The Hall effect

With some fine tuning of these numbers, a conductivity of 50 (fl m) is achieved when N = p = 8 X 10 m at this N value, remains approximately 0.04 rn /V S. 

It next becomes necessary to calculate the concentration of acceptor impurity in atom percent. This computation first requires the determination of the number of silicon atoms per cubic meter, Ns using Equation 4.2, which is given as follows  

The concentration of acceptor impurities in atom percent (C ) is just the ratio of and + Nsi multiplied by 100, or 

a silicon material having a room-temperature p-type electrical conductivity of 50 (D m) must contain 1.60 X 10 at% boron, aluminum, gaUimn, or indium. 

For some materials, it is on occasion desired to determine the material s majority charge carrier type, concentration, and mobility. Such determinations are not possible from a simple electrical conductivity measurement a Hall effect experiment must also be conducted. This Hall effect is a result of the phenomenon by which a magnetic field applied perpendicular to the direction of motion of a charged particle exerts a force on the particle perpendicular to both the magnetic field and the particle motion directions. 

Combining this result with Eq. (31.2), the expression for the conductivity becomes 

Ohm s law requires that k be a constant it must be independent of the field E. Therefore one of the quantities in the numerator of Eq. (31.9) must be proportional to E to compensate for the presence of E in the denominator. Obviously the charge e on the electron does not depend on the field. The number of electrons per cubic metre could conceivably depend on the field, but it can be shown that such a dependence would not be a simple proportionality. It must be that the velocity of the carrier is proportional to the field and that the number of carriers is independent of the field. This is the condition that must be satisfied if any conductor is to obey Ohm s law. Therefore we write 

The constant of proportionality u is called the mobility, which is the velocity acquired by a carrier in a field of unit strength u = v/E. 

From the requirement that the velocity must be proportional to the field, we conclude that the main force of retardation of the carrier is due to friction. If the charge on the carrier is q, then the force due to the electrical field is qE, which must be balanced by the inertial force ma = m(dv/dt), and the frictional force/y, which is proportional to the velocity. Thus 

In a metal the frictional force arises from the scattering of the electrons by collisions with the metal ions in the lattice. 

The final transport measurement to be considered is the Hall effect. This is the most intriguing transport property, but has been so difiicult to imderstand that it has not contributed much towards the elucidation of the conduction mechanisms. The reason is that the Hall effect is anomalous and has the opposite sign from that which is normally expected. Thus holes give a negative Hall voltage and 

13 shows that the Hall mobility of a-Si H lies between 0.01 and 

Two theories have been proposed to explain the Hall effect in amorphous semiconductors. Both treat the strong scattering by expressing the result in terms of a transfer integral J between specific sites. Friedman s calculation is based on the random phase approximation in which there is assumed to be no phase correlation between the electron or hole wavefunction on adjacent sites (Friedman 1971). The calculation yields 

The transfer integral is estimated to be about 1 eV, so that the Hall mobility is predicted to be 10-100 times smaller than at room 

A magnetic field acts on the moving charges. The current passing through the conductive medium is produced hy charges (the free electrons) whose velocity of motion shall he represented by the symbol v. 

These electrons are therefore subject to a force F =-evxB (Lorentz force), where -e) corresponds to 

This electrical field is responsible for an electrical force which is exerted on the electrons F =-eE (Coulomb force). Equilibrium is reached when the sum of the two forces is zero (Newton s second law). Therefore, we can 

6 http //en.wikipedia.org/wiki/Hall Elffect gives the simplified formula  

The concept of the Debye length has already been touched upon in the chapter on metal/plasma interactions (Langmuir probe). 

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Hall effect If a current (I) is passed through a conducting crystal in a direction perpendicular to that of an applied magnetic field (H), the conductor develops a potential (V) between the faces which are mutually perpendicular to both the direction of the current and the magnetic field. This is known as the Hall effect the magnitude of the potential difference is given by... 

Due to the symmetrical construction the resulting magnetic field between the two coils is zero in y-direction, if a conductive structure is symmetrically situated in the area a (see fig. 3) in the near of the probe. A resulting field is detectable by the Hall-effect device, if there are unsym-metrics in the structure in area a. The value of the Hall voltage is proportional to the detected magnetic field. 

All measured signals include errors described in chapter 4.2.1.. Especially the data of the Hall-effect device, curve... 

Examples of even processes include heat conduction, electrical conduction, diflfiision and chemical reactions [4], Examples of odd processes include the Hall effect [12] and rotating frames of reference [4], Examples of the general setting that lacks even or odd synnnetry include hydrodynamics [14] and the Boltzmaim equation [15]. 

The first term on the right represents scalar conduction and the second term the Hall effect. This is generally expressed in terms of the Hall parameter l3 = so that... 

To resolve the problem applying methods of collimated atom beams, equilibrium vapour as well as radioactive isotopes, the Hall effect and measurement of conductivity in thin layers of semiconductor-adsorbents using adsorption of atoms of silver and sodium as an example the relationship between the number of Ag-atoms adsorbed on a film of zinc oxide and the increase in concentration of current carriers in the film caused by a partial ionization of atoms in adsorbed layer were examined. 

Several additional conclusions concerning the nature of the chemisorbed layer can be drawn from the Hall effect measurements (33, 34) The chemisorbed species, together with the surface metal atoms, represent complexes analogical to the ordinary chemical compounds and, consequently, one might expect that the metal atoms involved in these complexes will contribute to lesser extent or not at all to the bulk properties of the metal. Then we should speak about the demetallized surface layer (41). When the Hall voltage was measured as a function of the evaporated film thickness... 

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

The Hall Effect In the presence of an orthogonal magnetic field in the z-direction an x-directed electric current produces a y-directed gradient of the electrochemical potential. Similarly an x-directed thermal gradient produces a y-directed gradient of the electrochemical potential, known as the Nernst effect. 

We shall briefly discuss the electrical properties of the metal oxides. Thermal conductivity, electrical conductivity, the Seebeck effect, and the Hall effect are some of the electron transport properties of solids that characterize the nature of the charge carriers. On the basis of electrical properties, the solid materials may be classified into metals, semiconductors, and insulators as shown in Figure 2.1. The range of electronic structures of oxides is very wide and hence they can be classified into two categories, nontransition metal oxides and transition metal oxides. In nontransition metal oxides, the cation valence orbitals are of s or p type, whereas the cation valence orbitals are of d type in transition metal oxides. A useful starting point in describing the structures of the metal oxides is the ionic model.5 Ionic crystals are formed between highly electropositive... 

Soule D. Magnetic field dependence of the hall effect and magnetoresistance in graphite single crystals. Physical Review. 1958 112(3) 698-707. 

Because the iron ions carry a magnetic moment, the Hall data are difficult to interpret. The conventional theory of the Hall effect utilizes a spin-independent resonance (transfer-energy) integral, and an adequate theory incorporating a spin-dependent resonance integral needs to be developed for antiferromagnetic materials. 

The Hall effect, an electric field perpendicular to both the impressed current flow and to the applied magnetic field, gives information about the mobility of the charge carriers as well as their sign. The Hall coefficient RH - Ey/JxHe is proportional to the reciprocal of the carrier density. The Hall coefficient is negative for electron charge carriers. 

The effect increased with penetration of the wave front into the electric field. Addition of a magnetic field decreased the total current across the slug, by about 40% when the j x B force was in the direction of wave propagation, but by about 25% when the force was against this direction. There was no effect on the wave speed unless the j x B force was against the flow, in which case the wave speed was lowered by up to 10% on account of an increase of turbulence in the boundary layer. The changes in wave structure observed were attributed to the "Hall Effect ... 

The Hall Effect, in magnetohydrodynamics (MHD), rotates the current vector away from the direction of the electric field and generally reduces the level of the force that the magnetic field exerts on the flow. It is usually measured by the parameter cor, where co = eB/m is the angular velocity of the electron orbits around the field lines, and r is the mean time between scattering collisions for the electrons. The form of Ohm s law which accounts for the Hall Effect (See Ref 2a) is ... 

Mindt [29] described some properties of these films (thicker electroless films, not the initial purely CD ones). Electron diffraction showed that the film was a-PbOi. The crystal (more correctly the particle) size was found, by electron microscopy, to be ca. 200 nm. The carrier density, measured by the Hall effect, was ca. 10 cm. The resistivity was somewhat dependent on the pH of deposi-... 

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. 

The physical properties of the metal (Table II) resemble those of thallium, lead and bismuth, its neighbors in the Periodic Table, rather than those of tellurium, its lower homologue. The low melting and boiling points are particularly noteworthy an attempted study of the Hall effect in polonium metal has also been reported (90). In chemical properties the metal is very similar to tellurium, the most striking resemblance being in its reactions with concentrated sulfuric acid (or sulfur trioxide) and with concentrated selenic acid. The products are the bright red solids, PoSOs and... 

Like other organic compounds, dyes can be divided into n- and -type conductors. This may be confirmed by measuring the influence of oxygen or hydrogen ,14,84)> the Hall effect si,34,85) or the thermoelectric effect 66,86). Moreover, in agreement... 

The Hall effect for hopping conduction is discussed in Chapter 5. 

The Hall effect in the temperature range where conduction is by variable-range hopping is not well understood. Evidence from the early work by Fritzsche is discussed by Shklovksii and Efros (1984), who come to the conclusion that the Hall mobility must be small. Hopkins et al (1989) have investigated the behaviour of heavily doped Ge Sb, pushed into the non-metallic regime by magnetic fields up to 7 T, at temperatures down to 100 mK. Below 1 K the... 

Putley, E. H. (1968). The Hall Effect and Semiconductor Physics. Dover, New York. 

We must now answer the question of what experimental methods to use to investigate cases of chemisorption involving boundary layers. This is possible by means of suitable electric methods. According to measurements of the electrical conductivity and of the Hall effect of polycrystalline ZnO samples by Anderson (36), Hahn (27), Miller (26), and Volger... 

Morrison (31) has compared measurements of the Hall effect and of the resistance. The Hall voltage is inversely proportional to the average concentration of carriers in the material (24), and so, for zinc oxide, will be inversely proportional to the concentration of carriers in the large grains (Fig. 2) of the material. Figure 3 shows an example in which the resistance and the inverse of the Hall voltage measured on a sintered sample of zinc oxide are plotted as functions of the time. This illustrates that the number of carriers in the bulk of the sample may remain relatively constant, while the conductance varies widely, all at constant temperature. 

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