Download 11. Quantum Transport in Low Dimensional 11.1

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
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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).
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