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2
Historical Background
In the 1980's advanced epitaxial growth techniques such as molecular beam epitaxy
(MBE) enabled the creation of GaAs-AlGaAs semiconductor heterostructures with
very smooth interfaces. This ability to control the composition of crystalline semi-
conductors with atomic precision made possible the formation of a highly conducting
two-dimensional electron gas (2DEG) at the interface between AlGaAs and GaAs.
Moreover, the 2DEG, which was essentially a plane of confined electrons, could be
further patterned by placing lithographically-defined metal gates on the surface of the
semiconductor. A negative potential on the gates would deplete the 2DEG under the
gate regions. In 1988 two groups measured quantized conductance through a con-
striction connecting two 2DEG regions and found that it was quantized [
1
,
2
]. This
was convincingly explained by invoking the quantum-mechanical nature of the
electrons transiting the constriction. Using the effective mass approximation, one
could explain much of the behavior of this layer by solving the Schrödinger equation
in two dimensions.
The ability to engineer the effective wavefunction of electrons seemed very
promising for potential device applications. Throughout the 1990's (and beyond)
many wave-based device designs were proposed which used quantum interference
effects as their operating principle, often created in analogy with microwave devices.
Truly remarkable experimental demonstrations left little doubt that these quantum
mechanical effects were real and could be potentially exploited for device behavior. In
addition, it proved possible to create quantum dots by confining the 2DEG in both
lateral dimensions (the third dimension was already confined by the heterostructure
potential. These quantum dots could be viewed as artificial atoms [
3
,
4
], and also as
high-Q resonators for ballistic electron transport [
5
].
Into the optimism that these new abilities engendered, Rolf Landauer injected a
ray of pessimism and realism. In a talk at the first International Symposium on
Nanostructure Physics and Fabrication in 1991, Landauer cautioned that interference
devices were unlikely to make it in the real world [
6
]. A ''rich'' response with many
peaks and valleys did not, he argued, make a robust basis for devices, which would
have to be tolerant of fabrication variations and environmental perturbations. He
argued for devices whose transfer function is nonlinear and saturates at two distinct
levels, as does a CMOS inverter. This input signal should be of the same type as the
output signal, so that information can be transferred from device to devices.
Another stream of research at the time was the newly emerging and promising
phenomenon of Coulomb blockade in small structures. Electrons tunneling onto small
metal islands can raise the potential of the island by e2/C, where C is the total
capacitance of the island [
7
]. For very small structures this charging energy could be
significant compared to thermal energies. The ''orthodox'' theories of the Coulomb
blockade, even when treating the system quantum mechanically, characterized the
island by this macroscopic quantity—the capacitance [
8
]. While this is quite adequate
for metal structures containing very many free electrons, in small semiconductors one
should really use a multi-particle approach. In such a model the effective capacitance
is a result of the calculation of Coulomb effects, rather than being an input to it.
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