~ Pergamon Solid State Communications, Vol. 98, No. 5, pp. 457-461, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1098/96 $12.00 + .00 0038-1098(95)00802-0 HOPPING TRANSPORT THROUGH AMORPHOUS JUNCTIONS H. Bahlouli Physics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia (Received 20 October 1995; accepted 23 November 1995 by B. Lundqvist) We study electron tunneling through thin amorphous material and obtain the relative strength of different hopping channel contributions to tunneling compared to the elastic resonant contribution under high magnetic field. The order of magnitude of these contributions are in good agreement with the recent experimental data on amorphous silicon tunnel junctions. Keywords: A. heterojunctions, A. semiconductors, D. tunnelling. THE SUBJECT of electronic transport via localized states in tunnel junctions is attracting a lot of interest both theoretically [1] and experimentally [2]. For very thin barriers (thickness d less than 60 ,~) we know that direct tunneling dominates the transport properties of the junction, when the thickness increases other types of indirect tunneling processes take over. What seems to be an interesting feature from the experimental point of view is that each of these indirect tunneling processes has a well defined region in terms of thick- ness, d, and temperature range, T, where it dominates. For thicknesses greater than 60 ,~ and less than 100,~, resonant tunneling dominates, above this thickness an inelastic hopping process starts to take over. First, the two impurity channel opens up for d>~100,~ and T ~<15 K, then for d ~>120 A the three impurity chan- nel becomes effective within the same range of low temperatures. One expects that when the junction becomes very thick (d i> 300,~) Mott's variable range hopping process takes over. The transition from an inelastic hopping to variable range hopping regime has been seen experimentally. Thus there are two regions, in terms of temperature and barrier thickness, in which tunnel junction conductance is well under- stood from the theoretical point of view. For high temperatures and thick barriers, the conduction is well described by variable range hopping as predicted by Mott [3] and the conductance varies as: GVRH(T) = GO exp[-(T*/T)l/4], (1) where Go is a constant, T* is a parameter which is related to the density and width of the localized states in the amorphous material. For low temperatures and thinner barriers, some forward-directed, one dimen- sional chain-like hopping dominates the conduction [4]. It is clear from the experimental point of view that some cross-over takes place between these two regimes but no theoretical work gave clear evidence for this cross-over. In this work we will study hopping conduction at intermediate thicknesses where inelastic hopping dominates the transport. Generally speaking, because of the small localization length (a = 6.7A in amor- phous silicon), electron-electron correlation plays an important role, we expect highly correlated transport via these localized states as it is seen experimentally. We shall show that processes of inelastic tunneling in channels containing two and three impurity states with a scatter of the energies of the order of KBT play an important role in low temperature conduction of intermediate thickness junctions. Assuming the width of the impurity level, F, to be small compared to temperatures of interest, we can use the usual kinetic equation approach to evaluate the linear conductance of a single chain containing n impurities joining the metal contacts. In spite of the fact that such chains are encountered less frequently, it is they that determine the conduction of junctions of intermediate thicknesses (d < AVRH, AVRH being the characteristic length in Mott's variable range hopping process). Let us order the energies of the n-impurity levels in the chain so that ~1 < £2 < £ 3 " ' ' < 6n 1 < £n, (2) where el and en are the closest to the left and right leads, respectively. In general there are many chains 457