Electron Hall mobility

Fio. 3. Dependence on hydrogenation temperature of the free-electron concentration (a) and the electron Hall mobility (b) in phosphorus-implanted n-type silicon (Johnson et al., 1987c). 

Fig.tr.1-35 Si cGei c. Composition dependence of the electron Hall mobility at room temperature [1.26]... 

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. 

Baird and Rehfeld express A ° in terms of the trap concentration and the chemical potentials of the empty trap and of the electron in the quasi-free and trapped states. Further, they indicate a statistical-mechanical procedure to calculate these chemical potentials. Although straightforward in principle, their actual evaluation is hampered by the paucity of experimental data. Nevertheless, Eq. (10.13) is of great importance in determining the relative stability of the quasi-free versus the trapped states of the electron if data on time-of-flight and Hall mobilities are available. 

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. 

The drift mobility of electrons in nonpolar liquids ranges from high values such as that for liquid xenon of 2000 cm /Vs to low values like that for tetradecane of 0.02 cm /Vs. It has often been suggested that the mobility is high for symmetrical molecules and low for straight chain molecules like -alkanes. Inspection of Table 2 shows that liquids with symmetrical molecules are indeed at the top of the list. However, other less symmetrical molecules like A-trimethylsilylmethane and 2,2,4,4-tetramethylpentane also show high drift mobility. A more important factor may be the existence of many methyl groups in the molecule. In any case, for liquids for which 10 cm /Vs, the electron is considered to be quasi-free. This is supported by the Hall mobility studies, as discussed below. 

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. 

Semiconducting Properties. Silicon carbide is a semiconductor it has a conductivity between that of metals and insulators or dielectrics (4,13,46,47). Because of the thermal stability of its electronic structure, silicon carbide has been studied for uses at high (>500° C) temperature. The Hall mobility in silicon carbide is a function of polytype (48,49), temperature (41,42,45—50), impurity, and concentration (49). In n-type crystals, activation energy for ionization of nitrogen impurity varies with polytype (50,51). 

This scattering process is due to the interaction of electrons with the electric field induced by the lattice vibration polarization (polar longitudinal-optical phonons) occurring in polar semiconductors with partially ionic bonding. According to Devlin [55], the optical Hall mobility can be calculated by... 

Although Fe304 is cited as the classical example of this effect, it should be noted that the transition temperature is about four times smaller than is predicted from electrostatic considerations. Also the room-temperature Hall mobilities of the charge carriers are 0.5 cm2/V-sec (719), which might be thought to represent narrow-band conductivity. (In Fe304 there arc 3.5 t2g electrons per B-site cation, so that if R < Rc, and upper H-site t2g band, which is split from a lower t2g band by intraatomic exchange via the localized eg electrons, would be one-sixth filled.) However, intermediate mobil-... 

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