Hall mobility experimental values

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)... 

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). 

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 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. 

Hall-Effect Measurements. Bullemer and Riehl (16) made these measurements. The experimental difficulties are great because of high electrode resistance, polarization effects, surface conductivity, and a low signal-to-noise ratio. Special palladium-black electrodes were used. The majority carriers were found to have a positive sign, as they should if they are protons. At —2°C. and —8°C., respectively, their concentration was 1.0 and 0.4 X 10 cm."", and the Hall mobility was 0.8 and 1.4 cm. /volt-sec. These values are 10 to 20 times lower and higher, respectively, than the results found by Eigen and De Maeyer from the saturation current and dissociation field effect (Table IV). 

Fig.H.l -127 InSb. Hole Hall mobility vs. temperature [1.111]. The vertical bars indicate the ranges of the experimental values. The solid line has a slope —1.8...

In crystalline semiconductors, the most common technique for the measurement of carrier mobility involves the Hall effect. However, in noncrystalline materials, experimental data are both fragmentary and anomalous (see, for example. Ref. [5]). Measured HaU mobility is typically of the order of 10 - 10 cm A /s and is frequently found to exhibit an anomalous sign reversal with respect to other properties providing information concerning the dominant charge carrier. Thus, apart from some theoretical interest, the Hall effect measurements are of minimal value in the study of macroscopic transport in amorphous semiconductors. 

---