The Hall effect in polycrystalline and powdered semiconductors

Abstract

T h e characterisation of the transport properties of semiconducting material through a combination of Hall effect and resistivity measurements is as important in understanding the electrical transport properties of polycrystalline and powdered semiconductors as it is for single-crystal semiconductors. However, the interpretation of these measurements for polycrystalline and powdered semiconductors is more complicated due to the presence of grain boundaries and trapped interface charges which lead to inter-grain band bending and potential barriers. I n recent years a resurgence of interest in these materials, due to their potential for large-area device applications, has led to a much better understanding of the influence of grain boundaries on these properties.This review surveys the development of this subject from its origins in the early 1950s to the recent advances of the last few years, showing the extent to which a considerable body of experimental results can now be understood in terms of simple theoretical models.We give a critical review of idealised two-phase geometrical models which, though first considered nearly 30 years ago, still form the basis of the subject. These treatments derive expressions for the resistivity and Hall coefficient of a composite material in terms of the properties of its constituents. We show that these models can be applied to the interpretation of transport measurements in polycrystalline films and powder layers.Important distinctions are made depending on whether the depletion layers extend completely or partially through the grains, whether the Debye length is greater or less than the grain size and whether the mean free path is greater or less than the grain size. When the depletion region extends only partially through the grain, the Hall effect measures the carrier concentration in the bulk of the grain while the Hall mobility should be given by p= po exp (-+b/kT) where +b is the bandbending and ,uo is related to the grain diameter 1. When the depletion region extends right through the grain, the carrier concentration measured may be very much lower than the bulk doping level but is still close to the carrier concentration in the centre of the grains. Band-bending is related to doping level N and interface trap density Nt. It reaches a maximum value when Nt=Nl, and ,u therefore shows a minimum.Consideration of the possibility of the mean free path being greater than the grain size 0034-4885/80/111263

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“…To test this hypothesis and generalize the conclusions of our model, we prepared electrodes from colloidal particles with several different carrier concentrations and interfacial state densities (Supplementary Information), which are the two parameters that most influence the formation of potential barriers 44 . When the doping level is low and the interface state concentration is high, large potential barriers are expected to form; conversely, high doping levels and low interface state concentrations yield negligible barriers 44 . These predictions agreed with the experimentally measured photocurrent and charge transport characteristics measured by C-AFM (Supplementary Information).…”

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