Download 12. Quantum Transport in Low Dimensional 12.1

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