculation, the authors used xt to evaluate the mobility. This is reasonable in this case since for liquids, there is little dilference between the adiabatic and isothermal compressibilities. A similar calculation for neopentane showed that the Basak-Cohen theory predicted the Hall mobility of the electron quite well for temperatures between 295 and 400 K [151]. Itoh... 

The variation in the measured electron mobilities from sample to sample in sintered materials (also observed by Hahn, ref. 24), may be due to any of several effects. The most probable reason for this variation in the well-sintered samples studied is a difference in history the individual samples are obtained with different numbers of conduction electrons per cm. frozen in in the necks. That is, the different history has allowed different amounts of oxygen to be adsorbed on the surface. Thus the concentration of electrons in the grain, as measured by the Hall coefficient, will have little relation to the concentration of electrons in the neck, as measured by the conductivity, and the mobility, obtained from the product of the Hall coefficient and the conductivity, will be neither the true mobility nor constant from sample to sample. The different samples may also end up with varying geometry of their necks, according to their previous treatment. 

At the end of the discussion of electrochemical measurement techniques, let us, however, briefly mention that there are other techniques that are not exclusively electrochemical in nature but related to the above methods such as thermoelectric measurements and Hall-effect measurements. Both techniques are extremely helpful in combination with conductivity experiments as they then allow the splitting of the conductivities into carrier concentration and mobilities. The first method relies on the emf formed as a sheer consequence of temperature differences (crosseffects in the thermal and chemical flux-force relations), while the second technique refers to concentration changes upon application of magnetic fields. Both techniques are particularly worked out for electronic carriers but are more tricky and much less straightforward for ionic carriers. For more details the reader is referred to Ref.16 301 302... 

Hall effect measurements indicate mobilities of— 10-1 cm2 V-Isec-1 for both electrons (Dresner, 1980) and holes (E>resner, 1983). Tiedje et al. (1981) have measured drift mobilities of 1 cm2 V-1 for electrons and 10-3 cm2 V-1 sec-1 for holes. However, Silver et al. (1982) have estimated that the electron mobility is s 100 cm2 V-1 sec-1 by using the reverse recovery technique. 

In a reactive sputtering process the oxygen flow rate f(02) is the most relevant parameter. Fig. 1 displays a typical example of the influence of f(02) on physical properties and structure. Hall effect measurements show that the free carrier concentration n decreases continuously with f(02) whereas the electron mobility attains a maximum at medium values of f(02). This variation of the n and p clearly reflects the change from metallic behavior at low f(02) (region I) to oxide formation (region III) at high f(02) which is related with an increase of the optical transmission T. These changes are accompanied by structural variations in the ZnO layers. The SEM... 

This is also confirmed by a decrease on the optical transmittance, especially for rf power densities lower than 5 W/cm. For the films with lower resistivity (< 10 Qcm), we measured Hall mobilities of about 2 cm A s and a carrier concentration of 3xl0 cm (n-type). For these undoped films an excess of interstitial Zn ions or/and oxygen vacancies can contribute with free electrons to the electrical conduction. Concerning the ZnO films used for the TFTs, due to the high value of the electrical resistivity ( 10 Qcm) it was not possible to measure the Hall. 

Hall effect measurements are reported for three single crystals of the charge transfer salt HMTSF-TCNQ in the temperature range 1.4-200 K at ambient pressure and under hydrostatic pressures of approximately 6 Kbars. There is evidence that the high conductivity of this material at low temperatures arises from a small number of electrons with a high mobility and a low degeneracy temperature as suggested by other experiments and a recent band-structure calculation. 

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