Information Technology Reference
In-Depth Information
Fig. 3.12 Tunneling of
electrons in the system of
potential barriers
sequence of
N
-dimensional barriers
V
(
x
) of arbitrary shape, separated (
N
1)
potential well, with
x !1
,
V
(
x
)
!
0, as considered by Carter.
The qualitative properties of this process were calculated analytically for the
barriers of the type
functions. It turned out that they did not depend on the
particular kind of potential energy. In 1962, the Soviet physicist Pshenichnov
showed that in quasi classical approximation for barriers of arbitrary shape under
certain conditions the passage may be abnormally large (Fig.
3.12
).
Pshenichnov calculated for a system of identical barriers the transmission
coefficient for a particle with the mass
ʴ
ʼ
and energy with energy
E
lower than the
height of the barrier
V
0
.
The study showed that when 0
<
V
0
stationary states arise in each of the
minima whose spectrum is, roughly speaking, the spectrum of one of the individual
minima, with all levels split into (
N
1) sublevels.
Moreover, if the energy of the incident particle equals the energy
E
of one of the
sublevels, the transmission coefficient shows a non-monotonic dependency on
E
and has (
N
1) maxima in which the values of the transmission coefficient are
equal to unity. Thus, the possibility of free electron passage through a succession of
barriers arises. At the same time, a change in the form of at least one of the barriers
causes the change in the position of the levels (relative to the energy of the passing
particle), and the transmission coefficient drops sharply. Therefore, in such a
system both the mechanism of signal transmission over long distances and effective
interruption of the signal are possible.
It should be noted that Pshenichnov's calculations were not confirmed experi-
mentally in a particular molecular system. However, in 1973 Chu and Esaki
performed similar calculations for multilayer semiconductor heterostructures
using one-dimensional approximations. Their results fully reproduced the findings
E
<
