On the degree of dispersion to be expected for the mechanism of carrier hopping in spatially disordered systems

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Abstract
Adler and Silver (1982) have recently presented the results of a Monte Carlo simulation study of transport by hopping between sites in a random spatial array. As a consequence of their modified simulation procedures, these authors obtain a higher degree of dispersion than that previously reported by Marshall (1978). On the basis of their data, Adler and Silver argue that the ‘r-hopping’ mechanism is capable of providing the highly dispersive transit pulses observed in time-of-flight studies of carrier mobility. In the present paper, the origins of the differing degrees of dispersion found in the two studies are re-examined. It is argued that Adler and Silver’s technique, in which a composite transit pulse is produced by combining data obtained for a collection of different small arrays, is inappropriate and will yield an erroneously high degree of dispersion. This assertion is supported by the fact that Adler and Silver’s study is performed for an array of such site density that anomalous dispersion would not be expected on theoretical grounds. On the basis of these simulation studies, it is argued that the highly dispersive transit pulses observed in many studies of carrier transport are not consistent with hopping in the presence of spatial disorder alone.