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Quantum Transport in Low Dimensional Disordered Systems 11. Quantum Transport in Low Dimensional Disordered Systems Academic and Research Staff Prof. P.A. Lee 11.1 Variable Range Hopping in Quasi-One-Dimensional MOSFET's Joint Services Electronics Program (Contract DAAG29-83-K-0003) Patrick A. Lee 1 In the past two or three years, several groups, including the group at M.I.T., have fabricated narrow channel Si-MOSFET's with a channel width of the order of 1000 A and a length of several microns. The most striking experimental finding was the appearance of irregular structures in the conductivity as a function of gate voltage. The structure is reproducible upon temperature and gate voltage cycling and increases in magnitude as the temperature is decreased. Highly non-ohmic behavior was also reported. In the past year, we provided a theoretical explanation of this phenomenon in terms of variable range hopping in one dimension. 2 Conductivity occurs via phonon assisted hopping between localized states. The process can be approximated by an equivalent resistor network connecting all pairs of localized states. Such resistors have a very broad distribution of resistance because each individual resistance depends exponentially on temperature, site energy, and the spacing between 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 point out that as the gate voltage (or chemical potential) is changed, the dominant resistor makes sudden switches from one pair to another. The result of the switching is observed as the irregular structure discussed earlier. We did a computer simulation of this model. The results compare very favorably with the data and account for the shape of the structure as well as its magnitude. This explanation of the structure opens the door to many further investigations. We see here the first example of a physical process which is not self-averaging. Indeed, the observed structure provides a map of the microscopic process of hopping between a particular pair of localized states. The non-ohmic effect can now be accounted for, because all the voltage drop is across the dominant resistor. Our result also suggests the possibility of measuring the properties of a single hop between an individual pair of states, such as its behavior in the presence of a magnetic field. Without a doubt, we will see a lot of experimental activities along these directions RLE P.R. No. 127 Quantum Transport in Low Dimensional Disordered Systems in the next few years. References 1. R.F. Kwasnick, M.A. Kastner, J. Meingailis, and P.A. Lee, Phys. Rev. Lett. 52, 224 (1984). 2. P.A. Lee, Phys. Rev. Lett. 53, 2042 (1984). RLE P.R. No. 127