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Quantum Transport in Low Dimensional Disordered Systems 12. Quantum Transport in Low Dimensional Disordered Systems Academic and Research Staff Prof. P.A. Lee Graduate Students R.A. Serota 12.1 Variable Range Hopping in Quasi-One-Dimensional MOSFET's Joint Services Electronics Program (Contract DAAG29-83-K-0003) Patrick A. Lee Recently it has become possible to fabricate narrow channel Si-MOSFET's with a channel width of less than 1000 A and a length of several microns. An unexpected feature is the appearance of irregular structures in the resistance as a function of gate voltage.' These structures are reproducible upon temperature and gate voltage cycling, but change from sample to sample. In 1984, we proposed an explanation of this phenomenon based on a model of variable range hopping in one dimension. 2 In this model conductivity occurs via phonon assisted hopping between localized states. The hopping process can be approximated by an equivalent resistor network connecting all pairs of localized states. At a given gate voltage, a particular resistor dominates the entire resistor network and is responsible for the resistance of the entire sample. We noted that as the gate voltage is changed, the dominant resistor makes sudden switches from one pair to another, thus giving rise to the observed irregular structure. Our computer simulation is in excellent agreement with the experimental results and account for the temperature dependence and magnitude of the irregular structures as well as the non-linear dependence of the current on source-drain voltage. A fundamental question remains to be addressed. In any finite size sample, one expects to find fluctuations in observed quantities simply due to the lack of complete averaging. Is the observed structure due simply to such finite size effect, or are we dealing with something more fundamental? In the past year we succeeded in answering this question by a combination of analytic and numerical techniques.3 We show that in one dimension while the resistance fluctuation decreases with increasing sample length L, it decreases extremely slowly, being proportional to (log L) - 1/2 . This shows that the irregular structure is not a finite size effect, which would be expected to decrease as a power law. At the same time, the average of the logarithm of resistance increases with sample size, as (log L) 1/ 2 so that its product with the fluctuation RLE Progress Report No. 128 Quantum Transport in Low Dimensional DisorderedSystems amplitude is independent of sample length. This remarkable result should be tested experimentally. The most important consequence of our conclusion is that the observed irregular structure is not simply a finite size effect and should continue to be observable in very long quasi-one-dimensional structure. It will be very interesting to fabricate long and narrow MOSFET's to test our theory. References 1. R.F. Kwasnick, M.A. Kastner, J. Melngailis, and P.A. Lee, Phys. Rev. Lett. 52, 224 (1984). 2. P.A. Lee, Phys. Rev. Lett. 53, 2024 (1984). 3. R.A. Serota, R. Kalia, and P.A. Lee, Phys. Rev. B33, to be published. RLE Progress Report No. 128