On the Hall effect in polycrystalline semiconductors
Journal of Applied Physics
Some problems involved in the interpretation of Hall-effect measurements in polycrystalline semiconductors have not been resolved, especially when the contribution of the boundaries is appreciable. Using the Herring theory of transport properties in inhomogeneous semiconductors, we present an alternative interpretation to that previously proposed. This model permits the calculation of the Hall coefficient under general conditions. Extensive measurements of the Han effect in polycrys-taHine
... olycrys-taHine semiconductors have been carried out. Nevertheless the interpretation of these measurements is not simple. Theoretical analysis has been done. One such is the model proposed by Voiger. 1 He considered a material consisting oflow-resistivity grains [region (1) in Fig. 1 , with resistivity PI and dimension II]' separated by boundaries [region (2) with resistivity pz and dimension 'z]. For one such material wherep2 » PI' II » Iz, and i/i z = 1/12 [ii' i 2 , being the mean current densities in regions (1) and (2) , respectively], theory showed that the measured Han coefficient was [ ' ]'Z R = RI + I: Rz, where R I is the Han coefficient of the grain and R z the Han coefficient of the boundary region. From this result Volger concluded that Ii was approximately R I. Bube z proposed an equivalent circuit of the basic unit in the Volger model, and modified versions of the Bube model were considered by other workers.  Volger's result has been frequently cited when it has been assumed that in a polycrystalline semiconductor the Hall coefficient is a measure of the carrier concentration in the grain, i.e., R = (qn.J -I. However, the conductivity models developed by Petritz,6 Seto/ and other authors,IO-I3 indicate that the assumptions of the Volger model are not always valid. In fact, if the region (2) is the boundary between grains, the conditionpz > Pt will be true only for light depletion of the grain; in generalpz can be comparable tOPt, depending on the trap states density, the doping level, the grain size, and surface scattering effects. In addition, the consideration of two different current densities seems to us only justified in the quite simplified model ofVolger. In spite of this, no theoretica! work on the Hall effect not based on the Volger model, has been reported. The depletion of the grain was considered by Seto; he assumed Ii = R I' but, since the carrier concentration is not uniform, he calculated n I from the onedimensional average of the carrier concentration in the grain 1 ill n l = -n(x) dx.