Drift and Hall Mobilities

In the joint presence of an electric field E and a magnetic field B in a medium, the stationary electron velocity can be written as 

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) 

Specific values of r are helpful for identifying the nature of the scattering process. For example, if the momentum relaxation time is proportional to a given 

It is important to realize that even in the presence of traps, the measured Hall mobility refers to that in the higher conducting state (Munoz, 1991). Thus, a value of r significantly 1.0, and increasing with temperature in a certain interval, has been taken as an evidence in favor of traps in NP near the critical point (Munoz, 1988 Munoz and Ascarelli, 1983). Similarly, a nearly constant value of r near 1.0 in TMS over the temperature interval 22-164°C has been taken to indicate absence of trapping in that liquid. The scattering mechanism in TMS is consistent with that by optical phonons (Doldissen and Schmidt, 1979 Munoz and Holroyd, 1987). 

Munoz and Holroyd (1987) have measured Hall mobility in TMS from 22 to 164° C. This measurement parallels very well the variation of drift mobility with temperature in this liquid, and the Hall ratio remains essentially constant at 1.0 0.1. Both the drift and Hall mobilities in TMS decrease with temperature beyond 100°C, becoming 50 cmV s-1 at 164°C. The overall conclusion is that TMS is essentially trap-free in this temperature range, and the decrease of mobilities is due not to trapping, but to some other scattering mechanism that is more effective at higher temperatures. 

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Fig. tr.1-39 Diamond. Hole mobility vs. temperature. Open circles, drift mobility data from [1.31] filled circles and filled triangles. Hall mobility data from [1.29, 30] and [1.32], respectively. Solid and dashed curves calculated drift and Hall mobilities, respectively [1.33]... 

M d/ M H denote the drift and Hall mobility, respectively. In principle, for a given type of charge carrier, both mobilities are different because they reflect different elementary processes of interaction. The measurement of lLh can give additional insight into the physics of the transport process. Two methods for the measurement of Ph have been reported in the literature. 

It should be bom in mind that the drift and Hall carrier mobility, as well as the diffusion constant, are dependent on the concrete scattering mechanisms in a given semiconductor and thus in a general case on the intensity of the applied electric and magnetic fields. Since the electric field generally depends on the position within the sample, this means that the mobility and the diffusion constant are the fimctions of the spatial coordinate. 

The following table presents values for the carrier concentration n calculated from lattice constants assuming that n is equal to the number of rare earth ions per cm of the compound, carrier concentration nn calculated from the Hall effect (for M " Se by the formula for the one-band model), effective mass mVmo of current carriers estimated from the position of the Fermi level and n, drift mobility and Hall mobility i (n and nn both in cm and hh both in cm --s" ) ... 

Hall mobility in NP has been measured by Munoz and Ascarelli (1983,1984) as a function of temperature up to the critical point (160°C). It falls relatively slowly from 220 cmV s-1 at 140°C to 170 cmV s-1 at the critical temperature. The drift mobility, however, falls precipitously over that temperature interval to -30 cmV s-1 at the critical temperature. Consequently the Hall ratio r increases sharply from 1.5 at 130° to 5.5 at 160°C. This has been taken as evidence for intrinsic trapping in this liquid. 

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. 

Mobility and leachability of diflubenzuron in soils is low, and residues are usually not detectable after 7 days. In water, half-time persistence (Tb 1/2) is usually less than 8 days and lowest at elevated temperatures, alkaline pH, and high sediment loadings (Fischer and Hall 1992) (Table 17.2). Increased concentrations of diflubenzuron in soils and waters are associated with increased application frequency, flooding of treated supratidal areas, wind drift, and excessive rainfall (Cunningham 1986). 

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... 

FIGURE 1 Electron drift (solid lines) and Hall (broken lines) mobilities calculated for InN as a function of temperature. Left for n = 5 x 10 6 cm-3 and compensation ratios of zero (upper) and 0.60 right for n = 8 x 1016 cm 3 and compensation ratios zero (upper), 0.30, 0.60 and 0.75. Calculated curves from [6], experimental data from [9],... 

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... 

Measurements of the Hall mobility in liquid argon as a function of density and in solid argon (Ascarelli, 1989) are explained by scattering on phonons and static density fluctuations. A problem exists at the mobility maximum in liquid argon where r values of about 2.5 were measured. The drift mobility at this density is rather high, about 1500 cm V s" so that trapping should not be important (Lamp, 1993). 

We introduce here the notation Ob = and ObPh = q K2lm Ob is effective conductivity, i.e., the semiconductor conductivity in the direction of electric field when there is an influence of magnetic field. In a general case its value depends on the intensity of magnetic induction vector, is Hall mobility, representing effective drift mobility under the influence of transversal electric field with an... 

Hall effect is the most widely used technique to measure the transport properties and assess the quality of epitaxial layers. For semiconductor materials, it yields the carrier concentration, its type, and carrier mobility. More specifically, experimental data on Hall measurements over a wide temperature range (4.2-300 K) provide quantitative information on impurities, imperfections, uniformity, scattering mechanisms, and so on. The Hall coefficient and resistivity (p) are experimentally determined and then related to the electrical parameters through (for n-type conduction) ffn = fulne and M-h = f n/P. where n is the free electron concentration, e is the unit electronic charge, Ph is the Hall mobility, and Th is the Hall scattering factor that depends on the particular scattering mechanism. The drift mobility is the average velocity per unit electric field in the limit of zero electric field and is related to the Hall mobility... 

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. 

There are four experimental techniques that are commonly used to gain information about the electronic transport in a-Si H dc conductivity, the drift mobility, thermopower, and the Hall effect. Sections 7.1 and 7.2 describe these measurements and how the information about electronic conduction in Sections 7.3 and 7.4. 

Further information on the transport processes in a-Si H and on the influence of doping can be obtained, e.g., from measurements of the drift mobility (Allan et al., 1977 Moore, 1977), of the photoconductivity (Rehm et al., 1977 Anderson and Spear, 1977), as well as of the magnetic field dependence of the photo- and dark conductivity (Weller et al., 1981). In this chapter, however, we shall confine ourselves mainly to results of conductivity and thermopower measurements. Some results from Hall effect and photoconductivity studies are also discussed. 

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