Silicon Atomic Quantum Dots Enable Beyond-CMOS Electronics - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 40

5 Fabricating and Controlling a Quantum Dot Cellular
Automata Cell

Figure 6 a shows two DBs. The distinct dark halo indicates the DBs are nega-
tively charged. Figure 4 b shows that when an additional DB is created by a tip
directed H removal at a nearby site, both the new DB and the nearby pre-existing
DB appear very differently, while the somewhat removed DB is unaltered. After
extensive study it became clear that such a closely placed pair of DBs experi-
ences a great Coulombic repulsive interaction, destabilizing the bound electrons
and enabling one electron to leave the ensemble [ 12 , 14 ]. The reduced net charge
simultaneously stabilizes the remaining bound electron and creates an unoccu-
pied energy level on one of the atoms. Because the barrier separating the DBs
is low, of order several 100 meV, and is also very narrow, of order 2 nm, tunnel-
ing to the vacant state is very facile. Such a pair of DBs may be referred to as
tunnel coupled. Our WKB and ab initio calculations agree that the tunneling
rate for the 3.84 A separated DBs corresponds to an extremely short tunneling
period of order 10 fs [ 22 , 23 ]. Conventional relatively large and necessarily widely
spaced dots would have a tunnel rate many orders of magnitude lower. Figure 7
shows the energy landscape schematically [ 14 ]. Each DB is represented by a
potential well. The well is within the silicon bandgap. In Fig. 7 a the separation
between DBs is su ciently large for the Coulombic interaction to be diminished
by distance and by screening by conduction band electrons. In Fig. 7 b the high
energy repulsive relationship existing between two negatively charged DBs is
represented. Figure 7 b also shows the relaxed situation resulting after removal of
one electron to the conduction band. In that final scenario one vacant electron
state is shown. That state and the low and narrow barrier enables tunneling
between the DBs.
The pairing result demonstrates a “self-biasing” effect. That is, by using
fabrication geometry and repulsion to adjust electron filling, the need for capac-
itively coupled filling electrodes is removed [ 14 ]. Figure 8 a shows several pairs of
DBs of different separations and therefore different average net occupations. It
can be readily seen that closer spaced DBs more fully reject one electron, leading
to less local charge induced band bending and therefore to a lighter appearance
in the STM image. The increasingly widely spaced pairs look increasingly dark
as the net charge approaches 2 electrons. A statistical mechanical model of the
paired DBs reproduces the effect as shown in Fig. 8 b. The graph stresses that
occupation is a time averaged quantity and that pairs in the cross-over region
will at any instant be either 1 charged [ 14 ].

Figure 9 shows a 4 dot ensemble or artificial molecule. The 4 dot cell was fabri-
cated to result in an average net filling of 2 extra electrons. The graphs in Fig. 9 b
show the result of a statistical mechanical description of average occupation versus
distance of separation in such a square cell at different temperatures [ 12 ].
One way to localize and thereby visualize the occupying electrons is to make
an irregular shaped cell as is shown in Fig. 10 [ 14 ]. Figure 10 a shows three dots,
two of which look darker indicating greater negative charge localization Upon

− or 2 −