Measurement of Hall mobility

While Hall measurements have been performed on metals and semiconductors, the adaptation of the method to insulators is rather difficult since the magnitude of the effect depends on the magnitude of the current flowing in the magnetic field (Red-field, 1954). In insulators, per definitionem, the currents are small. In insulating liquids, charge carriers have to be introduced in a given volume by external means. 

Charge carriers moving in crossed electric and magnetic fields are imder the influence of two forces. The electric field provides an acceleration in the direction of the field. In the magnetic field the charge carriers are imder the influence of the Lorentz force. The sum of the forces is given as 

In matter, the charge carriers interact with the atoms or molecules and a constant average velocity results. 

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. 

An electric field E is applied which cancels the influence of the magnetic field leading to v = 0. From Equation 88a LLh is then obtained as 

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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)... 

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